The qoutient by a central radical and the structure of flag manifolds

Question

Let $G=R\times S$ be a real Lie group where $R$ is a central connected subgroup and $S$ is a semisimple normal subgroup. Let $H$ be a closed subgroup such that it contains $R$.

Now if $G/H$ is compact complex manifold. Is it true that $G/H$ is a flag manifold?