Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
147 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 147 conjugacy classes of subgroups — too many to draw. Only its 41 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23 |
| prime radical | #493 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #446 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3390 | C2 | semidirect |
| 5. #1363 | C2 | semidirect |
| 6. #1338 | C2 | semidirect |
| 7. #1334 | C2 | semidirect |
| 68. Q16 | SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3390 | 2 |
| #2244 | 2 |
| #2207 | 2 |
| #1688 | 2 |
| #1363 | 2 |
| #1338 | 2 |
| #1334 | 2 |