Linear groups of degree four containing the subgroup SL2(k)⊗SL2(k)

Let a field K be an algebraic extension of a field k. Assume that the characteristic of k is different from 2 and k contains more than 9 elements. In the article, we study subgroups of the general linear group GL4(K) that contain the subgroup SL2(k)⊗SL2(k).