ABSTRACT Within lambda cold dark matter ($Λ$CDM), dwarf galaxies like the Large Magellanic Cloud (LMC) are expected to host numerous dark matter subhaloes, several of which should host faint dwarf companions. Recent Gaia proper motions confirm new members of the LMC system in addition to the previously known SMC, including two classical dwarf galaxies ($M_*$$\gt 10^5$ M$_{⊙ }$; Carina and Fornax) as well as several ultrafaint dwarfs (Car2, Car3, Hor1, and Hyd1). We use the Feedback In Realistic Environments (FIRE) simulations to study the dark and luminous (down to ultrafaint masses, $M_*$$∼$6$\times 10^ {3}$ M$_{⊙ }$) substructure population of isolated LMC-mass hosts ($M_{\text{200m}}$ = 1–3$\times 10^ {11}$ M$_{⊙ }$) and place the Gaia + DES results in a cosmological context. By comparing number counts of subhaloes in simulations with and without baryons, we find that, within 0.2 $r_{\text{200m}}$, LMC-mass hosts deplete $∼$30 per cent of their substructure, significantly lower than the $∼$70 per cent of substructure depleted by Milky Way (MW) mass hosts. For our highest resolution runs ($m_\text{bary}$ = 880 M$_{⊙ }$), $∼ 5\!-\!10$ subhaloes form galaxies with $M_*$$\ge 10^{4}$ M$_{⊙ }$ , in agreement with the seven observationally inferred pre-infall LMC companions. However, we find steeper simulated luminosity functions than observed, hinting at observation incompleteness at the faint end. The predicted DM content for classical satellites in FIRE agrees with observed estimates for Carina and Fornax, supporting the case for an LMC association. We predict that tidal stripping within the LMC potential lowers the inner dark matter density of ultrafaint companions of the LMC. Thus, in addition to their orbital consistency, the low densities of dwarfs Car2, Hyd1, and Hyd2 reinforce their likelihood of Magellanic association.