Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 120 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×C83 | C22⋊C4 |
| commutator | C2×C4 | C22×C4×C83 |
| Frattini, cosocle | C22×C4 | C23×C83 |
| prime radical | C2×#121×C83 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C23×C4×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C8×C83 | C2 | semidirect |
| 3. C2×#95×C83 | C2 | semidirect |
| 4. #327×C83 | C2 | direct (N × H) |
| 6. C22×D4×C83 | C4 | semidirect |
| 12. #121×C83 | C4 | semidirect |
| 14. C2×C4⋊C4×C83 | C4 | semidirect |
| 17. C22⋊C8×C83 | C22 | semidirect |
| 19. #95×C83 | C22 | semidirect |
| 28. C2×D4×C83 | C2×C4 | semidirect |
| 44. C4⋊C4×C83 | C2×C4 | semidirect |
| 107. C2×C83 | #327 | direct (N × H) |
| 111. C2×#327 | C83 | direct (N × H) |
| 112. C83 | C2×#327 | direct (N × H) |
| 114. C2×C22⋊C8 | C2×C83 | semidirect |
| 115. C2×#95 | C2×C83 | semidirect |
| 116. #327 | C2×C83 | direct (N × H) |
| 118. C22×D4 | C4×C83 | semidirect |
| 124. #121 | C4×C83 | semidirect |
| 126. C2×C4⋊C4 | C4×C83 | semidirect |
| 129. C22⋊C8 | C22×C83 | semidirect |
| 131. #95 | C22×C83 | semidirect |
| 140. C2×D4 | C2×C4×C83 | semidirect |
| 156. C4⋊C4 | C2×C4×C83 | semidirect |
| 219. C2 | #327×C83 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#121×C83 | 2 |
| C2×C22⋊C8×C83 | 2 |
| C2×#95×C83 | 2 |
| #327×C83 | 2 |
| C2×#327 | 83 |