Finite Group Databasebeta

← D33×D231 #44479217

Subgroups — D33×D231 #44479217

Order 30492.

296 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 46 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×C11×D231C211yesmaximal, characteristic, complemented
3C3⋊(C3⋊(C7⋊(C11⋊D11)))C211yesmaximal, characteristic, complemented
4D33×D77—31nomaximal
5D11×D231—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C3⋊(C7⋊(C11⋊D11))—31no—
8C3⋊(C7⋊(C11⋊D11))—31no—
9C3⋊(C7⋊(C11⋊D11))—61no—
10C11×D231D311yescharacteristic, complemented
11C7×C11×D33D311yescharacteristic, complemented
12C3×C11×D77—31no—
13C3×C7×C11×D11—31no—
14D332—71nomaximal, Hall
15D11×D77—91noHall
16D21×D33—111nomaximal
17D3×D231—111nomaximal
18C3×C7×C112—21no—
19C3×C7×C112C2×D311yescharacteristic, complemented
20C3×C7×C112C2×D311yescharacteristic, complemented
21C3⋊(C3⋊(C11⋊D11))—71no—
22C3×C11×D33—71no—
23C3×C11×D33D711yescharacteristic, complemented
24C7⋊(C11⋊D11)—91no—
25C11×D77—31no—
26C7×C11×D11—31no—
27D11×D33—211no—
28D11×D33—211no—
29C3⋊D231—111no—
30C3⋊D231—111no—
31C3⋊D231—225no—
32C3×D231D1111yescharacteristic, complemented
33C3×C11×D21—111no—
34C3×C7×D33D1111yescharacteristic, complemented
35C3×D3×C7×C11—111no—
36C32×C112C2×D711yescharacteristic, complemented, Hall
37C2×D231—331no—
38D3×D77—331no—
39D7×D33—331no—
40D11×D21—331no—
41C7×C112D3211yescharacteristic, complemented, Hall
42C3⋊(C11⋊D11)—211no—
43C3⋊(C11⋊D11)—211no—
44C3⋊(C11⋊D11)—421no—
45C11×D33—71no—
46C11×D33D2111yescharacteristic, complemented
47C3×C11×D11—31no—
48C3×C11×D11—211no—
49C32×C7×C11—25no—
50C32×C7×C11C2×D1111yescharacteristic, complemented
51C32×C7×C11C2×D1111yescharacteristic, complemented
52D112—631noHall
53C2×C3×C7×C11—331no—
54D231—331no—
55D231—331no—
56D231—331no—
57D231—331no—
58D231—661no—
59D231—661no—
60D231—665no—
61D231—665no—
62D231—6610no—
63D231D3311yescharacteristic, direct product factor
64C11×D21—111no—
65C7×D33D3311yescharacteristic, complemented
66D3×C7×C11—111no—
67C3×D77—31no—
68C3×C11×D7—331no—
69C3×C7×D11—31no—
70D3×D33—771no—
71D3×D33—771no—
72C3×C112—21no—
73C3×C112D3×D711yescharacteristic, complemented
74C3×C112C2×D2111yescharacteristic, complemented
75C2×D77—991no—
76D7×D11—991no—
77D3×D21—1211noHall
78C11⋊D11—631no—
79C11×D11—31no—
80C11×D11—211no—
81C3×C7×C11—210no—
82C3×C7×C11—21no—
83C3×C7×C11—21no—
84C3×C7×C11—25no—
85C3×C7×C11—25no—
86C3×C7×C11D3×D1111yescharacteristic, complemented
87C3×C7×C11D3×D1111yescharacteristic, complemented
88C3×C7×C11C2×D3311yescharacteristic, complemented
89C3×C7×C11C2×D3311yescharacteristic, complemented
90C3⋊D33—771no—
91C3⋊D33—771no—
92C3⋊D33—1545no—
93C3×D33—71no—
94C3×D33D7711yescharacteristic, complemented
95C3×D3×C11—111no—
96C3×D3×C11—771no—
97C2×C7×C11—331no—
98D77—31no—
99D77—991no—
100D77—991no—
101D77—1985no—
102C7×D11—31no—
103C11×D7—331no—
104C2×D33—2311no—
105C2×D33—2311no—
106D3×D11—2311no—
107D3×D11—2311no—
108C3⋊D21—1211no—
109C3×D21—111no—
110C3×D3×C7—111no—
111C112D3×D2111yescharacteristic, complemented, Sylow
112C32×C11—25no—
113C32×C11D7×D1111yescharacteristic, complemented
114C32×C11C2×D7711yescharacteristic, complemented
115C2×D21—3631no—
116D3×D7—3631no—
117C7×C11—25no—
118C7×C11D3×D3311yescharacteristic, complemented
119C7×C11D3×D3311yescharacteristic, complemented
120C2×C3×C11—331no—
121C2×C3×C11—2311no—
122D33—71no—
123D33—46210no—
124D33—4621no—
125D33—4621no—
126D33—4625no—
127D33—4625no—
128D33—2311no—
129D33—2311no—
130D33—2311no—
131D33—2311no—
132D33D23111yescharacteristic, direct product factor
133C3×D11—31no—
134C3×D11—211no—
135D3×C11—111no—
136D3×C11—771no—
137C32×C7D11211yescharacteristic, complemented, Hall
138C2×D11—6931no—
139C2×D11—6931no—
140C2×C3×C7—331no—
141D21—111no—
142D21—3631no—
143D21—3631no—
144D21—7261no—
145C3×D7—331no—
146D3×C7—111no—
147D32—8471noHall
148C3×C11—210no—
149C3×C11—21no—
150C3×C11—21no—
151C3×C11—25no—
152C3×C11—25no—
153C3×C11D11×D2111yescharacteristic, complemented
154C3×C11D7×D3311yescharacteristic, complemented
155C3×C11D3×D7711yescharacteristic, complemented
156C3×C11C2×D23111yescharacteristic, complemented
157C2×D7—10891noHall
158C2×C11—331no—
159C2×C11—2311no—
160D11—31no—
161D11—211no—
162D11—13865no—
163D11—6931no—
164D11—6931no—
165C3×C7—21no—
166C3×C7D11×D3311yescharacteristic, complemented
167C3×C7D11×D3311yescharacteristic, complemented
168C3⋊D3—8471no—
169C3×D3—111no—
170C3×D3—771no—
171C2×C7—331no—
172D7—331no—
173D7—10891no—
174C2×D3—25411no—
175C2×D3—25411no—
176C11—25no—
177C11D3×D23111yescharacteristic, complemented
178C11D21×D3311yescharacteristic, complemented
179C32D11×D7711yescharacteristic, complemented, Sylow
180C7D33211yescharacteristic, complemented, Sylow
181C2×C3—331no—
182C2×C3—2311no—
183D3—111no—
184D3—771no—
185D3—50821no—
186D3—25411no—
187D3—25411no—
188C22—76231noSylow
189C3—21no—
190C3D11×D23111yescharacteristic, complemented
191C3D33×D7711yescharacteristic, complemented
192C2—331no—
193C2—76231no—
194C2—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×C11×D33C2semidirect
2. C3×C11×D231C2semidirect
3. C3⋊(C3⋊(C7⋊(C11⋊D11)))C2semidirect
6. C32×C7×C112C22semidirect
10. C11×D231D3semidirect
11. C7×C11×D33D3semidirect
19. C3×C7×C112C2×D3semidirect
20. C3×C7×C112C2×D3semidirect
23. C3×C11×D33D7semidirect
32. C3×D231D11semidirect
34. C3×C7×D33D11semidirect
36. C32×C112C2×D7semidirect
41. C7×C112D32semidirect
46. C11×D33D21semidirect
50. C32×C7×C11C2×D11semidirect
51. C32×C7×C11C2×D11semidirect
63. D231D33direct (N × H)
65. C7×D33D33semidirect
73. C3×C112D3×D7semidirect
74. C3×C112C2×D21semidirect
86. C3×C7×C11D3×D11semidirect
87. C3×C7×C11D3×D11semidirect
88. C3×C7×C11C2×D33semidirect
89. C3×C7×C11C2×D33semidirect
94. C3×D33D77semidirect
111. C112D3×D21semidirect
113. C32×C11D7×D11semidirect
114. C32×C11C2×D77semidirect
118. C7×C11D3×D33semidirect
119. C7×C11D3×D33semidirect
132. D33D231direct (N × H)
137. C32×C7D112semidirect
153. C3×C11D11×D21semidirect
154. C3×C11D7×D33semidirect
155. C3×C11D3×D77semidirect
156. C3×C11C2×D231semidirect
166. C3×C7D11×D33semidirect
167. C3×C7D11×D33semidirect
177. C11D3×D231semidirect
178. C11D21×D33semidirect
179. C32D11×D77semidirect
180. C7D332semidirect
190. C3D11×D231semidirect
191. C3D33×D77semidirect

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×C11×D2312
C3⋊(C3⋊(C7⋊(C11⋊D11)))2
D33×D773
D11×D2313
D3327
D21×D3311
D3×D23111