Objection 1. It would seem that the subject of continence is the concupiscible power. For the subject of a virtue should be proportionate to the virtue's matter. Now the matter of continence, as stated (2), is desires for the pleasures of touch, which pertain to the concupiscible power. Therefore continence is in the concupiscible power.
Objection 2. Further, "Opposites are referred to one same thing" [Categ. viii]. But incontinence is in the concupiscible, whose passions overcome reason, for Andronicus says [De Affectibus] that "incontinence is the evil inclination of the concupiscible, by following which it chooses wicked pleasures in disobedience to reason." Therefore continence is likewise in the concupiscible.
Objection 3. Further, the subject of a human virtue is either the reason, or the appetitive power, which is divided into the will, the concupiscible and the irascible. Now continence is not in the reason, for then it would be an intellectual virtue; nor is it in the will, since continence is about the passions which are not in the will; nor again is it in the irascible, because it is not properly about the passions of the irascible, as stated above (2, ad 2). Therefore it follows that it is in the concupiscible.
On the contrary, Every virtue residing in a certain power removes the evil act of that power. But continence does not remove the evil act of the concupiscible: since "the continent man has evil desires," according to the Philosopher (Ethic. vii, 9). Therefore continence is not in the concupiscible power.
I answer that, Every virtue while residing in a subject, makes that subject have a different disposition from that which it has while subjected to the opposite vice. Now the concupiscible has the same disposition in one who is continent and in one who is incontinent, since in both of them it breaks out into vehement evil desires. Wherefore it is manifest that continence is not in the concupiscible as its subject. Again the reason has the same disposition in both, since both the continent and the incontinent have right reason, and each of them, while undisturbed by passion, purposes not to follow his unlawful desires. Now the primary difference between them is to be found in their choice: since the continent man, though subject to vehement desires, chooses not to follow them, because of his reason; whereas the incontinent man chooses to follow them, although his reason forbids. Hence continence must needs reside in that power of the soul, whose act it is to choose; and that is the will, as stated above (I-II, 13, 1).
Reply to Objection 1. Continence has for its matter the desires for pleasures of touch, not as moderating them (this belongs to temperance which is in the concupiscible), but its business with them is to resist them. For this reason it must be in another power, since resistance is of one thing against another.
Reply to Objection 2. The will stands between reason and the concupiscible, and may be moved by either. On the continent man it is moved by the reason, in the incontinent man it is moved by the concupiscible. Hence continence may be ascribed to the reason as to its first mover, and incontinence to the concupiscible power: though both belong immediately to the will as their proper subject.
Reply to Objection 3. Although the passions are not in the will as their subject, yet it is in the power of the will to resist them: thus it is that the will of the continent man resists desires.
Source: Summa Theologica (New Advent)