Finite Group Databasebeta

← C3×D3×C11×D77 #44479198

Subgroups — C3×D3×C11×D77 #44479198

Order 30492.

266 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 64 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×D3×C7×C112C211yesmaximal, characteristic, complemented
3C3×C11×D231C211yesmaximal, characteristic, complemented
4C2×C3×C11×D77—31nomaximal
5D3×C11×D77C311yesmaximal, characteristic, direct product factor
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C11×D231C2×C311yescharacteristic, complemented
8D3×C7×C112C2×C311yescharacteristic, complemented
9C3×C11×D77—21no—
10C3×C11×D77—31no—
11C3×C11×D77D311yescharacteristic, direct product factor
12C3×C11×D77C2×C311yescharacteristic, complemented
13C2×C3×C7×C112—31no—
14C3×D3×C11×D11—71nomaximal, Hall
15C2×C11×D77—31noHall
16C3×D3×D77C1111yesmaximal, 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×D33—71no—
22C3×D3×C112D711yescharacteristic, complemented
23C32×C11×D11—71no—
24C2×C7×C112—31no—
25C11×D77—31no—
26C11×D77C3×D311yescharacteristic, direct product factor
27C2×C3×C11×D11—211no—
28D3×C11×D11—71no—
29C3×D231C2×C1111yescharacteristic, complemented
30C3×C11×D21—111no—
31C3×D3×C7×C11—25no—
32C3×D3×C7×C11D1111yescharacteristic, complemented
33C3×D3×C7×C11C2×C1111yescharacteristic, complemented
34C32×D77C2×C1111yescharacteristic, complemented
35C32×C11×D7—111no—
36C32×C112C2×D711yescharacteristic, complemented, Hall
37C2×C3×D77—31no—
38C2×C3×C11×D7—331no—
39D3×D77C3×C1111yescharacteristic, direct product factor
40D3×C11×D7—111no—
41C7×C112C2×C3×D311yescharacteristic, complemented, Hall
42C2×C3×C112—31no—
43C11×D33—71no—
44D3×C112C3×D711yescharacteristic, complemented
45C3×C11×D11—71no—
46C3×C11×D11—71no—
47C3×C11×D11—141no—
48C3×C11×D11—211no—
49C32×C7×C11—25no—
50C32×C7×C11C2×D1111yescharacteristic, complemented
51C32×C7×C11C22×C1111yescharacteristic, complemented
52C2×C11×D11—211noHall
53C2×C3×C7×C11—31no—
54C2×C3×C7×C11—31no—
55C2×C3×C7×C11—65no—
56D231C2×C3×C1111yescharacteristic, complemented
57C11×D21—111no—
58D3×C7×C11—25no—
59D3×C7×C11C3×D1111yescharacteristic, complemented
60D3×C7×C11C2×C3×C1111yescharacteristic, complemented
61C3×D77—21no—
62C3×D77—31no—
63C3×D77D3×C1111yescharacteristic, direct product factor
64C3×D77C2×C3×C1111yescharacteristic, complemented
65C3×C11×D7—111no—
66C3×C11×D7—111no—
67C3×C11×D7—221no—
68C3×C11×D7—331no—
69C2×C3×D3×C11—771no—
70C3×D3×D11—71no—
71C3×C112—21no—
72C3×C112D3×D711yescharacteristic, complemented
73C3×C112C2×C3×D711yescharacteristic, complemented
74C2×D77—31no—
75C2×C11×D7—331no—
76C3×D3×D7—111noHall
77C2×C112—31no—
78C11×D11—71no—
79C11×D11—211no—
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×D33—71no—
91C3×D3×C11—25no—
92C3×D3×C11—771no—
93C3×D3×C11C11×D711yescharacteristic, complemented
94C3×D3×C11D7711yescharacteristic, direct product factor
95C32×D11—71no—
96C2×C7×C11—31no—
97C2×C7×C11—31no—
98C2×C7×C11—65no—
99D77—31no—
100D77C3×D3×C1111yescharacteristic, direct product factor
101C11×D7—111no—
102C11×D7—331no—
103C22×C3×C11—2311no—
104C2×D3×C11—771no—
105C2×C3×D11—211no—
106D3×D11—71no—
107C3×D21—111no—
108C3×D3×C7C11×D1111yescharacteristic, complemented
109C32×D7—111no—
110C112C3×D3×D711yescharacteristic, complemented, Sylow
111C32×C11—25no—
112C32×C11C2×C11×D711yescharacteristic, complemented
113C32×C11C2×D7711yescharacteristic, 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—31no—
120C2×C3×C11—31no—
121C2×C3×C11—65no—
122C2×C3×C11—771no—
123C2×C3×C11—771no—
124C2×C3×C11—1541no—
125C2×C3×C11—2311no—
126D33—71no—
127C3×D11—71no—
128C3×D11—71no—
129C3×D11—141no—
130C3×D11—211no—
131D3×C11—25no—
132D3×C11—771no—
133D3×C11C3×C11×D711yescharacteristic, complemented
134D3×C11C3×D7711yescharacteristic, direct product factor
135C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
136C22×C11—2311no—
137C2×D11—211no—
138C2×C3×C7—31no—
139D21—111no—
140C3×D7—111no—
141C3×D7—111no—
142C3×D7—221no—
143C3×D7—331no—
144D3×C7C3×C11×D1111yescharacteristic, complemented
145C2×C3×D3—771noHall
146C3×C11—21no—
147C3×C11—21no—
148C3×C11—25no—
149C3×C11—25no—
150C3×C11—45no—
151C3×C11D3×C11×D711yescharacteristic, complemented
152C3×C11D3×D7711yescharacteristic, direct product factor
153C3×C11C2×C3×C11×D711yescharacteristic, complemented
154C3×C11C2×C3×D7711yescharacteristic, complemented
155C2×D7—331noHall
156C2×C11—31no—
157C2×C11—31no—
158C2×C11—65no—
159C2×C11—771no—
160C2×C11—2311no—
161D11—71no—
162D11—211no—
163C3×C7—21no—
164C3×C7D3×C11×D1111yescharacteristic, complemented
165C3×C7C2×C3×C11×D1111yescharacteristic, complemented
166C2×C32—771no—
167C3×D3—771no—
168C3×D3C11×D7711yescharacteristic, direct product factor
169C2×C7—31no—
170D7—111no—
171D7—331no—
172C22×C3—2311no—
173C2×D3—771no—
174C11—25no—
175C11C3×D3×C11×D711yescharacteristic, complemented
176C11C3×D3×D7711yescharacteristic, direct product factor
177C32C2×C11×D7711yescharacteristic, complemented, Sylow
178C7C3×D3×C11×D1111yescharacteristic, complemented, Sylow
179C2×C3—31no—
180C2×C3—771no—
181C2×C3—771no—
182C2×C3—1541no—
183C2×C3—2311no—
184D3—771no—
185D3C3×C11×D7711yescharacteristic, direct product factor
186C22—2311noSylow
187C3—21no—
188C3D3×C11×D7711yescharacteristic, direct product factor
189C3C2×C3×C11×D7711yescharacteristic, complemented
190C2—31no—
191C2—771no—
192C2—2311no—
subgroupG/H
center, hypercenterC3×C11D3×D77
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×D3×C7×C112C2semidirect
3. C3×C11×D231C2semidirect
5. D3×C11×D77C3direct (N × H)
6. C32×C7×C112C22semidirect
7. C11×D231C2×C3semidirect
8. D3×C7×C112C2×C3semidirect
11. C3×C11×D77D3direct (N × H)
12. C3×C11×D77C2×C3semidirect
16. C3×D3×D77C11direct (N × H)
19. C3×C7×C112C2×D3semidirect
20. C3×C7×C112C22×C3semidirect
22. C3×D3×C112D7semidirect
26. C11×D77C3×D3direct (N × H)
29. C3×D231C2×C11semidirect
32. C3×D3×C7×C11D11semidirect
33. C3×D3×C7×C11C2×C11semidirect
34. C32×D77C2×C11semidirect
36. C32×C112C2×D7semidirect
39. D3×D77C3×C11direct (N × H)
41. C7×C112C2×C3×D3semidirect
44. D3×C112C3×D7semidirect
50. C32×C7×C11C2×D11semidirect
51. C32×C7×C11C22×C11semidirect
56. D231C2×C3×C11semidirect
59. D3×C7×C11C3×D11semidirect
60. D3×C7×C11C2×C3×C11semidirect
63. C3×D77D3×C11direct (N × H)
64. 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
93. C3×D3×C11C11×D7semidirect
94. C3×D3×C11D77direct (N × H)
100. D77C3×D3×C11direct (N × H)
108. C3×D3×C7C11×D11semidirect
110. C112C3×D3×D7semidirect
112. C32×C11C2×C11×D7semidirect
113. C32×C11C2×D77semidirect
117. C7×C11C3×D3×D11semidirect
118. C7×C11C2×C3×D3×C11semidirect
133. D3×C11C3×C11×D7semidirect
134. D3×C11C3×D77direct (N × H)
135. C32×C7C2×C11×D11semidirect
144. D3×C7C3×C11×D11semidirect
151. C3×C11D3×C11×D7semidirect
152. C3×C11D3×D77direct (N × H)
153. C3×C11C2×C3×C11×D7semidirect
154. C3×C11C2×C3×D77semidirect
164. C3×C7D3×C11×D11semidirect
165. C3×C7C2×C3×C11×D11semidirect
168. C3×D3C11×D77direct (N × H)
175. C11C3×D3×C11×D7semidirect
176. C11C3×D3×D77direct (N × H)
177. C32C2×C11×D77semidirect
178. C7C3×D3×C11×D11semidirect
185. D3C3×C11×D77direct (N × H)
188. C3D3×C11×D77direct (N × H)
189. C3C2×C3×C11×D77semidirect

Maximal subgroups

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

subgroupindex
C32×C11×D772
C3×D3×C7×C1122
C3×C11×D2312
C2×C3×C11×D773
D3×C11×D773
C3×D3×C11×D117
C3×D3×D7711
C3×D3×C11×D711