Finite Group Databasebeta

← #21457501

Subgroups — #21457501

Order 7808.

526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14519800C211yesmaximal, characteristic, complemented
2C22×D488C211yesmaximal, characteristic, complemented
3#16840403C212yesmaximal, complemented
4#16840147C211yesmaximal, characteristic, complemented
5#16839999C211yesmaximal, characteristic, complemented
6#16839980C212yesmaximal, complemented
7#16839912C212yesmaximal, complemented
8#16839910C212yesmaximal, complemented
9#16839844C211yesmaximal, characteristic, complemented
10C8×C22⋊D61C211yesmaximal, characteristic, complemented
11C61×#467C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yescomplemented
13C22×D244C2212yes—
14#14519800—24no—
15C2×#11758201C2212yescomplemented
16C2×#11758201C2212yescomplemented
17C2×D488—24no—
18C2×D488C2212yes—
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic, complemented
22#14519766C2212yescomplemented
23#14519762—22no—
24#14519752—22no—
25#14519752C2212yescomplemented
26#14519747—22no—
27#14519739C2212yescomplemented
28C4×C22⋊D61C2211yescharacteristic
29C22⋊C4×D61—22no—
30#14519706C2211yescharacteristic, complemented
31#14519697C2212yescomplemented
32#14519697C2212yescomplemented
33C22⋊#92418C2211yescharacteristic
34#14519689C2211yescharacteristic, complemented
35C8×Dic61C2211yescharacteristic, complemented
36C2×Q16×C61C2211yescharacteristic, complemented
37C22×C8×C61C2211yescharacteristic
38C22⋊Q8×C61C2212yes—
39#107×C61C2211yescharacteristic, complemented
40#103×C61C2212yescomplemented
41C23×D61—22no—
42C2×Q8×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61D411yescharacteristic
45#11758226—24no—
46#11758226—42no—
47C2×D244—24no—
48C2×D244—22no—
49C2×D244—22no—
50C2×D244—22no—
51C2×D244—42no—
52C2×D244C2312yes—
53C2×D244C2312yes—
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61C2311yescharacteristic
57Q16×C61—22no—
58C2×C8×C61—22no—
59C2×C8×C61C2311yescharacteristic
60C2×C8×C61C2311yescharacteristic
61C4⋊C4×C61—22no—
62C4⋊C4×C61C2312yes—
63C22⋊C4×C61—22no—
64C22⋊Dic61D411yescharacteristic
65#11758201—24no—
66#11758201—42no—
67#11758198—22no—
68#11758198—22no—
69#11758198—22no—
70#11758198—22no—
71#11758198D411yescharacteristic
72#11758196D411yescharacteristic
73C4×Dic61C2311yescharacteristic
74C2×#92418C2311yescharacteristic
75C2×#92418C2311yescharacteristic
76D488—24no—
77D488—22no—
78D488D414yescomplemented
79C8×D61—22no—
80C23×C61C2×D411yescharacteristic
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—44no—
84C22×D61—44no—
85C22×D61—82no—
86C22×D61C2×D411yescharacteristic
87Q8×C61—22no—
88Q8×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C22⋊D61—22no—
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99D244—22no—
100D244—22no—
101D244—22no—
102D244—44no—
103D244—44no—
104D244—82no—
105D244C2×D414yes—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—44no—
109C4×D61—82no—
110C8×C61—21no—
111C8×C61C2×D412yes—
112#92418—21no—
113#92418—21no—
114C22×C61—21no—
115C22×C61—21no—
116C22×C61#13512yescomplemented
117C22×C61C22×D411yescharacteristic
118C2×D61—21no—
119C2×D61—24no—
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—88no—
128C4×C61—21no—
129C4×C61—42no—
130C4×C61—42no—
131C4×C61C22×D411yescharacteristic
132C4×C61H(5,𝔽2)11yescharacteristic
133Dic61—21no—
134Dic61—21no—
135Dic61—21no—
136#3280—611nomaximal, Sylow
137C2×C61—22no—
138C2×C61D4211yescharacteristic
139C2×C61C2×#13511yescharacteristic
140C2×C61#57611yescharacteristic
141D61—41no—
142D61—44no—
143D61—82no—
144C2×#135—611no—
145C22×D8—611no—
146#546—612no—
147#495—611no—
148#467D6111yescharacteristic, complemented
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×D4—612no—
158#135—1224no—
159C2×Q16C2×D6111yescharacteristic, complemented
160C2×SD16—612no—
161C2×SD16—612no—
162C2×D8—611no—
163C2×D8—612no—
164C2×D8—611no—
165C2×D8—1224no—
166C22×C8—611no—
167C22×C8C2×D6111yescharacteristic
168#124—612no—
169#123—1222no—
170C22⋊Q8C2×D6112yes—
171#121—612no—
172#121—1222no—
173#120—1222no—
174C4×D4—611no—
175C4×D4—612no—
176C2×C22⋊C4—1222no—
177#107C2×D6111yescharacteristic, complemented
178C4⋊C8—611no—
179#103C2×D6112yescomplemented
180#102—612no—
181#102—612no—
182C22⋊C8—611no—
183C22⋊C8—611no—
184C4×C8—611no—
185C24—1222no—
186#41—1224no—
187#41—2442no—
188C2×Q8C22×D6112yes—
189C2×D4—611no—
190C2×D4—612no—
191C2×D4—612no—
192C2×D4—1224no—
193C2×D4—1222no—
194C2×D4—1222no—
195C2×D4—1222no—
196C2×D4—2442no—
197C22×C4—611no—
198C22×C4—1222no—
199C22×C4—1222no—
200C22×C4C22×D6111yescharacteristic
201Q16—22no—
202SD16—1224no—
203SD16—2442no—
204D8—614no—
205D8—1224no—
206D8—1222no—
207C2×C8—22no—
208C2×C8—611no—
209C2×C8—611no—
210C2×C8—1222no—
211C2×C8C22×D6111yescharacteristic
212C2×C8C22×D6111yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—611no—
215C4⋊C4C22×D6112yes—
216C22⋊C4—22no—
217C22⋊C4—611no—
218C22⋊C4—611no—
219C22⋊C4—1222no—
220C22⋊C4—1222no—
221C22⋊C4—1222no—
222C22⋊C4—1222no—
223C42—611no—
224C23—611no—
225C23—1222no—
226C23—1222no—
227C23—4882no—
228C23—2444no—
229C23—2444no—
230C23D4×D6111yescharacteristic
231Q8—22no—
232Q8—22no—
233D4—614no—
234D4—1222no—
235D4—1222no—
236D4—1222no—
237D4—1222no—
238D4—4882no—
239D4—2444no—
240D4—2444no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—4882no—
251C2×C4—2444no—
252C2×C4D4×D6111yescharacteristic
253C2×C4C23×D6111yescharacteristic
254C8—21no—
255C8—1221no—
256C8—1221no—
257C8D4×D6112yes—
258C22—21no—
259C22—21no—
260C22—1221no—
261C22—1221no—
262C22—1221no—
263C22—1224no—
264C22—4888no—
265C22—2442no—
266C22—2442no—
267C22—2442no—
268C22—2442no—
269C22—2442no—
270C22#1451980012yescomplemented
271C22C2×D4×D6111yescharacteristic
272C4—21no—
273C4—42no—
274C4—42no—
275C4—1221no—
276C4—1221no—
277C4—1221no—
278C4C2×D4×D6111yescharacteristic
279C4#1451982311yescharacteristic
280C2—22no—
281C2—4882no—
282C2—2441no—
283C2—2444no—
284C2#1684039611yescharacteristic
285C2C2×#1451980011yescharacteristic
286C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#467C2
socleC22×C61C22×D4
hypercenter#467D61
hypocenterC61#3280
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#14519800C2semidirect
2. C22×D488C2semidirect
3. #16840403C2semidirect
4. #16840147C2semidirect
5. #16839999C2semidirect
6. #16839980C2semidirect
7. #16839912C2semidirect
8. #16839910C2semidirect
9. #16839844C2semidirect
10. C8×C22⋊D61C2semidirect
11. C61×#467C2semidirect
12. C2×#11758226C22semidirect
15. C2×#11758201C22semidirect
16. C2×#11758201C22semidirect
21. C2×C8×D61C22semidirect
22. #14519766C22semidirect
25. #14519752C22semidirect
27. #14519739C22semidirect
30. #14519706C22semidirect
31. #14519697C22semidirect
32. #14519697C22semidirect
34. #14519689C22semidirect
35. C8×Dic61C22semidirect
36. C2×Q16×C61C22semidirect
39. #107×C61C22semidirect
40. #103×C61C22semidirect
78. D488D4semidirect
116. C22×C61#135semidirect
148. #467D61semidirect
155. C61#3280semidirect
159. C2×Q16C2×D61semidirect
177. #107C2×D61semidirect
179. #103C2×D61semidirect
270. C22#14519800semidirect