I'd say that classification of subgroups of GL$_2(F_p)$ plays a big part in Serre's result about the almost surjectivity of $\ell$-adic Galois representations of CM Elliptic curves.

Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. (French) Invent. Math. 15 (1972), no. 4, 259-331.