The paper investigates the combinatorial structure of the dual Lorimer plane. The authors prove that the dual Lorimer plane is single generated by quadrangles and that its Baer subplanes contain the centre for shears. The authors characterize some quadrangles which generate Fano subplanes and classify the subplanes of order 2 depending on whether they are extendable to Baer subplanes or not. Three inequivalent types of complete 14-arcs in the dual Lorimer plane are shown.