This paper analyzes the irreducible unitary representations of SU(2,1) in a basis labeled as |p, q; jmy>, where p,q correspond to quantum numbers associated with the quadratic and cubic Casimir operators, j,m label states of the SU(2) subgroup, and y labels the quantum number with respect to the U(1) subgroup. All the irreducible representations are found and the allowed range of these quantum numbers for each representation are given. The results are expressed in the form of diagrams that show the allowed values in a (j,y) plot for fixed values of p,q. A (p,q) plot is also provided that indicates the allowed values of these quantum numbers. [ABSTRACT FROM AUTHOR]