can the subject or the object in a sentence be a complete phrase

In the sentence: "I think Joe hates me", what is the object of the sentence?
Is it the whole phrase: "Joe hates me"?
If so, then does that mean that a complete phrase can be an object?
If not, then is "me" the object and "Joe" is the subject and "I think" modifies "hate"-- so the sentence would be better written as: "Joe hates me, I think."?--in terms of being able to identify its component parts.
So, what is the subject? "I" or "Joe" and what is the object? "Joe hates me" or "me"? And, does "I think" modify "hates" or are they the subject and predicate of the sentence?