Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
825 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 825 conjugacy classes of subgroups — too many to draw. Only its 167 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, Frattini, cosocle | C22×C4 | C24 |
| prime radical | #2541 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×Q8 | C2 | semidirect |
| 2. C2×#492 | C2 | semidirect |
| 3. C2×#460 | C2 | semidirect |
| 4. C2×#448 | C2 | semidirect |
| 6. #2000 | C2 | semidirect |
| 7. #1981 | C2 | semidirect |
| 8. #1954 | C2 | semidirect |
| 9. C4×#103 | C2 | semidirect |
| 61. C4⋊Q8 | D4 | semidirect |
| 71. C4×Q8 | D4 | semidirect |
| 90. #103 | D4 | semidirect |
| 124. C2×D4 | SD16 | semidirect |
| 179. Q8 | #127 | semidirect |
| 234. C4 | #448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Q8 | 2 |
| C2×#492 | 2 |
| C2×#460 | 2 |
| C2×#448 | 2 |
| #2541 | 2 |
| #2000 | 2 |
| #1981 | 2 |
| #1954 | 2 |
| C4×#103 | 2 |