Finite Group Databasebeta

← C3⋊(C3⋊(C7⋊(C11⋊#261))) #49114978

Subgroups — C3⋊(C3⋊(C7⋊(C11⋊#261))) #49114978

Order 36036.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11×D13C211yesmaximal, characteristic
2C3⋊(C7⋊(C11⋊#261))—34nomaximal
3C32×C7×C11×C13C411yescharacteristic, complemented, Hall
4C3×C7×C11×D13D314yes—
5C3⋊(C3⋊(C11⋊#261))—71nomaximal, Hall
6C7⋊(C11⋊#261)—91noHall
7C3⋊(C3⋊(C7⋊#261))—111nomaximal, Hall
8C3×C7×C11×C13Dic314yescomplemented
9C3⋊Dic231—131nomaximal, Hall
10C32×C11×D13D711yescharacteristic
11C7×C11×D13C3⋊D311yescharacteristic
12C3⋊(C11⋊#261)—214no—
13C32×C7×D13D1111yescharacteristic
14C2×C32×C7×C11—131no—
15C32×C11×C13Dic711yescharacteristic, complemented, Hall
16C3⋊(C7⋊#261)—334no—
17C7×C11×C13C3⋊Dic311yescharacteristic, complemented, Hall
18Dic231—394no—
19C3×C11×D13D2114yes—
20C32×C7×C13Dic1111yescharacteristic, complemented, Hall
21C32×C7×C11#26111yescharacteristic, complemented, Hall
22C11⋊#261—631noHall
23C3×C7×D13D3314yes—
24C3⋊(C3⋊#261)—771noHall
25C2×C3×C7×C11—134no—
26C3×C11×C13Dic2114yescomplemented
27C3⋊Dic33—911noHall
28C7⋊#261—991noHall
29Dic77—1171noHall
30C11×D13C3⋊D2111yescharacteristic
31C3×C7×C13Dic3314yescomplemented
32C3⋊Dic21—1431noHall
33C32×D13D7711yescharacteristic
34C3×C7×C11C3⋊#26114yescomplemented
35C2×C32×C11—131no—
36C7×D13C3⋊D3311yescharacteristic
37C3⋊#261—2314no—
38C2×C7×C11—131no—
39C11×C13C3⋊Dic2111yescharacteristic, complemented, Hall
40Dic33—2734no—
41C2×C32×C7—131no—
42C32×C13Dic7711yescharacteristic, complemented, Hall
43C32×C11C7⋊#26111yescharacteristic, complemented, Hall
44C7×C13C3⋊Dic3311yescharacteristic, complemented, Hall
45Dic21—4294no—
46C3×D13D23114yes—
47C7×C11C3⋊(C3⋊#261)11yescharacteristic, complemented, Hall
48C2×C3×C11—134no—
49C32×C7C11⋊#26111yescharacteristic, complemented, Hall
50#261—6931noHall
51Dic11—8191noHall
52C2×C3×C7—134no—
53C3×C13Dic23114yescomplemented
54C3⋊Dic3—10011noHall
55C3×C11C3⋊(C7⋊#261)14yescomplemented
56Dic7—12871noHall
57D13C3⋊D23111yescharacteristic
58C2×C11—131no—
59C3×C7C3⋊(C11⋊#261)14yescomplemented
60C2×C32—131no—
61C2×C7—131no—
62C13C3⋊Dic23111yescharacteristic, complemented, Sylow
63Dic3—30034no—
64C11C3⋊(C3⋊(C7⋊#261))11yescharacteristic, complemented, Sylow
65C32C7⋊(C11⋊#261)11yescharacteristic, complemented, Sylow
66C7C3⋊(C3⋊(C11⋊#261))11yescharacteristic, complemented, Sylow
67C2×C3—134no—
68C4—90091noSylow
69C3C3⋊(C7⋊(C11⋊#261))14yescomplemented
70C2—131no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C7×C11×C13C4
prime radical, cosocleC32×C7×C11×D13C2
LCSG ▷ C32×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
3. C32×C7×C11×C13C4semidirect
8. C3×C7×C11×C13Dic3semidirect
15. C32×C11×C13Dic7semidirect
17. C7×C11×C13C3⋊Dic3semidirect
20. C32×C7×C13Dic11semidirect
21. C32×C7×C11#261semidirect
26. C3×C11×C13Dic21semidirect
31. C3×C7×C13Dic33semidirect
34. C3×C7×C11C3⋊#261semidirect
39. C11×C13C3⋊Dic21semidirect
42. C32×C13Dic77semidirect
43. C32×C11C7⋊#261semidirect
44. C7×C13C3⋊Dic33semidirect
47. C7×C11C3⋊(C3⋊#261)semidirect
49. C32×C7C11⋊#261semidirect
53. C3×C13Dic231semidirect
55. C3×C11C3⋊(C7⋊#261)semidirect
59. C3×C7C3⋊(C11⋊#261)semidirect
62. C13C3⋊Dic231semidirect
64. C11C3⋊(C3⋊(C7⋊#261))semidirect
65. C32C7⋊(C11⋊#261)semidirect
66. C7C3⋊(C3⋊(C11⋊#261))semidirect
69. C3C3⋊(C7⋊(C11⋊#261))semidirect

Maximal subgroups

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

subgroupindex
C32×C7×C11×D132
C3⋊(C7⋊(C11⋊#261))3
C3⋊(C3⋊(C11⋊#261))7
C3⋊(C3⋊(C7⋊#261))11
C3⋊Dic23113