Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
948 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | C2×C4×D4×C83 | C2 |
| hypercenter | C2×C4×D4 | D83 |
| hypocenter | C83 | #2541 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14581789 | C2 | semidirect |
| 2. C2×#14581788 | C2 | semidirect |
| 3. C2×#14581766 | C2 | semidirect |
| 4. #19127610 | C2 | semidirect |
| 5. #19127602 | C2 | semidirect |
| 6. C4×C4⋊Dic83 | C2 | semidirect |
| 7. C2×C4×D4×C83 | C2 | semidirect |
| 37. C4⋊Dic83 | D4 | semidirect |
| 43. C2×D4×C83 | D4 | semidirect |
| 52. C42×C83 | D4 | semidirect |
| 99. C4×C83 | #121 | semidirect |
| 100. C4×C83 | #127 | semidirect |
| 110. C83 | #2541 | semidirect |
| 114. C2×C4×D4 | D83 | semidirect |
| 149. C2×D4 | D332 | semidirect |
| 162. C42 | C22⋊D83 | semidirect |
| 210. C4 | #14581766 | semidirect |
| 211. C4 | #14581788 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581789 | 2 |
| C2×#14581788 | 2 |
| C2×#14581766 | 2 |
| #19127610 | 2 |
| #19127602 | 2 |
| C4×C4⋊Dic83 | 2 |
| C2×C4×D4×C83 | 2 |
| #2541 | 83 |