If $H$ is a finite subgroup of $GL(n,\mathbb{Z})$ then by Minkowskie's theorem, it injects to a subgroup of $GL(n,\mathbb{Z}/p\mathbb{Z})$ under the natural map from $GL(n,\mathbb{Z})$ to $GL(n,\mathbb{Z}/p\mathbb{Z})$, where $p$ is an odd prime.
What are restrictions on subgroups $H$ that can inject to a subgroup of $GL(n,\mathbb{Z}/2\mathbb{Z})$ under the natural map from $GL(n,\mathbb{Z})$ to $GL(n,\mathbb{Z}/2\mathbb{Z})$