Magnetic actuation of microscopic devices in a liquid environment has been achieved in various ways, which can be grouped into rolling, propelling and swimming. Previous actuators were designed with a focus on one particular type of magnetic actuation. We have shown earlier that efficient magnetic propellers can be selected from randomly shaped magnetic nanostructures synthesized in solution. Here we show that these synthesized nanostructures can be used for all three types of magnetic actuation. Whereas it might not be surprising that single structures can roll in addition to propelling, swimming is unexpectedly also observed using the same material. In this case, however, the magnetically guided self-assembly of several individual particles into chain-like structures is necessary to obtain swimmers, since individual rigid nanostructures cannot swim. Interestingly, the direction of the swimming motion is not necessarily parallel to the long axis of the chain-like assembly, a finding that had been theoretically expected but experimentally not observed so far. Our findings show that the range of structures that can be effectively actuated by external magnetic fields is much broader than assumed until now. This could open up new opportunities for the design of magnetically actuated devices.