The gluteal muscles are a group of three muscles which make up the buttocks: the gluteus maximus, gluteus medius and gluteus minimus.The three muscles originate from the ilium and sacrum and insert on the femur.tructure [edit]. The gluteus maximus is the largest of the gluteal muscles and one of the strongest muscles in the human body. It inserts at the iliotibial band and the gluteal tuberosity of the femur. Its action is to extend and to laterally rotate the hip, and also to extend the trunk.