prove that a Lie algebra is semisimple

Question

Let $$J_3=\begin{pmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{pmatrix}$$ $$J=\begin{pmatrix} 0_3 & J_3 \\ J_3 & 0_3 \end{pmatrix}$$ Consider the Lie algebra $L=\{x \in gl(6,\mathbb{C})|^txJ+Jx=0\}$ I have to prove that $L$ is semisimple and find a a maximal total subalgebra $H$ of $L$. I now what a semisimple Lie algebra is and I know a series of equivalent condition ($Rad L=0$, killing form non degenerate, no abelian ideals). But I don’t know how to use this condition. In general how can I prove that a Lie algebra is semisimple?