Discrete gauging and Hasse diagrams

We analyse the Higgs branch of 4d $\mathcal{N}=2$ SQCD gauge theories with non-connected groups $\widetilde{\mathrm{SU}}(N) = \mathrm{SU}(N) \rtimes_{I,II} \mathbb{Z}_2$ whose study was initiated in arXiv:1804.01108. derive Hasse diagrams corresponding to mechanism using adapted characters for representations groups. propose 3d $\mathcal{N}=4$ magnetic quivers branches type $I$ discrete gauging case, form recently introduced wreathed quivers, and provide extensive checks by means Coulomb Hilbert series computations.