  The nontrivial band topology can influence the Hofstadter spectrum. We
investigate the Hofstadter spectrum for various models of Chern insulators
under a rational flux $\frac{\phi_{0}}{q}$, here $\phi_{0}=\frac{h}{e}$ and $q$
being an integer. We find two major features. First, the number of splitting
subbands is $|q-C|$ with Chern number $C$. Second, the anomalous open-orbit
subbands with Chern numbers $q-1$ and $-q-1$ emerge, which are beyond the
parameter window $(-q/2,q/2)$ of the Diophantine equation studied by
Thouless-Kohmoto-Nightingale-den Nijs [Phys. Rev. Lett. \textbf{49}, 405
(1982)]. These two findings are explained by semiclassical dynamics. We propose
that the number of splitting subbands can be utilized to determine Chern number
in cold atom systems, and the open-orbit subbands can provide routes to study
exotic features beyond the Landau level physics.
