Finite Group Databasebeta

← C2×C3×D11×#63270 #49114838

Subgroups — C2×C3×D11×#63270 #49114838

Order 36036.

240 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 84 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, complemented
2C3×D11×#63270C212yesmaximal, direct product factor
3C2×C3×C7×C13×D11C311yesmaximal, characteristic, complemented
4C2×D11×#63270C313yesmaximal, direct product factor
5C3×C11×#63270C2211yescharacteristic, complemented, Hall
6D11×#63270C2×C316yesdirect product factor
7C3×C7×C13×D11C2×C312yescomplemented
8C2×C11×#63270C2×C313yescomplemented
9C2×C3×C7×C11×C13C2×C311yescharacteristic, complemented
10C2×C3×D11×C13⋊C3—71nomaximal, Hall
11C2×C7×C13×D11C3211yescharacteristic, complemented, Hall
12C22×C3×#63270—111nomaximal, Hall
13C11×#63270C22×C313yescomplemented
14C3×C7×C11×C13C22×C311yescharacteristic, complemented
15C2×C3×ΓL(1,𝔽8)×D11—131nomaximal, Hall
16C2×C3×C11×C13⋊C3—71no—
17C3×D11×C13⋊C3—72no—
18C7×C13×D11C2×C3212yescomplemented
19C2×C7×C11×C13C2×C3211yescharacteristic, complemented
20C2×C3×C13×D11ΓL(1,𝔽8)11yescharacteristic, complemented
21C2×D11×C13⋊C3—73no—
22C2×C3×#63270—112no—
23C2×C3×#63270D1111yescharacteristic, direct product factor
24C2×C3×C11×ΓL(1,𝔽8)—131no—
25C3×ΓL(1,𝔽8)×D11—132no—
26C3×C11×C13⋊C3—71noHall
27C22×C3×C7×C13—111no—
28C22×#63270—113no—
29C7×C11×C13C22×C3211yescharacteristic, complemented, Hall
30C2×C3×C7×D11C13⋊C311yescharacteristic, complemented
31C2×ΓL(1,𝔽8)×D11—133no—
32C2×C3×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic, complemented
33C3×C13×D11C2×ΓL(1,𝔽8)12yescomplemented
34C2×C11×C13⋊C3—73no—
35D11×C13⋊C3—76no—
36C3×#63270C2×D1111yescharacteristic, direct product factor, Hall
37C3×C11×ΓL(1,𝔽8)—131noHall
38C2×C13×D11C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
39C2×C3×C7×C13—112no—
40C2×C3×C7×C13C3×D1111yescharacteristic, complemented
41C2×#63270—116no—
42C2×#63270C3×D1113yesdirect product factor
43C22×C3×C13⋊C3—771noHall
44C2×C3×C7×C11C2×C13⋊C311yescharacteristic, complemented
45C3×C7×D11C2×C13⋊C312yescomplemented
46C2×C11×ΓL(1,𝔽8)—133no—
47ΓL(1,𝔽8)×D11—136no—
48C3×C11×C13C22×ΓL(1,𝔽8)11yescharacteristic, complemented
49C11×C13⋊C3—73no—
50C2×C32×D11—911noHall
51C22×C7×C13—111noHall
52C2×C7×D11C3×C13⋊C311yescharacteristic, complemented, Hall
53C2×C11×C13C2×C3×ΓL(1,𝔽8)11yescharacteristic, complemented
54C13×D11C2×C3×ΓL(1,𝔽8)12yescomplemented
55C3×C7×C13C2×C3×D1111yescharacteristic, complemented
56#63270C2×C3×D1113yesdirect product factor
57C22×C3×ΓL(1,𝔽8)—1431noHall
58C2×C3×C13⋊C3—71no—
59C2×C3×C13⋊C3—772no—
60C3×C7×C11C22×C13⋊C311yescharacteristic, complemented
61C11×ΓL(1,𝔽8)—133no—
62C2×C32×C11—911no—
63C32×D11—912no—
64C2×C7×C13—112no—
65C2×C7×C13C32×D1111yescharacteristic, complemented
66C22×C3×C13—111no—
67C22×C13⋊C3—773no—
68C2×C7×C11C2×C3×C13⋊C311yescharacteristic, complemented
69C7×D11C2×C3×C13⋊C312yescomplemented
70C11×C13C22×C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
71C2×C3×D11—913no—
72C2×C3×D11#6327011yescharacteristic, direct product factor
73C2×C3×ΓL(1,𝔽8)—131no—
74C2×C3×ΓL(1,𝔽8)—1432no—
75C3×C13⋊C3—71noHall
76C32×C11—911noHall
77C7×C13C2×C32×D1111yescharacteristic, complemented, Hall
78C22×C3×C7—111no—
79C22×ΓL(1,𝔽8)—1433no—
80C2×C3×C13—112no—
81C2×C3×C13ΓL(1,𝔽8)×D1111yescharacteristic, complemented
82C2×C13⋊C3—73no—
83C2×C13⋊C3—776no—
84C7×C11C22×C3×C13⋊C311yescharacteristic, complemented, Hall
85C2×C3×C11—913no—
86C2×C3×C11C2×#6327011yescharacteristic, complemented
87C3×D11—916no—
88C3×D11C2×#6327012yesdirect product factor
89C3×ΓL(1,𝔽8)—131noHall
90C22×C13—111noHall
91C2×D11C3×#6327011yescharacteristic, direct product factor, Hall
92C2×C3×C7—112no—
93C2×C3×C7D11×C13⋊C311yescharacteristic, complemented
94C2×ΓL(1,𝔽8)—133no—
95C2×ΓL(1,𝔽8)—1436no—
96C3×C13C2×ΓL(1,𝔽8)×D1111yescharacteristic, complemented
97C13⋊C3—73no—
98C22×C32—10011noHall
99C3×C11—913no—
100C3×C11C22×#6327011yescharacteristic, complemented
101C22×C7—111noHall
102C2×C13—112no—
103C2×C13C3×ΓL(1,𝔽8)×D1111yescharacteristic, complemented
104C2×C11C2×C3×#6327011yescharacteristic, complemented
105D11C2×C3×#6327012yesdirect product factor
106C3×C7C2×D11×C13⋊C311yescharacteristic, complemented
107ΓL(1,𝔽8)—133no—
108C2×C32—911no—
109C2×C32—10012no—
110C2×C7—112no—
111C2×C7C3×D11×C13⋊C311yescharacteristic, complemented
112C13C2×C3×ΓL(1,𝔽8)×D1111yescharacteristic, complemented, Sylow
113C22×C3—111no—
114C22×C3—10013no—
115C11C22×C3×#6327011yescharacteristic, complemented, Sylow
116C32—911noSylow
117C7C2×C3×D11×C13⋊C311yescharacteristic, complemented, Sylow
118C2×C3—112no—
119C2×C3—913no—
120C2×C3—10016no—
121C2×C3D11×#6327011yescharacteristic, direct product factor
122C22—111noSylow
123C3—913no—
124C3C2×D11×#6327011yescharacteristic, direct product factor
125C2—112no—
126C2C3×D11×#6327011yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D11×#63270
commutator, cosocle, hypocenterC7×C11×C13C22×C32
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C11×#63270C2semidirect
2. C3×D11×#63270C2direct (N × H)
3. C2×C3×C7×C13×D11C3semidirect
4. C2×D11×#63270C3direct (N × H)
5. C3×C11×#63270C22semidirect
6. D11×#63270C2×C3direct (N × H)
7. C3×C7×C13×D11C2×C3semidirect
8. C2×C11×#63270C2×C3semidirect
9. C2×C3×C7×C11×C13C2×C3semidirect
11. C2×C7×C13×D11C32semidirect
13. C11×#63270C22×C3semidirect
14. C3×C7×C11×C13C22×C3semidirect
18. C7×C13×D11C2×C32semidirect
19. C2×C7×C11×C13C2×C32semidirect
20. C2×C3×C13×D11ΓL(1,𝔽8)semidirect
23. C2×C3×#63270D11direct (N × H)
29. C7×C11×C13C22×C32semidirect
30. C2×C3×C7×D11C13⋊C3semidirect
32. C2×C3×C11×C13C2×ΓL(1,𝔽8)semidirect
33. C3×C13×D11C2×ΓL(1,𝔽8)semidirect
36. C3×#63270C2×D11direct (N × H)
38. C2×C13×D11C3×ΓL(1,𝔽8)semidirect
40. C2×C3×C7×C13C3×D11semidirect
42. C2×#63270C3×D11direct (N × H)
44. C2×C3×C7×C11C2×C13⋊C3semidirect
45. C3×C7×D11C2×C13⋊C3semidirect
48. C3×C11×C13C22×ΓL(1,𝔽8)semidirect
52. C2×C7×D11C3×C13⋊C3semidirect
53. C2×C11×C13C2×C3×ΓL(1,𝔽8)semidirect
54. C13×D11C2×C3×ΓL(1,𝔽8)semidirect
55. C3×C7×C13C2×C3×D11semidirect
56. #63270C2×C3×D11direct (N × H)
60. C3×C7×C11C22×C13⋊C3semidirect
65. C2×C7×C13C32×D11semidirect
68. C2×C7×C11C2×C3×C13⋊C3semidirect
69. C7×D11C2×C3×C13⋊C3semidirect
70. C11×C13C22×C3×ΓL(1,𝔽8)semidirect
72. C2×C3×D11#63270direct (N × H)
77. C7×C13C2×C32×D11semidirect
81. C2×C3×C13ΓL(1,𝔽8)×D11semidirect
84. C7×C11C22×C3×C13⋊C3semidirect
86. C2×C3×C11C2×#63270semidirect
88. C3×D11C2×#63270direct (N × H)
91. C2×D11C3×#63270direct (N × H)
93. C2×C3×C7D11×C13⋊C3semidirect
96. C3×C13C2×ΓL(1,𝔽8)×D11semidirect
100. C3×C11C22×#63270semidirect
103. C2×C13C3×ΓL(1,𝔽8)×D11semidirect
104. C2×C11C2×C3×#63270semidirect
105. D11C2×C3×#63270direct (N × H)
106. C3×C7C2×D11×C13⋊C3semidirect
111. C2×C7C3×D11×C13⋊C3semidirect
112. C13C2×C3×ΓL(1,𝔽8)×D11semidirect
115. C11C22×C3×#63270semidirect
117. C7C2×C3×D11×C13⋊C3semidirect
121. C2×C3D11×#63270direct (N × H)
124. C3C2×D11×#63270direct (N × H)
126. C2C3×D11×#63270direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C11×#632702
C3×D11×#632702
C2×C3×C7×C13×D113
C2×D11×#632703
C2×C3×D11×C13⋊C37
C22×C3×#6327011
C2×C3×ΓL(1,𝔽8)×D1113