  Like the LR-tableau, a socle tableau is given as a skew diagram with certain
entries. Unlike in the LR-tableau, the entries in the socle tableau are weakly
increasing in each row, strictly increasing in each column and satisfy a
modified lattice permutation property. In the study of embeddings of a subgroup
in a finite abelian $p$-group, socle tableaux occur as isomorphism invariants,
they are given by the socle series of the subgroup. We show that each socle
tableau can be realized by some embedding. Moreover, the socle tableau of an
embedding and the LR-tableau of the dual embedding determine each other.
