what are the deep six hip muscles

The lateral rotator group is a group of six small muscles of the hip which all externally (laterally) rotate the femur in the hip joint. It consists of the following muscles: Piriformis, gemellus superior, obturator internus, gemellus inferior, quadratus femoris and the obturator externus

All muscles in the lateral rotator group originate from the hip bone and insert on to the upper extremity of the femur. The muscles are innervated by the sacral plexus (L4-S2), except the obturator externus, which is innervated by the lumbar plexus

This group does not include all muscles which aid in lateral rotation of the hip joint: rather it is a collection of ones which are known for primarily performing this action. Other muscles that contribute to lateral rotation of the hip include:

Gluteus maximus muscle (lower fibres)
Gluteus medius muscle and gluteus minimus muscle when the hip is extended (become medial rotators when hip is flexed)
Psoas major muscle
Psoas minor muscle