  Using the Lawson's existence theorem of minimal surfaces and the symmetries
of the Hopf fibration, we will construct symmetric embedded closed minimal
surfaces in the three dimensional sphere. These surfaces contain the Clifford
torus, the Lawson's minimal surfaces, and seven new minimal surfaces with
genera 9, 25, 49, 121, 121, 361 and 841. We will also discuss the relation
between such surfaces and the maximal extendable group actions on subsurfaces
of the three dimensional sphere.
