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We reveal a low-temperature duality between the hyperbolic lattice modelfeaturing fractons and infinite decoupled copies of Zabrodin's $p$-adic modelof AdS/CFT. The core of the duality is the subsystem symmetries of thehyperbolic fracton model, which always act on both the boundary and the bulk.These subsystem symmetries are associated with fractal trees embedded in thehyperbolic lattice, which have the same geometry as Zabrodin's model. Thefracton model, rewritten as electrostatics theory on these trees, matches theequation of motion of Zabrodin's model. The duality extends from the action tolattice defects as $p$-adic black holes.

$p$-adic Holography from the Hyperbolic Fracton Model