Finite Group Databasebeta

← C11×D33⋊D21 #44479215

Subgroups — C11×D33⋊D21 #44479215

Order 30492.

296 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 50 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
3C112×C3⋊D21C211yesmaximal, characteristic, complemented
4C11×D21⋊D11—31nomaximal
5C11×D11×D21—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C11×D231D311yescharacteristic, complemented
8C112×D21—31no—
9C112×D21—31no—
10C112×D21—61no—
11C7×C11×D33D311yescharacteristic, complemented
12C3×C11×D77—31no—
13C3×C7×C11×D11—31no—
14C11×(C3⋊D3)⋊D11—71nomaximal, Hall
15C11×D7×D11—91noHall
16D33⋊D21C1111yesmaximal, characteristic, direct product factor
17D3×C11×D21—111nomaximal
18C3×C7×C112—21no—
19C3×C7×C112C2×D311yescharacteristic, complemented
20C3×C7×C112C2×D311yescharacteristic, complemented
21C112×C3⋊D3—71no—
22C3×C11×D33—71no—
23C3×C11×D33D711yescharacteristic, complemented
24C11×D77—31no—
25C112×D7—91no—
26C7×C11×D11—31no—
27D3×C11×D11—211no—
28D3×C11×D11—211no—
29C11×C3⋊D21—25no—
30C11×C3⋊D21D1111yescharacteristic, complemented
31C11×C3⋊D21C2×C1111yescharacteristic, complemented
32C3×D231C2×C1111yescharacteristic, complemented
33C3×C11×D21—111no—
34C3×C7×D33C2×C1111yescharacteristic, complemented
35C3×D3×C7×C11—111no—
36C32×C112C2×D711yescharacteristic, complemented, Hall
37C2×C11×D21—331no—
38D21⋊D11—31no—
39D3×C11×D7—331no—
40D11×D21—31no—
41C7×C112D3211yescharacteristic, complemented, Hall
42C11×D33—71no—
43C11×D33D2111yescharacteristic, complemented
44D3×C112—211no—
45D3×C112—211no—
46D3×C112—421no—
47C3×C11×D11—31no—
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—331no—
54D231D3×C1111yescharacteristic, complemented
55C11×D21—31no—
56C11×D21—31no—
57C11×D21—31no—
58C11×D21—31no—
59C11×D21—61no—
60C11×D21—61no—
61C11×D21—65no—
62C11×D21—65no—
63C11×D21—610no—
64C11×D21—111no—
65C7×D33D3×C1111yescharacteristic, complemented
66D3×C7×C11—111no—
67C3×D77—31no—
68C3×C11×D7—331no—
69C3×C7×D11—31no—
70(C3⋊D3)⋊D11—71no—
71D32×C11—771no—
72C3×C112—21no—
73C3×C112D3×D711yescharacteristic, complemented
74C3×C112C2×D2111yescharacteristic, complemented
75C2×C11×D7—991no—
76D7×D11—91no—
77D3×D21—111noHall
78C2×C112—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×D3×C1111yescharacteristic, complemented
89C3×C7×C11C2×D3×C1111yescharacteristic, complemented
90C11×C3⋊D3—71no—
91C11×C3⋊D3—71no—
92C11×C3⋊D3—145no—
93C3×D33—71no—
94C3×D33C11×D711yescharacteristic, complemented
95C3×D3×C11—111no—
96C3×D3×C11—771no—
97C2×C7×C11—331no—
98D77—31no—
99C7×D11—31no—
100C11×D7—91no—
101C11×D7—91no—
102C11×D7—185no—
103C11×D7—331no—
104C2×D3×C11—2311no—
105C2×D3×C11—2311no—
106D3×D11—211no—
107D3×D11—211no—
108C3⋊D21C11×D1111yescharacteristic, complemented
109C3×D21—111no—
110C3×D3×C7—111no—
111C112D3×D2111yescharacteristic, complemented, Sylow
112C32×C11—25no—
113C32×C11D7×D1111yescharacteristic, complemented
114C32×C11C2×C11×D711yescharacteristic, complemented
115C2×D21—331no—
116D3×D7—331no—
117C7×C11—25no—
118C7×C11D32×C1111yescharacteristic, complemented
119C7×C11(C3⋊D3)⋊D1111yescharacteristic, complemented
120C2×C3×C11—331no—
121C2×C3×C11—2311no—
122D33—71no—
123D33C11×D2111yescharacteristic, complemented
124C3×D11—31no—
125C3×D11—211no—
126D3×C11—111no—
127D3×C11—211no—
128D3×C11—211no—
129D3×C11—211no—
130D3×C11—211no—
131D3×C11—425no—
132D3×C11—425no—
133D3×C11—421no—
134D3×C11—421no—
135D3×C11—4210no—
136D3×C11—771no—
137C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
138C22×C11—6931no—
139C2×D11—631no—
140C2×C3×C7—331no—
141D21—31no—
142D21—31no—
143D21—61no—
144D21—111no—
145C3×D7—331no—
146D3×C7—111no—
147D32—771noHall
148C3×C11—210no—
149C3×C11—21no—
150C3×C11—21no—
151C3×C11—25no—
152C3×C11—25no—
153C3×C11D11×D2111yescharacteristic, complemented
154C3×C11D3×C11×D711yescharacteristic, complemented
155C3×C11D21⋊D1111yescharacteristic, complemented
156C3×C11C2×C11×D2111yescharacteristic, complemented
157C2×D7—991noHall
158C2×C11—331no—
159C2×C11—631no—
160C2×C11—631no—
161C2×C11—1265no—
162C2×C11—2311no—
163D11—31no—
164D11—211no—
165C3×C7—21no—
166C3×C7D3×C11×D1111yescharacteristic, complemented
167C3×C7D3×C11×D1111yescharacteristic, complemented
168C3⋊D3—71no—
169C3×D3—111no—
170C3×D3—771no—
171C2×C7—331no—
172D7—91no—
173D7—331no—
174C2×D3—2311no—
175C2×D3—2311no—
176C11—25no—
177C11D3×C11×D2111yescharacteristic, complemented
178C11D33⋊D2111yescharacteristic, direct product factor
179C32C11×D7×D1111yescharacteristic, complemented, Sylow
180C7C11×(C3⋊D3)⋊D1111yescharacteristic, complemented, Sylow
181C2×C3—331no—
182C2×C3—2311no—
183D3—111no—
184D3—211no—
185D3—211no—
186D3—421no—
187D3—771no—
188C22—6931noSylow
189C3—21no—
190C3C11×D11×D2111yescharacteristic, complemented
191C3C11×D21⋊D1111yescharacteristic, complemented
192C2—331no—
193C2—631no—
194C2—2311no—
subgroupG/H
center, hypercenterC11D33⋊D21
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×C7×C11×D33C2semidirect
2. C3×C11×D231C2semidirect
3. C112×C3⋊D21C2semidirect
6. C32×C7×C112C22semidirect
7. C11×D231D3semidirect
11. C7×C11×D33D3semidirect
16. D33⋊D21C11direct (N × H)
19. C3×C7×C112C2×D3semidirect
20. C3×C7×C112C2×D3semidirect
23. C3×C11×D33D7semidirect
30. C11×C3⋊D21D11semidirect
31. C11×C3⋊D21C2×C11semidirect
32. C3×D231C2×C11semidirect
34. C3×C7×D33C2×C11semidirect
36. C32×C112C2×D7semidirect
41. C7×C112D32semidirect
43. C11×D33D21semidirect
50. C32×C7×C11C2×D11semidirect
51. C32×C7×C11C22×C11semidirect
54. D231D3×C11semidirect
65. C7×D33D3×C11semidirect
73. C3×C112D3×D7semidirect
74. C3×C112C2×D21semidirect
86. C3×C7×C11D3×D11semidirect
87. C3×C7×C11D3×D11semidirect
88. C3×C7×C11C2×D3×C11semidirect
89. C3×C7×C11C2×D3×C11semidirect
94. C3×D33C11×D7semidirect
108. C3⋊D21C11×D11semidirect
111. C112D3×D21semidirect
113. C32×C11D7×D11semidirect
114. C32×C11C2×C11×D7semidirect
118. C7×C11D32×C11semidirect
119. C7×C11(C3⋊D3)⋊D11semidirect
123. D33C11×D21semidirect
137. C32×C7C2×C11×D11semidirect
153. C3×C11D11×D21semidirect
154. C3×C11D3×C11×D7semidirect
155. C3×C11D21⋊D11semidirect
156. C3×C11C2×C11×D21semidirect
166. C3×C7D3×C11×D11semidirect
167. C3×C7D3×C11×D11semidirect
177. C11D3×C11×D21semidirect
178. C11D33⋊D21direct (N × H)
179. C32C11×D7×D11semidirect
180. C7C11×(C3⋊D3)⋊D11semidirect
190. C3C11×D11×D21semidirect
191. C3C11×D21⋊D11semidirect

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
C112×C3⋊D212
C11×D21⋊D113
C11×D11×D213
C11×(C3⋊D3)⋊D117
D33⋊D2111
D3×C11×D2111