Isoscalar (T = 0) plus isovector (T = 1) pairing hamiltonian in LS-coupling, which is important for heavy N=Z nuclei, is solvable in terms of a O(8) algebra for some special values of the mixing parameter that measures the competition between T = 0 and T = 1 pairing. The O(8) algebra is generated, amongst others, by the S = 1, T = 0 and S = 0, T = 1 pair creation and annihilation operators . Shell model algebras, with only number conserving operators, that are complementary to theThe problem of classification of states for a given number of