Fixed points subgroups $G^{\sigma ,{\sigma }^{\mathrm{\prime }}}$ by two involutive automorphisms $\sigma$, ${\sigma }^{\mathrm{\prime }}$ of exceptional compact Lie group $G$, Part II, $G=E_8$

For the simply connected compact exceptional Lie group $E_8$, we determine the structure of subgroup $(E_8{)}^{\sigma ,{\sigma }^{\mathrm{\prime }}}$ of $E_8$ which is the intersection $(E_8{)}^{\sigma }\cap (E_8{)}^{{\sigma }^{\mathrm{\prime }}}$. Then the space $E_8\mathrm{/}(E_8{)}^{\sigma ,{\sigma }^{\mathrm{\prime }}}$ is the exceptional $$\mathbb{Z}$_2 \times $\mathbb{Z}$_2$- symmetric space of type EVIII-VIII-VIII, and that we give two involutions $\sigma ,{\sigma }^{\mathrm{\prime }}$ for the space $E_8\mathrm{/}(E_8{)}^{\sigma ,{\sigma }^{\mathrm{\prime }}}$ concretely.