There are 38 vassals that have a household troop, as well as the 5 monarchs and 1 claimant. 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.
Note: Since 3.9.0, all claimants now have a household troop.
*: Only since 3.9.0. Previously, they had none.