Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
344 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #129029 |
| commutator | C2×C16 | C2×C42 |
| Frattini, cosocle | C4×M32 | C23 |
| prime radical | #2218 | C2×C4 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C4×C8 ◁ #11406 ◁ G | |
| LECS | G ▷ C4×M32 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #149516 | C2 | semidirect |
| 5. #129170 | C2 | semidirect |
| 6. #94417 | C2 | semidirect |
| 7. #94408 | C2 | semidirect |
| 14. #12089 | C4 | semidirect |
| 15. #12088 | C4 | semidirect |
| 17. #12067 | C4 | semidirect |
| 18. #12066 | C4 | semidirect |
| 24. #7454 | C4 | semidirect |
| 25. #7447 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #483962 | 2 |
| #150979 | 2 |
| #150390 | 2 |
| #149516 | 2 |
| #129170 | 2 |
| #94417 | 2 |
| #94408 | 2 |