2nd ID is the Indian head on a white star on a black shield.
The patch of the US Army Second Infantry Division consists of a blue Indian head with feathers, representing Native American traditions, on a white circular background. Surrounding the circle is a black border with "Second to None" written at the top and "2D INF DIV" at the bottom. The patch symbolizes the division's strength, courage, and dedication to service.
1st Infantry Division. The patch is a GREEN square with a point on the bottom and a RED "1".
3rd Infantry Division, US Army shoulder patch
The 81st Infantry Division is usually considered the first to be authorised to wear a unit insignia on their shoulder. They may or may not be the first to actually do it.
15th Infantry regiment, 3rd Infantry Division (US Army) and 36th Infantry Division (Texas National Guard)
Army, 82nd Infantry Division.
Not in WW2. Before 1939, each US Army Infantry Division had 4 infantry regiments. This proved to be too large for use on the battlefield. So the size the division was reduced and one regiment was removed. So the 3rd Infantry Regiment could have been part of a Division before then. However, during WW2 the 3rd Infantry Regiment was not part of an infantry division. Source: http://www.custermen.com/ItalyWW2/ArmyOrg/OrgChart/Divisions.htm
WW2 History The "Big Red One" referred to the US 1st Infantry Division which had a shoulder patch that included a Red "1". It is one of the US Army's oldest divisions.
In WWII it belonged to the 26th Yankee Division. Part of the 3 rd Army.
For WW2: Armored Infantry Divisions were equiped with half-tracks. Regular Infantry Divisions walked (or trucked). During the Vietnam War those Armored Infantry Divisions gave way to the new MECHANIZED INFANTRY DIVISIONS, equipped with M-113 APC/ACAV (Armored Personnel Carriers/Armored Cavalry Assault Vehicles). Only one US Army Mechanized Infantry Division was in Vietnam (and only it's 1st Brigade); the 5th Mechanized Infantry Division (Red Diamond Patch). Regular Infantry Divisions in Vietnam were called "Straight Legs", "Straight" meaning...straight foot soldiering.
Omaha beach was seized by the US 1st Infantry Division along with the 116th Infantry Brigade Team (29th Infantry Division) and the 16th Infantry Brigade Team (1st Infantry Division). US Army Rangers also took part in the invasion force.
You need to be more specific about whether you're referring to the 7th Infantry Division, or the 7th Infantry Regiment before this question can be answered.
8th Infantry Division