There are many subjects covered in Computer Science studies. we should do the discussion on Which subject is most important in Computer Science? and why?
Data Structures and Algorithms is perhaps the most important subject for a computer scientist (not computer programmer) as it provides the basic skills and background for creating efficient algorithms and writing code using appropriate data structures. Other subjects that a computer scientist is expected to know are Operating systems and database systems to some extent.
I think it slightly depends on what specialty one is going to consider in computer science. However, for any specialty data structures and algorithms is absolutely crucial, it is almost an axiom that this subject is the basis of computer science. Another important subject, in my opinion, is computer systems and organisation, because it provides the basic knowledge of how computers actually work at the lowest level (i.e. the interface between software and hardware). Additionally, something that is not obligatory but I think is very important, is discrete mathematics in computer science as it provides the mathematical foundation of computer science using logic, principles of computing, proofs etc.