A clutch unit for a powertrain of a motor vehicle is disclosed, comprising a torque input component acting as a drive element, a torque output component acting as an output element, being connectable so as to transmit a torque to the torque input component via a clutch that can be shifted using friction elements, and with a torsional vibration damper having two masses damped relative to one another to reduce rotational irregularities, which is arranged between the torque input component and the torque output component, at least one of the two masses of the torsional vibration damper being simultaneously designed as a support for a friction partner. The disclosure further relates to a hybrid module comprising a first drive machine, the output shaft of which can be connected to an output shaft of a second drive machine or a transmission input shaft via such a clutch unit.