TITLE: Subgroups of GL_2 over a finite field
QUESTION [10 upvotes]: I've come across the phrase "by the classification of subgroups of $GL_2(F_q)$" in multiple papers, but never with a reference.  Here $F_q$ is a finite field of size $q$.  Does anyone know a good reference for this (ideally for someone who is not a group theorist)?

REPLY [4 votes]: Dickson is responsible for the classification of subgroups of $SL_2(\mathbb{F}_q)$ (and once you've got this the subgroups of $GL_2(\mathbb{F}_q)$ are easy). You can find a full proof in Suzuki's "Group Theory Part I". It's Chapter 6, Section 3 of that book. If you email me I'll even send you a copy :-)