Finite Group DatabasebetaFinite Group DatabasebetaOrder 256.
410 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 149 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 | #2328 |
| commutator | C2×C4 | C23×C4 |
| Frattini, cosocle | C22×C4 | C24 |
| prime radical | #3155 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ 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. #2957 | C2 | semidirect |
| 3. #2948 | C2 | semidirect |
| 4. #1978 | C2 | semidirect |
| 5. #1976 | C2 | semidirect |
| 6. #1911 | C2 | semidirect |
| 7. #1910 | C2 | semidirect |
| 8. #1904 | C2 | semidirect |
| 9. #1903 | C2 | semidirect |
| 10. #1833 | C2 | semidirect |
| 11. #1747 | C2 | semidirect |
| 18. #496 | C4 | semidirect |
| 19. #495 | C4 | semidirect |
| 20. #493 | C4 | semidirect |
| 50. C2×Q16 | C2×C4 | semidirect |
| 51. C2×SD16 | C2×C4 | semidirect |
| 52. C2×SD16 | C2×C4 | semidirect |
| 59. C2×D8 | C2×C4 | semidirect |
| 60. C2×D8 | C2×C4 | semidirect |
| 69. #127 | C2×C4 | semidirect |
| 70. #124 | C2×C4 | semidirect |
| 91. #97 | C2×C4 | semidirect |
| 92. #97 | D4 | semidirect |
| 94. C4×C8 | C2×C4 | semidirect |
| 95. C4×C8 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3155 | 2 |
| #2957 | 2 |
| #2948 | 2 |
| #1978 | 2 |
| #1976 | 2 |
| #1911 | 2 |
| #1910 | 2 |
| #1904 | 2 |
| #1903 | 2 |
| #1833 | 2 |
| #1747 | 2 |