C := CharacterTable("Th");
worked for me.

Some of the maximal subgroups are stored, and you can access these with

    > a,M := MaximalSubgroups(G, "Th");
    Note: Generators for Max6 - Max11, Max 14, Max 15 are unknown
    
    > #M;
    8

It appears to have defined eight of them. They are stored as M[i]`group. For example:

    > LMGChiefFactors(M[1]`group);
        G
        |  Cyclic(3)
        *
        |  3D(4, 2)
        1




In principal you can find this data in the website

https://brauer.maths.qmul.ac.uk/Atlas/v3/

but it is not always easy to interpret.