Finite Group Databasebeta

← #24918251

Subgroups — #24918251

Order 10624.

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#19128212C211yesmaximal, characteristic, complemented
2#19128042C211yesmaximal, characteristic, complemented
3#19128039C211yesmaximal, characteristic, complemented
4#19128025C211yesmaximal, characteristic, complemented
5#19128022C211yesmaximal, characteristic, complemented
6#19127940C211yesmaximal, characteristic, complemented
7#19127935C211yesmaximal, characteristic, complemented
8#19127932C211yesmaximal, characteristic, complemented
9#19127928C211yesmaximal, characteristic, complemented
10#19127863C211yesmaximal, characteristic, complemented
11#19127861C211yesmaximal, characteristic, complemented
12#19127846C211yesmaximal, characteristic, complemented
13#19127844C211yesmaximal, characteristic, complemented
14C2×C22⋊(C83⋊C8)C211yesmaximal, characteristic, complemented
15#525×C83C211yesmaximal, characteristic, complemented
16C2×#13050590C2211yescharacteristic
17C2×#13050580C2211yescharacteristic, complemented
18C2×#13050578C2211yescharacteristic, complemented
19C2×#13050577C2211yescharacteristic, complemented
20C2×#13050575C2211yescharacteristic, complemented
21C22×C83⋊C8C2211yescharacteristic
22C22×C83⋊C8C2211yescharacteristic
23#14581775—21no—
24#14581771C2211yescharacteristic
25#14581771C2211yescharacteristic
26#14581766C2211yescharacteristic
27#14581766C2211yescharacteristic
28#14581761—21no—
29C4×C22⋊D83—21no—
30C4×C22⋊D83—21no—
31#14581751C2211yescharacteristic
32#14581725C2211yescharacteristic, complemented
33#14581725C2211yescharacteristic, complemented
34#14581723C2211yescharacteristic, complemented
35#14581723C2211yescharacteristic, complemented
36#14581716C2211yescharacteristic, complemented
37#14581716C2211yescharacteristic, complemented
38#14581715C2211yescharacteristic, complemented
39#14581715C2211yescharacteristic, complemented
40#14581713C2211yescharacteristic, complemented
41#14581713C2211yescharacteristic, complemented
42#14581712C2211yescharacteristic, complemented
43#14581712C2211yescharacteristic, complemented
44C22⋊(C83⋊C8)C2211yescharacteristic
45C22⋊(C83⋊C8)C2211yescharacteristic
46C22⋊(C83⋊C8)C2211yescharacteristic
47C22⋊(C83⋊C8)C2211yescharacteristic
48C2×#41×C83C2211yescharacteristic
49C23×C4×C83C2211yescharacteristic
50#123×C83—21no—
51C22⋊Q8×C83C2211yescharacteristic
52C22⋊Q8×C83C2211yescharacteristic
53#121×C83C2211yescharacteristic
54#121×C83C2211yescharacteristic
55#120×C83—21no—
56C4×D4×C83—21no—
57C4×D4×C83—21no—
58#117×C83C2211yescharacteristic
59#13050590—41no—
60#13050590—41no—
61C2×Dic166C2311yescharacteristic
62C2×D332C2311yescharacteristic
63C2×C22⋊D83—21no—
64C2×C22⋊D83—21no—
65C2×C22⋊D83—21no—
66C2×C4×D83—21no—
67#13050580—41no—
68#13050578—41no—
69#13050577—41no—
70#13050575—41no—
71C2×C83⋊C8—41no—
72C2×C83⋊C8—41no—
73C2×C83⋊C8C2311yescharacteristic
74C2×C83⋊C8C2311yescharacteristic
75C2×C83⋊C8C2311yescharacteristic
76C2×C83⋊C8C2311yescharacteristic
77C4⋊Dic83C2311yescharacteristic
78C4⋊Dic83C2311yescharacteristic
79Dic83⋊C4—21no—
80Dic83⋊C4—21no—
81C22⋊Dic83—21no—
82C22⋊Dic83—21no—
83C22⋊Dic83—21no—
84(C2×D83)⋊C4—21no—
85(C2×D83)⋊C4—21no—
86C4×Dic83—21no—
87C24×C83D411yescharacteristic
88#41×C83—41no—
89#41×C83—41no—
90C2×Q8×C83C2311yescharacteristic
91C2×D4×C83—21no—
92C2×D4×C83—21no—
93C2×D4×C83—21no—
94C2×D4×C83C2311yescharacteristic
95C22×C4×C83—21no—
96C22×C4×C83—41no—
97C22×C4×C83—41no—
98C22×C4×C83D411yescharacteristic
99C22×C4×C83D411yescharacteristic
100C22×C4×C83D411yescharacteristic
101C22×C4×C83C2311yescharacteristic
102C22×C4×C83C2311yescharacteristic
103C22×C4×C83C2311yescharacteristic
104C4⋊C4×C83—21no—
105C4⋊C4×C83—21no—
106C4⋊C4×C83C2311yescharacteristic
107C4⋊C4×C83C2311yescharacteristic
108C22⋊C4×C83—21no—
109C22⋊C4×C83—21no—
110C22⋊C4×C83—21no—
111C22⋊C4×C83—21no—
112C22⋊C4×C83—21no—
113C42×C83—21no—
114C23×C83—22no—
115C23×C83—21no—
116C23×C83—41no—
117C23×C83—41no—
118C23×C83C2×D411yescharacteristic
119C23×C83C2×D411yescharacteristic
120C23×C83C2×D411yescharacteristic
121C22×D83—21no—
122Q8×C83—21no—
123Q8×C83—21no—
124D4×C83—21no—
125D4×C83—21no—
126D4×C83—42no—
127D4×C83—42no—
128D4×C83—42no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—41no—
139C2×C4×C83—41no—
140C2×C4×C83—41no—
141C2×C4×C83—42no—
142C2×C4×C83C2×D411yescharacteristic
143C2×C4×C83C2×D411yescharacteristic
144C2×C4×C83C2×D411yescharacteristic
145C2×C4×C83C2411yescharacteristic
146C22⋊D83—42no—
147C22⋊D83—42no—
148C22⋊D83—42no—
149C2×Dic83—21no—
150C2×Dic83—21no—
151C2×Dic83—21no—
152D332—21no—
153D332—21no—
154C4×D83—42no—
155Dic166—21no—
156Dic166—21no—
157C83⋊C8—21no—
158C83⋊C8—21no—
159C83⋊C8—21no—
160C83⋊C8—21no—
161C22×C83—21no—
162C22×C83—21no—
163C22×C83—21no—
164C22×C83—21no—
165C22×C83—21no—
166C22×C83—21no—
167C22×C83—21no—
168C22×C83—21no—
169C22×C83—44no—
170C22×C83—41no—
171C22×C83—41no—
172C22×C83—41no—
173C22×C83#13512yes—
174C22×C83C22×D411yescharacteristic
175C2×D83—41no—
176C2×D83—41no—
177C2×D83—41no—
178C4×C83—21no—
179C4×C83—21no—
180C4×C83—21no—
181C4×C83—41no—
182C4×C83—41no—
183C4×C83—41no—
184C4×C83H(5,𝔽2)11yescharacteristic
185C4×C83H(5,𝔽2)11yescharacteristic
186Dic83—41no—
187Dic83—41no—
188Dic83—41no—
189C2×C83—22no—
190C2×C83—41no—
191C2×C83—41no—
192C2×C83—81no—
193C2×C83#53411yescharacteristic
194C2×C83C2×#13511yescharacteristic
195C2×C83#57511yescharacteristic
196D83—81no—
197#3191—831nomaximal, Sylow
198C83#319111yescharacteristic, complemented, Sylow
199#525—831no—
200#525D8311yescharacteristic, complemented
201#485—831no—
202#485—831no—
203#482—831no—
204#482—831no—
205#467—831no—
206#466—831no—
207#465—831no—
208#465—831no—
209#452—831no—
210#452—831no—
211#449—831no—
212#449—831no—
213C2×C22⋊C8—831no—
214C2×#41—831no—
215C2×#41C2×D8311yescharacteristic
216C23×C4C2×D8311yescharacteristic
217C2×Q16—831no—
218C2×SD16—831no—
219C2×SD16—831no—
220C2×D8—831no—
221C22×C8—831no—
222C22×C8—831no—
223#123—21no—
224#123—1661no—
225C22⋊Q8—831no—
226C22⋊Q8—831no—
227C22⋊Q8C2×D8311yescharacteristic
228C22⋊Q8C2×D8311yescharacteristic
229#121—831no—
230#121—831no—
231#121C2×D8311yescharacteristic
232#121C2×D8311yescharacteristic
233#120—21no—
234#120—1661no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—1661no—
238C4×D4—1661no—
239#117—831no—
240#117C2×D8311yescharacteristic
241#107—831no—
242#107—831no—
243#106—831no—
244#106—831no—
245#103—831no—
246#103—831no—
247#103—831no—
248#103—831no—
249#102—831no—
250#102—831no—
251#102—831no—
252#102—831no—
253C22⋊C8—831no—
254C22⋊C8—831no—
255C22⋊C8—831no—
256C22⋊C8—831no—
257C24C22⋊D8311yescharacteristic
258#41—41no—
259#41—41no—
260#41—3321no—
261#41—3321no—
262C2×Q8—831no—
263C2×Q8C22×D8311yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—831no—
268C2×D4—1661no—
269C2×D4—1661no—
270C2×D4—1661no—
271C2×D4C22×D8311yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—1661no—
276C22×C4C22⋊D8311yescharacteristic
277C22×C4C22⋊D8311yescharacteristic
278C22×C4C22⋊D8311yescharacteristic
279C22×C4C22×D8311yescharacteristic
280C22×C4C22×D8311yescharacteristic
281C22×C4C22×D8311yescharacteristic
282Q16—3321no—
283SD16—3321no—
284SD16—3321no—
285D8—3321no—
286C2×C8—3321no—
287C2×C8—3321no—
288C2×C8—831no—
289C2×C8—831no—
290C2×C8—831no—
291C2×C8—831no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—831no—
295C4⋊C4—831no—
296C4⋊C4—1661no—
297C4⋊C4—1661no—
298C4⋊C4C22×D8311yescharacteristic
299C4⋊C4C22×D8311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—1661no—
306C22⋊C4—1661no—
307C22⋊C4—1661no—
308C22⋊C4—1661no—
309C22⋊C4—1661no—
310C42—21no—
311C42—1661no—
312C23—22no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—1661no—
317C23C2×C22⋊D8311yescharacteristic
318C23C2×C22⋊D8311yescharacteristic
319C23C2×C22⋊D8311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1661no—
323Q8—1661no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—3322no—
330D4—3322no—
331D4—3322no—
332D4—1661no—
333D4—1661no—
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—3322no—
348C2×C4—1661no—
349C2×C4—1661no—
350C2×C4—1661no—
351C2×C4C2×C22⋊D8311yescharacteristic
352C2×C4C2×C22⋊D8311yescharacteristic
353C2×C4C2×C22⋊D8311yescharacteristic
354C2×C4C23×D8311yescharacteristic
355C8—1661no—
356C8—1661no—
357C8—1661no—
358C8—1661no—
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—3321no—
372C22—3321no—
373C22—3321no—
374C22#1458181212yes—
375C22C22×C22⋊D8311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3321no—
383C4—3321no—
384C4—3321no—
385C4#1458183711yescharacteristic
386C4#1458183711yescharacteristic
387C2—22no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—6641no—
392C2#1912826011yescharacteristic
393C2C2×#1458181211yescharacteristic
394C2#1912849911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#525×C83C2
socleC22×C83C22×D4
hypercenter#525D83
hypocenterC83#3191
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #19128212C2semidirect
2. #19128042C2semidirect
3. #19128039C2semidirect
4. #19128025C2semidirect
5. #19128022C2semidirect
6. #19127940C2semidirect
7. #19127935C2semidirect
8. #19127932C2semidirect
9. #19127928C2semidirect
10. #19127863C2semidirect
11. #19127861C2semidirect
12. #19127846C2semidirect
13. #19127844C2semidirect
14. C2×C22⋊(C83⋊C8)C2semidirect
15. #525×C83C2semidirect
17. C2×#13050580C22semidirect
18. C2×#13050578C22semidirect
19. C2×#13050577C22semidirect
20. C2×#13050575C22semidirect
32. #14581725C22semidirect
33. #14581725C22semidirect
34. #14581723C22semidirect
35. #14581723C22semidirect
36. #14581716C22semidirect
37. #14581716C22semidirect
38. #14581715C22semidirect
39. #14581715C22semidirect
40. #14581713C22semidirect
41. #14581713C22semidirect
42. #14581712C22semidirect
43. #14581712C22semidirect
198. C83#3191semidirect
200. #525D83semidirect

Maximal subgroups

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

subgroupindex
#191282122
#191280422
#191280392
#191280252
#191280222
#191279402
#191279352
#191279322
#191279282
#191278632
#191278612
#191278462
#191278442
C2×C22⋊(C83⋊C8)2
#525×C832
#319183