The commutator subalgebra is perfect of dimension 3. The radical of equals its center and is .
This Lie algebra is solvable. has dimension 2. Its center is 2-dimensional; its nilpotent radical is 4-dimensional.
The commutator subalgebra is abelian of dimension 3 and so is solvable. Its center is . Its nilpotent radical is 4-dimensional.
This Lie algebra is solvable. Its nilpotent radical is 4-dimensional. Its center is .
The solvable radical of this Lie algebra is 7-dimensional. There is a 3-dimensional Levi subalgebra. The center is .