An algebra $A$ has the congruence extension property (CEP) if for every $B\le A$ and $\theta \in \operatorname{Con} B$ there is a $\phi \in \operatorname{Con} A$ such that $\theta = \phi \cap (B\times B)$. A class $K$ of algebras has the CEP if every algebra in the class has the CEP.
I must show that the class of Abelian groups has the CEP and find an example of lattice that doesn't have the CEP.
For Abelian groups: I consider it doing by induction on number of elements in a group and use inductive proposition on quotient groups. This is just an idea and I don't know how to use it.
Lattices: I know that counterexample for lattices should be some non distributive lattice because all distributive are CEP. But I can't find any example of congruence in a sublattice that wouldn't be also a subset of a congruence of a lattice. Maybe my understanding of basic terms isn't correct...
Tnx in advance for any help