Cluster and satellite demographics in TNG-Cluster. Top panels: we plot the number of satellite galaxies of the 352 clusters in bins of satellite stellar $M_{\star }^{\mathrm{sat}}$ and host halo $M_{200\mathrm{c}}^{\mathrm{host}}$ mass at z = 0. The one-dimensional histograms for $M_{\star }^{\mathrm{sat}}$ and $M_{200\mathrm{c}}^{\mathrm{host}}$ are included in the right and top panels. The number of satellites per stellar mass bin decreases with satellite stellar mass, where there is a sharp decrease in the number of super-L_⋆ galaxies $M_{\star }^{\mathrm{sat}}>{10}^{10.5}{M}_{\odot }$. The number of satellites per host mass bin increases at lower cluster masses $M_{200\mathrm{c}}^{\mathrm{host}}\sim {10}^{14.3-15}{M}_{\odot }$, and then decreases for the most massive clusters $M_{200\mathrm{c}}^{\mathrm{host}}\sim {10}^{15-15.4}{M}_{\odot }$, which reflects the TNG-Cluster halo mass function (see text and Nelson et al. 2024 for details). Bottom panels: for each of the 352 hosts, we plot the number of FoF satellites above given stellar masses (left), where the medians and 16th and 84th percentiles are the solid curves and shaded regions respectively. Additionally, we qualitatively compare the TNG-Cluster results to spectroscopic (GalWCat19; Abdullah et al. 2020, 2023) and photometric (redMaPPer; Costanzi et al. 2019) SDSS observations, considering all galaxies brighter than r_mag < −20.4 and within a projected distance $d_{\mathrm{sat}}^{\mathrm{host}}<R_{200\mathrm{c}}$ as satellites (right panel; see text for details). The TNG-Cluster mass-richness relation is qualitatively consistent with observations.