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, 3-fold 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 3-fold symmetric molecule and the 6-fold 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.