  Non-trivial extensions of the three dimensional Poincar\'e algebra, beyond
the supersymmetric one, are explicitly constructed. These algebraic structures
are the natural three dimensional generalizations of fractional supersymmetry
of order $F$ already considered in one and two dimensions. Representations of
these algebras are exhibited, and unitarity is explicitly checked. It is then
shown that these extensions generate symmetries which connect fractional spin
states or anyons. Finally, a natural classification arises according to the
decomposition of $F$ into its product of prime numbers leading to sub-systems
with smaller symmetries.
