Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
482 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C131 | AΣL(1,𝔽16) |
| commutator | C2×Q8 | C22×C4×C131 |
| Frattini, cosocle | C4⋊Q8 | C23×C131 |
| socle | C2×C131 | C2×AΣL(1,𝔽16) |
| prime radical | #3018×C131 | C2 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C131 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ #532×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2132×C131 | C2 | semidirect |
| 3. #1543×C131 | C2 | semidirect |
| 4. #1405×C131 | C2 | semidirect |
| 16. #356×C131 | C22 | semidirect |
| 18. #333×C131 | C22 | semidirect |
| 172. #13572 | C131 | direct (N × H) |
| 173. C131 | #13572 | direct (N × H) |
| 175. #2132 | C2×C131 | semidirect |
| 176. #1543 | C2×C131 | semidirect |
| 177. #1405 | C2×C131 | semidirect |
| 189. #356 | C22×C131 | semidirect |
| 191. #333 | C22×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3018×C131 | 2 |
| #2132×C131 | 2 |
| #1543×C131 | 2 |
| #1405×C131 | 2 |
| #13572 | 131 |