The superficial layer has 4 muscles, the pronator teres, flexor carpi radialis, palmaris longus, and the flexor carpi ulnaris. (all-about-arm-exercises.com)
While doing pullups you will activate the musculature of your trapiezus (traps, all parts), pectorials (pecs, all parts), deltoids (shoulder, all parts), latissimus dorsi (lats), rhomboids, flexor carpi ulnaris, palmaris longus, flexor digitorum profundus, flexor digitorum superficialis, and flexor pollicis longus (just the anatomical way of saying the muscles in the forearm). (tomcoffeyfitness.com)
This group of muscles has 6 heads which include; flexor digitorum profundus, flexor digitorium superfisialis, flexor carpi ulnaris, flexor carpi radialis, palmaris longus and flexor pillicis longus. (weightlosstriumph.com)