Let $G=Sp(4,2^f)$ with $f>1$. Based on the facts when $f$ is small, I would feel the following:


$G$ has two conjugacy classes of subgroups isomorphic to $SO^+(4,2^f)$. One is in Aschbacher's class C8, and the other is $Sp(2,2^f)\wr2$ in C2. These two classes of subgroups are swapped by the graph automorphism of $G$.


Is this right and where can I find the related stuff? Thanks!



The action of graph automorphism of finite symplectic group on maximal subgroups
Yes it is right (for $f>1$), and it is (14.1)(2) of Aschbacher's paper


M. Aschbacher. On the maximal subgroups of the finite classical groups. Invent.
Math. 76 (1984), 469–514.


