Finite Group Databasebeta

← C2×C11×#13089649 #44540792

Subgroups — C2×C11×#13089649 #44540792

Order 31746.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#13089649C211yesmaximal, characteristic, direct product factor, Hall
2C2×C11×C13×C37C311yesmaximal, characteristic, complemented, Hall
3C11×C13×C37C2×C311yescharacteristic, complemented, Hall
4C2×#13089649C1111yesmaximal, characteristic, direct product factor, Hall
5C2×C11×C37⋊C3—131nomaximal, Hall
6#13089649C2×C1111yescharacteristic, direct product factor, Hall
7C11×C37⋊C3—131noHall
8C2×C13×C37C3×C1111yescharacteristic, complemented, Hall
9C2×C11×C13⋊C3—371nomaximal, Hall
10C2×C11×C37C13⋊C311yescharacteristic, complemented, Hall
11C13×C37C2×C3×C1111yescharacteristic, complemented, Hall
12C11×C13⋊C3—371noHall
13C11×C37C2×C13⋊C311yescharacteristic, complemented, Hall
14C2×C11×C13C37⋊C311yescharacteristic, complemented, Hall
15C2×C37⋊C3—131noHall
16C11×C13C2×C37⋊C311yescharacteristic, complemented, Hall
17C37⋊C3—131noHall
18C2×C13⋊C3—371noHall
19C2×C37C11×C13⋊C311yescharacteristic, complemented, Hall
20C2×C3×C11—4811noHall
21C13⋊C3—371noHall
22C37C2×C11×C13⋊C311yescharacteristic, complemented, Sylow
23C3×C11—4811noHall
24C2×C13C11×C37⋊C311yescharacteristic, complemented, Hall
25C2×C11#1308964911yescharacteristic, direct product factor, Hall
26C13C2×C11×C37⋊C311yescharacteristic, complemented, Sylow
27C11C2×#1308964911yescharacteristic, direct product factor, Sylow
28C2×C3—4811noHall
29C3—4811noSylow
30C2C11×#1308964911yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C11#13089649
commutator, cosocle, hypocenterC13×C37C2×C3×C11
FrattiniC1G
Fitting, socleC2×C11×C13×C37C3
LCSG ▷ C13×C37
UCSC1 ◁ C2×C11

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#13089649C2direct (N × H)
2. C2×C11×C13×C37C3semidirect
3. C11×C13×C37C2×C3semidirect
4. C2×#13089649C11direct (N × H)
6. #13089649C2×C11direct (N × H)
8. C2×C13×C37C3×C11semidirect
10. C2×C11×C37C13⋊C3semidirect
11. C13×C37C2×C3×C11semidirect
13. C11×C37C2×C13⋊C3semidirect
14. C2×C11×C13C37⋊C3semidirect
16. C11×C13C2×C37⋊C3semidirect
19. C2×C37C11×C13⋊C3semidirect
22. C37C2×C11×C13⋊C3semidirect
24. C2×C13C11×C37⋊C3semidirect
25. C2×C11#13089649direct (N × H)
26. C13C2×C11×C37⋊C3semidirect
27. C11C2×#13089649direct (N × H)
30. C2C11×#13089649direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C11×#130896492
C2×C11×C13×C373
C2×#1308964911
C2×C11×C37⋊C313
C2×C11×C13⋊C337