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.
$\mathbf{Added\ later}$: here are definitions of all but one of the missing maximals, taken from the above website. The only missing one now is max15 of order 465 with structure $31:15$. I will have a go at constructing that one.
a := G.1; b := G.2;
max6 := sub< Generic(G) | a^((a*b)^8*(a*b*b)^6),
((a*b*a*b*a*b*a*b*b*a*b*a*b*b*a*b*b)^3)^((a*b*b)^13*(a*b)^5) >;
max7 := sub< Generic(G) | a^((a*b*b)^3*(a*b)^11),
((a*b*a*b*a*b*b)^3)^((a*b)^14*(a*b*b)^6) >;
max8 := sub< Generic(G) | a^((a*b*b)^4*(a*b)^4*(a*b*b)^14),
(a*b*a*b*a*b*a*b*b*a*b*b)^((a*b*b)^12*(a*b)^4) >;
max9 := sub< Generic(G) |
(((a*b)^4*(a*b*a*b*b)^2*a*b*b)^10)^((a*b)^8*(a*b*b)^5*(a*b)^7),
((a*b*a*b*a*b*a*b*a*b*b)^5)^((a*b)^16*(a*b*b)^11) >;
max10 := sub< Generic(G) | a^((a*b)^3*(a*b*b)^15),
((a*b*a*b*a*b*a*b*a*b*b)^5)^((a*b*b)^8*(a*b)^9) >;
max11 := sub< Generic(G) | b^((a*b)^5*(a*b*b)^8*(a*b)^2),
((a*b*a*b*a*b*a*b*a*b*b)^5)^((a*b)^10*(a*b*b)^9) >;
max14 := sub< Generic(G) | a^((a*b)^4*(a*b*b)^4),
((a*b*a*b*a*b*a*b*a*b*b)^5)^((a*b*b)^17*(a*b)^6) >;