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A dcpo $P$ is continuous if and only if the lattice $C\left(P\right)$ of all Scott-closed subsets of $P$ is completely distributive. However, in the case where $P$ is a non-continuous dcpo, little is known about the order structure of $C\left(P\right)$. In this paper, we study the order-theoretic properties of $C\left(P\right)$ for general dcpo’s $P$. The main results are: (i) every $C\left(P\right)$ is C-continuous; (ii) a complete lattice $L$ is isomorphic to $C\left(P\right)$ for a complete semilattice $P$ if and only if $L$ is weak-stably C-algebraic; (iii) for any two complete semilattices...