  We study the effect of interactions on the Hofstadter butterfly of the
honeycomb lattice. We show that the interactions induce charge ordering that
breaks the translational and rotational symmetries of the system. These phase
transitions are prolific and occur at many values of the flux and particle
density. The breaking of the translational symmetry introduces a new length
scale in the problem and this affects the energy band diagram resulting in the
disintegration of the fractal structure in the energy flux plot, the Hofstadter
butterfly. This disintegration increases with increase in the interaction
strength. Many of these phase transitions are accompanied with change in the
Hall conductivity. Consequently, the disintegration of the Hofstadter butterfly
is manifested in the Landau fan diagram also.
