Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
174 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C11×C16 | C22 |
| commutator | C2 | C22×C11×C16 |
| Frattini, cosocle | C2×C8 | C23×C11 |
| socle | C22×C11 | C22×C8 |
| prime radical | C2×D4×C11 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C11×C16 | C2 | semidirect |
| 3. C11×C4⋊C16 | C2 | semidirect |
| 4. C11×C22⋊C16 | C2 | semidirect |
| 5. C4×C11×C16 | C2 | semidirect |
| 27. C11×C16 | D4 | direct (N × H) |
| 28. D4×C16 | C11 | direct (N × H) |
| 30. D4×C11 | C16 | direct (N × H) |
| 41. C22×C16 | C2×C11 | semidirect |
| 43. C4⋊C16 | C2×C11 | semidirect |
| 44. C22⋊C16 | C2×C11 | semidirect |
| 45. C4×C16 | C2×C11 | semidirect |
| 48. C22×C11 | C2×C16 | semidirect |
| 52. C4×C11 | C2×C16 | semidirect |
| 80. C16 | D4×C11 | direct (N × H) |
| 81. C11 | D4×C16 | direct (N × H) |
| 83. D4 | C11×C16 | direct (N × H) |
| 96. C22 | C2×C11×C16 | semidirect |
| 100. C4 | C2×C11×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×C16 | 2 |
| C8×D4×C11 | 2 |
| C11×C4⋊C16 | 2 |
| C11×C22⋊C16 | 2 |
| C4×C11×C16 | 2 |
| D4×C16 | 11 |