Finite Group Databasebeta

← #24915269

Subgroups — #24915269

Order 10624.

378 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127642C211yesmaximal, characteristic, complemented
2#19127631C211yesmaximal, characteristic, complemented
3#19127629C211yesmaximal, characteristic
4#19127629C211yesmaximal, characteristic
5#19127624C211yesmaximal, characteristic
6#19127624C211yesmaximal, characteristic
7#19127595C211yesmaximal, characteristic
8#19127589C211yesmaximal, characteristic
9#19127588C211yesmaximal, characteristic, complemented
10#19127588C211yesmaximal, characteristic, complemented
11#19127585C211yesmaximal, characteristic, complemented
12#19127585C211yesmaximal, characteristic, complemented
13#19127583C211yesmaximal, characteristic, complemented
14#19127570C211yesmaximal, characteristic, complemented
15#388×C83C211yesmaximal, characteristic
16C2×C4⋊Dic83C2211yescharacteristic
17C2×C4⋊Dic83C2211yescharacteristic
18C2×Dic83⋊C4C2211yescharacteristic
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×Dic83⋊C4C2211yescharacteristic
26C2×C22⋊Dic83C2211yescharacteristic
27C2×C22⋊Dic83C2211yescharacteristic
28C2×C22⋊Dic83C2211yescharacteristic
29C2×C22⋊Dic83C2211yescharacteristic
30C2×C4×Dic83C2211yescharacteristic
31C2×C4×Dic83C2211yescharacteristic
32C83⋊#95C2211yescharacteristic
33C83⋊#95C2211yescharacteristic
34C83⋊#95C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C2×C4⋊C4×C83C2211yescharacteristic
45C2×C22⋊C4×C83C2211yescharacteristic
46C2×C22⋊C4×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48C2×C42×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×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—22no—
62Dic83⋊C4—22no—
63Dic83⋊C4—22no—
64Dic83⋊C4—22no—
65Dic83⋊C4—22no—
66Dic83⋊C4—41no—
67Dic83⋊C4—41no—
68Dic83⋊C4—41no—
69C22⋊Dic83—22no—
70C22⋊Dic83—22no—
71C22⋊Dic83—41no—
72C22⋊Dic83—41no—
73C4×Dic83—22no—
74C4×Dic83—41no—
75C24×C83C2311yescharacteristic
76C22×C4×C83C2311yescharacteristic
77C22×C4×C83C2311yescharacteristic
78C22×C4×C83C2311yescharacteristic
79C22×C4×C83C2311yescharacteristic
80C22×C4×C83C2311yescharacteristic
81C22×C4×C83C2311yescharacteristic
82C4⋊C4×C83—41no—
83C22⋊C4×C83—22no—
84C22⋊C4×C83—41no—
85C22⋊C4×C83—41no—
86C42×C83—41no—
87C23×C83—21no—
88C23×C83—21no—
89C23×C83—21no—
90C23×C83—21no—
91C23×C83—21no—
92C23×C83—21no—
93C23×C83—21no—
94C23×C83C2411yescharacteristic
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83#4112yes—
113C2×Dic83—21no—
114C2×Dic83—21no—
115C2×Dic83—21no—
116C2×Dic83—21no—
117C2×Dic83—21no—
118C2×Dic83—21no—
119C2×Dic83—21no—
120C2×Dic83—21no—
121C2×Dic83—21no—
122C2×Dic83—21no—
123C2×Dic83—21no—
124C2×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—21no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83—21no—
133C2×Dic83—21no—
134C2×Dic83—21no—
135C2×Dic83#4112yes—
136C2×Dic83#4112yes—
137C22×C83—41no—
138C22×C83—41no—
139C22×C83—41no—
140C22×C83—41no—
141C22×C83—41no—
142C22×C83—41no—
143C22×C83—41no—
144C22×C83C2×#4111yescharacteristic
145C22×C83C2×#4111yescharacteristic
146C22×C83C2×#4111yescharacteristic
147C22×C83H(5,𝔽2)11yescharacteristic
148C22×C83H(5,𝔽2)11yescharacteristic
149C22×C832−1+411yescharacteristic
150C22×C832−1+411yescharacteristic
151C4×C83—22no—
152C4×C83—41no—
153C4×C83—41no—
154C4×C83—41no—
155C4×C83—41no—
156C4×C83—41no—
157Dic83—22no—
158Dic83—22no—
159Dic83—41no—
160Dic83—41no—
161Dic83—41no—
162Dic83—41no—
163Dic83—41no—
164Dic83—41no—
165C2×C83—81no—
166C2×C83#53911yescharacteristic
167C2×C83#54011yescharacteristic
168C2×C83#54211yescharacteristic
169C2×C83#55211yescharacteristic
170C2×C83#55311yescharacteristic
171C2×C83#55611yescharacteristic
172C2×C83#56311yescharacteristic
173#2793—831nomaximal, Sylow
174C83#279311yescharacteristic, complemented, Sylow
175#400—831no—
176#398—831no—
177#397—831no—
178#397—831no—
179#396—831no—
180#396—831no—
181#388—831no—
182#388—831no—
183#388D8311yescharacteristic
184#387—831no—
185#387—831no—
186#387—831no—
187#387—831no—
188#387—831no—
189#384—831no—
190C2×C4⋊C4—831no—
191C2×C4⋊C4—831no—
192C2×C4⋊C4—831no—
193C2×C4⋊C4—831no—
194C2×C4⋊C4—831no—
195C2×C4⋊C4—831no—
196C2×C4⋊C4—831no—
197C2×C4⋊C4—831no—
198C2×C4⋊C4—831no—
199C2×C4⋊C4—831no—
200C2×C4⋊C4C2×D8311yescharacteristic
201C2×C22⋊C4—831no—
202C2×C22⋊C4—831no—
203C2×C22⋊C4—831no—
204C2×C22⋊C4—831no—
205C2×C22⋊C4C2×D8311yescharacteristic
206C2×C22⋊C4C2×D8311yescharacteristic
207C2×C22⋊C4C2×D8311yescharacteristic
208C2×C42—831no—
209C2×C42—831no—
210C2×C42C2×D8311yescharacteristic
211#95—831no—
212#95—831no—
213#95—831no—
214#95—831no—
215#95—831no—
216#95—831no—
217#95—831no—
218#95—831no—
219#95—831no—
220#95—831no—
221#95—831no—
222#95—831no—
223#95C2×D8311yescharacteristic
224#95C2×D8311yescharacteristic
225C24C22×D8311yescharacteristic
226C22×C4—831no—
227C22×C4—831no—
228C22×C4—831no—
229C22×C4—831no—
230C22×C4—831no—
231C22×C4—831no—
232C22×C4—831no—
233C22×C4—831no—
234C22×C4C22×D8311yescharacteristic
235C22×C4C22×D8311yescharacteristic
236C22×C4C22×D8311yescharacteristic
237C22×C4C22×D8311yescharacteristic
238C22×C4C22×D8311yescharacteristic
239C22×C4C22×D8311yescharacteristic
240C4⋊C4—41no—
241C4⋊C4—3321no—
242C4⋊C4—3321no—
243C4⋊C4—3321no—
244C4⋊C4—3321no—
245C4⋊C4—3321no—
246C4⋊C4—1662no—
247C4⋊C4—1662no—
248C4⋊C4—1662no—
249C4⋊C4—1662no—
250C4⋊C4—1662no—
251C22⋊C4—22no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—3321no—
255C22⋊C4—3321no—
256C22⋊C4—1662no—
257C22⋊C4—1662no—
258C42—41no—
259C42—3321no—
260C42—1662no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23C23×D8311yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—832no—
287C2×C4—832no—
288C2×C4—1661no—
289C2×C4—1661no—
290C2×C4—1661no—
291C2×C4—1661no—
292C2×C4—1661no—
293C2×C4—1661no—
294C2×C4—1661no—
295C2×C4—1661no—
296C2×C4—1661no—
297C2×C4—1661no—
298C2×C4—1661no—
299C2×C4—1661no—
300C2×C4—1661no—
301C2×C4—1661no—
302C2×C4—1661no—
303C2×C4—1661no—
304C2×C4—1661no—
305C2×C4—1661no—
306C2×C4—1661no—
307C2×C4—1661no—
308C2×C4—1661no—
309C2×C4—1661no—
310C2×C4#1305059012yes—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#41×D8311yescharacteristic
319C22#41×D8311yescharacteristic
320C22C2×#1305059011yescharacteristic
321C22#1458183711yescharacteristic
322C22#1458183711yescharacteristic
323C22#1458183911yescharacteristic
324C22#1458183911yescharacteristic
325C4—22no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—3321no—
332C4—3321no—
333C4—3321no—
334C4—3321no—
335C4—3321no—
336C4—3321no—
337C4—1662no—
338C4—1662no—
339C2—81no—
340C2#1912829411yescharacteristic
341C2#1912830111yescharacteristic
342C2#1912831611yescharacteristic
343C2#1912838711yescharacteristic
344C2#1912840011yescharacteristic
345C2#1912841911yescharacteristic
346C2#1912845111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#388×C83C2
prime radicalC24×C83C23
hypercenter#388D83
hypocenterC83#2793
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #19127642C2semidirect
2. #19127631C2semidirect
9. #19127588C2semidirect
10. #19127588C2semidirect
11. #19127585C2semidirect
12. #19127585C2semidirect
13. #19127583C2semidirect
14. #19127570C2semidirect
174. C83#2793semidirect

Maximal subgroups

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

subgroupindex
#191276422
#191276312
#191276292
#191276242
#191275952
#191275892
#191275882
#191275852
#191275832
#191275702
#388×C832
#279383