A hybrid drive includes a control unit, an internal combustion engine, an electrical machine and a dual clutch transmission having an output shaft. The dual clutch transmission includes a first sub-transmission and a second sub-transmission, each couplable to the output shaft. A drive shaft of the internal combustion engine is couplable to a first input shaft of the first sub-transmission via a first clutch and to a second input shaft of the second sub-transmission via a second clutch. The control unit is configured to permit the second clutch to be closed even when the hybrid drive is being operated purely electrically so that the driveshaft of the internal combustion engine is driven by the electrical machine. A control unit and a method for operation of a hybrid drive are also provided.