What a great idea! The Mathematics Genealogy Project traces over 116,000 mathematicians along with their “descendants” — the students they have mentored, their grandstudents (I just made that word up) and so on. Tracing memes instead of genes! Try it at http://genealogy.math.ndsu.nodak.edu/ .
I did a keyword search for Schubert and got 21 results, listing names, institutions, and what looks like the year graduate work was completely. Clicking on Cedric Shubert showed me a guy who’d gotten his PhD at the University of Toronto in 1962.
Also listed were two of his students (those who note him as advisor on their dissertations) with their own information and links. He has a total of two students who are also his two “descendants.” Then you have someone like John Archibald Wheeler, who has only 11 students listed, but 458 “descendants”.
As you might imagine, this is a pretty extensive project; be sure to check out the FAQ for additional information (like where the contact information for the mathematicians is, how often the databases are updated, and where you can get the dissertations listed on the information pages.)