  Two-dimensional (2D) generalization of the Su-Schriffer-Heeger (SSH) model
serves as a platform for exploring higher-order topological insulators (HOTI).
We investigate this model in a magnetic field which interpolates two models
studied so far with zero flux and $\pi$ flux per plaquette. We show that in the
Hofstadter butterfly there appears a wide gap around the $\pi$ flux, which
belongs to the same HOTI discovered by Benalcazar-Bernevig-Hughes (BBH). It
turns out that in a weak field regime HOTI could exist even within a small gap
disconnected from the wider gap around $\pi$ flux. To characterize HOTI, we
employ the entanglement polarization (eP) technique which is useful even if the
basic four bands split into many Landau levels under a magnetic field.
