  The structure of the 64-dimensional extended real Clifford-Dirac (ERCD)
algebra, which has been introduced in our paper Phys. Lett. A. 375 (2011) 2479,
is under consideration. The subalgebras of this algebra are investigated: the
29-dimensional proper ERCD algebra and 32-dimensional pure matrix algebra of
invariance of the Dirac equation in the Foldy-Wouthuysen representation. The
last one is the maximal pure matrix algebra of invariance of this equation. The
different realizations of the proper ERCD algebra are given. The application of
proper ERCD algebra is illustrated on the example of the derivation of the
hidden spin (1,0) Poincare symmetry of the Dirac equation.
