Finite Group Databasebeta

← #21456607

Subgroups — #21456607

Order 7808.

424 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#16840273C211yesmaximal, characteristic, complemented
2#16840103C211yesmaximal, characteristic, complemented
3#16840100C211yesmaximal, characteristic, complemented
4#16840086C211yesmaximal, characteristic, complemented
5#16840083C211yesmaximal, characteristic, complemented
6#16840001C211yesmaximal, characteristic, complemented
7#16839996C211yesmaximal, characteristic, complemented
8#16839993C211yesmaximal, characteristic, complemented
9#16839989C211yesmaximal, characteristic, complemented
10#16839924C211yesmaximal, characteristic, complemented
11#16839922C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic, complemented
13#16839905C211yesmaximal, characteristic, complemented
14C2×C22⋊#92418C211yesmaximal, characteristic, complemented
15C61×#525C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C2×#11758202C2211yescharacteristic, complemented
18C2×#11758200C2211yescharacteristic, complemented
19C2×#11758201C2211yescharacteristic, complemented
20C2×#11758199C2211yescharacteristic, complemented
21C22×#92418C2211yescharacteristic
22C22×#92418C2211yescharacteristic
23#14519760—21no—
24#14519756C2211yescharacteristic
25#14519756C2211yescharacteristic
26#14519751C2211yescharacteristic
27#14519751C2211yescharacteristic
28#14519746—21no—
29C4×C22⋊D61—21no—
30C4×C22⋊D61—21no—
31#14519736C2211yescharacteristic
32#14519710C2211yescharacteristic, complemented
33#14519710C2211yescharacteristic, complemented
34#14519708C2211yescharacteristic, complemented
35#14519708C2211yescharacteristic, complemented
36#14519701C2211yescharacteristic, complemented
37#14519701C2211yescharacteristic, complemented
38#14519700C2211yescharacteristic, complemented
39#14519700C2211yescharacteristic, complemented
40#14519698C2211yescharacteristic, complemented
41#14519698C2211yescharacteristic, complemented
42#14519697C2211yescharacteristic, complemented
43#14519697C2211yescharacteristic, complemented
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic
47C22⋊#92418C2211yescharacteristic
48C2×#41×C61C2211yescharacteristic
49C23×C4×C61C2211yescharacteristic
50#123×C61—21no—
51C22⋊Q8×C61C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#121×C61C2211yescharacteristic
54#121×C61C2211yescharacteristic
55#120×C61—21no—
56C4×D4×C61—21no—
57C4×D4×C61—21no—
58#117×C61C2211yescharacteristic
59C24×C61D411yescharacteristic
60#41×C61—41no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×D4×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61D411yescharacteristic
71C22×C4×C61D411yescharacteristic
72C22×C4×C61D411yescharacteristic
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C2×C22⋊D61—21no—
77C2×C22⋊D61—21no—
78C2×C22⋊D61—21no—
79#11758222—41no—
80#11758222—41no—
81C2×D244C2311yescharacteristic
82C2×C4×D61—21no—
83C2×Dic122C2311yescharacteristic
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C42×C61—21no—
94C22⋊Dic61—21no—
95C22⋊Dic61—21no—
96C22⋊Dic61—21no—
97#11758202—41no—
98#11758201—41no—
99#11758200—41no—
100#11758199—41no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107C4×Dic61—21no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—22no—
115C23×C61—21no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61C2×D411yescharacteristic
119C23×C61C2×D411yescharacteristic
120C23×C61C2×D411yescharacteristic
121C22×D61—21no—
122Q8×C61—21no—
123Q8×C61—21no—
124D4×C61—21no—
125D4×C61—21no—
126D4×C61—42no—
127D4×C61—42no—
128D4×C61—42no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2×D411yescharacteristic
144C2×C4×C61C2×D411yescharacteristic
145C2×C4×C61C2411yescharacteristic
146C22⋊D61—42no—
147C22⋊D61—42no—
148C22⋊D61—42no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152D244—21no—
153D244—21no—
154C4×D61—42no—
155Dic122—21no—
156Dic122—21no—
157#92418—21no—
158#92418—21no—
159#92418—21no—
160#92418—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—44no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61#13512yes—
174C22×C61C22×D411yescharacteristic
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—41no—
182C4×C61—41no—
183C4×C61—41no—
184C4×C61H(5,𝔽2)11yescharacteristic
185C4×C61H(5,𝔽2)11yescharacteristic
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189#3191—611nomaximal, Sylow
190C2×C61—22no—
191C2×C61—41no—
192C2×C61—41no—
193C2×C61—81no—
194C2×C61#53411yescharacteristic
195C2×C61C2×#13511yescharacteristic
196C2×C61#57511yescharacteristic
197D61—81no—
198#525—611no—
199#525D6111yescharacteristic, complemented
200#485—611no—
201#485—611no—
202#482—611no—
203#482—611no—
204#467—611no—
205#466—611no—
206#465—611no—
207#465—611no—
208#452—611no—
209#452—611no—
210#449—611no—
211#449—611no—
212C2×C22⋊C8—611no—
213C61#319111yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C2×#41C2×D6111yescharacteristic
216C23×C4C2×D6111yescharacteristic
217C2×Q16—611no—
218C2×SD16—611no—
219C2×SD16—611no—
220C2×D8—611no—
221C22×C8—611no—
222C22×C8—611no—
223#123—21no—
224#123—1221no—
225C22⋊Q8—611no—
226C22⋊Q8—611no—
227C22⋊Q8C2×D6111yescharacteristic
228C22⋊Q8C2×D6111yescharacteristic
229#121—611no—
230#121—611no—
231#121C2×D6111yescharacteristic
232#121C2×D6111yescharacteristic
233#120—21no—
234#120—1221no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—1221no—
238C4×D4—1221no—
239#117—611no—
240#117C2×D6111yescharacteristic
241#107—611no—
242#107—611no—
243#106—611no—
244#106—611no—
245#103—611no—
246#103—611no—
247#103—611no—
248#103—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252#102—611no—
253C22⋊C8—611no—
254C22⋊C8—611no—
255C22⋊C8—611no—
256C22⋊C8—611no—
257C24C22⋊D6111yescharacteristic
258#41—41no—
259#41—41no—
260#41—2441no—
261#41—2441no—
262C2×Q8—611no—
263C2×Q8C22×D6111yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—611no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4C22×D6111yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—1221no—
276C22×C4C22⋊D6111yescharacteristic
277C22×C4C22⋊D6111yescharacteristic
278C22×C4C22⋊D6111yescharacteristic
279C22×C4C22×D6111yescharacteristic
280C22×C4C22×D6111yescharacteristic
281C22×C4C22×D6111yescharacteristic
282Q16—2441no—
283SD16—2441no—
284SD16—2441no—
285D8—2441no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—611no—
289C2×C8—611no—
290C2×C8—2441no—
291C2×C8—2441no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—611no—
295C4⋊C4—611no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4C22×D6111yescharacteristic
299C4⋊C4C22×D6111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C42—21no—
311C42—1221no—
312C23—22no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—1221no—
317C23C2×C22⋊D6111yescharacteristic
318C23C2×C22⋊D6111yescharacteristic
319C23C2×C22⋊D6111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1221no—
323Q8—1221no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—1221no—
330D4—1221no—
331D4—2442no—
332D4—2442no—
333D4—2442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—2442no—
351C2×C4C2×C22⋊D6111yescharacteristic
352C2×C4C2×C22⋊D6111yescharacteristic
353C2×C4C2×C22⋊D6111yescharacteristic
354C2×C4C23×D6111yescharacteristic
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—44no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—2441no—
372C22—2441no—
373C22—2441no—
374C22#1451979712yes—
375C22C22×C22⋊D6111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—2441no—
383C4—2441no—
384C4—2441no—
385C4#1451982211yescharacteristic
386C4#1451982211yescharacteristic
387C2—22no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—4881no—
392C2#1684032111yescharacteristic
393C2C2×#1451979711yescharacteristic
394C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#525C2
socleC22×C61C22×D4
hypercenter#525D61
hypocenterC61#3191
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #16840273C2semidirect
2. #16840103C2semidirect
3. #16840100C2semidirect
4. #16840086C2semidirect
5. #16840083C2semidirect
6. #16840001C2semidirect
7. #16839996C2semidirect
8. #16839993C2semidirect
9. #16839989C2semidirect
10. #16839924C2semidirect
11. #16839922C2semidirect
12. #16839907C2semidirect
13. #16839905C2semidirect
14. C2×C22⋊#92418C2semidirect
15. C61×#525C2semidirect
17. C2×#11758202C22semidirect
18. C2×#11758200C22semidirect
19. C2×#11758201C22semidirect
20. C2×#11758199C22semidirect
32. #14519710C22semidirect
33. #14519710C22semidirect
34. #14519708C22semidirect
35. #14519708C22semidirect
36. #14519701C22semidirect
37. #14519701C22semidirect
38. #14519700C22semidirect
39. #14519700C22semidirect
40. #14519698C22semidirect
41. #14519698C22semidirect
42. #14519697C22semidirect
43. #14519697C22semidirect
199. #525D61semidirect
213. C61#3191semidirect