Finite Group Databasebeta

← D3×C11×D231 #44479214

Subgroups — D3×C11×D231 #44479214

Order 30492.

266 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 56 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×D3×C7×C112C211yesmaximal, characteristic, complemented
2C3×C11×D231C211yesmaximal, characteristic, complemented
3C11×C3⋊D231C211yesmaximal, characteristic, complemented
4C2×C11×D231—31nomaximal
5D3×C11×D77—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C11×D231—31no—
8C11×D231—31no—
9C11×D231—61no—
10C11×D231D311yescharacteristic, direct product factor
11D3×C7×C112D311yescharacteristic, complemented
12C3×C11×D77—31no—
13C2×C3×C7×C112—31no—
14D3×C11×D33—71nomaximal, Hall
15C2×C11×D77—91noHall
16D3×D231C1111yesmaximal, characteristic, direct product factor
17D3×C11×D21—111nomaximal
18C3×C7×C112—21no—
19C3×C7×C112C2×D311yescharacteristic, complemented
20C3×C7×C112C2×D311yescharacteristic, complemented
21C11×C3⋊D33—71no—
22C3×C11×D33—71no—
23C3×D3×C112D711yescharacteristic, complemented
24C2×C7×C112—31no—
25C11×D77—31no—
26C11×D77—91no—
27C2×C11×D33—211no—
28D3×C11×D11—211no—
29C3⋊D231C2×C1111yescharacteristic, complemented
30C11×C3⋊D21—111no—
31C3×D231C2×C1111yescharacteristic, complemented
32C3×C11×D21—111no—
33C3×D3×C7×C11—25no—
34C3×D3×C7×C11D1111yescharacteristic, complemented
35C3×D3×C7×C11C2×C1111yescharacteristic, complemented
36C32×C112C2×D711yescharacteristic, complemented, Hall
37C2×D231—31no—
38C2×C11×D21—331no—
39D3×D77—31no—
40D3×C11×D7—331no—
41C7×C112D3211yescharacteristic, complemented, Hall
42C2×C3×C112—31no—
43C11×D33—71no—
44C11×D33—211no—
45C11×D33—211no—
46C11×D33—421no—
47D3×C112D2111yescharacteristic, complemented
48C3×C11×D11—211no—
49C32×C7×C11—25no—
50C32×C7×C11C2×D1111yescharacteristic, complemented
51C32×C7×C11C22×C1111yescharacteristic, complemented
52C2×C11×D11—631noHall
53C2×C3×C7×C11—31no—
54C2×C3×C7×C11—31no—
55C2×C3×C7×C11—65no—
56D231—31no—
57D231—31no—
58D231—61no—
59D231D3×C1111yescharacteristic, direct product factor
60C11×D21—111no—
61C11×D21—331no—
62C11×D21—331no—
63C11×D21—661no—
64D3×C7×C11—25no—
65D3×C7×C11D3×C1111yescharacteristic, complemented
66D3×C7×C11D3311yescharacteristic, complemented
67C3×D77—31no—
68C3×C11×D7—331no—
69D3×D33—71no—
70D32×C11—771no—
71C3×C112—21no—
72C3×C112D3×D711yescharacteristic, complemented
73C3×C112C2×D2111yescharacteristic, complemented
74C2×D77—91no—
75C2×C11×D7—991no—
76D3×D21—111noHall
77C2×C112—31no—
78C11×D11—211no—
79C11×D11—631no—
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×D3×C1111yescharacteristic, complemented
87C3×C7×C11C2×D3×C1111yescharacteristic, complemented
88C3×C7×C11C2×D3311yescharacteristic, complemented
89C3⋊D33—71no—
90C11×C3⋊D3—771no—
91C3×D33—71no—
92C3×D3×C11—25no—
93C3×D3×C11—771no—
94C3×D3×C11C11×D711yescharacteristic, complemented
95C3×D3×C11D7711yescharacteristic, complemented
96C2×C7×C11—31no—
97C2×C7×C11—31no—
98C2×C7×C11—65no—
99D77—31no—
100D77—91no—
101C11×D7—331no—
102C11×D7—991no—
103C2×D33—211no—
104C2×D3×C11—2311no—
105C2×D3×C11—2311no—
106D3×D11—211no—
107C3⋊D21—111no—
108C3×D21—111no—
109C3×D3×C7C11×D1111yescharacteristic, complemented
110C112D3×D2111yescharacteristic, complemented, Sylow
111C32×C11—25no—
112C32×C11C2×C11×D711yescharacteristic, complemented
113C32×C11C2×D7711yescharacteristic, complemented
114C2×D21—331no—
115D3×D7—331no—
116C7×C11—25no—
117C7×C11D32×C1111yescharacteristic, complemented
118C7×C11D3×D3311yescharacteristic, complemented
119C2×C3×C11—31no—
120C2×C3×C11—31no—
121C2×C3×C11—65no—
122C2×C3×C11—2311no—
123D33—71no—
124D33—211no—
125D33—211no—
126D33—421no—
127C3×D11—211no—
128D3×C11—25no—
129D3×C11—771no—
130D3×C11—4621no—
131D3×C11—2311no—
132D3×C11—2311no—
133D3×C11C11×D2111yescharacteristic, complemented
134D3×C11D23111yescharacteristic, direct product factor
135C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
136C22×C11—6931no—
137C2×D11—631no—
138C2×C3×C7—31no—
139D21—111no—
140D21—331no—
141D21—331no—
142D21—661no—
143C3×D7—331no—
144D3×C7C11×D3311yescharacteristic, complemented
145D32—771noHall
146C3×C11—21no—
147C3×C11—21no—
148C3×C11—25no—
149C3×C11—25no—
150C3×C11—45no—
151C3×C11D3×C11×D711yescharacteristic, complemented
152C3×C11D3×D7711yescharacteristic, complemented
153C3×C11C2×C11×D2111yescharacteristic, complemented
154C3×C11C2×D23111yescharacteristic, complemented
155C2×D7—991noHall
156C2×C11—31no—
157C2×C11—31no—
158C2×C11—65no—
159C2×C11—6931no—
160C2×C11—2311no—
161D11—211no—
162D11—631no—
163C3×C7—21no—
164C3×C7D3×C11×D1111yescharacteristic, complemented
165C3×C7C2×C11×D3311yescharacteristic, complemented
166C3⋊D3—771no—
167C3×D3—771no—
168C3×D3C11×D7711yescharacteristic, complemented
169C2×C7—31no—
170D7—331no—
171D7—991no—
172C2×D3—2311no—
173C2×D3—2311no—
174C11—25no—
175C11D3×C11×D2111yescharacteristic, complemented
176C11D3×D23111yescharacteristic, direct product factor
177C32C2×C11×D7711yescharacteristic, complemented, Sylow
178C7D3×C11×D3311yescharacteristic, complemented, Sylow
179C2×C3—31no—
180C2×C3—2311no—
181D3—771no—
182D3—4621no—
183D3—2311no—
184D3—2311no—
185D3C11×D23111yescharacteristic, direct product factor
186C22—6931noSylow
187C3—21no—
188C3D3×C11×D7711yescharacteristic, complemented
189C3C2×C11×D23111yescharacteristic, complemented
190C2—31no—
191C2—6931no—
192C2—2311no—
subgroupG/H
center, hypercenterC11D3×D231
commutator, cosocle, hypocenterC32×C7×C11C22×C11
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C32×C7×C11
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C3×D3×C7×C112C2semidirect
2. C3×C11×D231C2semidirect
3. C11×C3⋊D231C2semidirect
6. C32×C7×C112C22semidirect
10. C11×D231D3direct (N × H)
11. D3×C7×C112D3semidirect
16. D3×D231C11direct (N × H)
19. C3×C7×C112C2×D3semidirect
20. C3×C7×C112C2×D3semidirect
23. C3×D3×C112D7semidirect
29. C3⋊D231C2×C11semidirect
31. C3×D231C2×C11semidirect
34. C3×D3×C7×C11D11semidirect
35. C3×D3×C7×C11C2×C11semidirect
36. C32×C112C2×D7semidirect
41. C7×C112D32semidirect
47. D3×C112D21semidirect
50. C32×C7×C11C2×D11semidirect
51. C32×C7×C11C22×C11semidirect
59. D231D3×C11direct (N × H)
65. D3×C7×C11D3×C11semidirect
66. D3×C7×C11D33semidirect
72. C3×C112D3×D7semidirect
73. C3×C112C2×D21semidirect
85. C3×C7×C11D3×D11semidirect
86. C3×C7×C11C2×D3×C11semidirect
87. C3×C7×C11C2×D3×C11semidirect
88. C3×C7×C11C2×D33semidirect
94. C3×D3×C11C11×D7semidirect
95. C3×D3×C11D77semidirect
109. C3×D3×C7C11×D11semidirect
110. C112D3×D21semidirect
112. C32×C11C2×C11×D7semidirect
113. C32×C11C2×D77semidirect
117. C7×C11D32×C11semidirect
118. C7×C11D3×D33semidirect
133. D3×C11C11×D21semidirect
134. D3×C11D231direct (N × H)
135. C32×C7C2×C11×D11semidirect
144. D3×C7C11×D33semidirect
151. C3×C11D3×C11×D7semidirect
152. C3×C11D3×D77semidirect
153. C3×C11C2×C11×D21semidirect
154. C3×C11C2×D231semidirect
164. C3×C7D3×C11×D11semidirect
165. C3×C7C2×C11×D33semidirect
168. C3×D3C11×D77semidirect
175. C11D3×C11×D21semidirect
176. C11D3×D231direct (N × H)
177. C32C2×C11×D77semidirect
178. C7D3×C11×D33semidirect
185. D3C11×D231direct (N × H)
188. C3D3×C11×D77semidirect
189. C3C2×C11×D231semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C7×C1122
C3×C11×D2312
C11×C3⋊D2312
C2×C11×D2313
D3×C11×D773
D3×C11×D337
D3×D23111
D3×C11×D2111