Finite Group DatabasebetaFinite Group DatabasebetaOrder 128.
235 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 235 conjugacy classes of subgroups — too many to draw. Only its 140 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 | C4 | C23×C4 |
| Frattini, cosocle | C2×C4 | C24 |
| prime radical | C2×#41 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ G | |
| LECS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #519 | C2 | semidirect |
| 4. #441 | C2 | semidirect |
| 5. #440 | C2 | semidirect |
| 6. C4×Q16 | C2 | semidirect |
| 7. C4×SD16 | C2 | semidirect |
| 8. #428 | C2 | semidirect |
| 10. C2×#103 | C2 | semidirect |
| 11. #405 | C2 | semidirect |
| 14. #137 | C4 | semidirect |
| 46. C2×Q8 | C2×C4 | semidirect |
| 56. Q16 | C2×C4 | semidirect |
| 57. SD16 | C2×C4 | semidirect |
| 58. M16 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#137 | 2 |
| #520 | 2 |
| #519 | 2 |
| #441 | 2 |
| #440 | 2 |
| C4×Q16 | 2 |
| C4×SD16 | 2 |
| #428 | 2 |
| #416 | 2 |
| C2×#103 | 2 |
| #405 | 2 |