  We study gradings by noncommutative groups on finite dimensional Lie algebras
over an algebraically closed field of characteristic zero. It is shown that if
$L$ is gradeg by a non-abelian finite group $G$ then the solvable radical $R$
of $L$ is $G$-graded and there exists a Levi subalgebra
$B=H_1\oplus\cdots\oplus H_m$ homogeneous in $G$-grading with graded simple
summands $H_1, \ldots, H_m$. All supports $Supp~H_i, i=1\ldots, m$, are
commutative subsets of $G$.
