  We study the abundance of satellite galaxies around 198 Milky Way- (MW) and
M31-like hosts in TNG50, the final instalment in the IllustrisTNG suite of
cosmological magnetohydrodynamical simulations. MW/M31-like analogues are
defined as disky galaxies with stellar masses of Mstar = 10^10.5-11.2 Msun in
relative isolation at z = 0. By defining satellites as galaxies with Mstar >
5*10^6 Msun within 300 kpc (3D) of their host, we find a remarkable level of
diversity and host-to-host scatter across individual host galaxies. The median
(16th - 84th percentiles) TNG50 MW/M31-like galaxy hosts a total of 5 (2-11)
satellites with Mstar > 5*10^6 Msun, reaching up to Mstar ~ 10^8.5 Msun
(10^7.4-9.4 Msun). The abundance of subhaloes with Mdyn > 5*10^7 Msun is larger
by a factor of more than 10. The number of all satellites (subhaloes) ever
accreted is larger by a factor of 4-5 (3-5) than those surviving to z = 0.
Hosts with larger galaxy stellar mass, brighter K-band luminosity, larger total
halo mass, and more recent halo assembly typically have a larger number of
surviving satellites. The satellite abundances around TNG50 MW/M31-like
galaxies are consistent with similar hosts from observational surveys (e.g.
SAGA) and previous simulations (e.g. Latte). While the observed MW satellite
system falls within the TNG50 scatter across all stellar masses considered, M31
is slightly more satellite-rich than our 1 sigma scatter, possibly due to
volume and mass limitations. We find a handful of systems with both a Large and
a Small Magellanic Cloud-like satellite. There is no missing satellites problem
with TNG50.
