  We describe an easy way how to find supercharacter theories for a finite
group, if its character table is known. Namely, we show how an arbitrary
partition of the conjugacy classes or of the irreducible characters can be
refined to the coarsest partition that belongs to a supercharacter theory. Our
constructions emphasize the duality between superclasses and supercharacters.
An algorithm is presented to find all supercharacter theories on a given
character table. The algorithm is used to compute the number of supercharacter
theories for some nonabelian simple groups with up to 26 conjugacy classes.
