Most lifters feel squats only in their quads because of foot placement. Widen your stance to shoulder-width, angle your toes slightly out, and push your hips back as you bend your knees. This shift targets your glutes instead.
I only feel my quads when I squat. Here's how to fix it. When you squat, if you place your feet in front of you with a narrow stance, you'll feel it in your quads. If you place your feet very far out with your toes pointed out, you will feel it in your abductors. And if you place your feet shoulder-width apart, toes slightly pointing out, push your bum back and knees at the same time, you'll feel it in your glutes. Try this and let me know what your partner thinks.
