Thanks to the implementation of an order-N semiempirical Hartree-Fock method, which at the same time is accurate enough to allow a determination of electronic and structural properties of complex insulating systems with atoms in a wide range of environments, and is fast enough to tackle large size systems and repeated calculations, generic properties of monolayer and bilayer MgO square islands, deposited on a weakly interacting metal substrate, are studied. The presence of interfacial dislocations is evidenced, and their periodicity related to the two-dimensional lattice parameter of the unsupported islands. Two size regimes are identified: a small size regime, with no dislocations present (nanometric or subnanometric regime), in which edge effects play a prominent role and the island properties are driven by the small average coordination number of the atoms. At larger sizes, the properties present an oscillating behavior as a function of size, associated with the periodicity of interfacial dislocations. As regards electronic properties, their inhomogeneity inside the islands is expected to yield specific site reactivity or inhomogeneous surface potentials. Most stable islands are identified and their (magic) sizes have been related to the dislocation network periodicity, in agreement with existing experimental results for MgO on Ag(100) and Mo(100).