The atomic sublattices occupying different Wyckoff positions in a host crystal are shown to be subdivided in the supercell model owing to the splitting of the occupied Wyckoff positions. The site symmetries of the split Wyckoff positions are in general different, which significantly increases the number of possible occupation schemes for impurities and defects in the supercell model. It is demonstrated that the use of the programs and retrieval tools of the Bilbao Crystallographic Server considerably simplifies the group-theoretical analysis of Wyckoff position splittings in the supercell model of a crystal with a point defect. Ab initio calculations of electronic states of single defects in ZnO (Zn and O neutral vacancies) within the supercell model are performed to demonstrate the influence of Wyckoff position splittings on the results.