Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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 | #386 |
| commutator | C22×C4 | C22×C4 |
| Frattini, cosocle | C23×C4 | C23 |
| prime radical | #3194 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ G | |
| LECS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2978 | C2 | semidirect |
| 3. #1516 | C2 | semidirect |
| 4. #1510 | C2 | semidirect |
| 5. #1471 | C2 | semidirect |
| 6. #1306 | C2 | semidirect |
| 7. #1293 | C2 | semidirect |
| 10. #483 | C4 | semidirect |
| 12. #480 | C4 | semidirect |
| 15. #450 | C4 | semidirect |
| 17. #447 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3194 | 2 |
| #2978 | 2 |
| #1516 | 2 |
| #1510 | 2 |
| #1471 | 2 |
| #1306 | 2 |
| #1293 | 2 |