Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
292 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×AGL(1,ℤ/8) | C2 | semidirect |
| 2. C2×#127 | C2 | semidirect |
| 3. C4×#41 | C2 | semidirect |
| 4. #460 | C2 | semidirect |
| 5. #459 | C2 | semidirect |
| 6. #423 | C2 | semidirect |
| 7. #418 | C2 | semidirect |
| 12. C2×SD16 | C22 | semidirect |
| 13. C2×D8 | C22 | semidirect |
| 18. C4×Q8 | C22 | semidirect |
| 20. C4×D4 | C22 | semidirect |
| 25. C4⋊C8 | C22 | semidirect |
| 26. #102 | C22 | semidirect |
| 29. #41 | D4 | semidirect |
| 63. Q8 | C2×D4 | semidirect |
| 71. D4 | C2×D4 | semidirect |
| 96. C4 | AGL(1,ℤ/8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,ℤ/8) | 2 |
| C2×#127 | 2 |
| C4×#41 | 2 |
| #460 | 2 |
| #459 | 2 |
| #423 | 2 |
| #418 | 2 |