Dedicated to Professor Jorge Sotomayor on his 60th birthday
A phase portrait of a vector field on a plane is called completely symmetric if it is invariant with respect to the group consisting of four involutions $i_1, i_2, i_1i_2, id$. The simplest example is a local center defined by the germ of an analytic vector field with a non-degenerate linear approximation. By the Poincare-Lyapunov theorem such a center is diffeomorphic to the center defined by the vector field $\dot x_1 = x_2, \dot x_2 = -x_1$ and consequently it is is completely symmetric. The paper is devoted to the classification of completely symmetric centers defined by germs of vector fields with a nilpotent linear approximation and by germs of vector fields with zero 2-jet and generic 3-jet.