Finite Group Databasebeta

← C3×C3⋊(C7⋊(C11⋊#261)) #49114910

Subgroups — C3×C3⋊(C7⋊(C11⋊#261)) #49114910

Order 36036.

112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C7×C11×D13C211yesmaximal, characteristic
2C3⋊(C7⋊(C11⋊#261))C311yesmaximal, characteristic, direct product factor
3C3×C7⋊(C11⋊#261)—31nomaximal
4C32×C7×C11×C13C411yescharacteristic, complemented, Hall
5C3×C7×C11×D13—21no—
6C3×C7×C11×D13D311yescharacteristic
7C3×C7×C11×D13C2×C311yescharacteristic
8C3×C3⋊(C11⋊#261)—71nomaximal, Hall
9C7⋊(C11⋊#261)—31noHall
10C3×C3⋊(C7⋊#261)—111nomaximal, Hall
11C3×C7×C11×C13—21no—
12C3×C7×C11×C13Dic311yescharacteristic, complemented
13C3×C7×C11×C13C3×C411yescharacteristic, complemented
14C3×Dic231—131nomaximal, Hall
15C32×C11×D13D711yescharacteristic
16C7×C11×D13C3×D311yescharacteristic
17C3⋊(C11⋊#261)—71no—
18C3×C11⋊#261—211no—
19C32×C7×D13D1111yescharacteristic
20C2×C32×C7×C11—131no—
21C32×C11×C13Dic711yescharacteristic, complemented, Hall
22C3⋊(C7⋊#261)—111no—
23C3×C7⋊#261—331no—
24C7×C11×C13C3×Dic311yescharacteristic, complemented, Hall
25Dic231—131no—
26C3×Dic77—391no—
27C3×C11×D13—21no—
28C3×C11×D13C3×D711yescharacteristic
29C3×C11×D13D2111yescharacteristic
30C32×C7×C13Dic1111yescharacteristic, complemented, Hall
31C32×C7×C11#26111yescharacteristic, complemented, Hall
32C11⋊#261—211noHall
33C3×C7×D13—21no—
34C3×C7×D13C3×D1111yescharacteristic
35C3×C7×D13D3311yescharacteristic
36C3×C3⋊#261—771noHall
37C2×C3×C7×C11—131no—
38C2×C3×C7×C11—131no—
39C2×C3×C7×C11—261no—
40C3×C11×C13—21no—
41C3×C11×C13C3×Dic711yescharacteristic, complemented
42C3×C11×C13Dic2111yescharacteristic, complemented
43C3×Dic33—911noHall
44C7⋊#261—331noHall
45Dic77—391noHall
46C11×D13C3×D2111yescharacteristic
47C3×C7×C13—21no—
48C3×C7×C13C3×Dic1111yescharacteristic, complemented
49C3×C7×C13Dic3311yescharacteristic, complemented
50C3×Dic21—1431noHall
51C32×D13D7711yescharacteristic
52C3×C7×C11—21no—
53C3×C7×C11C3×#26111yescharacteristic, complemented
54C3×C7×C11C3⋊#26111yescharacteristic, complemented
55C2×C32×C11—131no—
56C7×D13C3×D3311yescharacteristic
57C3⋊#261—771no—
58C3×#261—2311no—
59C2×C7×C11—131no—
60C11×C13C3×Dic2111yescharacteristic, complemented, Hall
61Dic33—911no—
62C3×Dic11—2731no—
63C2×C32×C7—131no—
64C32×C13Dic7711yescharacteristic, complemented, Hall
65C32×C11C7⋊#26111yescharacteristic, complemented, Hall
66C7×C13C3×Dic3311yescharacteristic, complemented, Hall
67Dic21—1431no—
68C3×Dic7—4291no—
69C3×D13—21no—
70C3×D13C3×D7711yescharacteristic
71C3×D13D23111yescharacteristic
72C7×C11C3×C3⋊#26111yescharacteristic, complemented, Hall
73C2×C3×C11—131no—
74C2×C3×C11—131no—
75C2×C3×C11—261no—
76C32×C7C11⋊#26111yescharacteristic, complemented, Hall
77#261—2311noHall
78Dic11—2731noHall
79C2×C3×C7—131no—
80C2×C3×C7—131no—
81C2×C3×C7—261no—
82C3×C13—21no—
83C3×C13C3×Dic7711yescharacteristic, complemented
84C3×C13Dic23111yescharacteristic, complemented
85C3×Dic3—10011noHall
86C3×C11—21no—
87C3×C11C3×C7⋊#26111yescharacteristic, complemented
88C3×C11C3⋊(C7⋊#261)11yescharacteristic, complemented
89Dic7—4291noHall
90D13C3×D23111yescharacteristic
91C2×C11—131no—
92C3×C7—21no—
93C3×C7C3×C11⋊#26111yescharacteristic, complemented
94C3×C7C3⋊(C11⋊#261)11yescharacteristic, complemented
95C2×C32—131no—
96C2×C7—131no—
97C13C3×Dic23111yescharacteristic, complemented, Sylow
98C3×C4—30031no—
99Dic3—10011no—
100C11C3×C3⋊(C7⋊#261)11yescharacteristic, complemented, Sylow
101C32C7⋊(C11⋊#261)11yescharacteristic, complemented, Sylow
102C7C3×C3⋊(C11⋊#261)11yescharacteristic, complemented, Sylow
103C2×C3—131no—
104C2×C3—131no—
105C2×C3—261no—
106C4—30031noSylow
107C3—21no—
108C3C3×C7⋊(C11⋊#261)11yescharacteristic, complemented
109C3C3⋊(C7⋊(C11⋊#261))11yescharacteristic, direct product factor
110C2—131no—
subgroupG/H
center, hypercenterC3C3⋊(C7⋊(C11⋊#261))
commutator, hypocenterC3×C7×C11×C13C3×C4
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC3×C7×C11×D13C2×C3
LCSG ▷ C3×C7×C11×C13
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
2. C3⋊(C7⋊(C11⋊#261))C3direct (N × H)
4. C32×C7×C11×C13C4semidirect
12. C3×C7×C11×C13Dic3semidirect
13. C3×C7×C11×C13C3×C4semidirect
21. C32×C11×C13Dic7semidirect
24. C7×C11×C13C3×Dic3semidirect
30. C32×C7×C13Dic11semidirect
31. C32×C7×C11#261semidirect
41. C3×C11×C13C3×Dic7semidirect
42. C3×C11×C13Dic21semidirect
48. C3×C7×C13C3×Dic11semidirect
49. C3×C7×C13Dic33semidirect
53. C3×C7×C11C3×#261semidirect
54. C3×C7×C11C3⋊#261semidirect
60. C11×C13C3×Dic21semidirect
64. C32×C13Dic77semidirect
65. C32×C11C7⋊#261semidirect
66. C7×C13C3×Dic33semidirect
72. C7×C11C3×C3⋊#261semidirect
76. C32×C7C11⋊#261semidirect
83. C3×C13C3×Dic77semidirect
84. C3×C13Dic231semidirect
87. C3×C11C3×C7⋊#261semidirect
88. C3×C11C3⋊(C7⋊#261)semidirect
93. C3×C7C3×C11⋊#261semidirect
94. C3×C7C3⋊(C11⋊#261)semidirect
97. C13C3×Dic231semidirect
100. C11C3×C3⋊(C7⋊#261)semidirect
101. C32C7⋊(C11⋊#261)semidirect
102. C7C3×C3⋊(C11⋊#261)semidirect
108. C3C3×C7⋊(C11⋊#261)semidirect
109. C3C3⋊(C7⋊(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
C32×C7×C11×D132
C3⋊(C7⋊(C11⋊#261))3
C3×C7⋊(C11⋊#261)3
C3×C3⋊(C11⋊#261)7
C3×C3⋊(C7⋊#261)11
C3×Dic23113