  Reductive W-algebras which are generated by bosonic fields of spin-1, a
single spin-2 field and fermionic fields of spin-3/2 are classified. Three new
cases are found: a `symplectic' family of superconformal algebras which are
extended by $su(2)\oplus sp(n)$, an $N=7$ and an $N=8$ superconformal algebra.
The exceptional cases can be viewed as arising a Drinfeld-Sokolov type
reduction of the exceptional Lie superalgebras $G(3)$ and $F(4)$, and have an
octonionic description. The quantum versions of the superconformal algebras are
constructed explicitly in all three cases.
