Finite Group Databasebeta

← C11×D21⋊D33 #44479224

Subgroups — C11×D21⋊D33 #44479224

Order 30492.

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

normal subgroups only

This group has 266 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×C112×D21C211yesmaximal, characteristic, complemented
2C3×C11×D231C211yesmaximal, characteristic, complemented
3C7×C11×C3⋊D33C211yesmaximal, characteristic, complemented
4C11×D21⋊D11—31nomaximal
5C11×D7×D33—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C11×D231D311yescharacteristic, complemented
8C112×D21D311yescharacteristic, complemented
9C7×C11×D33—31no—
10C7×C11×D33—31no—
11C7×C11×D33—61no—
12C3×C11×D77—31no—
13C3×C112×D7—31no—
14D3×C11×D33—71nomaximal, Hall
15C11×D7×D11—91noHall
16D21⋊D33C1111yesmaximal, characteristic, direct product factor
17C11×(C3⋊D3)⋊D7—111nomaximal
18C3×C7×C112—21no—
19C3×C7×C112C2×D311yescharacteristic, complemented
20C3×C7×C112C2×D311yescharacteristic, complemented
21C11×C3⋊D33D711yescharacteristic, complemented
22C3×C11×D33—71no—
23C3×D3×C112—71no—
24C11×D77—31no—
25C112×D7—31no—
26C7×C11×D11—91no—
27C2×C11×D33—211no—
28D3×C11×D11—211no—
29C7×C3⋊D33C2×C1111yescharacteristic, complemented
30C7×C11×C3⋊D3—111no—
31C3×D231C2×C1111yescharacteristic, complemented
32C3×C11×D21—25no—
33C3×C11×D21—111no—
34C3×C11×D21D1111yescharacteristic, complemented
35C3×C11×D21C2×C1111yescharacteristic, complemented
36C32×C112C2×D711yescharacteristic, complemented, Hall
37D21⋊D11—31no—
38D7×D33—31no—
39D3×C11×D7—331no—
40D3×C11×D7—331no—
41C7×C112D3211yescharacteristic, complemented, Hall
42C2×C3×C112—211no—
43C11×D33—31no—
44C11×D33—31no—
45C11×D33—61no—
46C11×D33—71no—
47D3×C112—71no—
48C3×C11×D11—211no—
49C32×C7×C11—25no—
50C32×C7×C11C2×D1111yescharacteristic, complemented
51C32×C7×C11C22×C1111yescharacteristic, complemented
52C2×C11×D11—631noHall
53D231D3×C1111yescharacteristic, complemented
54C11×D21—25no—
55C11×D21—111no—
56C11×D21D3×C1111yescharacteristic, complemented
57C11×D21D3311yescharacteristic, complemented
58C7×D33—31no—
59C7×D33—31no—
60C7×D33—61no—
61D3×C7×C11—331no—
62D3×C7×C11—331no—
63D3×C7×C11—661no—
64C3×D77—31no—
65C3×C11×D7—31no—
66C3×C11×D7—31no—
67C3×C11×D7—65no—
68C3×C11×D7—331no—
69D3×D33—71no—
70D32×C11—771no—
71C3×C112—21no—
72C3×C112D3×D711yescharacteristic, complemented
73C3×C112D3×D711yescharacteristic, complemented
74C2×C11×D7—991no—
75D7×D11—91no—
76(C3⋊D3)⋊D7—111noHall
77C2×C112—211no—
78C11×D11—91no—
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×D3×C1111yescharacteristic, complemented
87C3×C7×C11C2×D3×C1111yescharacteristic, complemented
88C3×C7×C11C2×D3311yescharacteristic, complemented
89C3⋊D33C11×D711yescharacteristic, complemented
90C11×C3⋊D3—111no—
91C3×D33—71no—
92C3×D3×C11—71no—
93C3×D3×C11—71no—
94C3×D3×C11—145no—
95C3×D3×C11—771no—
96C2×C7×C11—991no—
97D77—31no—
98C7×D11—91no—
99C11×D7—31no—
100C11×D7—31no—
101C11×D7—65no—
102C11×D7—331no—
103C2×D33—211no—
104C2×D3×C11—2311no—
105C2×D3×C11—2311no—
106D3×D11—211no—
107C7×C3⋊D3—111no—
108C3×D21—111no—
109C3×D21C11×D1111yescharacteristic, complemented
110C112(C3⋊D3)⋊D711yescharacteristic, complemented, Sylow
111C32×C11—25no—
112C32×C11D7×D1111yescharacteristic, complemented
113C32×C11C2×C11×D711yescharacteristic, complemented
114D3×D7—331no—
115D3×D7—331no—
116C7×C11—25no—
117C7×C11D32×C1111yescharacteristic, complemented
118C7×C11D3×D3311yescharacteristic, complemented
119C2×C3×C11—211no—
120C2×C3×C11—211no—
121C2×C3×C11—425no—
122C2×C3×C11—2311no—
123D33—31no—
124D33—31no—
125D33—61no—
126D33—71no—
127C3×D11—211no—
128D3×C11—71no—
129D3×C11—71no—
130D3×C11—145no—
131D3×C11—331no—
132D3×C11—331no—
133D3×C11—661no—
134D3×C11—771no—
135C32×C7C2×C11×D1111yescharacteristic, complemented, Hall
136C22×C11—6931no—
137C2×D11—631no—
138D21—111no—
139D21C11×D3311yescharacteristic, complemented
140C3×D7—31no—
141C3×D7—331no—
142D3×C7—331no—
143D3×C7—331no—
144D3×C7—661no—
145D32—771noHall
146C3×C11—21no—
147C3×C11—21no—
148C3×C11—25no—
149C3×C11—25no—
150C3×C11—45no—
151C3×C11D3×C11×D711yescharacteristic, complemented
152C3×C11D3×C11×D711yescharacteristic, complemented
153C3×C11D7×D3311yescharacteristic, complemented
154C3×C11D21⋊D1111yescharacteristic, complemented
155C2×D7—991noHall
156C2×C11—211no—
157C2×C11—211no—
158C2×C11—425no—
159C2×C11—991no—
160C2×C11—2311no—
161D11—91no—
162D11—211no—
163C3×C7—21no—
164C3×C7D3×C11×D1111yescharacteristic, complemented
165C3×C7C2×C11×D3311yescharacteristic, complemented
166C3⋊D3—111no—
167C3×D3—71no—
168C3×D3—771no—
169C2×C7—991no—
170D7—31no—
171D7—331no—
172C2×D3—2311no—
173C2×D3—2311no—
174C11—25no—
175C11C11×(C3⋊D3)⋊D711yescharacteristic, complemented
176C11D21⋊D3311yescharacteristic, direct product factor
177C32C11×D7×D1111yescharacteristic, complemented, Sylow
178C7D3×C11×D3311yescharacteristic, complemented, Sylow
179C2×C3—211no—
180C2×C3—2311no—
181D3—71no—
182D3—331no—
183D3—331no—
184D3—661no—
185D3—771no—
186C22—6931noSylow
187C3—21no—
188C3C11×D7×D3311yescharacteristic, complemented
189C3C11×D21⋊D1111yescharacteristic, complemented
190C2—211no—
191C2—991no—
192C2—2311no—
subgroupG/H
center, hypercenterC11D21⋊D33
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×C112×D21C2semidirect
2. C3×C11×D231C2semidirect
3. C7×C11×C3⋊D33C2semidirect
6. C32×C7×C112C22semidirect
7. C11×D231D3semidirect
8. C112×D21D3semidirect
16. D21⋊D33C11direct (N × H)
19. C3×C7×C112C2×D3semidirect
20. C3×C7×C112C2×D3semidirect
21. C11×C3⋊D33D7semidirect
29. C7×C3⋊D33C2×C11semidirect
31. C3×D231C2×C11semidirect
34. C3×C11×D21D11semidirect
35. C3×C11×D21C2×C11semidirect
36. C32×C112C2×D7semidirect
41. C7×C112D32semidirect
50. C32×C7×C11C2×D11semidirect
51. C32×C7×C11C22×C11semidirect
53. D231D3×C11semidirect
56. C11×D21D3×C11semidirect
57. C11×D21D33semidirect
72. C3×C112D3×D7semidirect
73. C3×C112D3×D7semidirect
85. C3×C7×C11D3×D11semidirect
86. C3×C7×C11C2×D3×C11semidirect
87. C3×C7×C11C2×D3×C11semidirect
88. C3×C7×C11C2×D33semidirect
89. C3⋊D33C11×D7semidirect
109. C3×D21C11×D11semidirect
110. C112(C3⋊D3)⋊D7semidirect
112. C32×C11D7×D11semidirect
113. C32×C11C2×C11×D7semidirect
117. C7×C11D32×C11semidirect
118. C7×C11D3×D33semidirect
135. C32×C7C2×C11×D11semidirect
139. D21C11×D33semidirect
151. C3×C11D3×C11×D7semidirect
152. C3×C11D3×C11×D7semidirect
153. C3×C11D7×D33semidirect
154. C3×C11D21⋊D11semidirect
164. C3×C7D3×C11×D11semidirect
165. C3×C7C2×C11×D33semidirect
175. C11C11×(C3⋊D3)⋊D7semidirect
176. C11D21⋊D33direct (N × H)
177. C32C11×D7×D11semidirect
178. C7D3×C11×D33semidirect
188. C3C11×D7×D33semidirect
189. C3C11×D21⋊D11semidirect

Maximal subgroups

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

subgroupindex
C3×C112×D212
C3×C11×D2312
C7×C11×C3⋊D332
C11×D21⋊D113
C11×D7×D333
D3×C11×D337
D21⋊D3311
C11×(C3⋊D3)⋊D711