There are 38 vassals that have a household troop, as well as all monarchs and claimants. This mean that they will recruit that troop in large numbers as well as the normal faction recruitment they do. All of these vassals and some more are also in the List of notable lords, which should be looked at to review which of these lords might make good vassals for the player's kingdom.
*: Only since 3.9.0. Previously, they had none.