Finite Group Databasebeta

← C3×C7⋊(C11⋊#261) #26046537

Subgroups — C3×C7⋊(C11⋊#261) #26046537

Order 12012.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C11×D13C211yesmaximal, characteristic
2C7⋊(C11⋊#261)C311yesmaximal, characteristic, direct product factor, Hall
3C3×C7×C11×C13C411yescharacteristic, complemented, Hall
4C7×C11×D13C2×C311yescharacteristic
5C3×C11⋊#261—71nomaximal, Hall
6C3×C7⋊#261—111nomaximal, Hall
7C7×C11×C13C3×C411yescharacteristic, complemented, Hall
8C3×Dic77—131nomaximal, Hall
9C3×C11×D13D711yescharacteristic
10C11⋊#261—71noHall
11C3×C7×D13D1111yescharacteristic
12C2×C3×C7×C11—131no—
13C3×C11×C13Dic711yescharacteristic, complemented, Hall
14C7⋊#261—111noHall
15Dic77—131noHall
16C11×D13C3×D711yescharacteristic
17C3×C7×C13Dic1111yescharacteristic, complemented, Hall
18C3×C7×C11#26111yescharacteristic, complemented, Hall
19C7×D13C3×D1111yescharacteristic
20C3×#261—771noHall
21C2×C7×C11—131no—
22C11×C13C3×Dic711yescharacteristic, complemented, Hall
23C3×Dic11—911noHall
24C7×C13C3×Dic1111yescharacteristic, complemented, Hall
25C3×Dic7—1431noHall
26C3×D13D7711yescharacteristic
27C7×C11C3×#26111yescharacteristic, complemented, Hall
28C2×C3×C11—131no—
29#261—771noHall
30Dic11—911noHall
31C2×C3×C7—131no—
32C3×C13Dic7711yescharacteristic, complemented, Hall
33C3×C11C7⋊#26111yescharacteristic, complemented, Hall
34Dic7—1431noHall
35D13C3×D7711yescharacteristic
36C2×C11—131no—
37C3×C7C11⋊#26111yescharacteristic, complemented, Hall
38C2×C7—131no—
39C13C3×Dic7711yescharacteristic, complemented, Sylow
40C3×C4—10011noHall
41C11C3×C7⋊#26111yescharacteristic, complemented, Sylow
42C7C3×C11⋊#26111yescharacteristic, complemented, Sylow
43C2×C3—131no—
44C4—10011noSylow
45C3C7⋊(C11⋊#261)11yescharacteristic, direct product factor, Sylow
46C2—131no—
subgroupG/H
center, hypercenterC3C7⋊(C11⋊#261)
commutator, hypocenterC7×C11×C13C3×C4
FrattiniC1G
Fitting, socleC3×C7×C11×C13C4
prime radicalC3×C7×C11×D13C2
cosocleC7×C11×D13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C7⋊(C11⋊#261)C3direct (N × H)
3. C3×C7×C11×C13C4semidirect
7. C7×C11×C13C3×C4semidirect
13. C3×C11×C13Dic7semidirect
17. C3×C7×C13Dic11semidirect
18. C3×C7×C11#261semidirect
22. C11×C13C3×Dic7semidirect
24. C7×C13C3×Dic11semidirect
27. C7×C11C3×#261semidirect
32. C3×C13Dic77semidirect
33. C3×C11C7⋊#261semidirect
37. C3×C7C11⋊#261semidirect
39. C13C3×Dic77semidirect
41. C11C3×C7⋊#261semidirect
42. C7C3×C11⋊#261semidirect
45. C3C7⋊(C11⋊#261)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×C11×D132
C7⋊(C11⋊#261)3
C3×C11⋊#2617
C3×C7⋊#26111
C3×Dic7713