  We study the four-dimensional {\it N}=8 maximal supergravity in the context
of Lie superalgebra SU(8/1). All possible successive superalgebraic truncations
from four-dimensional {\it N}=8 theory to {\it N}=7, 6, $\cdots$, 1
supergravity theories are systematically realized as sub-superalgebra chains of
SU(8/1) by using the Kac-Dynkin weight techniques.
