Finite Group Databasebeta

← #24918315

Subgroups — #24918315

Order 10624.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128279C211yesmaximal, characteristic, complemented
2#19128042C211yesmaximal, characteristic, complemented
3#19128025C211yesmaximal, characteristic, complemented
4#19128017C211yesmaximal, characteristic, complemented
5#19128012C211yesmaximal, characteristic, complemented
6#19127952C211yesmaximal, characteristic, complemented
7#19127945C211yesmaximal, characteristic, complemented
8#19127935C211yesmaximal, characteristic, complemented
9#19127928C211yesmaximal, characteristic, complemented
10#19127852C211yesmaximal, characteristic, complemented
11#19127844C211yesmaximal, characteristic, complemented
12#19127844C211yesmaximal, characteristic, complemented
13#19127835C211yesmaximal, characteristic, complemented
14#19127668C211yesmaximal, characteristic, complemented
15#535×C83C211yesmaximal, characteristic, complemented
16C2×#13050590C2211yescharacteristic, complemented
17C2×#13050578C2211yescharacteristic
18C2×#13050578C2211yescharacteristic
19C2×#13050575C2211yescharacteristic
20C2×#13050575C2211yescharacteristic
21C2×#13050574C2211yescharacteristic, complemented
22C22×C83⋊C8C2211yescharacteristic, complemented
23#14581771C2211yescharacteristic
24#14581771C2211yescharacteristic, complemented
25#14581768—21no—
26#14581766C2211yescharacteristic
27#14581766C2211yescharacteristic, complemented
28#14581764—21no—
29#14581764—21no—
30#14581763—21no—
31C2×C4⋊Dic83C2211yescharacteristic, complemented
32#14581725C2211yescharacteristic, complemented
33#14581725C2211yescharacteristic, complemented
34#14581723C2211yescharacteristic, complemented
35#14581723C2211yescharacteristic, complemented
36#14581715C2211yescharacteristic, complemented
37#14581715C2211yescharacteristic, complemented
38#14581713C2211yescharacteristic
39#14581713C2211yescharacteristic
40#14581713C2211yescharacteristic
41#14581713C2211yescharacteristic
42#14581712C2211yescharacteristic, complemented
43#14581712C2211yescharacteristic, complemented
44C22⋊(C83⋊C8)C2211yescharacteristic
45C22⋊(C83⋊C8)C2211yescharacteristic
46C22⋊(C83⋊C8)C2211yescharacteristic, complemented
47C22⋊(C83⋊C8)C2211yescharacteristic, complemented
48C2×#41×C83C2211yescharacteristic
49C22×D4×C83C2211yescharacteristic
50#127×C83—21no—
51#124×C83—21no—
52#121×C83C2211yescharacteristic
53#121×C83C2211yescharacteristic
54#121×C83C2211yescharacteristic
55#121×C83C2211yescharacteristic
56#120×C83—21no—
57#120×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—
66C22×Dic83—21no—
67C2×C4×D83—21no—
68#13050578—41no—
69#13050578—41no—
70#13050575—41no—
71#13050575—41no—
72#13050574—41no—
73C2×C83⋊C8—41no—
74C2×C83⋊C8C2311yescharacteristic
75C2×C83⋊C8C2311yescharacteristic
76C2×C83⋊C8C2311yescharacteristic
77C2×C83⋊C8C2311yescharacteristic
78C4⋊Dic83—21no—
79C4⋊Dic83C2311yescharacteristic
80C4⋊Dic83C2311yescharacteristic
81Dic83⋊C4—21no—
82Dic83⋊C4—21no—
83C22⋊Dic83—21no—
84C22⋊Dic83—21no—
85(C2×D83)⋊C4—21no—
86(C2×D83)⋊C4—21no—
87C24×C83—21no—
88#41×C83—41no—
89#41×C83—41no—
90C2×Q8×C83D411yescharacteristic
91C2×D4×C83—21no—
92C2×D4×C83—21no—
93C2×D4×C83—21no—
94C2×D4×C83—21no—
95C2×D4×C83—21no—
96C2×D4×C83—41no—
97C2×D4×C83—41no—
98C2×D4×C83D411yescharacteristic
99C2×D4×C83D411yescharacteristic
100C2×D4×C83D411yescharacteristic
101C2×D4×C83C2311yescharacteristic
102C2×D4×C83C2311yescharacteristic
103C22×C4×C83C2311yescharacteristic
104C22×C4×C83C2311yescharacteristic
105C22×C4×C83C2311yescharacteristic
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—21no—
115C23×C83—21no—
116C23×C83—42no—
117C23×C83—81no—
118C23×C83—81no—
119C23×C83C2×D411yescharacteristic
120C23×C83C2×D411yescharacteristic
121C23×C83C2×D411yescharacteristic
122C22×D83—21no—
123Q8×C83—41no—
124D4×C83—21no—
125D4×C83—21no—
126D4×C83—21no—
127D4×C83—21no—
128D4×C83—41no—
129D4×C83—41no—
130D4×C83—41no—
131D4×C83—42no—
132D4×C83—81no—
133D4×C83—81no—
134D4×C83—81no—
135D4×C83—81no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—21no—
139C2×C4×C83—21no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—21no—
143C2×C4×C83—21no—
144C2×C4×C83C2×D411yescharacteristic
145C2×C4×C83C2×D411yescharacteristic
146C2×C4×C83C2×D411yescharacteristic
147C2×C4×C83C2411yescharacteristic
148C22⋊D83—42no—
149C22⋊D83—81no—
150C22⋊D83—81no—
151C2×Dic83—21no—
152C2×Dic83—21no—
153C2×Dic83—21no—
154C2×Dic83—81no—
155D332—21no—
156D332—21no—
157C4×D83—42no—
158Dic166—21no—
159Dic166—21no—
160C83⋊C8—21no—
161C83⋊C8—21no—
162C83⋊C8—21no—
163C83⋊C8—21no—
164C22×C83—21no—
165C22×C83—21no—
166C22×C83—21no—
167C22×C83—21no—
168C22×C83—21no—
169C22×C83—21no—
170C22×C83—21no—
171C22×C83—21no—
172C22×C83—21no—
173C22×C83—41no—
174C22×C83—41no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83—41no—
179C22×C83—84no—
180C22×C83C22×D411yescharacteristic
181C2×D83—41no—
182C2×D83—41no—
183C2×D83—41no—
184C4×C83—21no—
185C4×C83—21no—
186C4×C83—21no—
187C4×C83—41no—
188C4×C83—41no—
189C4×C83H(5,𝔽2)11yescharacteristic
190C4×C83H(5,𝔽2)11yescharacteristic
191Dic83—41no—
192Dic83—41no—
193Dic83—41no—
194C2×C83—41no—
195C2×C83—41no—
196C2×C83—41no—
197C2×C83—81no—
198C2×C83—81no—
199C2×C83#53411yescharacteristic
200C2×C83#57611yescharacteristic
201C2×C83#57711yescharacteristic
202D83—81no—
203#3198—831nomaximal, Sylow
204C83#319811yescharacteristic, complemented, Sylow
205#537—831no—
206#535D8311yescharacteristic, complemented
207#485—831no—
208#482—831no—
209#481—831no—
210#480—831no—
211#469—831no—
212#468—831no—
213#466—831no—
214#465—831no—
215#450—831no—
216#449—831no—
217#449—831no—
218#447—831no—
219#408—831no—
220C2×#41—831no—
221C2×#41C2×D8311yescharacteristic
222C22×D4C2×D8311yescharacteristic
223C2×SD16—831no—
224C2×SD16—831no—
225C2×D8—831no—
226C2×D8—831no—
227C2×M16—831no—
228C22×C8—831no—
229#127—21no—
230#124—21no—
231C22⋊Q8—831no—
232C22⋊Q8—831no—
233C22⋊Q8—1661no—
234#121—831no—
235#121—831no—
236#121—1661no—
237#121—1661no—
238#121—1661no—
239#121C2×D8311yescharacteristic
240#121C2×D8311yescharacteristic
241#121C2×D8311yescharacteristic
242#121C2×D8311yescharacteristic
243#120—21no—
244#120—21no—
245#117C2×D8311yescharacteristic
246C2×C4⋊C4—831no—
247#107—831no—
248#107—831no—
249#106—831no—
250#106—831no—
251#103—831no—
252#103—831no—
253#102—831no—
254#102—831no—
255#102—831no—
256#102—831no—
257#102—831no—
258#102—831no—
259C22⋊C8—831no—
260C22⋊C8—831no—
261C22⋊C8—831no—
262C22⋊C8—831no—
263C24—21no—
264#41—41no—
265#41—41no—
266#41—3321no—
267#41—3321no—
268C2×Q8—831no—
269C2×Q8C22⋊D8311yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—831no—
278C2×D4—1661no—
279C2×D4—1661no—
280C2×D4—1661no—
281C2×D4C22⋊D8311yescharacteristic
282C2×D4C22⋊D8311yescharacteristic
283C2×D4C22⋊D8311yescharacteristic
284C2×D4C22×D8311yescharacteristic
285C2×D4C22×D8311yescharacteristic
286C22×C4—1661no—
287C22×C4—1661no—
288C22×C4C22×D8311yescharacteristic
289C22×C4C22×D8311yescharacteristic
290C22×C4C22×D8311yescharacteristic
291SD16—3321no—
292SD16—3321no—
293D8—3321no—
294D8—3321no—
295M16—3321no—
296C2×C8—3321no—
297C2×C8—831no—
298C2×C8—831no—
299C2×C8—831no—
300C2×C8—831no—
301C4⋊C4—831no—
302C4⋊C4—831no—
303C4⋊C4—1661no—
304C4⋊C4—1661no—
305C4⋊C4—1661no—
306C4⋊C4C22×D8311yescharacteristic
307C4⋊C4C22×D8311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—1661no—
314C22⋊C4—1661no—
315C22⋊C4—1661no—
316C22⋊C4—1661no—
317C42—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—1661no—
324C23C2×C22⋊D8311yescharacteristic
325C23C2×C22⋊D8311yescharacteristic
326C23C2×C22⋊D8311yescharacteristic
327Q8—41no—
328Q8—1661no—
329Q8—1661no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—3322no—
343D4—6641no—
344D4—6641no—
345D4—1661no—
346D4—1661no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—3322no—
356C2×C4—6641no—
357C2×C4—1661no—
358C2×C4—1661no—
359C2×C4—1661no—
360C2×C4C2×C22⋊D8311yescharacteristic
361C2×C4C2×C22⋊D8311yescharacteristic
362C2×C4C2×C22⋊D8311yescharacteristic
363C2×C4C23×D8311yescharacteristic
364C8—1661no—
365C8—1661no—
366C8—1661no—
367C8—1661no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—84no—
384C22—3321no—
385C22—3321no—
386C22—3321no—
387C22C22×C22⋊D8311yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—3321no—
394C4—3321no—
395C4—3321no—
396C4#1458183711yescharacteristic
397C4#1458183711yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—81no—
403C2—6641no—
404C2#1912826011yescharacteristic
405C2#1912850411yescharacteristic
406C2#1912851211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#535×C83C2
socleC22×C83C22×D4
hypercenter#535D83
hypocenterC83#3198
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #19128279C2semidirect
2. #19128042C2semidirect
3. #19128025C2semidirect
4. #19128017C2semidirect
5. #19128012C2semidirect
6. #19127952C2semidirect
7. #19127945C2semidirect
8. #19127935C2semidirect
9. #19127928C2semidirect
10. #19127852C2semidirect
11. #19127844C2semidirect
12. #19127844C2semidirect
13. #19127835C2semidirect
14. #19127668C2semidirect
15. #535×C83C2semidirect
16. C2×#13050590C22semidirect
21. C2×#13050574C22semidirect
22. C22×C83⋊C8C22semidirect
24. #14581771C22semidirect
27. #14581766C22semidirect
31. C2×C4⋊Dic83C22semidirect
32. #14581725C22semidirect
33. #14581725C22semidirect
34. #14581723C22semidirect
35. #14581723C22semidirect
36. #14581715C22semidirect
37. #14581715C22semidirect
42. #14581712C22semidirect
43. #14581712C22semidirect
46. C22⋊(C83⋊C8)C22semidirect
47. C22⋊(C83⋊C8)C22semidirect
204. C83#3198semidirect
206. #535D83semidirect

Maximal subgroups

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

subgroupindex
#191282792
#191280422
#191280252
#191280172
#191280122
#191279522
#191279452
#191279352
#191279282
#191278522
#191278442
#191278352
#191276682
#535×C832
#319883