Finite Group Databasebeta

← #24912708

Subgroups — #24912708

Order 10624.

476 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127643C211yesmaximal, characteristic, complemented
2#19127617C211yesmaximal, characteristic
3#19127612C211yesmaximal, characteristic, complemented
4#19127608C211yesmaximal, characteristic, complemented
5#19127595C211yesmaximal, characteristic, complemented
6#19127590C211yesmaximal, characteristic, complemented
7#19127578C211yesmaximal, characteristic
8#19127577C211yesmaximal, characteristic
9#19127568C211yesmaximal, characteristic, complemented
10#19127568C211yesmaximal, characteristic, complemented
11#19127563C211yesmaximal, characteristic, complemented
12#19127562C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic83C211yesmaximal, characteristic, complemented
14#19127548C211yesmaximal, characteristic, complemented
15#393×C83C211yesmaximal, characteristic, complemented
16C22×C22⋊D83C2211yescharacteristic
17C23×Dic83C2211yescharacteristic
18C22×C4×D83C2211yescharacteristic
19C2×C4⋊Dic83C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×C22⋊Dic83C2211yescharacteristic
22C2×C22⋊Dic83C2211yescharacteristic
23C2×(C2×D83)⋊C4C2211yescharacteristic
24C2×(C2×D83)⋊C4C2211yescharacteristic
25C2×(C2×D83)⋊C4C2211yescharacteristic
26C2×(C2×D83)⋊C4C2211yescharacteristic
27C2×(C2×D83)⋊C4C2211yescharacteristic
28C2×C4×Dic83C2211yescharacteristic
29C2×C4×Dic83C2211yescharacteristic
30C2×C4×Dic83C2211yescharacteristic
31C83⋊#95C2211yescharacteristic
32C83⋊#95C2211yescharacteristic
33C83⋊#95C2211yescharacteristic
34C83⋊#95C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C22×Q8×C83C2211yescharacteristic
45C2×C22⋊C4×C83C2211yescharacteristic
46C2×C22⋊C4×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48#95×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51C23×D83C2311yescharacteristic
52C2×C22⋊D83—22no—
53C2×C22⋊D83—22no—
54C2×C22⋊D83—41no—
55C22×Dic83—22no—
56C22×Dic83—22no—
57C22×Dic83—41no—
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C22×Dic83C2311yescharacteristic
63C22×Dic83C2311yescharacteristic
64C22×Dic83C2311yescharacteristic
65C2×C4×D83—22no—
66C2×C4×D83—22no—
67C2×C4×D83—41no—
68C4⋊Dic83—41no—
69Dic83⋊C4—41no—
70C22⋊Dic83—22no—
71C22⋊Dic83—22no—
72(C2×D83)⋊C4—22no—
73(C2×D83)⋊C4—22no—
74(C2×D83)⋊C4—22no—
75(C2×D83)⋊C4—41no—
76(C2×D83)⋊C4—41no—
77C4×Dic83—22no—
78C4×Dic83—22no—
79C4×Dic83—41no—
80C24×C83C2311yescharacteristic
81C2×Q8×C83—22no—
82C2×Q8×C83—41no—
83C2×Q8×C83—41no—
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C22×C4×C83C2311yescharacteristic
89C22×C4×C83C2311yescharacteristic
90C22⋊C4×C83—22no—
91C22⋊C4×C83—41no—
92C22⋊C4×C83—41no—
93C23×C83—21no—
94C23×C83—21no—
95C23×C83—21no—
96C23×C83—21no—
97C23×C83—21no—
98C23×C83—21no—
99C23×C83#4112yes—
100C23×C83C2411yescharacteristic
101C22×D83—21no—
102C22×D83—21no—
103C22×D83—21no—
104C22×D83—21no—
105C22×D83—21no—
106C22×D83—21no—
107C22×D83#4112yes—
108Q8×C83—44no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×C4×C83—21no—
117C2×C4×C83—21no—
118C2×C4×C83—21no—
119C2×C4×C83—21no—
120C2×C4×C83—21no—
121C2×C4×C83—21no—
122C2×C4×C83—21no—
123C2×C4×C83—21no—
124C2×C4×C83—21no—
125C2×C4×C83—21no—
126C2×C4×C83#4112yes—
127C22⋊D83—44no—
128C2×Dic83—21no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83—21no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83—21no—
136C2×Dic83—21no—
137C2×Dic83—21no—
138C2×Dic83—21no—
139C2×Dic83—21no—
140C2×Dic83—21no—
141C2×Dic83—21no—
142C2×Dic83—21no—
143C2×Dic83—21no—
144C2×Dic83—21no—
145C2×Dic83—21no—
146C2×Dic83—21no—
147C2×Dic83—44no—
148C2×Dic83#4112yes—
149C2×Dic83#4112yes—
150C4×D83—44no—
151C22×C83—22no—
152C22×C83—22no—
153C22×C83—22no—
154C22×C83—41no—
155C22×C83—41no—
156C22×C83—41no—
157C22×C83—41no—
158C22×C83C2×#4111yescharacteristic
159C22×C83C2×#4111yescharacteristic
160C22×C83C2×#4111yescharacteristic
161C22×C83C2×#4111yescharacteristic
162C22×C83C2×#4111yescharacteristic
163C22×C83H(5,𝔽2)11yescharacteristic
164C22×C83H(5,𝔽2)11yescharacteristic
165C2×D83—22no—
166C2×D83—22no—
167C2×D83—22no—
168C2×D83—41no—
169C2×D83—41no—
170C2×D83—41no—
171C2×D83—41no—
172C4×C83—22no—
173C4×C83—41no—
174C4×C83—41no—
175C4×C83—41no—
176C4×C83—41no—
177C4×C83—41no—
178Dic83—22no—
179Dic83—22no—
180Dic83—41no—
181Dic83—41no—
182Dic83—41no—
183Dic83—41no—
184Dic83—41no—
185C2×C83—42no—
186C2×C83#52911yescharacteristic
187C2×C83#52911yescharacteristic
188C2×C83#53811yescharacteristic
189C2×C83#55111yescharacteristic
190C2×C83#55111yescharacteristic
191C2×C83#55111yescharacteristic
192C2×C83#55511yescharacteristic
193D83—42no—
194#2572—831nomaximal, Sylow
195C83#257211yescharacteristic, complemented, Sylow
196#400—831no—
197#394—831no—
198#393—831no—
199#393D8311yescharacteristic, complemented
200#391—831no—
201#388—831no—
202#388—831no—
203#386—831no—
204#386—831no—
205#383—831no—
206#383—831no—
207#381—831no—
208#381—831no—
209C4×C22⋊C4—831no—
210C4×C22⋊C4—831no—
211C22×Q8C2×D8311yescharacteristic
212C22×D4—831no—
213C23×C4—831no—
214C23×C4—831no—
215C2×C4⋊C4—831no—
216C2×C4⋊C4—831no—
217C2×C22⋊C4—831no—
218C2×C22⋊C4—831no—
219C2×C22⋊C4—831no—
220C2×C22⋊C4—831no—
221C2×C22⋊C4—831no—
222C2×C22⋊C4—831no—
223C2×C22⋊C4—831no—
224C2×C22⋊C4C2×D8311yescharacteristic
225C2×C22⋊C4C2×D8311yescharacteristic
226C2×C22⋊C4C2×D8311yescharacteristic
227C2×C42—831no—
228C2×C42—831no—
229C2×C42—831no—
230#95—831no—
231#95—831no—
232#95—831no—
233#95—831no—
234#95—831no—
235#95—831no—
236#95—831no—
237#95—831no—
238#95—831no—
239#95—831no—
240#95—831no—
241#95—831no—
242#95—831no—
243#95C2×D8311yescharacteristic
244#95C2×D8311yescharacteristic
245#95C2×D8311yescharacteristic
246C24—831no—
247C24C22×D8311yescharacteristic
248C2×Q8—22no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×D4—3321no—
252C2×D4—1662no—
253C2×D4—1662no—
254C22×C4—3321no—
255C22×C4—3321no—
256C22×C4—831no—
257C22×C4—831no—
258C22×C4—831no—
259C22×C4—831no—
260C22×C4—831no—
261C22×C4—831no—
262C22×C4—831no—
263C22×C4—1662no—
264C22×C4—1662no—
265C22×C4—1662no—
266C22×C4—1662no—
267C22×C4C22×D8311yescharacteristic
268C22×C4C22×D8311yescharacteristic
269C22×C4C22×D8311yescharacteristic
270C22×C4C22×D8311yescharacteristic
271C22×C4C22×D8311yescharacteristic
272C22×C4C22×D8311yescharacteristic
273C4⋊C4—3321no—
274C4⋊C4—3321no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—3321no—
279C22⋊C4—3321no—
280C22⋊C4—1662no—
281C22⋊C4—1662no—
282C22⋊C4—1662no—
283C22⋊C4—1662no—
284C22⋊C4—1662no—
285C42—3321no—
286C42—1662no—
287C42—1662no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—832no—
295C23—1661no—
296C23—1661no—
297C23—1661no—
298C23—1661no—
299C23—1661no—
300C23—1661no—
301C23#1305059112yes—
302C23C23×D8311yescharacteristic
303Q8—44no—
304D4—3324no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—3324no—
323C2×C4—3324no—
324C2×C4—832no—
325C2×C4—832no—
326C2×C4—1661no—
327C2×C4—1661no—
328C2×C4—1661no—
329C2×C4—1661no—
330C2×C4—1661no—
331C2×C4—1661no—
332C2×C4—1661no—
333C2×C4—1661no—
334C2×C4—1661no—
335C2×C4—1661no—
336C2×C4—1661no—
337C2×C4—1661no—
338C2×C4—1661no—
339C2×C4—1661no—
340C2×C4—1661no—
341C2×C4—1661no—
342C2×C4—1661no—
343C2×C4—1661no—
344C2×C4—1661no—
345C2×C4#1305058912yes—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—3321no—
354C22—3321no—
355C22—3321no—
356C22—3321no—
357C22—1662no—
358C22—1662no—
359C22—1662no—
360C22#41×D8311yescharacteristic
361C22#41×D8311yescharacteristic
362C22#41×D8311yescharacteristic
363C22C2×#1305058911yescharacteristic
364C22C2×#1305059111yescharacteristic
365C22#1458183711yescharacteristic
366C22#1458183711yescharacteristic
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—3321no—
374C4—3321no—
375C4—3321no—
376C4—3321no—
377C4—3321no—
378C4—1662no—
379C4—1662no—
380C2—42no—
381C2—3322no—
382C2#1912823011yescharacteristic
383C2#1912823711yescharacteristic
384C2#1912828611yescharacteristic
385C2#1912837811yescharacteristic
386C2#1912837811yescharacteristic
387C2#1912838111yescharacteristic
388C2#1912841311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#393×C83C2
prime radicalC22×C22⋊D83C22
hypercenter#393D83
hypocenterC83#2572
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #19127643C2semidirect
3. #19127612C2semidirect
4. #19127608C2semidirect
5. #19127595C2semidirect
6. #19127590C2semidirect
9. #19127568C2semidirect
10. #19127568C2semidirect
11. #19127563C2semidirect
12. #19127562C2semidirect
13. C22⋊C4×Dic83C2semidirect
14. #19127548C2semidirect
15. #393×C83C2semidirect
195. C83#2572semidirect
199. #393D83semidirect

Maximal subgroups

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

subgroupindex
#191276432
#191276172
#191276122
#191276082
#191275952
#191275902
#191275782
#191275772
#191275682
#191275632
#191275622
C22⋊C4×Dic832
#191275482
#393×C832
#257283