The offensive against the Reinosa pocket (prior to the battle for Santander) began on August 14th, 1937. The CTV had prepared a fast detachment to exploit the initial breakthrough carried out by the infantry units. This detachment included:

HQ of the Raggruppamento Reparti Specializzati
1 Tank Company (the others were attached to the infantry divisions for the initial attack)
1 lorried Infantry Battalion detached from the Littorio div (that was remaining in reserve)
1 MG motorcycle Company
1 Armoured Car Company
and, here they are, 5 Nationalist Cavalry Squadrons!

Also note that at this time the Raggruppamento had a Flame-thrower Tankette Platoon and an attached Spanish Tank Company (most likely, T26Bs from the ist Bandera Carros de Combate de la Legion Extranjera).

A small but interesting mobile force, I think. The cavalry is present and under command of the CTV, although these aren't Italian troopers. I assume the 5 squadrons form a regular regiment with 4 sabre and 1 MG squadrons.

Related

Italian CTV TO&E For Command Decision Rules