In a classic such as this book, there are may symbols. So, I will give one of the most recognizable symbols, which relate to some major themes in the book.
Perhaps the most recognizable symbol in the book is Holden's red cap. It is a sign that he wants to be different. He is an individual, not like the rest. We can say that he is not part of the herd and he wants people to know it. The dark side of this is that Holden is a very critical person. For example, one of Holden's favorite words in the book is the word, "phony."
As Holden sees it there is phoniness everywhere, especially in the adult world. To be sure, Holden's ideas are superficial in many ways, but he is also an accurate observer of society with all its pretensions. As we read the book, there are plenty examples of phoniness. Characters such as Carl Luce, Maurice and Sunny, and even Mr. Spencer can be seen to be phony. The irony of all of this is that Holden is also a phony, which he never quite seems to notice. The reader is supposed to pick up on this one.
The red cap also ties into the theme of loneliness. Holden wants to be so different that he does not have a companion. We can say that his desire to stand apart is the very thing that perpetuates his loneliness. On the one hand, he wants a meaningful companion; on the other hand, he is alienates people, like when he alienates Sally Hayes on a date.
Uniqueness is a lonely place.