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) >;