  We characterize the luminosity functions of galaxies residing in $z\sim0$
groups and clusters over the broadest ranges of luminosity and mass reachable
by the Sloan Digital Sky Survey. Our measurements cover four orders of
magnitude in luminosity, down to about $M_r=-12$ mag or $L=10^7\,L_\odot$, and
three orders of magnitude in halo mass, from $10^{12}$ to $10^{15} \, {\rm
M}_\odot$. We find a characteristic scale, $M_r\sim-18$ mag or $L\sim10^9\,
L_\odot$, below which the slope of the luminosity function becomes
systematically steeper. This trend is present for all halo masses and
originates mostly from red satellites. This ubiquitous faint-end upturn
suggests that it is formation, rather than halo-specific environmental effect,
that plays a major role in regulating the stellar masses of faint satellites.
We show that the satellite luminosity functions can be described in a simple
manner by a double Schechter function with amplitudes scaling with halo mass
over the entire range of observables. Combining these conditional luminosity
functions with the dark matter halo mass function, we accurately recover the
entire field luminosity function over 10 visual magnitudes and reveal that
satellite galaxies dominate the field luminosity function at magnitudes fainter
than $-17$. We find that the luminosity functions of blue and red satellite
galaxies show distinct shapes and we present estimates of the stellar mass
fraction as a function of halo mass and galaxy type. Finally, using a simple
model, we demonstrate that the abundances and the faint-end slopes of blue and
red satellite galaxies can be interpreted in terms of their formation history,
with two distinct modes separated by some characteristic time.
