Most US units occasinally obtained fancier, hand embroidered patches from local tailors or specialty shops in Europe, both during and after the War. Such insignia was often used on Service Coats and Ike jackets. This is one for the 101st.
Unit patches actually had no prescribed regulation position when sewn to the upper sleeve, but usually they were placed 1/2"-1" under the shoulder seam. The wearer's current unit was sewn to the left sleeve, while any previous unit might be placed on the right sleeve. Shoulder patches were seen on all troops in the Normandy invasion, but as the war progressed, it was more common to see no divisional patches (especially on field jackets).
Historical Reference: Combat Chronicles of US Army Divisions in WWII is a good website for basic divisional histories. They also have lists of the sub-units (regiments and support battalions) assigned to each division.