  We prove that a quotient of subspace of $C_p\oplus_pR_p$ ($1\le p<2$) embeds
completely isomorphically into a noncommutative $L_p$-space, where $C_p$ and
$R_p$ are respectively the $p$-column and $p$-row Hilbertian operator spaces.
We also represent $C_q$ and $R_q$ ($p<q\le2$) as quotients of subspaces of
$C_p\oplus_pR_p$. Consequently, $C_q$ and $R_q$ embed completely isomorphically
into a noncommutative $L_p(M)$. We further show that the underlying von Neumann
algebra $M$ cannot be semifinite.
