$C_w(L)$ is a set of all the weak congruences on a given lattice $L$, i.e. a set of all the congruences on all the sublattices of $L$. It is proved here that: a) the lattice $(C_w(L),\leq)$ is modular if and only if $L$ is a two-element chain; and b) if $L$ is a bounded lattice (with two disjoint constants 0 and 1) then $(C_w(L),s)$ is complemented if and only if its lattice of sublattices is complemented. (For lattice $L$ without constants, $(C_w(L),\leq)$ is never complemented).