The non-existence of stringless monopole solutions in the Weinberg-Salam theory (except in the case in which the electromagnetic U(1) is contained in the SU(2) factor of the gauge group) is usually ascribed to a combination of circumstances arising from the topology of the gauge group, from the underlying Lie algebra structure and from the nature of the Higgs mechanism. The author analyses this result from a geometric point of view, and shows that no electroweak theory based on a compact connected non-semisimple group can admit stringless monopoles, unless the charge operator lies in the semisimple part of the Lie algebra. The analysis is independent of the mechanisms used to break the symmetry.