1. Organization/Chain of Command

2. ARMY
The basic building block of all Army organizations is the individual soldier.
A small group of soldiers organized to maneuver and fire is called a squad. As elements of the Army's organizational structure become larger units, they contain more and more subordinate elements from combat arms, combat support and combat service support units.
A company is typically the smallest Army element to be given a designation and affiliation with higher headquarters at battalion and brigade level. This alphanumeric and branch designation causes an "element" to become a "unit."

3. Squad - 9 to 10 soldiers. Typically commanded by a sergeant or staff sergeant, a squad or section is the smallest element in the Army structure, and its size is dependent on its function.
Platoon - 16 to 44 soldiers. A platoon is led by a lieutenant with an NCO as second in command, and consists of two to four squads or sections.
Company - 62 to 190 soldiers. Three to five platoons form a company, which is commanded by a captain with a first sergeant as the commander's principle NCO assistant. An artillery unit of equivalent size is called a battery, and a comparable armored or air cavalry unit is called a troop.

4. Battalion - 300 to 1,000 soldiers
Battalion to 1,000 soldiers. Four to six companies make up a battalion, which is normally commanded by a lieutenant colonel with a command sergeant major as principle NCO assistant. A battalion is capable of independent operations of limited duration and scope. An armored or air cavalry unit of equivalent size is called a squadron.
Brigade - 3,000 to 5,000 solders. A brigade headquarters commands the tactical operation of two to five organic or attached combat battalions. Normally commanded by a colonel with a command sergeant major as senior NCO, brigades are employed on independent or semi-independent operations. Armored cavalry, ranger and special forces units this size are categorized as regiments or groups.
Division - 10,000 to 15,000 soldiers. Usually consisting of three brigade-sized elements and commanded by a major general, divisions are numbered and assigned missions based on their structures. The division performs major tactical operations for the corps and can conduct sustained battles and engagements.

5. Above Information Derived from DA Pamphlet 10-1
Corps - 20,000 to 45,000 soldiers. Two to five divisions constitute a corps, which is typically commanded by a lieutenant general. As the deployable level of command required to synchronize and sustain combat operations, the corps provides the framework for multi-national operations.
Army - 50,000 + soldiers. Typically commanded by a lieutenant general or higher, an army combines two or more corps. A theater army is the ranking Army component in a unified command, and it has operational and support responsibilities that are assigned by the theater commander in chief. The commander in chief and theater army commander may order formation of a field army to direct operations of assigned corps and divisions. An army group plans and directs campaigns in a theater, and is composed of two or more field armies under a designated commander. Army groups have not been employed by the Army since World War II.
Above Information Derived from DA Pamphlet 10-1

6. NAVY The Navy has a somewhat complicated organizational structure

7. Airman: (single Air Force member)
Section: Two or more airmen can form a "section." Generally, the section is the place (duty section) where the person works. For example, the Administrative Section, or the Life Support Section. It's not absolutely necessary to have a "section." For example, many aircrew members and Security Forces (Air Force "cops") don't have a "section." Instead, they belong (as a group) to a "flight." In Air Force Basic Training, it's called an "Element." Each basic training "flight" is divided into four "elements," each with an assigned "element leader."
Flight: Two or more airmen can form a flight. Two or more sections can also form a flight. It depends upon how the Squadron is organized. There are three types of flights: Numbered, Alpha, and Functional. Numbered flights incorporate small mission elements into an organized unit. For example, flights in basic training are numbered flights. While in basic, you could be assigned to "Flight 421," for instance.

8. Squadron: Two or more flights form a squadron
Squadron: Two or more flights form a squadron. The squadron is the lowest level of command with a headquarters element (example, a Squadron Commander, or Squadron First Sergeant). In the Air Force, a squadron commander is generally in the rank of Lt Col (O-5), although smaller squadrons may be commanded by majors, captains, and sometimes even lieutenants. Squadrons are usually identified both numerically, and by function. An example would be the 49th Security Forces Squadron, or the 501st Maintenance Squadron.
Group: Two or more Squadrons form a Group. In the Air Force, Groups are usually based upon assignment of squadrons with similar functions. For example, the Supply Squadron, Transportation, and Aircraft Maintenance Squadron would be assigned to the Logistics Group. The flying squadrons would be assigned to the Operations Group. The Dental Squadron and the Medical Squadron would be assigned to the Medical Group, etc. Usually, Groups take on the number of the Wing they are assigned to. The 49th Logistics Group, for example is assigned to the 49th Fighter Wing, at Holloman AFB in New Mexico. The group commander is usually a colonel (O-6).

9. Wing: Two or more groups compose a Wing
Wing: Two or more groups compose a Wing. There is only one Wing on an Air Force base, and the Wing Commander is quite often considered to be the "Installation Commander." There are two types of Wings: Composite and Objective.
Composite Wings operate more than one kind of aircraft.
Objective Wings streamline and consolidate responsibilities and clarify lines of command. They may have operational missions, such as air combat, flying training, or airlift, and they may provide support to a MAJCOM or a geographically separated unit (GSU). Wings may also have a specialized mission (e.g., an "Intelligence Wing").

10. Numbered Air Force: A numbered Air Force (Example, 7th Air Force) is usually assigned for geographical purposes, and primarily used only during wartime. In peacetime, they generally only consist of a limited number of headquarters staff who's job it is to prepare and maintain wartime plans.
Major Command (MAJCOM): Air Force Wings usually report directly to MAJCOMs. Air Force MAJCOMs within the Continental United States are primarily organized by mission. For example, Wings who's primary mission is to fly combat missions (fighters and bombers) would likely be assigned to the Air Combat Command. Wings who's primary mission is training would likely be assigned to the Air Force Education & Training Command (AETC). Overseas, MAJCOMs are generally organized by regional area. Examples would be PACAF (Pacific Air Forces). Wings located in the Pacific Region (Hawaii, Japan, Korea, etc.) would usually be assigned to PACAF. Another example would be USAFE (United States Air Forces Europe), which control most wings assigned to Europe.
Air Force: MAJCOMS report directly to Headquarters, Air Force.

11. MARINES
The Marine Corps has the "RULE of THREE.“
Three men to a fire team commanded by a Corporal (so there are actually a total of four on the team, when you count the team leader).
Three fire teams to a rifle squad commanded by a sergeant.
Three rifle squads to a platoon commanded by a Lt..
Three rifle platoons to a company commanded by a Capt.
Three companies to a battalion commanded by a Lt Col. etc.

12. Team: Four individual Marines assigned to a specific team (Three team members, plus the team leader).
Squad: Three Teams are assigned to a specific squad.
Platoon: Three squads are usually assigned to a specific platoon.
Company (or Battery): Three platoons are assigned to a Company (sometimes called a battery). The Company/battery is the lowest level of command with a headquarters element (example, a Company Commander, or Company First Sergeant).

13. Battalion: Three companies/batteries are assigned to form a battery a battalion.
Regiment: Three battalions form a Regiment (Sometimes called a Brigade).
Division: Three Brigades are assigned to make up a Division.
Marine Corps: Three or more divisions make up the Marine Corps.

14. COAST GUARD
Complicated, like the Navy.

15. Military Rank/Rate
Rank/Rate. There are three general categories of rank/rate (Note: The Navy/Coast Guard calls it "rate," the other services refer to it as "rank"): Enlisted personnel, Warrant Officers, and Commissioned Officers.
Enlisted personnel. Enlisted members are the "backbone" of the military. They perform the primary jobs that need to be done. Enlisted members are "specialists." They are trained to perform specific specialties in the military. As enlisted personnel progress up the ranks (there are nine enlisted ranks), they assume more responsibility, and provide direct supervision to their subordinates.

16. Warrant Officers. Warrant Officers are very highly-trained specialists
Warrant Officers. Warrant Officers are very highly-trained specialists. This is where they differ from commissioned officers. Unlike commissioned officers, warrant officers remain in their primary specialty to provide specialized knowledge, instruction, and leadership to enlisted members and commissioned officers alike.
With few exceptions, one must be an enlisted member with several years of experience, recommended by their commander, and pass a selection board to become a warrant officer. The Air Force is the only service which does not have warrant officers. The Air Force eliminated their warrant officer positions when Congress created the grades of E-8 and E-9 in the late 60s. The other services elected to retain the warrant ranks, and shifted the emphasis from a promotion process for E-7s to a highly selective system for highly-skilled technicians. There are five separate warrant ranks. Warrant Officers outrank all enlisted members.
Warrant officers are not required to have college degrees (they are selected primarily based upon technical skills and experience), but many of them do.

17. Commissioned Officers. Commissioned Officers are the "top brass
Commissioned Officers. Commissioned Officers are the "top brass." Their primary function is to provide overall management and leadership in their area of responsibility. Unlike enlisted members and warrant officers, commissioned officers do not specialize as much (with certain exceptions such as pilots, doctors, nurses, and lawyers). As he moves up the ranks, he gets more and more experience in the different areas of his branch, and is responsible for commanding more and more troops. All of this has the primary purpose of (ultimately) generating an experienced officer who can command an entire infantry company, battalion, or division.
Commissioned Officers must have a minimum of a four-year bachelor's degree. As they move up the ranks, if they want to get promoted, they will have to earn a masters degree. Commissioned Officers are commissioned through specific commissioning programs, such as one of the military academies (West Point, Naval Academy, Air Force Academy, Coast Guard Academy), ROTC (Reserve Officer Training Corps, or OCS (Officer Candidate School), called OTS (Officer Training School) for the Air Force.