There are a few papers by Gabriele Nebe and Wilhelm Plesken on this topic, eg:
Nebe, Gabriele Finite subgroups of ${\rm GL}_{24}(Q)$. Experiment. Math. 5 (1996), no. 3, 163--195.
Nebe, Gabriele Finite subgroups of ${\rm GL}_n(\bold Q)$ 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.