A description of the subgroups of the complete linear group that contain the group of diagonal matrices

Let $K$ be a field containing at least seven elements. In the group $G=GL(n,K)$ we describe the subgroups containing the group $D$ of all diagonal matrices. This description is given in terms of the concept of a $D$-net subgroup, defined as a subgroup of $G$ composed of matrices $(a_{ij})$ with zero elements $a_{ij}$ in some prescribed cells outside the main diagonal (the set of cells is subordinated to some condition of agreement). The main theorem is: Every subgroup of $G$ containing $D$ is contained between a uniquely determined $D$-net subgroup and its normalizer in $G$. The structure of all subgroups of $G$ containing $D$ is finite and does not depend on the field $K$ (when $\operatorname{card}k\geqslant7$).