The invention relates to a clutch system (1) for a drive train of a motor vehicle, comprising: a housing (2); a carrier (4) which is mounted so as to be rotatable about an axis of rotation (3) relative to the housing (2); an electric machine, the rotor of which is rotationally coupled to the carrier (4); a plurality of clutches (5, 6, 7), wherein each clutch (5, 6, 7) is accommodated in a rotationally fixed manner on the carrier (4) by means of a clutch component (8 b, 8 c, 9 a); and an actuating device (11) having two auxiliary cylinders (10 a, 10 b), wherein each auxiliary cylinder (10 a, 10b) acts on the clutch (5, 6, 7) in an actuating manner, wherein the carrier (4) is supported via a support bearing (12) on the radially inner side (13) of an actuator housing (14) of the actuating device (11). The invention further relates to a drive unit (30) having the clutch system (1).