Background: In heavy-ion-induced reactions the mechanism leading to the formation of the compound nucleus and the role of quasifission is still not clear. Purpose: Investigation of the quasifission process of superheavy composite systems with Z = 110-116 and comparison with properties of fusion-fission and quasifission of lighter composite systems. Method: Mass and energy distributions of fissionlike fragments formed in the reactions 48Ca +232 Th, 238U, 244Pu, and 248Cm at energies near the Coulomb barrier have been measured using the double-arm time-of-flight spectrometer CORSET at the U-400 cyclotron of the FLNR JINR. Results: The most probable fragment masses as well as total kinetic energies and their dispersions in dependence on the interaction energies and ion-target combinations have been studied for asymmetric and symmetric fragments formed in the reactions. The capture cross sections were obtained for the reactions 48Ca +244 Pu and 248Cm. The lower limits for fission barriers of 283−286Cn, 289−292Fl, and 293−296Lv compound nuclei were estimated. Conclusions: Analysis of the properties of symmetric fragments has shown that a significant part of these fragments may be attributed to fusion-fission process for the reactions 48Ca+238U, 244Pu, and 248Cm.