Is anyone aware of a result (or a counterexample) along the following lines: let $G$ be an algebraic group over $\mathbf Z$. Let $H$ be a finite group such that $H$ occurs as a subgroup of $G(\bar{\mathbf F}_p)$ for all but finitely many primes $p$. Then $H$ also occurs as a subgroup of $G(\mathbf C)$.

I only really need this for $H$ solvable and $G = \mathrm{GSp}(4)$ if that helps at all.