Manifold with largest symmetry group

Question

Is there any $n$-dimensional (smooth) manifold $M_{0}$ which has largest symmetry group, i.e. for any $n$-dimensional manifold $M$, $Sym(M)$ can be embedded in $Sym(M_{0})$? Intuitively, if it exists, I think sphere or whole euclidean space will give answer (because it looks highly symmetric), but I don't know how to show or even such manifold exists. Is there any known results with more specific conditions? (specific $n$, compact manifold, complex manifold, Riemannian manifold (with isometry group), ...) Thanks in advance.