Irreducible subgroups of symplectic groups in characteristic 2

Suppose that V is a finite dimensional vector space over a finite field of characteristic 2, G is the symplectic group on V and a is a non-zero vector of V. Here we classify irreducible subgroups of G containing a certain subgroup of O-2(Stab(G)) all of whose non-trivial elements are 2-transvections.