The experimental structure of AlOF is only partially known, given the limitations of XRD measurements. We have completed an extensive first principle theoretical study of the structure of AlOF. As a complement to experimental studies we investigate the structure of AlOF with density functional theory to identify the most stable distribution of oxide and fluoride ions on the lattice. Next to the experimentally found space group Pnma, we include its subgroups in our study for a deeper understanding of the structure-stability-relation. The theoretically identified most stable structure confirms the experimentally determined space group with a homogeneous distribution of the fluoride anions. Additionally, we determine Bader charges and elastic constants for two selected distributions to gain a deeper insight into the binding of this material.