With the help of density functional theory, a series of matryoshka superatoms X@Y-12@X-20 = Ge, Y = Zn; X = Sn, Y = Mg, Mn, Zn or Cd; X = Pb, Y = Mg, Mn, Cd or Hg) with icosahedral symmetry has been extensively studied, to focus on the influence of the spin orbit coupling on geometries, stabilities, electronic structures and magnetic moments for these clusters. Generally speaking, the effect of spin-orbit coupling is highly correlated with composition elements of these clusters. Ge@Zn-12@Ge-20 islittle affected by the spin orbit coupling, while clusters containing Sn atom will generally undergo a moderate influence on their atomization energy, HOMO-LUMO gap and projected density of states. For clusters with Pb atoms, the effect of spin-orbit coupling could be observed distinctly in most cases. Our results demonstrate that the spin-orbit coupling can play a substantial role in superatoms containing heavy elements.