Finite Group Databasebeta

← C7×D33⋊D33 #44479210

Subgroups — C7×D33⋊D33 #44479210

Order 30492.

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

normal subgroups only

This group has 266 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
1C3×C7×C11×D33C211yesmaximal, characteristic, complemented
2C3×C7×C3⋊(C11⋊D11)C211yesmaximal, characteristic, complemented
3C7×C11×C3⋊D33C211yesmaximal, characteristic, complemented
4C7×D33⋊D11—31nomaximal
5C7×D11×D33—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C7×C3⋊(C11⋊D11)D311yescharacteristic, complemented
8C7×C11×D33—31no—
9C7×C11×D33—31no—
10C7×C11×D33—61no—
11C7×C11×D33D311yescharacteristic, complemented
12C3×C7×C11⋊D11—31no—
13C3×C7×C11×D11—31no—
14D33⋊D33C711yesmaximal, characteristic, direct product factor, Hall
15C7×D112—91noHall
16C7×(C3⋊D3)⋊D11—111nomaximal
17D3×C7×D33—111nomaximal
18C3×C7×C112—21no—
19C3×C7×C112C2×D311yescharacteristic, complemented
20C3×C7×C112C2×D311yescharacteristic, complemented
21C11×C3⋊D33C2×C711yescharacteristic, complemented
22C3×C3⋊(C11⋊D11)C2×C711yescharacteristic, complemented
23C3×C11×D33C2×C711yescharacteristic, complemented
24C7×C11⋊D11—31no—
25C7×C11×D11—31no—
26C7×C11×D11—91no—
27D33⋊D11—31no—
28D11×D33—31no—
29C7×C3⋊D33D1111yescharacteristic, complemented
30C7×C11×C3⋊D3—111no—
31C3×C7×D33—111no—
32C3×C7×D33—111no—
33C3×C7×D33—225no—
34C3×C7×D33D1111yescharacteristic, complemented
35C3×D3×C7×C11—111no—
36C32×C112C22×C711yescharacteristic, complemented, Hall
37C2×C7×D33—331no—
38D3×C7×D11—331no—
39D3×C7×D11—331no—
40D3×C7×D11—331no—
41C7×C112D3211yescharacteristic, complemented, Hall
42C3⋊(C11⋊D11)D3×C711yescharacteristic, complemented
43C11×D33—31no—
44C11×D33—31no—
45C11×D33—61no—
46C11×D33D3×C711yescharacteristic, complemented
47C3×C11⋊D11—31no—
48C3×C11×D11—31no—
49C32×C7×C11—25no—
50C32×C7×C11C2×D1111yescharacteristic, complemented
51C32×C7×C11C2×D1111yescharacteristic, complemented
52D112—91noHall
53C2×C3×C7×C11—331no—
54C7×D33—31no—
55C7×D33—31no—
56C7×D33—61no—
57C7×D33—111no—
58C7×D33—111no—
59C7×D33—225no—
60C7×D33D3311yescharacteristic, complemented
61D3×C7×C11—111no—
62D3×C7×C11—331no—
63D3×C7×C11—331no—
64D3×C7×C11—661no—
65C3×C7×D11—31no—
66C3×C7×D11—331no—
67C3×C7×D11—331no—
68C3×C7×D11—665no—
69(C3⋊D3)⋊D11—111no—
70D3×D33—111no—
71C3×C112—21no—
72C3×C112C2×D3×C711yescharacteristic, complemented
73C3×C112C2×D3×C711yescharacteristic, complemented
74C2×C7×D11—991no—
75C2×C7×D11—991no—
76D32×C7—1211noHall
77C11⋊D11—31no—
78C11×D11—31no—
79C11×D11—91no—
80C3×C7×C11—21no—
81C3×C7×C11—21no—
82C3×C7×C11—25no—
83C3×C7×C11—25no—
84C3×C7×C11—45no—
85C3×C7×C11D3×D1111yescharacteristic, complemented
86C3×C7×C11D3×D1111yescharacteristic, complemented
87C3×C7×C11D3×D1111yescharacteristic, complemented
88C3×C7×C11C2×D3311yescharacteristic, complemented
89C3⋊D33C7×D1111yescharacteristic, complemented
90C11×C3⋊D3—111no—
91C3×D33—111no—
92C3×D33—111no—
93C3×D33—225no—
94C3×D33C7×D1111yescharacteristic, complemented
95C3×D3×C11—111no—
96C2×C7×C11—331no—
97C2×C7×C11—991no—
98C7×D11—31no—
99C7×D11—91no—
100C7×D11—331no—
101C7×D11—331no—
102C7×D11—665no—
103C2×D33—331no—
104D3×D11—331no—
105D3×D11—331no—
106D3×D11—331no—
107C7×C3⋊D3—111no—
108C3×D3×C7—111no—
109C3×D3×C7—1211no—
110C112D32×C711yescharacteristic, complemented, Sylow
111C32×C11—25no—
112C32×C11C2×C7×D1111yescharacteristic, complemented
113C32×C11C2×C7×D1111yescharacteristic, complemented
114C2×D3×C7—3631no—
115C2×D3×C7—3631no—
116C7×C11—25no—
117C7×C11D3×D3311yescharacteristic, complemented
118C7×C11(C3⋊D3)⋊D1111yescharacteristic, complemented
119C2×C3×C11—331no—
120D33—31no—
121D33—31no—
122D33—61no—
123D33—111no—
124D33—111no—
125D33—225no—
126D33C7×D3311yescharacteristic, complemented
127C3×D11—31no—
128C3×D11—331no—
129C3×D11—331no—
130C3×D11—665no—
131D3×C11—111no—
132D3×C11—331no—
133D3×C11—331no—
134D3×C11—661no—
135C32×C7D11211yescharacteristic, complemented, Hall
136C2×D11—991no—
137C2×D11—991no—
138C2×C3×C7—331no—
139C2×C3×C7—3631no—
140D3×C7—111no—
141D3×C7—331no—
142D3×C7—331no—
143D3×C7—661no—
144D3×C7—1211no—
145D32—1211noHall
146C3×C11—21no—
147C3×C11—21no—
148C3×C11—25no—
149C3×C11—25no—
150C3×C11—45no—
151C3×C11D3×C7×D1111yescharacteristic, complemented
152C3×C11D3×C7×D1111yescharacteristic, complemented
153C3×C11D3×C7×D1111yescharacteristic, complemented
154C3×C11C2×C7×D3311yescharacteristic, complemented
155C22×C7—10891noHall
156C2×C11—331no—
157C2×C11—991no—
158D11—31no—
159D11—91no—
160D11—331no—
161D11—331no—
162D11—665no—
163C3×C7—21no—
164C3×C7D11×D3311yescharacteristic, complemented
165C3×C7D33⋊D1111yescharacteristic, complemented
166C3⋊D3—111no—
167C3×D3—111no—
168C3×D3—1211no—
169C2×C7—331no—
170C2×C7—991no—
171C2×C7—3631no—
172C2×D3—3631no—
173C2×D3—3631no—
174C11—25no—
175C11D3×C7×D3311yescharacteristic, complemented
176C11C7×(C3⋊D3)⋊D1111yescharacteristic, complemented
177C32C7×D11211yescharacteristic, complemented, Sylow
178C7D33⋊D3311yescharacteristic, direct product factor, Sylow
179C2×C3—331no—
180C2×C3—3631no—
181D3—111no—
182D3—331no—
183D3—331no—
184D3—661no—
185D3—1211no—
186C22—10891noSylow
187C3—21no—
188C3C7×D11×D3311yescharacteristic, complemented
189C3C7×D33⋊D1111yescharacteristic, complemented
190C2—331no—
191C2—991no—
192C2—3631no—
subgroupG/H
center, hypercenterC7D33⋊D33
commutator, cosocle, hypocenterC32×C112C22×C7
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C32×C112
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C3×C7×C11×D33C2semidirect
2. C3×C7×C3⋊(C11⋊D11)C2semidirect
3. C7×C11×C3⋊D33C2semidirect
6. C32×C7×C112C22semidirect
7. C7×C3⋊(C11⋊D11)D3semidirect
11. C7×C11×D33D3semidirect
14. D33⋊D33C7direct (N × H)
19. C3×C7×C112C2×D3semidirect
20. C3×C7×C112C2×D3semidirect
21. C11×C3⋊D33C2×C7semidirect
22. C3×C3⋊(C11⋊D11)C2×C7semidirect
23. C3×C11×D33C2×C7semidirect
29. C7×C3⋊D33D11semidirect
34. C3×C7×D33D11semidirect
36. C32×C112C22×C7semidirect
41. C7×C112D32semidirect
42. C3⋊(C11⋊D11)D3×C7semidirect
46. C11×D33D3×C7semidirect
50. C32×C7×C11C2×D11semidirect
51. C32×C7×C11C2×D11semidirect
60. C7×D33D33semidirect
72. C3×C112C2×D3×C7semidirect
73. C3×C112C2×D3×C7semidirect
85. C3×C7×C11D3×D11semidirect
86. C3×C7×C11D3×D11semidirect
87. C3×C7×C11D3×D11semidirect
88. C3×C7×C11C2×D33semidirect
89. C3⋊D33C7×D11semidirect
94. C3×D33C7×D11semidirect
110. C112D32×C7semidirect
112. C32×C11C2×C7×D11semidirect
113. C32×C11C2×C7×D11semidirect
117. C7×C11D3×D33semidirect
118. C7×C11(C3⋊D3)⋊D11semidirect
126. D33C7×D33semidirect
135. C32×C7D112semidirect
151. C3×C11D3×C7×D11semidirect
152. C3×C11D3×C7×D11semidirect
153. C3×C11D3×C7×D11semidirect
154. C3×C11C2×C7×D33semidirect
164. C3×C7D11×D33semidirect
165. C3×C7D33⋊D11semidirect
175. C11D3×C7×D33semidirect
176. C11C7×(C3⋊D3)⋊D11semidirect
177. C32C7×D112semidirect
178. C7D33⋊D33direct (N × H)
188. C3C7×D11×D33semidirect
189. C3C7×D33⋊D11semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C11×D332
C3×C7×C3⋊(C11⋊D11)2
C7×C11×C3⋊D332
C7×D33⋊D113
C7×D11×D333
D33⋊D337
C7×(C3⋊D3)⋊D1111
D3×C7×D3311