Maximal subgroups of finite symplectic groups stabilizing spreads of lines

We prove that, for q odd, the group G=Un(q2)•2 is maximal in the symplectic group Sp2n(q) except when n=2 and q=3. The group G corresponds to the stabilizer of a spread of lines of PG(2n−1,q) in which some lines are isotropic and some are non-isotropic.