  We classify the solvable subalgebras, semisimple subalgebras, and Levi
decomposable subalgebras of $\mathfrak{so}(4,\mathbb{C})$, up to inner
automorphism. By Levi's Theorem, this is a full classification of the
subalgebras of $\mathfrak{so}(4,\mathbb{C})$.
