Every sentence has a subject, and that subject is always a noun. There are three nouns in the sentence, (the) girl, (the) plane and (the rear). If we look at the sentence, we see that the phrase 'who loves to touch the rear of the plane' is describing the girl, thus the plane is not the subject. 'The rear' is describing part of the plane, and is also therefore not the subject. We can also look at the end of the sentence, 'is jailed today', which clearly applies to the girl, and not the plane or rear. We can even remove the middle section, leaving us with 'The girl is jailed today', showing clearly that the girl is the subject.
