Finite Group DatabasebetaFinite Group DatabasebetaOrder 10496.
468 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C41 | #353 |
| commutator | C42 | C22×C4×C41 |
| Frattini, cosocle | #124 | C23×C41 |
| prime radical | C2×C41×#496 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C41 ◁ C23×C41 ◁ C22×C4×C41 ◁ C2×#124×C41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C41×#355 | C2 | semidirect |
| 3. C2×C41×#354 | C2 | semidirect |
| 4. C41×#1406 | C2 | direct (N × H) |
| 7. C2×#127×C41 | C4 | semidirect |
| 11. C41×#496 | C4 | semidirect |
| 15. C2×#97×C41 | C4 | semidirect |
| 17. C41×#355 | C22 | semidirect |
| 19. C41×#354 | C22 | semidirect |
| 36. #127×C41 | C2×C4 | semidirect |
| 50. #97×C41 | C2×C4 | semidirect |
| 132. C2×#1406 | C41 | direct (N × H) |
| 155. C2×#355 | C2×C41 | semidirect |
| 156. C2×#354 | C2×C41 | semidirect |
| 157. #1406 | C2×C41 | direct (N × H) |
| 163. C2×C41 | #1406 | direct (N × H) |
| 167. C2×#127 | C4×C41 | semidirect |
| 171. #496 | C4×C41 | semidirect |
| 175. C2×#97 | C4×C41 | semidirect |
| 177. #355 | C22×C41 | semidirect |
| 179. #354 | C22×C41 | semidirect |
| 180. C41 | C2×#1406 | direct (N × H) |
| 197. #127 | C2×C4×C41 | semidirect |
| 211. #97 | C2×C4×C41 | semidirect |
| 319. C2 | C41×#1406 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C41×#496 | 2 |
| C2×C41×#355 | 2 |
| C2×C41×#354 | 2 |
| C41×#1406 | 2 |
| C2×#1406 | 41 |