**Core Concept**
The superior gluteal nerve is a branch of the lumbosacral plexus that supplies the gluteus medius, gluteus minimus, and tensor fasciae latae muscles. It is a crucial nerve for hip abduction and external rotation.

**Why the Correct Answer is Right**
The superior gluteal nerve exits the pelvis through the greater sciatic notch, superior to the piriformis muscle. This nerve then innervates the gluteus medius, gluteus minimus, and tensor fasciae latae muscles, which are involved in hip abduction and external rotation. The gluteus maximus, on the other hand, is innervated by the inferior gluteal nerve.

**Why Each Wrong Option is Incorrect**
**Option A:** Gluteus medius - Incorrect because the gluteus medius is indeed innervated by the superior gluteal nerve.
**Option B:** Gluteus minimus - Incorrect because the gluteus minimus is also innervated by the superior gluteal nerve.
**Option C:** Tensor fasciae latae - Incorrect because the tensor fasciae latae is innervated by the superior gluteal nerve.
**Option D:** Gluteus maximus - Correct because the gluteus maximus is innervated by the inferior gluteal nerve, not the superior gluteal nerve.

**Clinical Pearl / High-Yield Fact**
Remember the mnemonic "GOLD" to recall the muscles innervated by the superior gluteal nerve: Gluteus medius, Obturator internus (not listed), and Tensor fasciae latae.

**Correct Answer: D. Gluteus maximus**