We studied the nanoscale structure of the short-range incommensurate magnetic order in La1.5 Sr0.5 CoO4 by elastic neutron scattering. We find that magnetic diffuse scattering is isotropic in the a-b plane, in contrast with the naive expectation based on the popular stripe model. Indeed, charge segregation into lines favoring certain lattice direction(s) would facilitate linear stacking faults in an otherwise robust antiferromagnetism of undoped material, leading to anisotropic disorder with a characteristic symmetry pattern present in the neutron scattering data.