Cross-characteristic representations of Sp6(2a) and their restrictions to proper subgroups

We classify all pairs (V,H), where H is a proper subgroup of G=Sp6(q), q even, and V is an ℓ-modular representation of G for ℓ≠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.