C := CharacterTable("Th");
worked for me.
Some of the maximal subgroups are stored, and you can access these with
> G := MatrixGroup("Th", 1);
> 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.