Finite Group Databasebeta

← #24914500

Subgroups — #24914500

Order 10624.

552 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127637C211yesmaximal, characteristic, complemented
2#19127629C211yesmaximal, characteristic, complemented
3#19127629C211yesmaximal, characteristic, complemented
4#19127626C211yesmaximal, characteristic, complemented
5#19127624C211yesmaximal, characteristic, complemented
6#19127624C211yesmaximal, characteristic, complemented
7#19127595C211yesmaximal, characteristic, complemented
8#19127595C211yesmaximal, characteristic, complemented
9#19127594C211yesmaximal, characteristic, complemented
10#19127594C211yesmaximal, characteristic, complemented
11#19127589C211yesmaximal, characteristic, complemented
12#19127589C211yesmaximal, characteristic, complemented
13#19127557C211yesmaximal, characteristic
14#19127557C211yesmaximal, characteristic
15#379×C83C211yesmaximal, characteristic
16C2×C4⋊Dic83C2211yescharacteristic, complemented
17C2×C4⋊Dic83C2211yescharacteristic, complemented
18C2×Dic83⋊C4C2211yescharacteristic, complemented
19C2×Dic83⋊C4C2211yescharacteristic, complemented
20C2×Dic83⋊C4C2211yescharacteristic, complemented
21C2×Dic83⋊C4C2211yescharacteristic, complemented
22C2×C22⋊Dic83C2211yescharacteristic
23C2×C22⋊Dic83C2211yescharacteristic
24C2×C22⋊Dic83C2211yescharacteristic
25C2×C22⋊Dic83C2211yescharacteristic
26C2×C22⋊Dic83C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C2×C22⋊Dic83C2211yescharacteristic
31C2×C22⋊Dic83C2211yescharacteristic
32C2×C22⋊Dic83C2211yescharacteristic
33C2×C22⋊Dic83C2211yescharacteristic
34C2×C4×Dic83C2211yescharacteristic, complemented
35C2×C4×Dic83C2211yescharacteristic, complemented
36C83⋊#95C2211yescharacteristic, complemented
37C83⋊#95C2211yescharacteristic, complemented
38C83⋊#95C2211yescharacteristic, complemented
39C83⋊#95C2211yescharacteristic, complemented
40C83⋊#95C2211yescharacteristic, complemented
41C83⋊#95C2211yescharacteristic, complemented
42C83⋊#95C2211yescharacteristic, complemented
43C83⋊#95C2211yescharacteristic, complemented
44C25×C83C2211yescharacteristic
45C2×C22⋊C4×C83C2211yescharacteristic
46C2×C22⋊C4×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48C2×C22⋊C4×C83C2211yescharacteristic
49C2×C22⋊C4×C83C2211yescharacteristic
50C2×C22⋊C4×C83C2211yescharacteristic
51C22×Dic83C2311yescharacteristic
52C22×Dic83C2311yescharacteristic
53C22×Dic83C2311yescharacteristic
54C22×Dic83C2311yescharacteristic
55C22×Dic83C2311yescharacteristic
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C4⋊Dic83—41no—
60C4⋊Dic83—41no—
61Dic83⋊C4—41no—
62Dic83⋊C4—41no—
63Dic83⋊C4—41no—
64Dic83⋊C4—41no—
65C22⋊Dic83—22no—
66C22⋊Dic83—22no—
67C22⋊Dic83—22no—
68C22⋊Dic83—22no—
69C22⋊Dic83—41no—
70C22⋊Dic83—41no—
71C22⋊Dic83—41no—
72C22⋊Dic83—41no—
73C22⋊Dic83—41no—
74C22⋊Dic83—41no—
75C22⋊Dic83—41no—
76C22⋊Dic83—41no—
77C4×Dic83—41no—
78C4×Dic83—41no—
79C24×C83—22no—
80C24×C83—22no—
81C24×C83—22no—
82C24×C83—41no—
83C24×C83—41no—
84C24×C83—41no—
85C24×C83—41no—
86C24×C83C2311yescharacteristic
87C24×C83C2311yescharacteristic
88C24×C83C2311yescharacteristic
89C22×C4×C83C2311yescharacteristic
90C22×C4×C83C2311yescharacteristic
91C22×C4×C83C2311yescharacteristic
92C22×C4×C83C2311yescharacteristic
93C22⋊C4×C83—22no—
94C22⋊C4×C83—22no—
95C22⋊C4×C83—41no—
96C22⋊C4×C83—41no—
97C22⋊C4×C83—41no—
98C22⋊C4×C83—41no—
99C23×C83—21no—
100C23×C83—21no—
101C23×C83—21no—
102C23×C83—21no—
103C23×C83—21no—
104C23×C83—21no—
105C23×C83—21no—
106C23×C83—21no—
107C23×C83—21no—
108C23×C83—21no—
109C23×C83—21no—
110C23×C83—21no—
111C23×C83—21no—
112C23×C83—21no—
113C23×C83—21no—
114C23×C83—21no—
115C23×C83—21no—
116C23×C83—21no—
117C23×C83—44no—
118C23×C83—44no—
119C23×C83—44no—
120C23×C83—44no—
121C23×C83—44no—
122C23×C83—44no—
123C23×C83—44no—
124C23×C83#4112yes—
125C23×C83#4112yes—
126C23×C83#4112yes—
127C23×C83C2411yescharacteristic
128C2×C4×C83—21no—
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—21no—
139C2×C4×C83—21no—
140C2×Dic83—21no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83—21no—
144C2×Dic83—21no—
145C2×Dic83—21no—
146C2×Dic83—21no—
147C2×Dic83—21no—
148C2×Dic83—21no—
149C2×Dic83—21no—
150C2×Dic83—21no—
151C2×Dic83—21no—
152C2×Dic83—21no—
153C2×Dic83—21no—
154C2×Dic83—21no—
155C2×Dic83—21no—
156C2×Dic83—21no—
157C2×Dic83—21no—
158C2×Dic83—21no—
159C2×Dic83—21no—
160C2×Dic83—21no—
161C2×Dic83—21no—
162C2×Dic83—21no—
163C2×Dic83—21no—
164C22×C83—22no—
165C22×C83—22no—
166C22×C83—22no—
167C22×C83—22no—
168C22×C83—22no—
169C22×C83—22no—
170C22×C83—22no—
171C22×C83—22no—
172C22×C83—22no—
173C22×C83—416no—
174C22×C83—41no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83—41no—
179C22×C83—41no—
180C22×C83—41no—
181C22×C83—41no—
182C22×C83—41no—
183C22×C83—41no—
184C22×C83—41no—
185C22×C83—41no—
186C22×C83C2×#4111yescharacteristic
187C22×C83C2×#4111yescharacteristic
188C22×C83C2×#4111yescharacteristic
189C22×C83H(5,𝔽2)11yescharacteristic
190C22×C83H(5,𝔽2)11yescharacteristic
191C22×C83H(5,𝔽2)11yescharacteristic
192C22×C83H(5,𝔽2)11yescharacteristic
193C4×C83—41no—
194C4×C83—41no—
195C4×C83—41no—
196C4×C83—41no—
197Dic83—41no—
198Dic83—41no—
199Dic83—41no—
200Dic83—41no—
201Dic83—41no—
202Dic83—41no—
203Dic83—41no—
204Dic83—41no—
205C2×C83—42no—
206C2×C83—42no—
207C2×C83—42no—
208C2×C83#53811yescharacteristic
209C2×C83#53811yescharacteristic
210C2×C83#53811yescharacteristic
211C2×C83#55111yescharacteristic
212C2×C83#55111yescharacteristic
213C2×C83#55111yescharacteristic
214C2×C83#56011yescharacteristic
215#2735—831nomaximal, Sylow
216C83#273511yescharacteristic, complemented, Sylow
217#399—831no—
218#397—831no—
219#397—831no—
220#397—831no—
221#396—831no—
222#396—831no—
223#388—831no—
224#388—831no—
225#388—831no—
226#388—831no—
227#388—831no—
228#388—831no—
229#379—831no—
230#379—831no—
231#379D8311yescharacteristic
232C25C2×D8311yescharacteristic
233C2×C4⋊C4—831no—
234C2×C4⋊C4—831no—
235C2×C4⋊C4—831no—
236C2×C4⋊C4—831no—
237C2×C4⋊C4—831no—
238C2×C4⋊C4—831no—
239C2×C22⋊C4—831no—
240C2×C22⋊C4—831no—
241C2×C22⋊C4—831no—
242C2×C22⋊C4—831no—
243C2×C22⋊C4—831no—
244C2×C22⋊C4—831no—
245C2×C22⋊C4—831no—
246C2×C22⋊C4—831no—
247C2×C22⋊C4—831no—
248C2×C22⋊C4—831no—
249C2×C22⋊C4—831no—
250C2×C22⋊C4—831no—
251C2×C22⋊C4C2×D8311yescharacteristic
252C2×C22⋊C4C2×D8311yescharacteristic
253C2×C22⋊C4C2×D8311yescharacteristic
254C2×C22⋊C4C2×D8311yescharacteristic
255C2×C22⋊C4C2×D8311yescharacteristic
256C2×C22⋊C4C2×D8311yescharacteristic
257C2×C42—831no—
258C2×C42—831no—
259#95—831no—
260#95—831no—
261#95—831no—
262#95—831no—
263#95—831no—
264#95—831no—
265#95—831no—
266#95—831no—
267C24—22no—
268C24—22no—
269C24—22no—
270C24—41no—
271C24—41no—
272C24—41no—
273C24—41no—
274C24C22×D8311yescharacteristic
275C24C22×D8311yescharacteristic
276C24C22×D8311yescharacteristic
277C22×C4—831no—
278C22×C4—831no—
279C22×C4—831no—
280C22×C4—831no—
281C22×C4—831no—
282C22×C4—831no—
283C22×C4—831no—
284C22×C4—831no—
285C22×C4C22×D8311yescharacteristic
286C22×C4C22×D8311yescharacteristic
287C22×C4C22×D8311yescharacteristic
288C22×C4C22×D8311yescharacteristic
289C4⋊C4—3321no—
290C4⋊C4—3321no—
291C4⋊C4—3321no—
292C4⋊C4—3321no—
293C4⋊C4—3321no—
294C4⋊C4—3321no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—3321no—
302C22⋊C4—3321no—
303C22⋊C4—3321no—
304C22⋊C4—3321no—
305C22⋊C4—3321no—
306C22⋊C4—3321no—
307C22⋊C4—3321no—
308C22⋊C4—3321no—
309C22⋊C4—1662no—
310C22⋊C4—1662no—
311C22⋊C4—1662no—
312C22⋊C4—1662no—
313C42—3321no—
314C42—3321no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—44no—
334C23—44no—
335C23—44no—
336C23—44no—
337C23—44no—
338C23—44no—
339C23—44no—
340C23#1305058912yes—
341C23#1305058912yes—
342C23#1305059012yes—
343C23C23×D8311yescharacteristic
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
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—21no—
356C2×C4—1661no—
357C2×C4—1661no—
358C2×C4—1661no—
359C2×C4—1661no—
360C2×C4—1661no—
361C2×C4—1661no—
362C2×C4—1661no—
363C2×C4—1661no—
364C2×C4—1661no—
365C2×C4—1661no—
366C2×C4—1661no—
367C2×C4—1661no—
368C2×C4—1661no—
369C2×C4—1661no—
370C2×C4—1661no—
371C2×C4—1661no—
372C2×C4—1661no—
373C2×C4—1661no—
374C2×C4—1661no—
375C2×C4—1661no—
376C2×C4—1661no—
377C2×C4—1661no—
378C2×C4—1661no—
379C2×C4—1661no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—22no—
389C22—416no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22C2×#1305058911yescharacteristic
403C22C2×#1305058911yescharacteristic
404C22C2×#1305059011yescharacteristic
405C22#1458183711yescharacteristic
406C22#1458183711yescharacteristic
407C22#1458183711yescharacteristic
408C22#1458183711yescharacteristic
409C4—41no—
410C4—41no—
411C4—41no—
412C4—41no—
413C4—3321no—
414C4—3321no—
415C4—3321no—
416C4—3321no—
417C4—3321no—
418C4—3321no—
419C4—3321no—
420C4—3321no—
421C2—42no—
422C2—42no—
423C2—42no—
424C2#1912828611yescharacteristic
425C2#1912828611yescharacteristic
426C2#1912828911yescharacteristic
427C2#1912837711yescharacteristic
428C2#1912837711yescharacteristic
429C2#1912838211yescharacteristic
430C2#1912844011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#379×C83C2
prime radicalC25×C83C22
hypercenter#379D83
hypocenterC83#2735
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #19127637C2semidirect
2. #19127629C2semidirect
3. #19127629C2semidirect
4. #19127626C2semidirect
5. #19127624C2semidirect
6. #19127624C2semidirect
7. #19127595C2semidirect
8. #19127595C2semidirect
9. #19127594C2semidirect
10. #19127594C2semidirect
11. #19127589C2semidirect
12. #19127589C2semidirect
16. C2×C4⋊Dic83C22semidirect
17. C2×C4⋊Dic83C22semidirect
18. C2×Dic83⋊C4C22semidirect
19. C2×Dic83⋊C4C22semidirect
20. C2×Dic83⋊C4C22semidirect
21. C2×Dic83⋊C4C22semidirect
34. C2×C4×Dic83C22semidirect
35. C2×C4×Dic83C22semidirect
36. C83⋊#95C22semidirect
37. C83⋊#95C22semidirect
38. C83⋊#95C22semidirect
39. C83⋊#95C22semidirect
40. C83⋊#95C22semidirect
41. C83⋊#95C22semidirect
42. C83⋊#95C22semidirect
43. C83⋊#95C22semidirect
216. C83#2735semidirect

Maximal subgroups

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

subgroupindex
#191276372
#191276292
#191276262
#191276242
#191275952
#191275942
#191275892
#191275572
#379×C832
#273583