Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
398 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C43 | #2196 |
| commutator, Frattini, cosocle | C4⋊Q8 | C23×C43 |
| LCS | G ▷ C4⋊Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C43 ◁ C22×C43 ◁ C2×C4×C43 ◁ C4⋊Q8×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#3291 | C2 | semidirect |
| 2. C43×#2204 | C2 | semidirect |
| 3. C43×#1624 | C2 | semidirect |
| 4. C43×#1410 | C2 | semidirect |
| 5. C43×#1405 | C2 | semidirect |
| 7. C43×#555 | C22 | semidirect |
| 15. C43×#356 | C22 | semidirect |
| 17. C43×#333 | C22 | semidirect |
| 114. #13681 | C43 | direct (N × H) |
| 129. #3291 | C2×C43 | semidirect |
| 130. #2204 | C2×C43 | semidirect |
| 131. #1624 | C2×C43 | semidirect |
| 132. #1410 | C2×C43 | semidirect |
| 133. #1405 | C2×C43 | semidirect |
| 140. #555 | C22×C43 | semidirect |
| 148. #356 | C22×C43 | semidirect |
| 150. #333 | C22×C43 | semidirect |
| 152. C43 | #13681 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#3291 | 2 |
| C43×#2204 | 2 |
| C43×#1624 | 2 |
| C43×#1410 | 2 |
| C43×#1405 | 2 |
| #13681 | 43 |