Supergroups of some hyperbolic space groups are classified as a continuation
of our former works. Fundamental domains will be integer parts of truncated
tetrahedra belonging to families F1 - F4, for a while, by the notation of E.
Moln?r et al. in 2006. Our paper relies basically on this work. As an
application, optimal congruent hyperball packings and coverings to the
truncation base planes with their very good densities are computed. This
covering density is better than the conjecture of L. Fejes T?th for balls
and horoballs in 1964.