In  we investigated the lattice ⋀(Df 2) of all subvarieties of the variety Df 2 of two-dimensional diagonal free cylindric algebras. In the present paper we investigate the lattice ⋀(CA 2) of all subvarieties of the variety CA 2 of two-dimensional cylindric algebras. We prove that the cardinality of ⋀(CA 2) is that of the continuum, give a criterion for a subvariety of CA 2 to be locally finite, and describe the only pre locally nite subvariety of CA2. We also characterize nitely generated subvarieties of CA2 by describing all fteen pre nitely generated subvarieties of CA 2. Finally, we give a rough picture of ⋀(CA 2), and investigate algebraic properties preserved and reected by the reduct functors F:CA2andΦ:Λ(CA2)→(Λ(Df2)
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