Finite Group Databasebeta

← #21457504

Subgroups — #21457504

Order 7808.

526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519796C211yesmaximal, characteristic, complemented
2#16840406C212yesmaximal, complemented
3#16840145C211yesmaximal, characteristic, complemented
4#16840003C211yesmaximal, characteristic, complemented
5#16839995C211yesmaximal, characteristic, complemented
6#16839975C212yesmaximal, complemented
7#16839913C212yesmaximal, complemented
8#16839904C212yesmaximal, complemented
9D8×Dic61C211yesmaximal, characteristic, complemented
10C8×C22⋊D61C211yesmaximal, characteristic, complemented
11C22×D8×C61C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yescomplemented
13#14519796—24no—
14C2×Dic244C2211yescharacteristic, complemented
15C2×#11758200C2212yescomplemented
16C2×#11758200C2212yescomplemented
17C2×C8×D61C2211yescharacteristic, complemented
18#14519764C2212yescomplemented
19#14519758—22no—
20#14519756C2212yes—
21#14519749—22no—
22#14519748C2212yescomplemented
23#14519746—22no—
24D4×Dic61C2212yescomplemented
25C4×C22⋊D61C2211yescharacteristic
26C2×C22⋊Dic61—22no—
27#14519711C2211yescharacteristic, complemented
28#14519706C2211yescharacteristic, complemented
29#14519702C2212yescomplemented
30#14519698C2212yescomplemented
31#14519698C2212yescomplemented
32C22⋊#92418C2211yescharacteristic
33#14519689C2211yescharacteristic, complemented
34C8×Dic61C2211yescharacteristic, complemented
35C22×D4×C61C2212yes—
36C2×D8×C61—24no—
37C2×D8×C61C2212yes—
38C2×D8×C61C2211yescharacteristic
39C2×D8×C61C2211yescharacteristic
40C22×C8×C61C2211yescharacteristic
41C24×C61—22no—
42C2×D4×C61—24no—
43C2×D4×C61—22no—
44C2×D4×C61—42no—
45C2×D4×C61C2312yes—
46C2×D4×C61C2312yes—
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—22no—
49C2×C22⋊D61—22no—
50C2×C22⋊D61D411yescharacteristic
51C22×Dic61—22no—
52C22×Dic61—22no—
53#11758224—24no—
54#11758224—42no—
55C2×C4×D61C2311yescharacteristic
56C2×Dic122C2312yes—
57D8×C61—24no—
58D8×C61—22no—
59D8×C61D414yescomplemented
60C2×C8×C61—22no—
61C2×C8×C61C2311yescharacteristic
62C2×C8×C61C2311yescharacteristic
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65C22⋊Dic61—22no—
66C22⋊Dic61—22no—
67C22⋊Dic61—22no—
68C22⋊Dic61D411yescharacteristic
69#11758200—24no—
70#11758200—42no—
71#11758198D411yescharacteristic
72C4⋊Dic61C2312yes—
73#11758196—22no—
74#11758196D411yescharacteristic
75C4×Dic61C2311yescharacteristic
76C2×#92418C2311yescharacteristic
77C2×#92418C2311yescharacteristic
78Dic244—22no—
79C8×D61—22no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—44no—
83C23×C61—44no—
84C23×C61—82no—
85C23×C61C2×D411yescharacteristic
86C22×D61C2×D411yescharacteristic
87D4×C61—22no—
88D4×C61—22no—
89D4×C61—22no—
90D4×C61—44no—
91D4×C61C2×D414yes—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—22no—
97C22⋊D61—44no—
98C22⋊D61—82no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—44no—
102C2×Dic61—82no—
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105C2×Dic61C2×D411yescharacteristic
106C4×D61—21no—
107C4×D61—21no—
108Dic122—22no—
109Dic122—22no—
110C8×C61—21no—
111C8×C61C2×D412yes—
112#92418—21no—
113#92418—21no—
114C22×C61—21no—
115C22×C61—21no—
116C22×C61—24no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—88no—
123C22×C61#13512yescomplemented
124C22×C61C22×D411yescharacteristic
125C2×D61—21no—
126C2×D61—21no—
127C2×D61—21no—
128C4×C61—21no—
129C4×C61C22×D411yescharacteristic
130C4×C61H(5,𝔽2)11yescharacteristic
131Dic61—21no—
132Dic61—21no—
133Dic61—21no—
134Dic61—42no—
135Dic61—42no—
136#3280—611nomaximal, Sylow
137C2×C61—22no—
138C2×C61—44no—
139C2×C61—82no—
140C2×C61D4211yescharacteristic
141C2×C61C2×#13511yescharacteristic
142C2×C61#57611yescharacteristic
143D61—41no—
144C2×#135—611no—
145C22×D8D6111yescharacteristic, complemented
146#546—612no—
147#495—611no—
148#467—611no—
149#466—611no—
150#463—612no—
151#450—612no—
152#449—612no—
153C4×D8—611no—
154C8×D4—611no—
155C61#328011yescharacteristic, complemented, Sylow
156C2×#41—612no—
157C22×D4C2×D6112yes—
158#135—1224no—
159C2×Q16—611no—
160C2×SD16—612no—
161C2×SD16—612no—
162C2×D8—24no—
163C2×D8C2×D6112yes—
164C2×D8C2×D6111yescharacteristic
165C2×D8C2×D6111yescharacteristic
166C22×C8—611no—
167C22×C8C2×D6111yescharacteristic
168#124—612no—
169#123—1222no—
170C22⋊Q8—612no—
171#121—612no—
172#121—1222no—
173#120—1222no—
174C4×D4—611no—
175C4×D4—612no—
176C2×C22⋊C4—1222no—
177#107—611no—
178C4⋊C8—611no—
179#103—612no—
180#102—612no—
181#102—612no—
182C22⋊C8—611no—
183C22⋊C8—611no—
184C4×C8—611no—
185C24—22no—
186#41—1224no—
187#41—2442no—
188C2×Q8—612no—
189C2×D4—24no—
190C2×D4—22no—
191C2×D4—42no—
192C2×D4—611no—
193C2×D4—1222no—
194C2×D4—1222no—
195C2×D4C22×D6112yes—
196C2×D4C22×D6112yes—
197C22×C4—611no—
198C22×C4—1222no—
199C22×C4—1222no—
200C22×C4C22×D6111yescharacteristic
201Q16—1222no—
202SD16—1224no—
203SD16—2442no—
204D8—24no—
205D8—22no—
206D8C22⋊D6114yescomplemented
207C2×C8—22no—
208C2×C8—611no—
209C2×C8—611no—
210C2×C8—1222no—
211C2×C8C22×D6111yescharacteristic
212C2×C8C22×D6111yescharacteristic
213C4⋊C4—611no—
214C4⋊C4—612no—
215C4⋊C4—1222no—
216C22⋊C4—611no—
217C22⋊C4—611no—
218C22⋊C4—1222no—
219C22⋊C4—1222no—
220C22⋊C4—1222no—
221C22⋊C4—1222no—
222C22⋊C4—1222no—
223C42—611no—
224C23—22no—
225C23—22no—
226C23—44no—
227C23—44no—
228C23—82no—
229C23—611no—
230C23D4×D6111yescharacteristic
231Q8—1222no—
232Q8—1222no—
233D4—22no—
234D4—22no—
235D4—22no—
236D4—44no—
237D4—1222no—
238D4—4882no—
239D4—2444no—
240D4C2×C22⋊D6114yes—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—4882no—
251C2×C4—2444no—
252C2×C4D4×D6111yescharacteristic
253C2×C4C23×D6111yescharacteristic
254C8—21no—
255C8—1221no—
256C8—1221no—
257C8C2×C22⋊D6112yes—
258C22—21no—
259C22—21no—
260C22—24no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—88no—
267C22—1221no—
268C22—1221no—
269C22—1221no—
270C22#1451979612yescomplemented
271C22C2×D4×D6111yescharacteristic
272C4—21no—
273C4—1221no—
274C4—1221no—
275C4—1221no—
276C4—2442no—
277C4—2442no—
278C4C22×C22⋊D6111yescharacteristic
279C4#1451982211yescharacteristic
280C2—22no—
281C2—44no—
282C2—82no—
283C2—2441no—
284C2D4×C22⋊D6111yescharacteristic
285C2C2×#1451979611yescharacteristic
286C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC22×D8×C61C2
socleC22×C61C22×D4
hypercenterC22×D8D61
hypocenterC61#3280
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14519796C2semidirect
2. #16840406C2semidirect
3. #16840145C2semidirect
4. #16840003C2semidirect
5. #16839995C2semidirect
6. #16839975C2semidirect
7. #16839913C2semidirect
8. #16839904C2semidirect
9. D8×Dic61C2semidirect
10. C8×C22⋊D61C2semidirect
11. C22×D8×C61C2semidirect
12. C2×#11758224C22semidirect
14. C2×Dic244C22semidirect
15. C2×#11758200C22semidirect
16. C2×#11758200C22semidirect
17. C2×C8×D61C22semidirect
18. #14519764C22semidirect
22. #14519748C22semidirect
24. D4×Dic61C22semidirect
27. #14519711C22semidirect
28. #14519706C22semidirect
29. #14519702C22semidirect
30. #14519698C22semidirect
31. #14519698C22semidirect
33. #14519689C22semidirect
34. C8×Dic61C22semidirect
59. D8×C61D4semidirect
123. C22×C61#135semidirect
145. C22×D8D61semidirect
155. C61#3280semidirect
206. D8C22⋊D61semidirect
270. C22#14519796semidirect