Lie rings of prime-cube order

The list
Let $$p$$ be a prime number. Up to isomorphism, here are the Lie rings of order $$p^3$$ (the table is not yet complete):

There are some more to be filled in

For the explanation of why these are precisely the Lie rings of prime-cube order, see classification of Lie rings of prime-cube order. If you are interested in only the nilpotent ones, see classification of nilpotent Lie rings of prime-cube order.

Baer correspondence for odd primes
If $$p$$ is an odd prime, then there is a correspondence between the nilpotent Lie rings among the above and the groups of prime-cube order, given below: