  This paper provides a short introduction to scalar, bosonic, and fermionic
superfield component expansion based on the branching rules of irreducible
representations in one Lie algebra (in our case, $\mathfrak{su}(32)$, and also
$\mathfrak{su}(16)$) into one of its Lie subalgebras ($\mathfrak{so}(11)$,
$\mathfrak{so}(10)$). This systematic method paves the way for expansion of
bosonic and fermionic superfields, in order to search for possible off-shell
supergravity supermultiplets. Furthermore, we implement such a decomposition
method in Mathematica in its simplest form, which can be used for superfield
component decompositions.
