  In the framework of Hofstadter`s approach we provide a detailed analysis of a
realization of exotic topological states such as the Chern insulator with large
Chern numbers. In a transverse homogeneous magnetic field a one-particle
spectrum of fermions transforms to an intricate spectrum with a fine
topological structure of the subbands. In a weak magnetic field $H$ for a
rational magnetic flux, a topological phase with a large Chern number is
realized near the half filling. There is an abnormal behavior of the Hall
conductance ${\sigma_{xy}\simeq \frac{e}{2 H}}$. At half-filling, the number of
chiral Majorana fermion edge states increases sharply forming a new state,
called the chiral Majorana fermion liquid.
