Subgroups of the general linear group over a local field

We describe subgroups of the general linear group $\mathrm{GL}(n,R)$ over the field of fractions $K$ of a local principal ideal domain $R$, containing the group $\mathrm{SD}(n,R)$ of diagonal matrices with entries from $R$ and determinant 1. Similar results for overgroups of $D(n,R)$ were obtained earlier by I. Hamdan and N. Vavilov. Results of the present paper generalize also some further known results, notably decription of parahoric subgroups by N. Iwahori and H. Matsumoto.