We measure neutrino charged-current quasielasticlike scattering on hydrocarbon at high statistics using the wideband Neutrinos at the Main Injector beam with neutrino energy peaked at 6 GeV. The double-differential cross section is reported in terms of muon longitudinal (p_{∥}) and transverse (p_{⊥}) momentum. Cross section contours versus lepton momentum components are approximately described by a conventional generator-based simulation, however, discrepancies are observed for transverse momenta above 0.5  GeV/c for longitudinal momentum ranges 3-5 and 9-20  GeV/c. The single differential cross section versus momentum transfer squared (dσ/dQ_{QE}^{2}) is measured over a four-decade range of Q^{2} that extends to 10  GeV^{2}. The cross section turnover and falloff in the Q^{2} range 0.3-10  GeV^{2} is not fully reproduced by generator predictions that rely on dipole form factors. Our measurement probes the axial-vector content of the hadronic current and complements the electromagnetic form factor data obtained using electron-nucleon elastic scattering. These results help oscillation experiments because they probe the importance of various correlations and final-state interaction effects within the nucleus, which have different effects on the visible energy in detectors.