Simple extensions of reflection subgroups of primitive complex   reflection groups
  If $G$ is a finite primitive complex reflection group, all reflection subgroups of $G$ and their inclusions are determined up to conjugacy. As a consequence, it is shown that if the rank of $G$ is $n$ and if $G$ can be generated by $n$ reflections, then for every set $R$ of $n$ reflections which generate $G$, every subset of $R$ generates a parabolic subgroup of $G$. 
D. E. Taylor
math.GR