Flag manifolds have the form $G/C(S)$ where $C(S)$ is the centralizer (in $G$) of its center $S$ (a torus).

Most $G/H$ in the [list](https://en.wikipedia.org/wiki/Quaternion-Kähler_symmetric_space) don't have this form, for $H$ has discrete center in each case except the complex Grassmannians $\mathrm{SU}(p+2)/\mathrm S(\mathrm{U}(p)\times\mathrm{U}(2))$ and $\mathrm{SO}(6)/\mathrm{SO}(2)\mathrm{SO}(4)$.