Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
221 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 221 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D4 |
| commutator | C2×C4 | C22×C4 |
| Frattini, cosocle | C22×C4 | C23 |
| socle | C22 | C2×C22⋊C4 |
| prime radical | #525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C42 | C2 | semidirect |
| 3. C2×#104 | C2 | semidirect |
| 4. #407 | C2 | semidirect |
| 5. #339 | C2 | semidirect |
| 11. C22⋊Q8 | C4 | semidirect |
| 12. #121 | C4 | semidirect |
| 24. C2×Q8 | C2×C4 | semidirect |
| 27. C2×D4 | C2×C4 | semidirect |
| 42. C4⋊C4 | C2×C4 | semidirect |
| 49. C42 | D4 | semidirect |
| 84. C22 | #104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #525 | 2 |
| C22×C42 | 2 |
| C2×#104 | 2 |
| #407 | 2 |
| #339 | 2 |