Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
485 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 485 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×D4 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | C24 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#441 | C2 | semidirect |
| 5. #1971 | C2 | semidirect |
| 6. #1943 | C2 | semidirect |
| 7. #1927 | C2 | semidirect |
| 9. #1865 | C2 | semidirect |
| 10. #1776 | C2 | semidirect |
| 17. #467 | C4 | semidirect |
| 47. C2×Q16 | C2×C4 | semidirect |
| 74. #107 | C2×C4 | semidirect |
| 80. #103 | C2×C4 | semidirect |
| 195. C22 | #441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#467 | 2 |
| C2×#441 | 2 |
| C22×#106 | 2 |
| #2360 | 2 |
| #1971 | 2 |
| #1943 | 2 |
| #1927 | 2 |
| #1872 | 2 |
| #1865 | 2 |
| #1776 | 2 |
| #1752 | 2 |