There are a few papers by Gabriele Nebe and Wilhelm Plesken on this topic, eg:

Nebe, Gabriele Finite subgroups of ${\rm GL}_{24}(\mathbb Q)$.  Experiment. Math.  5  (1996),  no. 3, 163--195.

Nebe, Gabriele Finite subgroups of ${\rm GL}_n(\mathbb Q)$ for $25\leq n\leq 31$.  Comm. Algebra  24  (1996),  no. 7, 2341--2397.

Nebe, G.; Plesken, W. Finite rational matrix groups.  Mem. Amer. Math. Soc.  116  (1995),  no. 556, viii+144 pp.