  The set of prime numbers $p$ such that the supersingular $j$-invariants in
characteristic $p$ are all contained in the prime field is finite. And it is
well known that this set of primes coincides with the set of prime divisors of
the order of the Monster simple group. In this paper, we will present analogous
coincidences of supersingular invariants in level 2 and 3 and the orders of the
Baby monster group and the Fischer's group. The proof uses a connection between
the number of supersingular invariants and class numbers of imaginary quadratic
fields.
