Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
Only the 306 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 306 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72209716 |
| commutator, Frattini, cosocle | C22×H(5,𝔽2) | C24 |
| prime radical | #72210025 | C2 |
| LCS | G ▷ C22×H(5,𝔽2) ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ C22×H(5,𝔽2) ◁ G | |
| LECS | G ▷ C22×H(5,𝔽2) ▷ C23 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72241005 | C2 | semidirect |
| 2. #72227300 | C2 | semidirect |
| 3. #72226369 | C2 | semidirect |
| 4. #72210035 | C2 | semidirect |
| 7. #8932880 | C22 | semidirect |
| 12. #213830 | C22 | semidirect |
| 13. #213828 | C22 | semidirect |
| 14. #128069 | C22 | semidirect |
| 16. #35446 | D4 | semidirect |
| 21. #20585 | D4 | semidirect |
| 38. C24×C4 | #120 | semidirect |
| 40. C22×C22⋊C4 | #120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72241005 | 2 |
| #72227300 | 2 |
| #72226369 | 2 |
| #72210035 | 2 |
| #72210025 | 2 |