Finite Group Databasebeta

← #13080302

Subgroups — #13080302

Order 1408.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#66965C211yesmaximal, characteristic, complemented
2C2×D8×D11C211yesmaximal, characteristic, complemented
3#10623085C212yesmaximal, complemented
4C4×C11×D8C211yesmaximal, characteristic, complemented
5#10622629C212yesmaximal, complemented
6#10622500C211yesmaximal, characteristic, complemented
7#10622496C211yesmaximal, characteristic, complemented
8#10622394C212yesmaximal, complemented
9#10622389C212yesmaximal, complemented
10#10622309C211yesmaximal, characteristic, complemented
11C8×D44C211yesmaximal, characteristic, complemented
12C2×#4341C2212yescomplemented
13C2×D4×D11C2212yes—
14C2×C11×D8C2211yescharacteristic
15C4×D4×C11C2212yescomplemented
16C2×#4324C2212yescomplemented
17C2×#4323C2212yes—
18#66983—22no—
19C2×(C2×D11)⋊C4—22no—
20#66965—24no—
21D8×D11—24no—
22C2×Dic44C2211yescharacteristic, complemented
23C2×D88C2211yescharacteristic
24C2×#4314C2212yescomplemented
25C2×C8×D11C2211yescharacteristic
26C2×C8×D11C2211yescharacteristic, complemented
27#66950C2212yes—
28#66948C2212yescomplemented
29#66939—22no—
30#66935—22no—
31#66928C2212yescomplemented
32C4×D44C2211yescharacteristic
33C11×#107C2211yescharacteristic, complemented
34C11×#102C2212yescomplemented
35C4×C8×C11C2211yescharacteristic, complemented
36(C2×D11)⋊C8C2211yescharacteristic
37(C2×D11)⋊C8C2211yescharacteristic, complemented
38#66874C2212yescomplemented
39#66873C2212yescomplemented
40C4⋊(C11⋊C8)C2211yescharacteristic, complemented
41C23×D11—22no—
42C2×D4×C11C2312yes—
43C22×C4×C11—22no—
44C2×C22⋊D11—22no—
45C2×C22⋊D11—22no—
46C22×Dic11—22no—
47#4341—24no—
48#4341—42no—
49D4×D11—24no—
50D4×D11—42no—
51C2×D44—22no—
52C2×D44D411yescharacteristic
53C2×D44C2312yes—
54C2×C4×D11C2311yescharacteristic
55C2×C4×D11C2311yescharacteristic
56C2×Dic22C2312yes—
57C11×D8D414yescomplemented
58C2×C8×C11C2311yescharacteristic
59C2×C8×C11C2311yescharacteristic
60C11×C4⋊C4C2312yes—
61C11×C22⋊C4—22no—
62C42×C11C2311yescharacteristic
63#4324—24no—
64#4323—24no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—22no—
69(C2×D11)⋊C4D411yescharacteristic
70(C2×D11)⋊C4D411yescharacteristic
71C4⋊Dic11—22no—
72C4⋊Dic11D411yescharacteristic
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75Dic44—22no—
76D88—22no—
77#4314—42no—
78C8×D11—22no—
79C8×D11—22no—
80#3280—111nomaximal, Sylow
81C23×C11—22no—
82C22×D11—22no—
83C22×D11—44no—
84C22×D11—44no—
85C22×D11—82no—
86C22×D11C2×D411yescharacteristic
87C22×D11C2×D411yescharacteristic
88D4×C11—22no—
89D4×C11C2×D414yes—
90C2×C4×C11—22no—
91C2×C4×C11—82no—
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2411yescharacteristic
95C22⋊D11—44no—
96C22⋊D11—44no—
97C2×Dic11—22no—
98C2×Dic11—44no—
99C2×Dic11C2×D411yescharacteristic
100C2×Dic11C2×D411yescharacteristic
101D44—22no—
102D44—22no—
103D44—22no—
104D44—82no—
105C4×D11—21no—
106C4×D11—21no—
107C4×D11—21no—
108C4×D11—21no—
109Dic22—22no—
110Dic22—22no—
111C8×C11—21no—
112C8×C11C2×D412yes—
113C11⋊C8—21no—
114C11⋊C8—21no—
115C2×#135—111no—
116C22×D8—111no—
117#546—112no—
118#495—111no—
119#467—111no—
120#466—111no—
121#463—112no—
122#450—112no—
123#449—112no—
124C4×D8D1111yescharacteristic, complemented
125C8×D4—111no—
126C22×C11—24no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11C22×D411yescharacteristic
130C2×D11—21no—
131C2×D11—21no—
132C2×D11—21no—
133C2×D11—21no—
134C2×D11—21no—
135C2×D11—42no—
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—88no—
139C2×D11#13512yescomplemented
140C4×C11—21no—
141C4×C11—21no—
142C4×C11—42no—
143C4×C11C22×D411yescharacteristic
144C4×C11H(5,𝔽2)11yescharacteristic
145Dic11—21no—
146Dic11—21no—
147Dic11—42no—
148C2×#41—112no—
149C22×D4—112no—
150#135—224no—
151C2×Q16—111no—
152C2×SD16—112no—
153C2×SD16—112no—
154C2×D8—112no—
155C2×D8—111no—
156C2×D8—224no—
157C2×D8C2×D1111yescharacteristic
158C22×C8—111no—
159C22×C8—111no—
160#124—112no—
161#123—222no—
162C22⋊Q8—112no—
163#121—112no—
164#121—222no—
165#120—222no—
166C4×D4—111no—
167C4×D4C2×D1112yescomplemented
168C2×C22⋊C4—222no—
169#107C2×D1111yescharacteristic, complemented
170C4⋊C8—111no—
171#103—112no—
172#102—112no—
173#102C2×D1112yescomplemented
174C22⋊C8—111no—
175C22⋊C8—111no—
176C4×C8C2×D1111yescharacteristic, complemented
177C2×C11—44no—
178C2×C11D4211yescharacteristic
179C2×C11C2×#13511yescharacteristic
180C2×C11#57611yescharacteristic
181D11—22no—
182D11—41no—
183D11—82no—
184C24—222no—
185#41—224no—
186#41—442no—
187C2×Q8—112no—
188C2×D4—111no—
189C2×D4—112no—
190C2×D4—222no—
191C2×D4—222no—
192C2×D4—224no—
193C2×D4—222no—
194C2×D4—442no—
195C2×D4C22×D1112yes—
196C22×C4—22no—
197C22×C4—111no—
198C22×C4—111no—
199C22×C4—222no—
200Q16—222no—
201SD16—224no—
202SD16—442no—
203D8—224no—
204D8—222no—
205D8D4414yescomplemented
206C2×C8—111no—
207C2×C8—111no—
208C2×C8—222no—
209C2×C8—222no—
210C2×C8C22×D1111yescharacteristic
211C2×C8C22×D1111yescharacteristic
212C4⋊C4—111no—
213C4⋊C4—222no—
214C4⋊C4C22×D1112yes—
215C22⋊C4—22no—
216C22⋊C4—111no—
217C22⋊C4—111no—
218C22⋊C4—222no—
219C22⋊C4—222no—
220C22⋊C4—222no—
221C22⋊C4—222no—
222C42C22×D1111yescharacteristic
223C11#328011yescharacteristic, complemented, Sylow
224C23—22no—
225C23—111no—
226C23—111no—
227C23—222no—
228C23—444no—
229C23—444no—
230C23—882no—
231Q8—222no—
232Q8—222no—
233D4—22no—
234D4—222no—
235D4—222no—
236D4—222no—
237D4—444no—
238D4—444no—
239D4—882no—
240D4C2×D4414yes—
241C2×C4—22no—
242C2×C4—82no—
243C2×C4—111no—
244C2×C4—111no—
245C2×C4—221no—
246C2×C4—221no—
247C2×C4—221no—
248C2×C4—221no—
249C2×C4—222no—
250C2×C4—444no—
251C2×C4D4×D1111yescharacteristic
252C2×C4D4×D1111yescharacteristic
253C2×C4C23×D1111yescharacteristic
254C8—21no—
255C8—221no—
256C8—221no—
257C8C2×D4412yes—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—112no—
262C22—221no—
263C22—221no—
264C22—221no—
265C22—221no—
266C22—221no—
267C22—442no—
268C22—442no—
269C22—442no—
270C22—888no—
271C22C2×D4×D1111yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—221no—
276C4—221no—
277C4—442no—
278C4C22×D4411yescharacteristic
279C4#6704211yescharacteristic
280C2—44no—
281C2—222no—
282C2—441no—
283C2—882no—
284C2D4×D4411yescharacteristic
285C2#1062328811yescharacteristic
286C2D11×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×D8C2
socleC22×C11C22×D4
hypercenterC4×D8D11
hypocenterC11#3280
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#66965C2semidirect
2. C2×D8×D11C2semidirect
3. #10623085C2semidirect
4. C4×C11×D8C2semidirect
5. #10622629C2semidirect
6. #10622500C2semidirect
7. #10622496C2semidirect
8. #10622394C2semidirect
9. #10622389C2semidirect
10. #10622309C2semidirect
11. C8×D44C2semidirect
12. C2×#4341C22semidirect
15. C4×D4×C11C22semidirect
16. C2×#4324C22semidirect
22. C2×Dic44C22semidirect
24. C2×#4314C22semidirect
26. C2×C8×D11C22semidirect
28. #66948C22semidirect
31. #66928C22semidirect
33. C11×#107C22semidirect
34. C11×#102C22semidirect
35. C4×C8×C11C22semidirect
37. (C2×D11)⋊C8C22semidirect
38. #66874C22semidirect
39. #66873C22semidirect
40. C4⋊(C11⋊C8)C22semidirect
57. C11×D8D4semidirect
124. C4×D8D11semidirect
139. C2×D11#135semidirect
167. C4×D4C2×D11semidirect
169. #107C2×D11semidirect
173. #102C2×D11semidirect
176. C4×C8C2×D11semidirect
205. D8D44semidirect
223. C11#3280semidirect

Maximal subgroups

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

subgroupindex
C2×#669652
C2×D8×D112
#106230852
C4×C11×D82
#106226292
#106225002
#106224962
#106223942
#106223892
#106223092
C8×D442
#328011