Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D44 |
| commutator, cosocle | C2×C4×C11 | C24 |
| Frattini | C2×C4 | C23×D11 |
| Fitting | C11×#443 | C2 |
| socle | C2×C11 | D42 |
| hypercenter | #443 | D11 |
| hypocenter | C11 | #3293 |
| LCS | G ▷ C2×C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10623302 | C2 | semidirect |
| 2. #10623284 | C2 | semidirect |
| 3. C11×#443 | C2 | semidirect |
| 4. #10622756 | C2 | semidirect |
| 5. #10622509 | C2 | semidirect |
| 6. #10622439 | C2 | semidirect |
| 7. #10622313 | C2 | semidirect |
| 8. #10622312 | C2 | semidirect |
| 94. #443 | D11 | semidirect |
| 162. C11 | #3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623302 | 2 |
| #10623284 | 2 |
| C11×#443 | 2 |
| #10622756 | 2 |
| #10622509 | 2 |
| #10622439 | 2 |
| #10622313 | 2 |
| #10622312 | 2 |
| #3293 | 11 |