Somehow, I managed to teach ESL for over 10 years before I learned what this is.  The expression “is supposed to” is called a semi-auxiliary verb.  In the sentence in the title, “study” is the main verb.

The expressions below are all called semi-auxiliary verbs.  They are followed by the main verb.

•  (have) to

•  (be) supposed to

•  (be) able to

•  (be) going to

Sample Sentences with Semi-Auxiliary Verbs

Example #1. Mario is supposed to study.

-“is supposed to” is a semi-auxiliary verb and “study” is the main verb.
-One way to look at this is you could substitute “is supposed to” with the auxiliary verb “should.”  For #1, you could write, “Mario should study.”
-And just like in Example #1, “study” is the main verb.

Example #2. She has to eat her soup.

-“has to” is a semi-auxiliary verb and “eat” is the main verb.
-One way to look at this is you could substitute “has to” with the auxiliary verb “must.” For #2, you could write, “She must eat her soup.”
-As in Example #2, “eat” is the main verb.

Example #3. We were able to finish early.

-“are able to” is a semi-auxiliary verb and “finish” is the main verb.
-One way to look at this is you could substitute “has to” with the auxiliary verb “could.” For #3, you could write, “We could finish early.”
-And just like in Example #3, “finish” is the main verb.

Example #4. I am going to look for a new roommate.

-“am going to” is a semi-auxiliary verb and “look” is the main verb.
-One way to look at this is you could substitute “am going to” with the auxiliary verb “will.” For #4, you could write, “I will look for a new roommate.” 
-And just like in Example #4, “look” is the main verb.

For an inductive approach to teaching semi-auxiliary verbs, see Unit 26 in Pro Lingua Learning–The Grammar Review Book) 

Thank you “Chris” for the question.

David