On the intermediate subgroups of the general linear group containing group of quaternions

Let $G=G(2,K)$ be a general linear group over a quadratic extention $K$ of the field $F$ (char $F\ne2$) and let $D=(\frac{a,b}F)$ be an algebra of quaternions with division containing $F$.
The subgroups $H$ of $G$ containing a matrix realisation of multiplicative group $D^*$ of the algebra $D$ considered. The discription of the rings of multipliers of the intermediate subgroups is gived.