We have studied by means of low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) single molecular spin hybrids formed upon chemisorbing a polycyclic aromatic, threefold symmetric hydrocarbon molecule on Co(111) nanoislands. The spin-dependent hybridization between the Co d states and the π orbitals of the molecule leads to a spin-imbalanced electronic structure of the chemisorbed organic molecule. Spin-sensitive measurements reveal that the spin polarization shows intramolecular variations among the different aromatic rings in spite of the highly symmetric adsorption geometry promoted by symmetry matching of the threefold symmetric molecule and the sixfold symmetric Co(111) lattice. Hence the varying degree of spin polarization on the organic molecule does not stem from a different hybridization of the aromatic rings with the Co atoms, but is proposed to be a consequence of the superposition of the spin polarization of the molecule and the spatially modulated spin polarization of the spin-dependent quantum interference pattern of the Co(111) surface state.