Here's the breakdown:
* Subject: The subject is the person or thing performing the action. While the sentence isn't complete, it's safe to assume the subject is the "girl" because the sentence implies she's doing the kissing.
* Object: The object is the person or thing receiving the action. The "boy" is the direct object of the verb "kissed."
So, even though the sentence is incomplete, the likely subject is "girl" and the object is "boy."