A hybrid drivetrain having an internal combustion engine which is designed for a maximum internal combustion engine rotational speed; a dual-clutch arrangement which has a first friction clutch and a second friction clutch with a common input element and in each case one output element; a transmission arrangement which has a first sub-transmission and a second sub-transmission; an electric machine connected to the output element of the second friction clutch via a machine transmission ratio (iM), in such a way that a purely electric driving mode can be established via the second sub-transmission. The electric machine is designed for a maximum machine rotational speed. The maximum machine rotational speed divided by the machine transmission ratio is greater than the maximum internal combustion engine rotational speed. The output element of the second friction clutch is structurally designed for the maximum machine rotational speed divided by the machine transmission ratio (iM).