  The moir\'e potential of graphene on hexagonal boron nitride (hBN) generates
a supercell sufficiently large as to thread a full magnetic flux quantum
$\Phi_0$ for experimentally accessible magnetic field strengths. Close to
rational fractions of $\Phi_0$, $p/q \cdot\Phi_0$, magnetotranslation
invariance is restored giving rise to Brown-Zak fermions featuring the same
dispersion relation as in the absence of the field. Employing a highly
efficient numerical approach we have performed the first realistic simulation
of the magnetoconductance for a 250 nm wide graphene ribbon on hexagonal boron
nitride using a full ab-initio derived parametrization including strain. The
resulting Hofstadter butterfly is analyzed in terms of a novel Wannier diagram
for Landau spectra of Dirac particles that includes the lifting of the spin and
valley degeneracy by the magnetic field and the moir\'e potential. This complex
diagram can account for many experimentally observed features on a
single-particle level, such as spin and valley degeneracy lifting and a
non-periodicidy in $\Phi_0$.
