Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
276 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 276 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 | C2 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#509 | C2 | semidirect |
| 2. #3067 | C2 | semidirect |
| 3. #3058 | C2 | semidirect |
| 4. C2×#361 | C2 | semidirect |
| 5. #2145 | C2 | semidirect |
| 6. #2117 | C2 | semidirect |
| 7. #1389 | C2 | semidirect |
| 43. C2×Q16 | D4 | semidirect |
| 51. C2×D8 | D4 | semidirect |
| 71. M32 | D4 | semidirect |
| 75. #108 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#509 | 2 |
| #3067 | 2 |
| #3058 | 2 |
| C2×#361 | 2 |
| #2145 | 2 |
| #2117 | 2 |
| #1389 | 2 |