Objection 1. It seems that vainglory is not a capital vice. For a vice that always arises from another vice is seemingly not capital. But vainglory always arises from pride. Therefore vainglory is not a capital vice.
Objection 2. Further, honor would seem to take precedence of glory, for this is its effect. Now ambition which is inordinate desire of honor is not a capital vice. Neither therefore is the desire of vainglory.
Objection 3. Further, a capital vice has a certain prominence. But vainglory seems to have no prominence, neither as a sin, because it is not always a mortal sin, nor considered as an appetible good, since human glory is apparently a frail thing, and is something outside man himself. Therefore vainglory is not a capital vice.
On the contrary, Gregory (Moral. xxxi) numbers vainglory among the seven capital vices.
I answer that, The capital vices are enumerated in two ways. For some reckon pride as one of their number: and these do not place vainglory among the capital vices. Gregory, however (Moral. xxxi), reckons pride to be the queen of all the vices, and vainglory, which is the immediate offspring of pride, he reckons to be a capital vice: and not without reason. For pride, as we shall state farther on (152, 1 and 2), denotes inordinate desire of excellence. But whatever good one may desire, one desires a certain perfection and excellence therefrom: wherefore the end of every vice is directed to the end of pride, so that this vice seems to exercise a kind of causality over the other vices, and ought not to be reckoned among the special sources of vice, known as the capital vices. Now among the goods that are the means whereby man acquires honor, glory seems to be the most conducive to that effect, inasmuch as it denotes the manifestation of a man's goodness: since good is naturally loved and honored by all. Wherefore, just as by the glory which is in God's sight man acquires honor in Divine things, so too by the glory which is in the sight of man he acquires excellence in human things. Hence on account of its close connection with excellence, which men desire above all, it follows that it is most desirable. And since many vices arise from the inordinate desire thereof, it follows that vainglory is a capital vice.
Reply to Objection 1. It is not impossible for a capital vice to arise from pride, since as stated above (in the body of the Article and I-II, 84, 2) pride is the queen and mother of all the vices.
Reply to Objection 2. Praise and honor, as stated above (Article 2), stand in relation to glory as the causes from which it proceeds, so that glory is compared to them as their end. For the reason why a man loves to be honored and praised is that he thinks thereby to acquire a certain renown in the knowledge of others.
Reply to Objection 3. Vainglory stands prominent under the aspect of desirability, for the reason given above, and this suffices for it to be reckoned a capital vice. Nor is it always necessary for a capital vice to be a mortal sin; for mortal sin can arise from venial sin, inasmuch as venial sin can dispose man thereto.
Source: Summa Theologica (New Advent)