Finite Group Databasebeta

← C11×Dic3×#63270 #49114577

Subgroups — C11×Dic3×#63270 #49114577

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
1C2×C3×C11×#63270C211yesmaximal, characteristic
2C7×C11×Dic3×C13C311yesmaximal, characteristic, complemented
3C4×C11×#63270—31nomaximal
4C3×C11×#63270C411yescharacteristic, complemented, Hall
5C2×C11×#63270—21no—
6C2×C11×#63270D311yescharacteristic
7C2×C3×C7×C11×C13C2×C311yescharacteristic
8C11×Dic3×C13⋊C3—71nomaximal, Hall
9C4×C7×C11×C13—31noHall
10Dic3×#63270C1111yesmaximal, characteristic, direct product factor, Hall
11C11×#63270—21no—
12C11×#63270Dic311yescharacteristic, direct product factor
13C3×C7×C11×C13C3×C411yescharacteristic, complemented
14C11×Dic3×ΓL(1,𝔽8)—131nomaximal, Hall
15C2×C3×C11×C13⋊C3—71no—
16C2×C7×C11×C13C3×D311yescharacteristic
17C11×Dic3×C13ΓL(1,𝔽8)11yescharacteristic, complemented
18C4×C11×C13⋊C3—211no—
19C2×C3×#63270C2×C1111yescharacteristic
20C2×C3×C11×ΓL(1,𝔽8)—131no—
21C3×C11×C13⋊C3—71noHall
22C7×Dic3×C13C3×C1111yescharacteristic, complemented
23C4×#63270—31no—
24C7×C11×C13C3×Dic311yescharacteristic, complemented, Hall
25C7×C11×Dic3C13⋊C311yescharacteristic, complemented
26C4×C11×ΓL(1,𝔽8)—391no—
27C2×C3×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic
28C2×C11×C13⋊C3—71no—
29C2×C11×C13⋊C3—141no—
30C3×#63270C4×C1111yescharacteristic, complemented, Hall
31C3×C11×ΓL(1,𝔽8)—131noHall
32C4×C11×C13—31noHall
33C2×C3×C7×C13C2×C3×C1111yescharacteristic
34C2×#63270—21no—
35C2×#63270D3×C1111yescharacteristic
36Dic3×C13⋊C3—71noHall
37C2×C3×C7×C11C2×C13⋊C311yescharacteristic
38C2×C11×ΓL(1,𝔽8)—131no—
39C2×C11×ΓL(1,𝔽8)—261no—
40C3×C11×C13C4×ΓL(1,𝔽8)11yescharacteristic, complemented
41C11×C13⋊C3—71no—
42C11×C13⋊C3—141no—
43C3×C11×Dic3—911noHall
44C4×C7×C13—31noHall
45C4×C7×C11—31noHall
46C2×C11×C13D3×ΓL(1,𝔽8)11yescharacteristic
47C3×C7×C13C3×C4×C1111yescharacteristic, complemented
48#63270—21no—
49#63270C11×Dic311yescharacteristic, direct product factor
50Dic3×ΓL(1,𝔽8)—131noHall
51C2×C3×C13⋊C3—71no—
52C3×C7×C11C4×C13⋊C311yescharacteristic, complemented
53C11×ΓL(1,𝔽8)—131no—
54C11×ΓL(1,𝔽8)—261no—
55C2×C32×C11—911no—
56C2×C7×C13C3×D3×C1111yescharacteristic
57Dic3×C13C11×ΓL(1,𝔽8)11yescharacteristic, complemented
58C4×C13⋊C3—211no—
59C2×C7×C11D3×C13⋊C311yescharacteristic
60C11×C13Dic3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
61C3×C4×C11—2731no—
62C11×Dic3#6327011yescharacteristic, direct product factor
63C2×C3×ΓL(1,𝔽8)—131no—
64C3×C13⋊C3—71noHall
65C32×C11—911noHall
66C7×C13C3×C11×Dic311yescharacteristic, complemented, Hall
67C7×Dic3C11×C13⋊C311yescharacteristic, complemented
68C4×ΓL(1,𝔽8)—391no—
69C2×C3×C13C2×C11×ΓL(1,𝔽8)11yescharacteristic
70C2×C13⋊C3—71no—
71C2×C13⋊C3—141no—
72C7×C11Dic3×C13⋊C311yescharacteristic, complemented, Hall
73C2×C3×C11—911no—
74C2×C3×C11—1821no—
75C2×C3×C11C2×#6327011yescharacteristic
76C3×ΓL(1,𝔽8)—131noHall
77C4×C13—31noHall
78C4×C11—31noHall
79C2×C3×C7C2×C11×C13⋊C311yescharacteristic
80C2×ΓL(1,𝔽8)—131no—
81C2×ΓL(1,𝔽8)—261no—
82C3×C13C4×C11×ΓL(1,𝔽8)11yescharacteristic, complemented
83C13⋊C3—71no—
84C13⋊C3—141no—
85C3×Dic3—911noHall
86C3×C11—911no—
87C3×C11—1821no—
88C3×C11C4×#6327011yescharacteristic, complemented
89C4×C7—31noHall
90C2×C13D3×C11×ΓL(1,𝔽8)11yescharacteristic
91C2×C11D3×#6327011yescharacteristic
92C3×C7C4×C11×C13⋊C311yescharacteristic, complemented
93ΓL(1,𝔽8)—131no—
94ΓL(1,𝔽8)—261no—
95C2×C32—911no—
96C2×C7D3×C11×C13⋊C311yescharacteristic
97C13C11×Dic3×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
98C3×C4—2731no—
99Dic3C11×#6327011yescharacteristic, direct product factor
100C11Dic3×#6327011yescharacteristic, direct product factor, Sylow
101C32—911noSylow
102C7C11×Dic3×C13⋊C311yescharacteristic, complemented, Sylow
103C2×C3—911no—
104C2×C3—1821no—
105C2×C3C2×C11×#6327011yescharacteristic
106C4—31noSylow
107C3—911no—
108C3—1821no—
109C3C4×C11×#6327011yescharacteristic, complemented
110C2D3×C11×#6327011yescharacteristic
subgroupG/H
center, hypercenterC2×C11D3×#63270
commutator, hypocenterC3×C7×C13C3×C4×C11
FrattiniC2D3×C11×#63270
Fitting, socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C11×#63270C2
cosocleC2×C3×C7×C13C2×C3×C11
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C11

Complements

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

NH ≅ G/Ntype
2. C7×C11×Dic3×C13C3semidirect
4. C3×C11×#63270C4semidirect
10. Dic3×#63270C11direct (N × H)
12. C11×#63270Dic3direct (N × H)
13. C3×C7×C11×C13C3×C4semidirect
17. C11×Dic3×C13ΓL(1,𝔽8)semidirect
22. C7×Dic3×C13C3×C11semidirect
24. C7×C11×C13C3×Dic3semidirect
25. C7×C11×Dic3C13⋊C3semidirect
30. C3×#63270C4×C11semidirect
40. C3×C11×C13C4×ΓL(1,𝔽8)semidirect
47. C3×C7×C13C3×C4×C11semidirect
49. #63270C11×Dic3direct (N × H)
52. C3×C7×C11C4×C13⋊C3semidirect
57. Dic3×C13C11×ΓL(1,𝔽8)semidirect
60. C11×C13Dic3×ΓL(1,𝔽8)semidirect
62. C11×Dic3#63270direct (N × H)
66. C7×C13C3×C11×Dic3semidirect
67. C7×Dic3C11×C13⋊C3semidirect
72. C7×C11Dic3×C13⋊C3semidirect
82. C3×C13C4×C11×ΓL(1,𝔽8)semidirect
88. C3×C11C4×#63270semidirect
92. C3×C7C4×C11×C13⋊C3semidirect
97. C13C11×Dic3×ΓL(1,𝔽8)semidirect
99. Dic3C11×#63270direct (N × H)
100. C11Dic3×#63270direct (N × H)
102. C7C11×Dic3×C13⋊C3semidirect
109. C3C4×C11×#63270semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C11×#632702
C7×C11×Dic3×C133
C4×C11×#632703
C11×Dic3×C13⋊C37
Dic3×#6327011
C11×Dic3×ΓL(1,𝔽8)13