Let F be the field with p elements, where p is of the form (2 t+ 1) for some square free odd integer t. In this article, we obtain the order of the symmetric and the unitary subgroup of U(FCq) , where q is a prime divisor of t. Consequently, we resolve the normal complement problem for the modular group algebra of a split extension of Cq by an abelian group of order pm with m≥ (q- 3) , over the field with p elements such that p= (2 q+ 1). Further, we study the normal complement problem in the finite semisimple group algebras of general linear groups.