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We propose a predictive $Q_4$ flavored 2HDM model, where the scalar sector isenlarged by the inclusion of several gauge singlet scalars and the fermionsector by the inclusion of right handed Majorana neutrinos. In our model, the$Q_4$ family symmetry is supplemented by several auxiliary cyclic symmetries,whose spontaneous breaking produces the observed pattern of SM charged fermionmasses and quark mixing angles. The light active neutrino masses are generatedfrom an inverse seesaw mechanism at one loop level thanks to a remnantpreserved $Z_2$ symmetry. Our model succesfully reproduces the measured darkmatter relic abundance and is consistent with direct detection constraints formasses of the DM candidate around $\sim$ 6.3 TeV. Furthermore, our model isalso consistent with the lepton and baryon asymmetries of the Universe as wellas with the muon anomalous magnetic moment

Fermion masses and mixings, dark matter, leptogenesis and $g-2$ muon anomaly in an extended 2HDM with inverse seesaw