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The Genealogica Arnulfi Comitis names (in order) "Hludovicum Karolum Karlomannum...
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The Genealogica Arnulfi Comitis names (in order) "Hludovicum Karolum Karlomannum et Hlotharium" as the four sons of "Karolus imperator…ex Hyrmentrudi regina". Cited at Medieval Lands Database: http://fmg.ac/Projects/MedLands/CAROLINGIANS.htm#_ftnref235. Accessed January 10, 2017