Previous neutron experiments on polycrystalline samples of UFe4Al8 have led to a series of conflicting proposals, including a spin-glass state, for the magnetic structure below the ordering temperature of similar to 150 K. Our experiments on a stoichiometric single crystal show that the principal interaction is a commensurate antiferromagnetic ordering of the Fe sublattice, with a moment at 4.2 K of 1.08(2)mu(B) per Fe atom in the basal plane of the tetragonal structure. However, symmetry arguments suggest that the Fe sublattice has a weak ferromagnetic component also in the basal plane. Experiments in a magnetic field with polarized neutrons establish that the ferromagnetic U moment is 0.47(2)mu(B) per U atom. In a magnetic field applied in the  direction (basal plane) the Fe sublattice antiferromagnetism is aligned perpendicular to the field in the basal plane, i.e., in the direction . Combining the neutron and magnetization results shows that the weak Fe ferromagnetic component in zero field is similar to 0.3 mu(B) so that the canting angle of the Fe moments is 16 degrees. Relatively small fields are sufficient to cause a further canting of the Fe moments towards the field direction; for example at 4.6 T this canting is 25 degrees. Polarized-neutron experiments in the paramagnetic state show that the Fe susceptibility is almost isotropic; however, the response of the U 5f electrons is much smaller along the c axis, so that it is the hybridization between the Fe 3d and U 5f electrons that gives rise to the measured anisotropy in this material. The weak ferromagnetism of the Fe sublattice, which may be a consequence of the interaction between the U 5f and Fe 3d electrons assures that the two sublattices develop their moments in the same manner. This is different from the situation in the RFe4Al8 (R = rare earth) compounds, in which the rare earth develops its full moment only at a lower temperature.