Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
308 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C79 |
| prime radical | D42×C79 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C42×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #486×C79 | C2 | semidirect |
| 3. #474×C79 | C2 | semidirect |
| 4. #461×C79 | C2 | semidirect |
| 5. #331×C79 | C2 | semidirect |
| 6. D4⋊C8×C79 | C2 | semidirect |
| 7. D4⋊C8×C79 | C2 | semidirect |
| 11. C4⋊Q8×C79 | C22 | semidirect |
| 19. C4⋊C8×C79 | C22 | semidirect |
| 20. C4⋊C8×C79 | C22 | semidirect |
| 24. C4×C8×C79 | C22 | semidirect |
| 70. D4×C79 | SD16 | semidirect |
| 109. #1639 | C79 | direct (N × H) |
| 110. C79 | #1639 | direct (N × H) |
| 112. #486 | C2×C79 | semidirect |
| 113. #474 | C2×C79 | semidirect |
| 114. #461 | C2×C79 | semidirect |
| 115. #331 | C2×C79 | semidirect |
| 116. D4⋊C8 | C2×C79 | semidirect |
| 117. D4⋊C8 | C2×C79 | semidirect |
| 121. C4⋊Q8 | C22×C79 | semidirect |
| 129. C4⋊C8 | C22×C79 | semidirect |
| 130. C4⋊C8 | C22×C79 | semidirect |
| 134. C4×C8 | C22×C79 | semidirect |
| 180. D4 | SD16×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D42×C79 | 2 |
| #486×C79 | 2 |
| #474×C79 | 2 |
| #461×C79 | 2 |
| #331×C79 | 2 |
| D4⋊C8×C79 | 2 |
| #1639 | 79 |