Finite Group Databasebeta

← C2×C3×C7×C11×D33 #44479263

Subgroups — C2×C3×C7×C11×D33 #44479263

Order 30492.

296 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 88 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×C7×C11×D33C212yesmaximal, direct product factor
2C2×C32×C7×C112C211yesmaximal, characteristic, complemented
3C2×C3×C7×C11×D11—31nomaximal
4C2×C7×C11×D33C311yesmaximal, characteristic, direct product factor
5C32×C7×C112C2211yescharacteristic, complemented, Hall
6C7×C11×D33C2×C312yesdirect product factor
7C3×C7×C11×D11—32no—
8C2×C3×C7×C112—21no—
9C2×C3×C7×C112D311yescharacteristic, complemented
10C2×C3×C7×C112C2×C311yescharacteristic, complemented
11C2×C3×C11×D33C711yesmaximal, characteristic, direct product factor, Hall
12C2×C7×C11×D11—31noHall
13C2×C3×D3×C7×C11—111nomaximal
14C2×C3×C7×D33C1111yesmaximal, characteristic, direct product factor
15C3×C7×C112—21no—
16C3×C7×C112C2×D311yescharacteristic, complemented
17C3×C7×C112C22×C311yescharacteristic, complemented
18C3×C11×D33C2×C712yesdirect product factor
19C2×C32×C112C2×C711yescharacteristic, complemented
20C2×C7×C112C3×D311yescharacteristic, complemented
21C7×C11×D11—32no—
22C2×C11×D33C3×C711yescharacteristic, direct product factor
23C2×C3×C11×D11—31no—
24C2×C32×C7×C11—25no—
25C2×C32×C7×C11D1111yescharacteristic, complemented
26C2×C32×C7×C11C2×C1111yescharacteristic, complemented
27C3×C7×D33C2×C1112yesdirect product factor
28C3×D3×C7×C11—112no—
29C32×C112C22×C711yescharacteristic, complemented, Hall
30C22×C3×C7×C11—331no—
31C2×C7×D33C3×C1111yescharacteristic, direct product factor
32C2×D3×C7×C11—111no—
33C2×C3×C7×D11—31no—
34C7×C112C2×C3×D311yescharacteristic, complemented, Hall
35C2×C3×C112—21no—
36C2×C3×C112D3×C711yescharacteristic, complemented
37C2×C3×C112C2×C3×C711yescharacteristic, complemented
38C11×D33C2×C3×C712yesdirect product factor
39C3×C11×D11—32no—
40C32×C7×C11—25no—
41C32×C7×C11C2×D1111yescharacteristic, complemented
42C32×C7×C11C22×C1111yescharacteristic, complemented
43C2×C11×D11—31noHall
44C2×C3×C7×C11—210no—
45C2×C3×C7×C11—25no—
46C2×C3×C7×C11—25no—
47C2×C3×C7×C11—21no—
48C2×C3×C7×C11—21no—
49C2×C3×C7×C11—332no—
50C2×C3×C7×C11D3×C1111yescharacteristic, complemented
51C2×C3×C7×C11C3×D1111yescharacteristic, complemented
52C2×C3×C7×C11D3311yescharacteristic, direct product factor
53C2×C3×C7×C11C2×C3×C1111yescharacteristic, complemented
54C7×D33C2×C3×C1112yesdirect product factor
55D3×C7×C11—112no—
56C3×C7×D11—32no—
57C2×C3×D33C7×C1111yescharacteristic, direct product factor
58C2×C3×D3×C11—111no—
59C3×C112—21no—
60C3×C112C2×D3×C711yescharacteristic, complemented
61C3×C112C22×C3×C711yescharacteristic, complemented
62C22×C7×C11—331no—
63C2×C7×D11—31no—
64C2×C3×D3×C7—111noHall
65C2×C112C3×D3×C711yescharacteristic, complemented
66C11×D11—32no—
67C3×C7×C11—210no—
68C3×C7×C11—21no—
69C3×C7×C11—21no—
70C3×C7×C11—25no—
71C3×C7×C11—25no—
72C3×C7×C11C2×C3×D1111yescharacteristic, complemented
73C3×C7×C11C2×D3×C1111yescharacteristic, complemented
74C3×C7×C11C2×D3311yescharacteristic, direct product factor
75C3×C7×C11C22×C3×C1111yescharacteristic, complemented
76C2×C32×C11—25no—
77C2×C32×C11C7×D1111yescharacteristic, complemented
78C2×C32×C11C2×C7×C1111yescharacteristic, complemented
79C3×D33C2×C7×C1112yesdirect product factor
80C3×D3×C11—112no—
81C2×C7×C11—25no—
82C2×C7×C11—332no—
83C2×C7×C11C3×D3×C1111yescharacteristic, complemented
84C2×C7×C11C3×D3311yescharacteristic, direct product factor
85C7×D11—32no—
86C22×C3×C11—331no—
87C2×D33C3×C7×C1111yescharacteristic, direct product factor
88C2×D3×C11—111no—
89C2×C3×D11—31no—
90C2×C32×C7C11×D1111yescharacteristic, complemented
91C3×D3×C7—112no—
92C112C2×C3×D3×C711yescharacteristic, complemented, Sylow
93C32×C11—25no—
94C32×C11C2×C7×D1111yescharacteristic, complemented
95C32×C11C22×C7×C1111yescharacteristic, complemented
96C22×C3×C7—331no—
97C2×D3×C7—111no—
98C7×C11—25no—
99C7×C11C2×C3×D3×C1111yescharacteristic, complemented
100C7×C11C2×C3×D3311yescharacteristic, direct product factor
101C2×C3×C11—210no—
102C2×C3×C11—21no—
103C2×C3×C11—21no—
104C2×C3×C11—25no—
105C2×C3×C11—25no—
106C2×C3×C11—332no—
107C2×C3×C11C3×C7×D1111yescharacteristic, complemented
108C2×C3×C11D3×C7×C1111yescharacteristic, complemented
109C2×C3×C11C7×D3311yescharacteristic, direct product factor
110C2×C3×C11C2×C3×C7×C1111yescharacteristic, complemented
111D33C2×C3×C7×C1112yesdirect product factor
112C3×D11—32no—
113D3×C11—112no—
114C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
115C22×C11—331no—
116C2×D11—31no—
117C2×C3×C7—21no—
118C2×C3×C7—332no—
119C2×C3×C7C3×C11×D1111yescharacteristic, complemented
120C2×C3×C7C11×D3311yescharacteristic, direct product factor
121D3×C7—112no—
122C2×C3×D3—111noHall
123C3×C11—210no—
124C3×C11—21no—
125C3×C11—21no—
126C3×C11—25no—
127C3×C11—25no—
128C3×C11C2×C3×C7×D1111yescharacteristic, complemented
129C3×C11C2×D3×C7×C1111yescharacteristic, complemented
130C3×C11C2×C7×D3311yescharacteristic, direct product factor
131C3×C11C22×C3×C7×C1111yescharacteristic, complemented
132C22×C7—331noHall
133C2×C11—25no—
134C2×C11—332no—
135C2×C11C3×D3×C7×C1111yescharacteristic, complemented
136C2×C11C3×C7×D3311yescharacteristic, direct product factor
137D11—32no—
138C3×C7—21no—
139C3×C7C2×C3×C11×D1111yescharacteristic, complemented
140C3×C7C2×C11×D3311yescharacteristic, direct product factor
141C2×C32C7×C11×D1111yescharacteristic, complemented
142C3×D3—112no—
143C2×C7—332no—
144C2×C7C3×C11×D3311yescharacteristic, direct product factor
145C22×C3—331no—
146C2×D3—111no—
147C11—25no—
148C11C2×C3×C7×D3311yescharacteristic, direct product factor
149C11C2×C3×D3×C7×C1111yescharacteristic, complemented
150C32C2×C7×C11×D1111yescharacteristic, complemented, Sylow
151C7C2×C3×C11×D3311yescharacteristic, direct product factor, Sylow
152C2×C3—21no—
153C2×C3—332no—
154C2×C3C3×C7×C11×D1111yescharacteristic, complemented
155C2×C3C7×C11×D3311yescharacteristic, direct product factor
156D3—112no—
157C22—331noSylow
158C3—21no—
159C3C2×C7×C11×D3311yescharacteristic, direct product factor
160C3C2×C3×C7×C11×D1111yescharacteristic, complemented
161C2—332no—
162C2C3×C7×C11×D3311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7×C11D33
commutator, cosocle, hypocenterC3×C11C22×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C112C2
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C7×C11

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×D33C2direct (N × H)
2. C2×C32×C7×C112C2semidirect
4. C2×C7×C11×D33C3direct (N × H)
5. C32×C7×C112C22semidirect
6. C7×C11×D33C2×C3direct (N × H)
9. C2×C3×C7×C112D3semidirect
10. C2×C3×C7×C112C2×C3semidirect
11. C2×C3×C11×D33C7direct (N × H)
14. C2×C3×C7×D33C11direct (N × H)
16. C3×C7×C112C2×D3semidirect
17. C3×C7×C112C22×C3semidirect
18. C3×C11×D33C2×C7direct (N × H)
19. C2×C32×C112C2×C7semidirect
20. C2×C7×C112C3×D3semidirect
22. C2×C11×D33C3×C7direct (N × H)
25. C2×C32×C7×C11D11semidirect
26. C2×C32×C7×C11C2×C11semidirect
27. C3×C7×D33C2×C11direct (N × H)
29. C32×C112C22×C7semidirect
31. C2×C7×D33C3×C11direct (N × H)
34. C7×C112C2×C3×D3semidirect
36. C2×C3×C112D3×C7semidirect
37. C2×C3×C112C2×C3×C7semidirect
38. C11×D33C2×C3×C7direct (N × H)
41. C32×C7×C11C2×D11semidirect
42. C32×C7×C11C22×C11semidirect
50. C2×C3×C7×C11D3×C11semidirect
51. C2×C3×C7×C11C3×D11semidirect
52. C2×C3×C7×C11D33direct (N × H)
53. C2×C3×C7×C11C2×C3×C11semidirect
54. C7×D33C2×C3×C11direct (N × H)
57. C2×C3×D33C7×C11direct (N × H)
60. C3×C112C2×D3×C7semidirect
61. C3×C112C22×C3×C7semidirect
65. C2×C112C3×D3×C7semidirect
72. C3×C7×C11C2×C3×D11semidirect
73. C3×C7×C11C2×D3×C11semidirect
74. C3×C7×C11C2×D33direct (N × H)
75. C3×C7×C11C22×C3×C11semidirect
77. C2×C32×C11C7×D11semidirect
78. C2×C32×C11C2×C7×C11semidirect
79. C3×D33C2×C7×C11direct (N × H)
83. C2×C7×C11C3×D3×C11semidirect
84. C2×C7×C11C3×D33direct (N × H)
87. C2×D33C3×C7×C11direct (N × H)
90. C2×C32×C7C11×D11semidirect
92. C112C2×C3×D3×C7semidirect
94. C32×C11C2×C7×D11semidirect
95. C32×C11C22×C7×C11semidirect
99. C7×C11C2×C3×D3×C11semidirect
100. C7×C11C2×C3×D33direct (N × H)
107. C2×C3×C11C3×C7×D11semidirect
108. C2×C3×C11D3×C7×C11semidirect
109. C2×C3×C11C7×D33direct (N × H)
110. C2×C3×C11C2×C3×C7×C11semidirect
111. D33C2×C3×C7×C11direct (N × H)
114. C32×C7C2×C11×D11semidirect
119. C2×C3×C7C3×C11×D11semidirect
120. C2×C3×C7C11×D33direct (N × H)
128. C3×C11C2×C3×C7×D11semidirect
129. C3×C11C2×D3×C7×C11semidirect
130. C3×C11C2×C7×D33direct (N × H)
131. C3×C11C22×C3×C7×C11semidirect
135. C2×C11C3×D3×C7×C11semidirect
136. C2×C11C3×C7×D33direct (N × H)
139. C3×C7C2×C3×C11×D11semidirect
140. C3×C7C2×C11×D33direct (N × H)
141. C2×C32C7×C11×D11semidirect
144. C2×C7C3×C11×D33direct (N × H)
148. C11C2×C3×C7×D33direct (N × H)
149. C11C2×C3×D3×C7×C11semidirect
150. C32C2×C7×C11×D11semidirect
151. C7C2×C3×C11×D33direct (N × H)
154. C2×C3C3×C7×C11×D11semidirect
155. C2×C3C7×C11×D33direct (N × H)
159. C3C2×C7×C11×D33direct (N × H)
160. C3C2×C3×C7×C11×D11semidirect
162. C2C3×C7×C11×D33direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×C11×D332
C2×C32×C7×C1122
C2×C3×C7×C11×D113
C2×C7×C11×D333
C2×C3×C11×D337
C2×C3×D3×C7×C1111
C2×C3×C7×D3311