Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
267 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 73 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 | C2×C42 | C23 |
| prime radical | C2×#127 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×M16 | C2 | semidirect |
| 5. #1487 | C2 | semidirect |
| 6. #1292 | C2 | semidirect |
| 7. #1283 | C2 | semidirect |
| 109. M16 | SD16 | semidirect |
| 142. Q8 | #100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#460 | 2 |
| Q8×M16 | 2 |
| #1965 | 2 |
| #1545 | 2 |
| #1487 | 2 |
| #1292 | 2 |
| #1283 | 2 |