  To any complex Hadamard matrix H one associates a spin model commuting
square, and therefore a hyperfinite subfactor. The standard invariant of this
subfactor captures certain "group-like" symmetries of H. To gain some insight,
we compute the first few relative commutants of such subfactors for Hadamard
matrices of small dimensions. Also, we show that subfactors arising from Dita
type matrices have intermediate subfactors, and thus their standard invariants
have some extra structure besides the Jones projections.
