Finite Group Databasebeta

← #11761395

Subgroups — #11761395

Order 1056.

332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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
1D4×D33C211yesmaximal, characteristic, complemented
2D3×D4×C11C211yesmaximal, characteristic, complemented
3C3×#4341C211yesmaximal, characteristic, complemented
4#10587252C212yesmaximal, complemented
5D3×C22⋊D11C212yesmaximal, complemented
6C2×#63142C212yesmaximal, complemented
7#10587244C212yesmaximal, complemented
8D11×D12C211yesmaximal, characteristic, complemented
9#10587233C211yesmaximal, characteristic, complemented
10#10587231C211yesmaximal, characteristic, complemented
11#10587230C211yesmaximal, characteristic, complemented
12#67037—31nomaximal, Hall
13C22×D33C2212yescomplemented
14C22×D3×C11C2212yescomplemented
15C2×D3×D11C2212yescomplemented
16C3×D4×C11C2211yescharacteristic, complemented
17#63159C2212yescomplemented
18D132C2211yescharacteristic, complemented
19C4×D33C2211yescharacteristic, complemented
20C11×#67C2212yescomplemented
21C11×D12C2211yescharacteristic, complemented
22C4×D3×C11C2211yescharacteristic, complemented
23C3×C22⋊D11C2212yescomplemented
24C2×C3×Dic11C2212yescomplemented
25C3×C4×D11C2211yescharacteristic, complemented
26C3×Dic22C2211yescharacteristic, complemented
27#63143C2211yescharacteristic, complemented
28#63142C2212yescomplemented
29#63142C2212yescomplemented
30#63142C2211yescharacteristic, complemented
31#63142C2212yescomplemented
32#63141C2211yescharacteristic, complemented
33#63140C2211yescharacteristic, complemented
34D33⋊C4C2212yescomplemented
35D3×Dic11C2212yescomplemented
36C2×D4×C11—31no—
37C2×C22⋊D11—32no—
38C2×C22⋊D11—32no—
39#4341—32no—
40#4341—31no—
41#4341D311yescharacteristic, complemented
42D4×D11—32no—
43D4×D11—31no—
44D4×D11—31no—
45#4339—31no—
46#4339—31no—
47C22×C3×C11C2312yes—
48C2×D33—42no—
49C2×D33C2312yes—
50C2×D33C2311yescharacteristic
51C2×D3×C11—42no—
52C2×D3×C11C2312yes—
53C2×D3×C11C2311yescharacteristic
54C2×C3×D11C2311yescharacteristic
55D3×D11—42no—
56C3×C4×C11C2311yescharacteristic
57Dic33C2311yescharacteristic
58C3×Dic11C2312yes—
59C3×Dic11C2311yescharacteristic
60C11×Dic3C2311yescharacteristic
61#1009—111nomaximal, Hall
62C23×C11—32no—
63C22×D11—32no—
64C22×D11—32no—
65D4×C11—32no—
66D4×C11—31no—
67D4×C11C2×D311yescharacteristic, complemented
68C2×C4×C11—31no—
69C22⋊D11—32no—
70C22⋊D11—31no—
71C22⋊D11—31no—
72C22⋊D11—32no—
73C22⋊D11—32no—
74C22⋊D11—32no—
75C22⋊D11C2×D312yescomplemented
76C2×Dic11—32no—
77C2×Dic11C2×D312yescomplemented
78D44—31no—
79D44—31no—
80C4×D11—31no—
81C4×D11—32no—
82C4×D11C2×D311yescharacteristic, complemented
83Dic22—31no—
84Dic22C2×D311yescharacteristic, complemented
85C2×C3×C11—22no—
86C2×C3×C11C2411yescharacteristic
87D33—22no—
88D33—21no—
89C3×D11—21no—
90D3×C11—22no—
91D3×C11—21no—
92C3×#41—111no—
93#239—111no—
94#239—111no—
95D3×D4—112no—
96D3×D4—111no—
97D3×D4—112no—
98D3×D4D1111yescharacteristic, complemented
99#235—112no—
100#235—111no—
101C2×D12—112no—
102C2×D12—111no—
103C22×C11—31no—
104C22×C11—32no—
105C22×C11—122no—
106C22×C11C22×D312yes—
107C2×D11—31no—
108C2×D11—32no—
109C2×D11—122no—
110C2×D11—122no—
111C2×D11C22×D311yescharacteristic
112C4×C11—31no—
113C4×C11C22×D311yescharacteristic
114Dic11—31no—
115Dic11C22×D311yescharacteristic
116Dic11C22×D312yes—
117C3×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
118H(5,𝔽2)—331noSylow
119C22×D3—112no—
120C22×D3—112no—
121C22×D3C2×D1112yescomplemented
122C3×Q8—111no—
123C3×D4—112no—
124C3×D4C2×D1111yescharacteristic, complemented
125C2×C3×C4—112no—
126C2×C3×C4—111no—
127#67—112no—
128#67—111no—
129#67—111no—
130#67C2×D1112yescomplemented
131D12—112no—
132D12—111no—
133D12—112no—
134D12—112no—
135D12—111no—
136D12C2×D1111yescharacteristic, complemented
137C4×D3—112no—
138C4×D3—111no—
139C4×D3—112no—
140C4×D3C2×D1111yescharacteristic, complemented
141Dic6—111no—
142C2×C11—22no—
143C2×C11—62no—
144C2×C11—61no—
145C2×C11C23×D311yescharacteristic
146D11—21no—
147D11—62no—
148D11—61no—
149#41—111no—
150#41—331no—
151#41—331no—
152#41—332no—
153#41—331no—
154C2×D4—31no—
155C2×D4—331no—
156C2×D4—332no—
157C2×D4—332no—
158C2×D4—332no—
159C2×D4—331no—
160C22×C3—111no—
161C22×C3C22×D1112yes—
162C2×D3—42no—
163C2×D3—112no—
164C2×D3—111no—
165C2×D3—442no—
166C2×D3—442no—
167C2×D3C22×D1112yes—
168C2×D3C22×D1111yescharacteristic
169C3×C4—111no—
170C3×C4—112no—
171C3×C4C22×D1111yescharacteristic
172Dic3—111no—
173Dic3C22×D1111yescharacteristic
174C11#100911yescharacteristic, complemented, Sylow
175C23—32no—
176C23—332no—
177C23—332no—
178Q8—111no—
179Q8—331no—
180D4—32no—
181D4—31no—
182D4—112no—
183D4—331no—
184D4—331no—
185D4—332no—
186D4—332no—
187D4—332no—
188D4—331no—
189D4—332no—
190D4—331no—
191D4D3×D1111yescharacteristic, complemented
192C2×C4—31no—
193C2×C4—112no—
194C2×C4—111no—
195C2×C4—332no—
196C2×C4—332no—
197C2×C4—331no—
198C2×C3—22no—
199C2×C3—221no—
200C2×C3C23×D1111yescharacteristic
201D3—21no—
202D3—22no—
203D3—222no—
204D3—221no—
205C22—31no—
206C22—32no—
207C22—111no—
208C22—122no—
209C22—332no—
210C22—331no—
211C22—1322no—
212C22—1322no—
213C22C2×D3×D1112yes—
214C4—31no—
215C4—111no—
216C4—112no—
217C4—331no—
218C4C2×D3×D1111yescharacteristic
219C3#6703711yescharacteristic, complemented, Sylow
220C2—22no—
221C2—61no—
222C2—62no—
223C2—221no—
224C2—661no—
225C2—662no—
226C2C22×D3×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D11
commutator, socle, cosocleC2×C3×C11C24
FittingC3×D4×C11C22
hypercenterD4D3×D11
hypocenterC3×C11H(5,𝔽2)
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. D4×D33C2semidirect
2. D3×D4×C11C2semidirect
3. C3×#4341C2semidirect
4. #10587252C2semidirect
5. D3×C22⋊D11C2semidirect
6. C2×#63142C2semidirect
7. #10587244C2semidirect
8. D11×D12C2semidirect
9. #10587233C2semidirect
10. #10587231C2semidirect
11. #10587230C2semidirect
13. C22×D33C22semidirect
14. C22×D3×C11C22semidirect
15. C2×D3×D11C22semidirect
16. C3×D4×C11C22semidirect
17. #63159C22semidirect
18. D132C22semidirect
19. C4×D33C22semidirect
20. C11×#67C22semidirect
21. C11×D12C22semidirect
22. C4×D3×C11C22semidirect
23. C3×C22⋊D11C22semidirect
24. C2×C3×Dic11C22semidirect
25. C3×C4×D11C22semidirect
26. C3×Dic22C22semidirect
27. #63143C22semidirect
28. #63142C22semidirect
29. #63142C22semidirect
30. #63142C22semidirect
31. #63142C22semidirect
32. #63141C22semidirect
33. #63140C22semidirect
34. D33⋊C4C22semidirect
35. D3×Dic11C22semidirect
41. #4341D3semidirect
67. D4×C11C2×D3semidirect
75. C22⋊D11C2×D3semidirect
77. C2×Dic11C2×D3semidirect
82. C4×D11C2×D3semidirect
84. Dic22C2×D3semidirect
98. D3×D4D11semidirect
117. C3×C11H(5,𝔽2)semidirect
121. C22×D3C2×D11semidirect
124. C3×D4C2×D11semidirect
130. #67C2×D11semidirect
136. D12C2×D11semidirect
140. C4×D3C2×D11semidirect
174. C11#1009semidirect
191. D4D3×D11semidirect
219. C3#67037semidirect

Maximal subgroups

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

subgroupindex
D4×D332
D3×D4×C112
C3×#43412
#105872522
D3×C22⋊D112
C2×#631422
#105872442
D11×D122
#105872332
#105872312
#105872302
#670373
#100911