Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
304 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | C2×D4 |
| commutator | C2×C4 | C22×C4×C11 |
| Frattini, cosocle | C22×C4 | C23×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×C11×Q16 | C4 | semidirect |
| 39. #1971 | C11 | direct (N × H) |
| 79. C2×Q16 | C4×C11 | semidirect |
| 113. C11 | #1971 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×Q16 | 2 |
| C2×C11×#106 | 2 |
| C2×C11×#103 | 2 |
| C2×C11×#97 | 2 |
| C11×#391 | 2 |
| #1971 | 11 |