While the word subject in grammar normally applies to a sentence, it is possible for an infinitive to have a subject.
When an infinitive or an infinitive phrase follows certain verbs, the action of the infinitive may be done by a different person or thing than the subject of the sentence. This doer of the infinitive's action follows the verb and comes before the infinitive. This is known as the subject of the infinitive.
Keep in mind that when an infinitive follows a verb, sometimes the word to is dropped from the infinitive.
A personal pronoun is in the objective case when it is a subject of the infinitive.
Examples: We wanted Bill to go to the airport.
Simon helped me to record the data.
No one saw the prisoner escape.
Simon helped me record the data.
(In the last two examples, the word to has been dropped.)