Dear Members of Mathoverflow,

I am interested about a Fact (if it is right) of the structure of parabolic subgroups of finite classical algebraic groups:

Let G be a classical algebraic group over the finite field of order $r^{e}$, and let $ P \leq G $ denote a maximal parabolic subgroup of G.

We regard the unipotent radical of P: $ R:=R_{U}(P) = O_{r}(P) $. Is it true, that R is a minimal normal subgroup of P? (For P being a parabolic subgroup which is not a maximal in G, it is not true. If we regard the PSL(3,$r^{e}$) and a Borel subgroup.)

If it is right for the maximal parabolic subgroups of G, are there any Theorems or Propositions about that?

Thank you much for your Answers.