  All 7-dimensional subalgebras of the 8-dimensional Clifford algebra over the
field C of complex numbers are found. Canonical bases are used throughout the
determination. It is found that the 8-dimensional Clifford algebra over C has
exactly eight 7-dimensional subalgebras and each of these eight is over the
complex numbers. It follows that the 8-dimensional Clifford algebra over C has
no 7-dimensional subalgebra over the real numbers. Another consequence is that
the eight 7-dimensional subalgebras of the 8-dimentional Clifford over C are in
fact 7-dimensional subalgebras of all greater dimensional Clifford algebras
over C.
