In LaAlO(3)/SrTiO(3) heterointerfaces, charge carriers migrate from the LaAlO(3) to the interface in an electronic reconstruction. Magnetism has been observed in LaAlO(3)/SrTiO(3), but its relationship to the interface conductivity is unknown. Here we show that reconstruction is necessary, but not sufficient, for the formation of magnetism. Using scanning superconducting quantum interference device microscopy we find that magnetism appears only above a critical LaAlO(3) thickness, similar to the conductivity. We observe no change in ferromagnetism with gate voltage, and detect ferromagnetism in a non-conducting p-type sample. These observations indicate that the carriers at the interface do not need to be itinerant to generate magnetism. The ferromagnetism appears in isolated patches whose density varies greatly between samples. This inhomogeneity strongly suggests that disorder or local strain generates magnetism in a population of the interface carriers.