A sublattice of a lattice 
is a nonempty subset
closed under the meet and join
of 
. It is itself a lattice
with the inherited operations (Burris and Sankappanavar
1981). Being a lattice under an inherited order alone
is insufficient, since the meet or join
computed in the subset might differ from that in 
.
For example, any nonempty subset of a chain is a sublattice. A sublattice of a congruence lattice need not be the full congruence lattice. The distinction matters in the finite lattice representation problem.
