Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
348 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C41 | #2127 |
| commutator | C42 | C22×C4×C41 |
| Frattini, cosocle | #127 | C23×C41 |
| prime radical | C41×#3220 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C41 ◁ C22×C41 ◁ C22×C4×C41 ◁ C41×#535 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C41×#2128 | C2 | semidirect |
| 3. C41×#2127 | C2 | semidirect |
| 4. C41×#1412 | C2 | semidirect |
| 5. C41×#1408 | C2 | semidirect |
| 6. C41×#540 | C4 | semidirect |
| 8. C41×#496 | C4 | semidirect |
| 11. C41×#488 | C4 | semidirect |
| 16. C41×#433 | C4 | semidirect |
| 29. #127×C41 | C2×C4 | semidirect |
| 32. #125×C41 | C2×C4 | semidirect |
| 54. #97×C41 | C2×C4 | semidirect |
| 55. C4×C8×C41 | C2×C4 | semidirect |
| 130. #13609 | C41 | direct (N × H) |
| 154. #2128 | C2×C41 | semidirect |
| 155. #2127 | C2×C41 | semidirect |
| 156. #1412 | C2×C41 | semidirect |
| 157. #1408 | C2×C41 | semidirect |
| 165. #540 | C4×C41 | semidirect |
| 167. #496 | C4×C41 | semidirect |
| 170. #488 | C4×C41 | semidirect |
| 175. #433 | C4×C41 | semidirect |
| 182. C41 | #13609 | direct (N × H) |
| 189. #127 | C2×C4×C41 | semidirect |
| 192. #125 | C2×C4×C41 | semidirect |
| 214. #97 | C2×C4×C41 | semidirect |
| 215. C4×C8 | C2×C4×C41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C41×#3220 | 2 |
| C41×#2128 | 2 |
| C41×#2127 | 2 |
| C41×#1412 | 2 |
| C41×#1408 | 2 |
| #13609 | 41 |