  Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8.
They can be obtained from appropriate conformal embeddings and the
corresponding graphs have self-fusion. From these embeddings, or from their
associated modular invariants, we determine the algebras of quantum symmetries,
obtain their generators, and, as a by-product, recover the known graphs
E4(SU4), E6(SU4) and E8(SU4) describing exceptional quantum subgroups of type
SU(4). We also obtain characteristic numbers (quantum cardinalities,
dimensions) for each of them and for their associated quantum groupoids.
