# Embedding of $F(4)$ in $OSp(8|4)$?

Is the superconformal algebra in five dimensions, $F(4)$, a subalgebra of the (maximal) six-dimensional superconformal algebra $OSp(8|4)$?

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The bosonic subalgebra of $F(4)$ is $SO(5,2)\times SU(2)$. This certainly can be embedded into the bosonic subalgebra of $OSp(8|4)$ which is $SO(6,2)\times SO(5)$. The tricky bit is indeed to figure out the fermionic generators.