Cross-Characteristic Representations of $Sp_6(2^a)$ and Their Restrictions to Maximal Subgroups

We classify all pairs $(V,H)$, where $H$ is a proper subgroup of $G=Sp_6(q)$, $q$ even, and $V$ is an $\ell$-modular representation of $G$ for $\ell\neq 2$ which is absolutely irreducible as a representation of $H$. This problem is motivated by the Aschbacher-Scott program on classifying maximal subgroups of finite classical groups.