This is, roughly (sometimes you might have to take the commutator subgroup), true if $n$ and/or $q$ are big enough. Wikipedia and sufficiently advanced textbooks on finite group theory spell it out in all the detail.

This is, roughly (sometimes you might have to take the commutator subgroup), true if $n$ and/or $q$ are big enough. Wikipedia and sufficiently advanced textbooks on finite group theory spell it out in all the detail.

EDIT: E.g., from the discussion in comments, $SO^+_{2n}(2^k)$ for $n\geq 3$ is not perfect, for it has a simple index 2 subgroup (specified by Dickson invariant).