Finite Group Databasebeta

← #21462685

Subgroups — #21462685

Order 7808.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840797C211yesmaximal, characteristic, complemented
2#16840795C211yesmaximal, characteristic, complemented
3#16840794C211yesmaximal, characteristic, complemented
4#16840793C211yesmaximal, characteristic, complemented
5#16840793C211yesmaximal, characteristic, complemented
6#16840791C211yesmaximal, characteristic, complemented
7#16840789C211yesmaximal, characteristic, complemented
8D4×#92420C211yesmaximal, characteristic, complemented
9#16840786C211yesmaximal, characteristic, complemented
10#16840786C211yesmaximal, characteristic, complemented
11#16840736C211yesmaximal, characteristic, complemented
12#16840735C211yesmaximal, characteristic, complemented
13#16840732C211yesmaximal, characteristic, complemented
14C2×C22⋊#92420C211yesmaximal, characteristic, complemented
15#16840268C211yesmaximal, characteristic
16C2×#11758213C2211yescharacteristic, complemented
17C2×#11758217C2211yescharacteristic
18C2×#11758217C2211yescharacteristic
19C2×#11758217C2211yescharacteristic, complemented
20C2×D61⋊C8C2211yescharacteristic, complemented
21C22×#92420C2211yescharacteristic
22C22×#92420C2211yescharacteristic
23C22×#92420C2211yescharacteristic, complemented
24#14519844C2211yescharacteristic, complemented
25#14519844C2211yescharacteristic, complemented
26C4⋊#92420C2211yescharacteristic, complemented
27C4⋊#92420C2211yescharacteristic, complemented
28#14519834C2211yescharacteristic, complemented
29#14519834C2211yescharacteristic, complemented
30C22⋊#92420C2211yescharacteristic
31C22⋊#92420C2211yescharacteristic
32C22⋊#92420C2211yescharacteristic
33C22⋊#92420C2211yescharacteristic
34C22⋊#92420C2211yescharacteristic
35C22⋊#92420C2211yescharacteristic
36C22⋊#92420C2211yescharacteristic
37C22⋊#92420C2211yescharacteristic
38C22⋊#92420C2211yescharacteristic, complemented
39C22⋊#92420C2211yescharacteristic, complemented
40#14519832C2211yescharacteristic, complemented
41#14519832C2211yescharacteristic, complemented
42C4×#92420C2211yescharacteristic, complemented
43C4×#92420C2211yescharacteristic, complemented
44C2×#11758224C2211yescharacteristic
45C23×Dic61C2211yescharacteristic
46#14519761C411yescharacteristic
47#14519758C411yescharacteristic
48#14519754C411yescharacteristic
49#14519754C411yescharacteristic
50#14519749C411yescharacteristic
51#14519749C411yescharacteristic
52#14519746C411yescharacteristic
53D4×Dic61C2211yescharacteristic
54D4×Dic61C2211yescharacteristic
55#14519737C2211yescharacteristic
56#14519737C2211yescharacteristic
57#14519733C2211yescharacteristic
58#120×C61C411yescharacteristic
59C24×C61C2×C411yescharacteristic
60C2×D4×C61C2×C411yescharacteristic
61C2×D4×C61C2×C411yescharacteristic
62C2×D4×C61C2×C411yescharacteristic
63C2×C22⋊D61C2×C411yescharacteristic
64C2×C22⋊D61C2×C411yescharacteristic
65C2×C22⋊D61C2×C411yescharacteristic
66C2×C22⋊D61C2×C411yescharacteristic
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61C2×C411yescharacteristic
70C22×Dic61C2×C411yescharacteristic
71C22×Dic61C2×C411yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76#11758224—41no—
77#11758224—41no—
78C2×C4×D61C2311yescharacteristic
79C2×Dic122C2×C411yescharacteristic
80#11758217—41no—
81#11758217—41no—
82#11758217—41no—
83C2×#92420—41no—
84C2×#92420—41no—
85C2×#92420—41no—
86C2×#92420C2311yescharacteristic
87C2×#92420C2311yescharacteristic
88C2×#92420C2311yescharacteristic
89C2×#92420C2311yescharacteristic
90C2×#92420C2311yescharacteristic
91C2×#92420C2311yescharacteristic
92C2×#92420C2311yescharacteristic
93C2×#92420C2311yescharacteristic
94#11758213—41no—
95D61⋊C8—41no—
96C22⋊C4×C61C2×C411yescharacteristic
97C22⋊C4×C61C2×C411yescharacteristic
98C22⋊C4×C61C2×C411yescharacteristic
99C22⋊Dic61C2×C411yescharacteristic
100C22⋊Dic61C2×C411yescharacteristic
101C22⋊Dic61C2×C411yescharacteristic
102C22⋊Dic61C2×C411yescharacteristic
103C22⋊Dic61C2×C411yescharacteristic
104#11758198C2×C411yescharacteristic
105#11758198C2×C411yescharacteristic
106C4⋊Dic61C2×C411yescharacteristic
107C4⋊Dic61C2×C411yescharacteristic
108#11758196C2×C411yescharacteristic
109#11758196C2×C411yescharacteristic
110#11758196C2×C411yescharacteristic
111#11758196C2×C411yescharacteristic
112C4×Dic61C2311yescharacteristic
113C4×Dic61C2311yescharacteristic
114C23×C61—22no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61C22×C411yescharacteristic
118C23×C61C22×C411yescharacteristic
119C23×C61C22×C411yescharacteristic
120C23×C61C22×C411yescharacteristic
121C22×D61C22×C411yescharacteristic
122D4×C61—22no—
123D4×C61—41no—
124D4×C61—41no—
125C2×C4×C61C22×C411yescharacteristic
126C2×C4×C61C22×C411yescharacteristic
127C2×C4×C61C22×C411yescharacteristic
128C22⋊D61—22no—
129C22⋊D61—41no—
130C22⋊D61—41no—
131C22⋊D61—41no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61C22×C411yescharacteristic
144C2×Dic61C22×C411yescharacteristic
145C2×Dic61C22×C411yescharacteristic
146C2×Dic61C22×C411yescharacteristic
147C2×Dic61C22×C411yescharacteristic
148C2×Dic61C22×C411yescharacteristic
149C2×Dic61C2411yescharacteristic
150C4×D61—21no—
151C4×D61—21no—
152Dic122—41no—
153#92420—21no—
154#92420—21no—
155#92420—21no—
156#92420—21no—
157#92420—21no—
158#92420—21no—
159#92420—21no—
160#92420—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—44no—
173C22×C61#13112yes—
174C22×C61C23×C411yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181Dic61—21no—
182Dic61—21no—
183Dic61—21no—
184Dic61—21no—
185Dic61—21no—
186Dic61—21no—
187Dic61H(5,𝔽2)11yescharacteristic
188Dic61H(5,𝔽2)11yescharacteristic
189#2976—611nomaximal, Sylow
190C2×C61—22no—
191C2×C61—41no—
192C2×C61—41no—
193C2×C61—41no—
194C2×C61#51811yescharacteristic
195C2×C61C2×#13111yescharacteristic
196C2×C61#56811yescharacteristic
197D61—41no—
198#525—611no—
199#436—611no—
200#436—611no—
201#435—611no—
202#435—611no—
203#435—611no—
204#435—611no—
205C8×D4—611no—
206C8×D4—611no—
207#433—611no—
208#433—611no—
209#408—611no—
210#408—611no—
211#407—611no—
212C2×C22⋊C8—611no—
213C61#297611yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C23×C4—611no—
216C2×M16—611no—
217C2×M16—611no—
218C2×M16—611no—
219C2×M16—611no—
220C22×C8—611no—
221C22×C8—611no—
222C22×C8—611no—
223C22×C8—611no—
224#123—611no—
225#123—611no—
226C22⋊Q8—611no—
227C22⋊Q8—611no—
228#121—611no—
229#121—611no—
230#120—611no—
231#120#692311yescharacteristic
232C4×D4—611no—
233C4×D4—611no—
234C4×D4—611no—
235C4×D4—611no—
236#117—611no—
237C4⋊C8—611no—
238C4⋊C8—611no—
239C4⋊C8—611no—
240C4⋊C8—611no—
241C22⋊C8—611no—
242C22⋊C8—611no—
243C22⋊C8—611no—
244C22⋊C8—611no—
245C22⋊C8—611no—
246C22⋊C8—611no—
247C22⋊C8—611no—
248C22⋊C8—611no—
249C22⋊C8—611no—
250C22⋊C8—611no—
251C22⋊C8—611no—
252C22⋊C8—611no—
253#97—611no—
254#97—611no—
255C4×C8—611no—
256C4×C8—611no—
257C24C2×#692311yescharacteristic
258#41—2441no—
259#41—2441no—
260C2×Q8—611no—
261C2×D4—611no—
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—611no—
265C2×D4C2×#692311yescharacteristic
266C2×D4C2×#692311yescharacteristic
267C2×D4C2×#692311yescharacteristic
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—2441no—
277C22×C4—2441no—
278M16—2441no—
279M16—2441no—
280M16—2441no—
281M16—2441no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8—611no—
285C2×C8—611no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—611no—
290C2×C8—2441no—
291C2×C8—2441no—
292C2×C8—2441no—
293C2×C8—2441no—
294C4⋊C4—611no—
295C4⋊C4—611no—
296C4⋊C4—611no—
297C4⋊C4—611no—
298C4⋊C4—611no—
299C4⋊C4—611no—
300C22⋊C4—611no—
301C22⋊C4—611no—
302C22⋊C4—611no—
303C22⋊C4—611no—
304C22⋊C4—611no—
305C22⋊C4—611no—
306C22⋊C4—611no—
307C22⋊C4C2×#692311yescharacteristic
308C22⋊C4C2×#692311yescharacteristic
309C22⋊C4C2×#692311yescharacteristic
310C42—611no—
311C42—611no—
312C23—22no—
313C23—41no—
314C23—41no—
315C23—611no—
316C23C22×#692311yescharacteristic
317C23C22×#692311yescharacteristic
318C23C22×#692311yescharacteristic
319C23C22×#692311yescharacteristic
320Q8—2441no—
321D4—22no—
322D4—41no—
323D4—41no—
324D4—1222no—
325D4—2441no—
326D4—2441no—
327D4—2441no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—611no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2441no—
348C2×C4C22×#692311yescharacteristic
349C2×C4C22×#692311yescharacteristic
350C2×C4C22×#692311yescharacteristic
351C8—1221no—
352C8—1221no—
353C8—1221no—
354C8—1221no—
355C8—1221no—
356C8—1221no—
357C8—1221no—
358C8—1221no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22—1221no—
372C22—1221no—
373C22—1221no—
374C22#1451986412yes—
375C22C23×#692311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—611no—
380C4—611no—
381C4—1221no—
382C4—1221no—
383C4—1221no—
384C4—1221no—
385C4—1221no—
386C4—1221no—
387C2—22no—
388C2—41no—
389C2—41no—
390C2—41no—
391C2—2441no—
392C2#1684082911yescharacteristic
393C2C2×#1451986411yescharacteristic
394C2#1684084011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#6923
commutator, socleC22×C61C23×C4
Fitting#120×C61C4
hypercenter#120#6923
hypocenterC61#2976
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #16840797C2semidirect
2. #16840795C2semidirect
3. #16840794C2semidirect
4. #16840793C2semidirect
5. #16840793C2semidirect
6. #16840791C2semidirect
7. #16840789C2semidirect
8. D4×#92420C2semidirect
9. #16840786C2semidirect
10. #16840786C2semidirect
11. #16840736C2semidirect
12. #16840735C2semidirect
13. #16840732C2semidirect
14. C2×C22⋊#92420C2semidirect
16. C2×#11758213C22semidirect
19. C2×#11758217C22semidirect
20. C2×D61⋊C8C22semidirect
23. C22×#92420C22semidirect
24. #14519844C22semidirect
25. #14519844C22semidirect
26. C4⋊#92420C22semidirect
27. C4⋊#92420C22semidirect
28. #14519834C22semidirect
29. #14519834C22semidirect
38. C22⋊#92420C22semidirect
39. C22⋊#92420C22semidirect
40. #14519832C22semidirect
41. #14519832C22semidirect
42. C4×#92420C22semidirect
43. C4×#92420C22semidirect
213. C61#2976semidirect