Finite Group Databasebeta

← C3×C11×D21⋊D11 #44479199

Subgroups — C3×C11×D21⋊D11 #44479199

Order 30492.

266 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C32×C11×D77C211yesmaximal, characteristic, complemented
2C3×C7×C11×D33C211yesmaximal, characteristic, complemented
3C3×C112×D21C211yesmaximal, characteristic, complemented
4C11×D21⋊D11C311yesmaximal, characteristic, direct product factor
5C3×C11×D7×D11—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C112×D21C2×C311yescharacteristic, complemented
8C7×C11×D33C2×C311yescharacteristic, complemented
9C3×C11×D77—21no—
10C3×C11×D77D311yescharacteristic, complemented
11C3×C11×D77C2×C311yescharacteristic, complemented
12C3×C112×D7—31no—
13C3×C7×C11×D11—31no—
14C3×D3×C11×D11—71nomaximal, Hall
15C11×D7×D11—31noHall
16C3×D21⋊D11C1111yesmaximal, characteristic, direct product factor
17C3×D3×C11×D7—111nomaximal
18C3×C7×C112—21no—
19C3×C7×C112C2×D311yescharacteristic, complemented
20C3×C7×C112C22×C311yescharacteristic, complemented
21C3×C11×D33D711yescharacteristic, complemented
22C3×D3×C112—71no—
23C32×C11×D11—71no—
24C11×D77C3×D311yescharacteristic, complemented
25C112×D7—31no—
26C7×C11×D11—31no—
27C2×C3×C11×D11—211no—
28D3×C11×D11—71no—
29C3×C11×D21—25no—
30C3×C11×D21D1111yescharacteristic, complemented
31C3×C11×D21C2×C1111yescharacteristic, complemented
32C3×C7×D33C2×C1111yescharacteristic, complemented
33C3×D3×C7×C11—111no—
34C32×D77C2×C1111yescharacteristic, complemented
35C32×C11×D7—111no—
36C32×C112C2×D711yescharacteristic, complemented, Hall
37C2×C3×C11×D7—331no—
38D21⋊D11C3×C1111yescharacteristic, direct product factor
39D3×C11×D7—111no—
40C3×D7×D11—31no—
41C7×C112C2×C3×D311yescharacteristic, complemented, Hall
42C2×C3×C112—211no—
43C11×D33C3×D711yescharacteristic, complemented
44D3×C112—71no—
45C3×C11×D11—31no—
46C3×C11×D11—71no—
47C3×C11×D11—71no—
48C3×C11×D11—141no—
49C32×C7×C11—25no—
50C32×C7×C11C2×D1111yescharacteristic, complemented
51C32×C7×C11C22×C1111yescharacteristic, complemented
52C2×C11×D11—211noHall
53C2×C3×C7×C11—331no—
54C11×D21—25no—
55C11×D21C3×D1111yescharacteristic, complemented
56C11×D21C2×C3×C1111yescharacteristic, complemented
57C7×D33C2×C3×C1111yescharacteristic, complemented
58D3×C7×C11—111no—
59C3×D77—21no—
60C3×D77D3×C1111yescharacteristic, complemented
61C3×D77C2×C3×C1111yescharacteristic, complemented
62C3×C11×D7—31no—
63C3×C11×D7—31no—
64C3×C11×D7—65no—
65C3×C11×D7—111no—
66C3×C11×D7—111no—
67C3×C11×D7—221no—
68C3×C7×D11—31no—
69C2×C3×D3×C11—771no—
70C3×D3×D11—71no—
71C3×C112—21no—
72C3×C112D3×D711yescharacteristic, complemented
73C3×C112C2×C3×D711yescharacteristic, complemented
74C2×C11×D7—331no—
75D7×D11—31no—
76C3×D3×D7—111noHall
77C2×C112—211no—
78C11×D11—31no—
79C11×D11—71no—
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×C11C2×C3×D1111yescharacteristic, complemented
87C3×C7×C11C2×D3×C1111yescharacteristic, complemented
88C3×C7×C11C22×C3×C1111yescharacteristic, complemented
89C2×C32×C11—771no—
90C3×D33C11×D711yescharacteristic, complemented
91C3×D3×C11—71no—
92C3×D3×C11—71no—
93C3×D3×C11—111no—
94C3×D3×C11—145no—
95C32×D11—71no—
96C2×C7×C11—331no—
97D77C3×D3×C1111yescharacteristic, complemented
98C7×D11—31no—
99C11×D7—31no—
100C11×D7—31no—
101C11×D7—65no—
102C11×D7—111no—
103C22×C3×C11—2311no—
104C2×D3×C11—771no—
105C2×C3×D11—211no—
106D3×D11—71no—
107C3×D21C11×D1111yescharacteristic, complemented
108C3×D3×C7—111no—
109C32×D7—111no—
110C112C3×D3×D711yescharacteristic, complemented, Sylow
111C32×C11—25no—
112C32×C11D7×D1111yescharacteristic, complemented
113C32×C11C2×C11×D711yescharacteristic, complemented
114C2×C3×D7—331no—
115D3×D7—111no—
116C7×C11—25no—
117C7×C11C3×D3×D1111yescharacteristic, complemented
118C7×C11C2×C3×D3×C1111yescharacteristic, complemented
119C2×C3×C11—211no—
120C2×C3×C11—211no—
121C2×C3×C11—331no—
122C2×C3×C11—425no—
123C2×C3×C11—771no—
124C2×C3×C11—771no—
125C2×C3×C11—1541no—
126D33C3×C11×D711yescharacteristic, complemented
127C3×D11—31no—
128C3×D11—71no—
129C3×D11—71no—
130C3×D11—141no—
131D3×C11—71no—
132D3×C11—71no—
133D3×C11—111no—
134D3×C11—145no—
135C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
136C22×C11—2311no—
137C2×D11—211no—
138C2×C3×C7—331no—
139D21C3×C11×D1111yescharacteristic, complemented
140C3×D7—31no—
141C3×D7—111no—
142C3×D7—111no—
143C3×D7—221no—
144D3×C7—111no—
145C2×C3×D3—771noHall
146C3×C11—21no—
147C3×C11—21no—
148C3×C11—25no—
149C3×C11—25no—
150C3×C11—45no—
151C3×C11C3×D7×D1111yescharacteristic, complemented
152C3×C11D3×C11×D711yescharacteristic, complemented
153C3×C11D21⋊D1111yescharacteristic, direct product factor
154C3×C11C2×C3×C11×D711yescharacteristic, complemented
155C2×D7—331noHall
156C2×C11—211no—
157C2×C11—211no—
158C2×C11—331no—
159C2×C11—425no—
160C2×C11—771no—
161D11—31no—
162D11—71no—
163C3×C7—21no—
164C3×C7D3×C11×D1111yescharacteristic, complemented
165C3×C7C2×C3×C11×D1111yescharacteristic, complemented
166C2×C32—771no—
167C3×D3—71no—
168C3×D3—111no—
169C2×C7—331no—
170D7—31no—
171D7—111no—
172C22×C3—2311no—
173C2×D3—771no—
174C11—25no—
175C11C3×D3×C11×D711yescharacteristic, complemented
176C11C3×D21⋊D1111yescharacteristic, direct product factor
177C32C11×D7×D1111yescharacteristic, complemented, Sylow
178C7C3×D3×C11×D1111yescharacteristic, complemented, Sylow
179C2×C3—211no—
180C2×C3—331no—
181C2×C3—771no—
182C2×C3—771no—
183C2×C3—1541no—
184D3—71no—
185D3—111no—
186C22—2311noSylow
187C3—21no—
188C3C3×C11×D7×D1111yescharacteristic, complemented
189C3C11×D21⋊D1111yescharacteristic, direct product factor
190C2—211no—
191C2—331no—
192C2—771no—
subgroupG/H
center, hypercenterC3×C11D21⋊D11
commutator, cosocle, hypocenterC3×C7×C11C22×C3×C11
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C3×C7×C11
UCSC1 ◁ C3×C11

Complements

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

NH ≅ G/Ntype
1. C32×C11×D77C2semidirect
2. C3×C7×C11×D33C2semidirect
3. C3×C112×D21C2semidirect
4. C11×D21⋊D11C3direct (N × H)
6. C32×C7×C112C22semidirect
7. C112×D21C2×C3semidirect
8. C7×C11×D33C2×C3semidirect
10. C3×C11×D77D3semidirect
11. C3×C11×D77C2×C3semidirect
16. C3×D21⋊D11C11direct (N × H)
19. C3×C7×C112C2×D3semidirect
20. C3×C7×C112C22×C3semidirect
21. C3×C11×D33D7semidirect
24. C11×D77C3×D3semidirect
30. C3×C11×D21D11semidirect
31. C3×C11×D21C2×C11semidirect
32. C3×C7×D33C2×C11semidirect
34. C32×D77C2×C11semidirect
36. C32×C112C2×D7semidirect
38. D21⋊D11C3×C11direct (N × H)
41. C7×C112C2×C3×D3semidirect
43. C11×D33C3×D7semidirect
50. C32×C7×C11C2×D11semidirect
51. C32×C7×C11C22×C11semidirect
55. C11×D21C3×D11semidirect
56. C11×D21C2×C3×C11semidirect
57. C7×D33C2×C3×C11semidirect
60. C3×D77D3×C11semidirect
61. C3×D77C2×C3×C11semidirect
72. C3×C112D3×D7semidirect
73. C3×C112C2×C3×D7semidirect
85. C3×C7×C11D3×D11semidirect
86. C3×C7×C11C2×C3×D11semidirect
87. C3×C7×C11C2×D3×C11semidirect
88. C3×C7×C11C22×C3×C11semidirect
90. C3×D33C11×D7semidirect
97. D77C3×D3×C11semidirect
107. C3×D21C11×D11semidirect
110. C112C3×D3×D7semidirect
112. C32×C11D7×D11semidirect
113. C32×C11C2×C11×D7semidirect
117. C7×C11C3×D3×D11semidirect
118. C7×C11C2×C3×D3×C11semidirect
126. D33C3×C11×D7semidirect
135. C32×C7C2×C11×D11semidirect
139. D21C3×C11×D11semidirect
151. C3×C11C3×D7×D11semidirect
152. C3×C11D3×C11×D7semidirect
153. C3×C11D21⋊D11direct (N × H)
154. C3×C11C2×C3×C11×D7semidirect
164. C3×C7D3×C11×D11semidirect
165. C3×C7C2×C3×C11×D11semidirect
175. C11C3×D3×C11×D7semidirect
176. C11C3×D21⋊D11direct (N × H)
177. C32C11×D7×D11semidirect
178. C7C3×D3×C11×D11semidirect
188. C3C3×C11×D7×D11semidirect
189. C3C11×D21⋊D11direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×D772
C3×C7×C11×D332
C3×C112×D212
C11×D21⋊D113
C3×C11×D7×D113
C3×D3×C11×D117
C3×D21⋊D1111
C3×D3×C11×D711