We investigate the correlation of star formation quenching with internal galaxy properties and environment by comparing observation and theoretical models. We first classify galaxies as the most massive “central” or “satellite” in each halo in order to investigate the environmental effect. For observed central galaxies, we are unable to determine whether star formation quenching is primarily connected with halo mass or stellar mass, because these two quantities are strongly correlated. For satellite galaxies, a nearly equal dependence on halo mass and stellar mass is seen. We find that theoretical models with AGN feedback reproduce the dependence on colours and specific star formation rates for central galaxies reasonably. However, the same models seriously fail to reproduce the star formation rates of satellite galaxies by over-quenching star formation via strong strangulation: satellite over-quenching problem.