**Core Concept**
The greater sciatic notch is a significant anatomical structure in the pelvis that allows passage of several nerves and blood vessels. The nerves passing through the greater sciatic notch play a crucial role in innervating the lower limb. Understanding the anatomy of the nerves in relation to the greater sciatic notch is essential for clinical practice.

**Why the Correct Answer is Right**
The obturator nerve is unique among the nerves listed as it does not pass through the greater sciatic notch. Instead, it passes through the obturator foramen, a separate opening in the pelvis. This distinction is clinically relevant as the obturator nerve innervates the medial compartment of the thigh, whereas the other nerves listed innervate the lateral compartment. The obturator nerve's passage through the obturator foramen allows it to innervate the adductor muscles of the thigh.

**Why Each Wrong Option is Incorrect**
**Option A:** The superior gluteal nerve passes through the greater sciatic notch and innervates the gluteus medius, gluteus minimus, and tensor fasciae latae muscles. It is responsible for hip abduction and external rotation.
**Option B:** The inferior gluteal nerve also passes through the greater sciatic notch and innervates the gluteus maximus muscle, which is responsible for hip extension.
**Option C:** The sciatic nerve, the largest nerve in the body, passes through the greater sciatic notch and divides into the common peroneal and tibial nerves, innervating the lower limb.

**Clinical Pearl / High-Yield Fact**
The obturator nerve is often tested in clinical exams due to its unique passage through the obturator foramen, making it an important landmark for diagnosing and treating lower limb injuries and conditions.

**✓ Correct Answer: D. Obturator nerve**