A clutch arrangement for a motor vehicle has a clutch housing that is filled with pumped medium in the form of fluid, a first friction element being rotatable in common with the clutch housing. Further, a second friction element is provided which is rotatable in common with a driven member and which can be brought into an operative connection with the at least one first friction element for producing a frictional interaction. At least one first friction element and at least one second friction element are each provided with a support component that can be provided for receiving at least one friction lining. The support components have support component segments which are arranged successively in circumferential direction and which are provided at a circumference-side terminating edge, respectively, with fluid delivery surfaces for generating a fluid circulation and are constructed in the form of friction lining segments to produce the frictional interaction with friction linings. The fluid delivery surfaces adjoin a cutout of the support component in each instance.