Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
422 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 74 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×C43 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C43 |
| prime radical | C43×#3199 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C43 ◁ C22×C4×C43 ◁ C43×#408 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C43×#2185 | C2 | semidirect |
| 3. C43×#2020 | C2 | semidirect |
| 4. C43×#1349 | C2 | semidirect |
| 5. C43×#1315 | C2 | semidirect |
| 7. C22×Q16×C43 | C22 | semidirect |
| 17. C43×C22⋊C16 | C22 | semidirect |
| 18. C43×#341 | C22 | semidirect |
| 119. #12111 | C43 | direct (N × H) |
| 136. #2185 | C2×C43 | semidirect |
| 137. #2020 | C2×C43 | semidirect |
| 138. #1349 | C2×C43 | semidirect |
| 139. #1315 | C2×C43 | semidirect |
| 146. C22×Q16 | C22×C43 | semidirect |
| 156. C22⋊C16 | C22×C43 | semidirect |
| 157. #341 | C22×C43 | semidirect |
| 158. C43 | #12111 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3199 | 2 |
| C43×#2185 | 2 |
| C43×#2020 | 2 |
| C43×#1349 | 2 |
| C43×#1315 | 2 |
| #12111 | 43 |