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In this paper we consider the divergence parabolic equation with bounded andmeasurable coefficients related to Hormander's vector fields and establish aNash type result, i.e., the local Holder regularity for weak solutions. Afterderiving the parabolic Sobolev inequality, (1,1) type Poincar\'e inequality ofHormander's vector fields and a De Giorgi type Lemma, the Holder regularityof weak solutions to the equation is proved based on the estimates ofoscillations of solutions and the isomorphism between parabolic Campanato spaceand parabolic Holder space. As a consequence, we give the Harnack inequalityof weak solutions by showing an extension property of positivity for functionsin the De Giorgi class.

A Nash Type result for Divergence Parabolic Equation related to Hormander's vector fields