Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
205 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 205 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24 |
| prime radical | C24 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #485 | C2 | semidirect |
| 4. #484 | C2 | semidirect |
| 5. #483 | C2 | semidirect |
| 6. #428 | C2 | semidirect |
| 7. #419 | C2 | semidirect |
| 27. #107 | C22 | semidirect |
| 28. #106 | C22 | semidirect |
| 29. #103 | C22 | semidirect |
| 30. #103 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Q8 | 2 |
| C2×#117 | 2 |
| #485 | 2 |
| #484 | 2 |
| #483 | 2 |
| #428 | 2 |
| #419 | 2 |
| #407 | 2 |