Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
512 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 192 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×C79 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C79 |
| prime radical | C22×D4×C79 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#125×C79 | C2 | semidirect |
| 3. #399×C79 | C2 | semidirect |
| 4. #398×C79 | C2 | semidirect |
| 5. #397×C79 | C2 | semidirect |
| 7. #385×C79 | C2 | semidirect |
| 8. #383×C79 | C2 | semidirect |
| 94. #2633 | C79 | direct (N × H) |
| 95. C79 | #2633 | direct (N × H) |
| 96. C2×#125 | C2×C79 | semidirect |
| 98. #399 | C2×C79 | semidirect |
| 99. #398 | C2×C79 | semidirect |
| 100. #397 | C2×C79 | semidirect |
| 102. #385 | C2×C79 | semidirect |
| 103. #383 | C2×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#125×C79 | 2 |
| C2×C4×D4×C79 | 2 |
| #399×C79 | 2 |
| #398×C79 | 2 |
| #397×C79 | 2 |
| #394×C79 | 2 |
| #385×C79 | 2 |
| #383×C79 | 2 |
| #2633 | 79 |