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The US Army is organized into Armies (3rd, 6th, 7th, etc.). Armies consist of subordinate units of Corps, Divisions, Regiments, Brigades, Battalions, Companies, Platoons and Squads.  The larger units are organized into Command structures consisting of Commander, Chief of Staff (XO) and Command Staff responsible for various functions.

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."

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.

Battalion - 300 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.

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. The Army has not employed army groups since World War II.

Command Staff Designations: 1-Personnel, 2-Intelligence, 3-Operations, 4-Logistics, 5-Civil/Military Operations, 6-Signals (communications, etc.)

"G" designations identify the officer (and corresponding staff) is at the Corps or Division level. "S" designations indicate Regiment, Brigade or Battalion level function.  Therefore An S2 would be the staff officer responsible for all intelligence activities in either a Regiment, Brigade or Battalion unit.  His counterpart at Division or Corps would be designated G4.

Above Information Derived from DA Pamphlet 10-1

There is no set size (number of troops) assigned to any specific element. The size of an element of command depends primarily upon the type of unit and mission. For example, an aviation company would have a different number of troops assigned than an infantry company because it has a different mission, different equipment, and therefore different requirements.

Note: The usual structure is battalion -> brigade -> division, with battalions organized into regiments as the exception. An example of this exception would be cavalry regiments. Calvary is unique in that battalions are called "squadrons" and companies are called "troops."

However, most battalions that are actually part of brigades still have a regimental affiliation, such as 1/34 IN Rgt. 1st Battalion of the 34th. This affiliation is pretty much just historical and symbolic these days. It has no real significance as far as the chain of command goes. For example, the infantry battalions of the 3d Brigade of the 2d Infantry Division are 1st Bn 23rd Infantry, 2d Bn 3d Infantry, and 5th Bn 20th Infantry. Each battalion is affiliated with a different regiment but part of the same brigade.

This goes back to the old days when the structure was battalion -> regiment -> brigade -> division. Up through the first part of the 20th century a division was made up of 2 brigades, each of which had 2 regiments. This was called a "square" division. During WW2, the U.S. Army transitioned to "triangular" divisions of 3 brigades each (most other armies had gone triangular during WW1). They did this by cutting out the regiment level, but since the regiment traditionally was thought of as a soldier's "home," battalions kept their regimental designation even though the regiments as functional units were no more.

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