Exceptional quantum subgroups for the rank two Lie algebras B 2 and G 2

Exceptional modular invariants for the Lie algebras B 2 (at levels 2, 3, 7, and 12) and G 2 (at levels 3 and 4) can be obtained from conformal embeddings. We determine the associated algebras of quantum symmetries and discover or recover, as a by-product, the graphs describing exceptional quantum subgroups of type B 2 or G 2 that encode their module structure over the associated fusion category. Global dimensions are given.