Serial group rings of finite simple groups of Lie type

Suppose that $F$ is a field whose characteristic $p$ divides the order of a finite group $G$. It is shown that if $G$ is one of the groups ${}^3 D_4(q)$, $E_6(q)$, ${}^2E_6(q)$, $E_7(q)$, $E_8(q)$, $F_4(q)$, ${}^2F_4(q)$, or ${}^2G_2(q)$, then the group ring $FG$ is not serial. If $G= G_2(q^2)$, then the ring $FG$ is serial if and only if either $p>2$ divides $q^2-1$, or $p=7$ divides $q^2 + \sqrt{3}q + 1$ but $49$ does not divide this number.