Finite Group Databasebeta

← #44479219

Subgroups — #44479219

Order 30492.

266 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 43 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×C3⋊(C11⋊D11)C211yesmaximal, characteristic, complemented
2C3×C11×D231C211yesmaximal, characteristic, complemented
3C11×C3⋊D231C211yesmaximal, characteristic, complemented
4D77⋊D33—31nomaximal
5#23779059—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C11×D231—31no—
8C11×D231—31no—
9C11×D231—61no—
10C11×D231D311yescharacteristic, complemented
11C7×C3⋊(C11⋊D11)D311yescharacteristic, complemented
12C3×C11×D77—31no—
13C3×C7×C11⋊D11—31no—
14D33⋊D33—71nomaximal, Hall
15D77⋊D11—91noHall
16D21×D33—111nomaximal
17D33⋊D21—111nomaximal
18C3×C7×C112—21no—
19C3×C7×C112C2×D311yescharacteristic, complemented
20C3×C7×C112C2×D311yescharacteristic, complemented
21C11×C3⋊D33—71no—
22C3×C3⋊(C11⋊D11)D711yescharacteristic, complemented
23C3×C11×D33—71no—
24C11×D77—31no—
25C11×D77—91no—
26C7×C11⋊D11—31no—
27D33⋊D11—211no—
28D11×D33—211no—
29C3⋊D231D1111yescharacteristic, complemented
30C11×C3⋊D21—111no—
31C3×D231D1111yescharacteristic, complemented
32C3×C11×D21—111no—
33C3×C7×D33—111no—
34C3×C7×D33—111no—
35C3×C7×D33—225no—
36C32×C112C2×D711yescharacteristic, complemented, Hall
37D21⋊D11—331no—
38D7×D33—331no—
39D11×D21—331no—
40D11×D21—331no—
41C7×C112D3211yescharacteristic, complemented, Hall
42C3⋊(C11⋊D11)D2111yescharacteristic, complemented
43C11×D33—71no—
44C11×D33—211no—
45C11×D33—211no—
46C11×D33—421no—
47C3×C11⋊D11—31no—
48C3×C11×D11—211no—
49C32×C7×C11—25no—
50C32×C7×C11C2×D1111yescharacteristic, complemented
51C32×C7×C11C2×D1111yescharacteristic, complemented
52D112—631noHall
53D231—31no—
54D231—31no—
55D231—61no—
56D231D3311yescharacteristic, complemented
57C11×D21—111no—
58C11×D21—331no—
59C11×D21—331no—
60C11×D21—661no—
61C7×D33—111no—
62C7×D33—111no—
63C7×D33—225no—
64C3×D77—31no—
65C3×C11×D7—331no—
66C3×C7×D11—331no—
67C3×C7×D11—331no—
68C3×C7×D11—665no—
69(C3⋊D3)⋊D11—771no—
70D3×D33—771no—
71C3×C112—21no—
72C3×C112D3×D711yescharacteristic, complemented
73C3×C112C2×D2111yescharacteristic, complemented
74D7×D11—991no—
75D7×D11—991no—
76D3×D21—1211noHall
77C11⋊D11—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×C11D3×D1111yescharacteristic, complemented
87C3×C7×C11D3×D1111yescharacteristic, complemented
88C3×C7×C11C2×D3311yescharacteristic, complemented
89C3⋊D33—71no—
90C11×C3⋊D3—771no—
91C3×D33—71no—
92C3×D33—111no—
93C3×D33—111no—
94C3×D33—225no—
95C3×D3×C11—771no—
96D77—31no—
97D77—91no—
98C7×D11—331no—
99C7×D11—331no—
100C7×D11—665no—
101C11×D7—331no—
102C11×D7—991no—
103C2×D33—2311no—
104D3×D11—2311no—
105D3×D11—2311no—
106D3×D11—2311no—
107C3⋊D21—111no—
108C3×D21—111no—
109C3×D3×C7—1211no—
110C112D3×D2111yescharacteristic, complemented, Sylow
111C32×C11—25no—
112C32×C11D7×D1111yescharacteristic, complemented
113C32×C11D7×D1111yescharacteristic, complemented
114C2×D21—3631no—
115D3×D7—3631no—
116C7×C11—25no—
117C7×C11D3×D3311yescharacteristic, complemented
118C7×C11(C3⋊D3)⋊D1111yescharacteristic, complemented
119C2×C3×C11—2311no—
120D33—71no—
121D33—111no—
122D33—111no—
123D33—211no—
124D33—211no—
125D33—225no—
126D33—421no—
127C3×D11—211no—
128C3×D11—331no—
129C3×D11—331no—
130C3×D11—665no—
131D3×C11—771no—
132D3×C11—4621no—
133D3×C11—2311no—
134D3×C11—2311no—
135C32×C7D11211yescharacteristic, complemented, Hall
136C2×D11—6931no—
137C2×D11—6931no—
138C2×C3×C7—3631no—
139D21—111no—
140D21—331no—
141D21—331no—
142D21—661no—
143C3×D7—331no—
144D3×C7—1211no—
145D32—8471noHall
146C3×C11—21no—
147C3×C11—21no—
148C3×C11—25no—
149C3×C11—25no—
150C3×C11—45no—
151C3×C11D11×D2111yescharacteristic, complemented
152C3×C11D11×D2111yescharacteristic, complemented
153C3×C11D7×D3311yescharacteristic, complemented
154C3×C11D21⋊D1111yescharacteristic, complemented
155C2×D7—10891noHall
156C2×C11—6931no—
157C2×C11—2311no—
158D11—211no—
159D11—331no—
160D11—331no—
161D11—631no—
162D11—665no—
163C3×C7—21no—
164C3×C7D11×D3311yescharacteristic, complemented
165C3×C7D33⋊D1111yescharacteristic, complemented
166C3⋊D3—771no—
167C3×D3—771no—
168C3×D3—1211no—
169C2×C7—3631no—
170D7—331no—
171D7—991no—
172C2×D3—25411no—
173C2×D3—25411no—
174C11—25no—
175C11D33⋊D2111yescharacteristic, complemented
176C11D21×D3311yescharacteristic, complemented
177C32D77⋊D1111yescharacteristic, complemented, Sylow
178C7D33⋊D3311yescharacteristic, complemented, Sylow
179C2×C3—3631no—
180C2×C3—2311no—
181D3—771no—
182D3—1211no—
183D3—4621no—
184D3—2311no—
185D3—2311no—
186C22—76231noSylow
187C3—21no—
188C3#2377905911yescharacteristic, complemented
189C3D77⋊D3311yescharacteristic, complemented
190C2—3631no—
191C2—6931no—
192C2—2311no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C7×C112C22
LCSG ▷ C32×C7×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C7×C3⋊(C11⋊D11)C2semidirect
2. C3×C11×D231C2semidirect
3. C11×C3⋊D231C2semidirect
6. C32×C7×C112C22semidirect
10. C11×D231D3semidirect
11. C7×C3⋊(C11⋊D11)D3semidirect
19. C3×C7×C112C2×D3semidirect
20. C3×C7×C112C2×D3semidirect
22. C3×C3⋊(C11⋊D11)D7semidirect
29. C3⋊D231D11semidirect
31. C3×D231D11semidirect
36. C32×C112C2×D7semidirect
41. C7×C112D32semidirect
42. C3⋊(C11⋊D11)D21semidirect
50. C32×C7×C11C2×D11semidirect
51. C32×C7×C11C2×D11semidirect
56. D231D33semidirect
72. C3×C112D3×D7semidirect
73. C3×C112C2×D21semidirect
85. C3×C7×C11D3×D11semidirect
86. C3×C7×C11D3×D11semidirect
87. C3×C7×C11D3×D11semidirect
88. C3×C7×C11C2×D33semidirect
110. C112D3×D21semidirect
112. C32×C11D7×D11semidirect
113. C32×C11D7×D11semidirect
117. C7×C11D3×D33semidirect
118. C7×C11(C3⋊D3)⋊D11semidirect
135. C32×C7D112semidirect
151. C3×C11D11×D21semidirect
152. C3×C11D11×D21semidirect
153. C3×C11D7×D33semidirect
154. C3×C11D21⋊D11semidirect
164. C3×C7D11×D33semidirect
165. C3×C7D33⋊D11semidirect
175. C11D33⋊D21semidirect
176. C11D21×D33semidirect
177. C32D77⋊D11semidirect
178. C7D33⋊D33semidirect
188. C3#23779059semidirect
189. C3D77⋊D33semidirect

Maximal subgroups

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

subgroupindex
C3×C7×C3⋊(C11⋊D11)2
C3×C11×D2312
C11×C3⋊D2312
D77⋊D333
#237790593
D33⋊D337
D21×D3311
D33⋊D2111