Continuum crystal plasticity finite element simulations are performed for archetypal pure and alloyed fcc crystals to investigate the role of the crystalline orientation, hardening response and dislocation interactions on the plastic flow patterns developing underneath spherical and pyramidal indenter tips. Following our prior analyses, the orientation of plastic features such as subsurface lobes and surface rosettes goes along that of specific in-plane and out-of-plane slip systems. Interestingly, however, we currently show that the activity of the closely oriented slip systems in such lobes and rosettes is, in general, unaccountable to their development. In highly symmetric (001), (011) and (111) indentations, it is found that the slip systems with a net out-of-plane slip direction may contribute to rosette formation at the surface, whereas in-plane slip directions lead to lobe formation in the subsurface. The present results also show that while the isocontours of maximum shear stress max from anisotropic elasticity analyses indeed provide an indication of the indentation-induced elastic field, it is the projection of the stress tensor in all slip systems that drives lobe formation. The isocontours of max may not therefore dictate the plastic zone shape, even though they are useful in explaining some of its features. Finally, a conical shear band shape is found to develop immediately underneath the imprint, dictating accumulation of shear strains and their spreading towards the thickness of the crystal. This feature varies depending on crystal orientation, hardening response and on whether or not the cross-section under analysis contains normal slip directions. ; Peer Reviewed ; Postprint (published version)