Finite Group Databasebeta

← C11×C3⋊(C7⋊#261) #26046551

Subgroups — C11×C3⋊(C7⋊#261) #26046551

Order 12012.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C7×C11×D13C211yesmaximal, characteristic
2C11×C7⋊#261—31nomaximal, Hall
3C3×C7×C11×C13C411yescharacteristic, complemented, Hall
4C7×C11×D13D311yescharacteristic
5C11×C3⋊#261—71nomaximal, Hall
6C3⋊(C7⋊#261)C1111yesmaximal, characteristic, direct product factor, Hall
7C7×C11×C13Dic311yescharacteristic, complemented, Hall
8C11×Dic21—131nomaximal, Hall
9C3×C11×D13D711yescharacteristic
10C11×#261—211noHall
11C3×C7×D13C2×C1111yescharacteristic
12C2×C3×C7×C11—131no—
13C3×C11×C13Dic711yescharacteristic, complemented, Hall
14C7⋊#261—31noHall
15C11×Dic7—391noHall
16C11×D13D2111yescharacteristic
17C3×C7×C13C4×C1111yescharacteristic, complemented, Hall
18C3×C7×C11#26111yescharacteristic, complemented, Hall
19C7×D13D3×C1111yescharacteristic
20C3⋊#261—71noHall
21C2×C7×C11—131no—
22C11×C13Dic2111yescharacteristic, complemented, Hall
23C11×Dic3—911noHall
24C7×C13C11×Dic311yescharacteristic, complemented, Hall
25Dic21—131noHall
26C3×D13C11×D711yescharacteristic
27C7×C11C3⋊#26111yescharacteristic, complemented, Hall
28C2×C3×C11—131no—
29#261—211noHall
30C4×C11—2731noHall
31C2×C3×C7—131no—
32C3×C13C11×Dic711yescharacteristic, complemented, Hall
33C3×C11C7⋊#26111yescharacteristic, complemented, Hall
34Dic7—391noHall
35D13C11×D2111yescharacteristic
36C2×C11—131no—
37C3×C7C11×#26111yescharacteristic, complemented, Hall
38C2×C7—131no—
39C13C11×Dic2111yescharacteristic, complemented, Sylow
40Dic3—911noHall
41C11C3⋊(C7⋊#261)11yescharacteristic, direct product factor, Sylow
42C7C11×C3⋊#26111yescharacteristic, complemented, Sylow
43C2×C3—131no—
44C4—2731noSylow
45C3C11×C7⋊#26111yescharacteristic, complemented, Sylow
46C2—131no—
subgroupG/H
center, hypercenterC11C3⋊(C7⋊#261)
commutator, hypocenterC3×C7×C13C4×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C4
prime radicalC3×C7×C11×D13C2
cosocleC3×C7×D13C2×C11
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
3. C3×C7×C11×C13C4semidirect
6. C3⋊(C7⋊#261)C11direct (N × H)
7. C7×C11×C13Dic3semidirect
13. C3×C11×C13Dic7semidirect
17. C3×C7×C13C4×C11semidirect
18. C3×C7×C11#261semidirect
22. C11×C13Dic21semidirect
24. C7×C13C11×Dic3semidirect
27. C7×C11C3⋊#261semidirect
32. C3×C13C11×Dic7semidirect
33. C3×C11C7⋊#261semidirect
37. C3×C7C11×#261semidirect
39. C13C11×Dic21semidirect
41. C11C3⋊(C7⋊#261)direct (N × H)
42. C7C11×C3⋊#261semidirect
45. C3C11×C7⋊#261semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C11×D132
C11×C7⋊#2613
C11×C3⋊#2617
C3⋊(C7⋊#261)11
C11×Dic2113