Finite Group Databasebeta

← C3×D3×C72×D11 #34084994

Subgroups — C3×D3×C72×D11 #34084994

Order 19404.

440 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 200 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
1C3×C72×D33C211yesmaximal, characteristic, complemented
2C3×D3×C72×C11C211yesmaximal, characteristic, complemented
3C32×C72×D11C211yesmaximal, characteristic, complemented
4C2×C3×C72×D11—31nomaximal
5D3×C72×D11C311yesmaximal, characteristic, direct product factor
6C32×C72×C11C2211yescharacteristic, complemented, Hall
7C72×D33C2×C311yescharacteristic, complemented
8D3×C72×C11C2×C311yescharacteristic, complemented
9C3×C72×D11—21no—
10C3×C72×D11—31no—
11C3×C72×D11D311yescharacteristic, direct product factor
12C3×C72×D11C2×C311yescharacteristic, complemented
13C2×C3×C72×C11—31no—
14C3×D3×C7×D11C718yesmaximal, direct product factor
15C2×C72×D11—31noHall
16C2×C3×D3×C72—111nomaximal, Hall
17C3×C72×C11—21no—
18C3×C72×C11C2×D311yescharacteristic, complemented
19C3×C72×C11C22×C311yescharacteristic, complemented
20C3×C7×D33C2×C718yescomplemented
21C3×D3×C7×C11C2×C718yescomplemented
22C32×C7×D11C2×C718yescomplemented
23C2×C72×C11—31no—
24C72×D11—31no—
25C72×D11C3×D311yescharacteristic, direct product factor
26C2×C3×C7×D11—38no—
27D3×C7×D11C3×C718yesdirect product factor
28C2×C32×C72—111no—
29C3×D3×C72—111no—
30C3×D3×C72D1111yescharacteristic, direct product factor
31C32×C7×C11C22×C718yescomplemented
32C22×C3×C72—331no—
33C2×D3×C72—111no—
34C72×C11C2×C3×D311yescharacteristic, complemented, Hall
35C2×C3×C7×C11—38no—
36C7×D33C2×C3×C718yescomplemented
37D3×C7×C11C2×C3×C718yescomplemented
38C3×C7×D11—28no—
39C3×C7×D11—38no—
40C3×C7×D11D3×C718yesdirect product factor
41C3×C7×D11C2×C3×C718yescomplemented
42C32×C72C2×D1111yescharacteristic, complemented, Hall
43C3×D3×D11C7211yescharacteristic, direct product factor, Hall
44C2×C7×D11—38no—
45C2×C3×C72—31no—
46C2×C3×C72—111no—
47C2×C3×C72—111no—
48C2×C3×C72—221no—
49C2×C3×C72—331no—
50D3×C72—111no—
51D3×C72C3×D1111yescharacteristic, direct product factor
52C2×C3×D3×C7—118no—
53C3×C7×C11—28no—
54C3×C7×C11C2×D3×C718yescomplemented
55C3×C7×C11C22×C3×C718yescomplemented
56C3×D33C2×C7211yescharacteristic, complemented
57C3×D3×C11C2×C7211yescharacteristic, complemented
58C32×D11C2×C7211yescharacteristic, complemented
59C22×C72—331noHall
60C2×C7×C11—38no—
61C7×D11—38no—
62C7×D11C3×D3×C718yesdirect product factor
63C3×C72—21no—
64C3×C72D3×D1111yescharacteristic, direct product factor
65C3×C72C2×C3×D1111yescharacteristic, complemented
66C2×C3×D11—31no—
67D3×D11C3×C7211yescharacteristic, direct product factor
68C2×C32×C7—118no—
69C3×D3×C7—118no—
70C3×D3×C7C7×D1118yesdirect product factor
71C32×C11C22×C7211yescharacteristic, complemented, Hall
72C2×C72—31no—
73C2×C72—111no—
74C2×C72—331no—
75C22×C3×C7—338no—
76C2×D3×C7—118no—
77C7×C11C2×C3×D3×C718yescomplemented
78C2×C3×C11—31no—
79D33C2×C3×C7211yescharacteristic, complemented
80C3×D11—21no—
81C3×D11—31no—
82C3×D11D3×C7211yescharacteristic, direct product factor
83C3×D11C2×C3×C7211yescharacteristic, complemented
84D3×C11C2×C3×C7211yescharacteristic, complemented
85C32×C7C2×C7×D1118yescomplemented
86C72C3×D3×D1111yescharacteristic, direct product factor, Sylow
87C2×D11—31noHall
88C2×C3×C7—38no—
89C2×C3×C7—118no—
90C2×C3×C7—118no—
91C2×C3×C7—228no—
92C2×C3×C7—338no—
93D3×C7—118no—
94D3×C7C3×C7×D1118yesdirect product factor
95C2×C3×D3—111noHall
96C3×C11—21no—
97C3×C11C2×D3×C7211yescharacteristic, complemented
98C3×C11C22×C3×C7211yescharacteristic, complemented
99C22×C7—338no—
100C2×C11—31no—
101D11—31no—
102D11C3×D3×C7211yescharacteristic, direct product factor
103C3×C7—28no—
104C3×C7D3×C7×D1118yesdirect product factor
105C3×C7C2×C3×C7×D1118yescomplemented
106C2×C32—111no—
107C3×D3—111no—
108C3×D3C72×D1111yescharacteristic, direct product factor
109C2×C7—38no—
110C2×C7—118no—
111C2×C7—338no—
112C22×C3—331no—
113C2×D3—111no—
114C11C2×C3×D3×C7211yescharacteristic, complemented, Sylow
115C32C2×C72×D1111yescharacteristic, complemented, Sylow
116C7C3×D3×C7×D1118yesdirect product factor
117C2×C3—31no—
118C2×C3—111no—
119C2×C3—111no—
120C2×C3—221no—
121C2×C3—331no—
122D3—111no—
123D3C3×C72×D1111yescharacteristic, direct product factor
124C22—331noSylow
125C3—21no—
126C3D3×C72×D1111yescharacteristic, direct product factor
127C3C2×C3×C72×D1111yescharacteristic, complemented
128C2—31no—
129C2—111no—
130C2—331no—
subgroupG/H
center, hypercenterC3×C72D3×D11
commutator, cosocle, hypocenterC3×C11C22×C3×C72
FrattiniC1G
Fitting, socleC32×C72×C11C22
LCSG ▷ C3×C11
UCSC1 ◁ C3×C72

Complements

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

NH ≅ G/Ntype
1. C3×C72×D33C2semidirect
2. C3×D3×C72×C11C2semidirect
3. C32×C72×D11C2semidirect
5. D3×C72×D11C3direct (N × H)
6. C32×C72×C11C22semidirect
7. C72×D33C2×C3semidirect
8. D3×C72×C11C2×C3semidirect
11. C3×C72×D11D3direct (N × H)
12. C3×C72×D11C2×C3semidirect
14. C3×D3×C7×D11C7direct (N × H)
18. C3×C72×C11C2×D3semidirect
19. C3×C72×C11C22×C3semidirect
20. C3×C7×D33C2×C7semidirect
21. C3×D3×C7×C11C2×C7semidirect
22. C32×C7×D11C2×C7semidirect
25. C72×D11C3×D3direct (N × H)
27. D3×C7×D11C3×C7direct (N × H)
30. C3×D3×C72D11direct (N × H)
31. C32×C7×C11C22×C7semidirect
34. C72×C11C2×C3×D3semidirect
36. C7×D33C2×C3×C7semidirect
37. D3×C7×C11C2×C3×C7semidirect
40. C3×C7×D11D3×C7direct (N × H)
41. C3×C7×D11C2×C3×C7semidirect
42. C32×C72C2×D11semidirect
43. C3×D3×D11C72direct (N × H)
51. D3×C72C3×D11direct (N × H)
54. C3×C7×C11C2×D3×C7semidirect
55. C3×C7×C11C22×C3×C7semidirect
56. C3×D33C2×C72semidirect
57. C3×D3×C11C2×C72semidirect
58. C32×D11C2×C72semidirect
62. C7×D11C3×D3×C7direct (N × H)
64. C3×C72D3×D11direct (N × H)
65. C3×C72C2×C3×D11semidirect
67. D3×D11C3×C72direct (N × H)
70. C3×D3×C7C7×D11direct (N × H)
71. C32×C11C22×C72semidirect
77. C7×C11C2×C3×D3×C7semidirect
79. D33C2×C3×C72semidirect
82. C3×D11D3×C72direct (N × H)
83. C3×D11C2×C3×C72semidirect
84. D3×C11C2×C3×C72semidirect
85. C32×C7C2×C7×D11semidirect
86. C72C3×D3×D11direct (N × H)
94. D3×C7C3×C7×D11direct (N × H)
97. C3×C11C2×D3×C72semidirect
98. C3×C11C22×C3×C72semidirect
102. D11C3×D3×C72direct (N × H)
104. C3×C7D3×C7×D11direct (N × H)
105. C3×C7C2×C3×C7×D11semidirect
108. C3×D3C72×D11direct (N × H)
114. C11C2×C3×D3×C72semidirect
115. C32C2×C72×D11semidirect
116. C7C3×D3×C7×D11direct (N × H)
123. D3C3×C72×D11direct (N × H)
126. C3D3×C72×D11direct (N × H)
127. C3C2×C3×C72×D11semidirect

Maximal subgroups

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

subgroupindex
C3×C72×D332
C3×D3×C72×C112
C32×C72×D112
C2×C3×C72×D113
D3×C72×D113
C3×D3×C7×D117
C2×C3×D3×C7211