Finite Group Databasebeta

← #24914527

Subgroups — #24914527

Order 10624.

392 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127643C211yesmaximal, characteristic, complemented
2#19127641C211yesmaximal, characteristic, complemented
3#19127637C211yesmaximal, characteristic
4#19127634C211yesmaximal, characteristic, complemented
5#19127632C211yesmaximal, characteristic, complemented
6#19127629C211yesmaximal, characteristic
7#19127599C211yesmaximal, characteristic, complemented
8#19127589C211yesmaximal, characteristic
9#19127584C211yesmaximal, characteristic, complemented
10#19127583C211yesmaximal, characteristic, complemented
11#19127576C211yesmaximal, characteristic
12#19127569C211yesmaximal, characteristic, complemented
13#19127562C211yesmaximal, characteristic
14#19127559C211yesmaximal, characteristic
15#388×C83C211yesmaximal, characteristic
16C23×Dic83C2211yescharacteristic
17C2×C4⋊Dic83C2211yescharacteristic
18C2×C4⋊Dic83C2211yescharacteristic
19C2×C4⋊Dic83C2211yescharacteristic
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×C4×Dic83C2211yescharacteristic
30C83⋊#95C2211yescharacteristic
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
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×Dic83—22no—
52C22×Dic83—22no—
53C22×Dic83—41no—
54C22×Dic83C2311yescharacteristic
55C22×Dic83C2311yescharacteristic
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C4⋊Dic83—22no—
63C4⋊Dic83—22no—
64C4⋊Dic83—41no—
65Dic83⋊C4—22no—
66Dic83⋊C4—41no—
67Dic83⋊C4—41no—
68Dic83⋊C4—41no—
69Dic83⋊C4—41no—
70Dic83⋊C4—41no—
71C22⋊Dic83—22no—
72C22⋊Dic83—41no—
73C22⋊Dic83—41no—
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—22no—
85C22⋊C4×C83—41no—
86C42×C83—22no—
87C23×C83—21no—
88C23×C83—21no—
89C23×C83—21no—
90C23×C83—21no—
91C23×C83—21no—
92C23×C83—21no—
93C23×C83#4112yes—
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—21no—
136C2×Dic83—44no—
137C2×Dic83#4112yes—
138C22×C83—22no—
139C22×C83—22no—
140C22×C83—22no—
141C22×C83—41no—
142C22×C83—41no—
143C22×C83—41no—
144C22×C83—41no—
145C22×C83C2×#4111yescharacteristic
146C22×C83C2×#4111yescharacteristic
147C22×C83C2×#4111yescharacteristic
148C22×C83H(5,𝔽2)11yescharacteristic
149C22×C83H(5,𝔽2)11yescharacteristic
150C22×C832−1+411yescharacteristic
151C22×C832−1+411yescharacteristic
152C4×C83—22no—
153C4×C83—41no—
154C4×C83—41no—
155C4×C83—41no—
156C4×C83—41no—
157C4×C83—41no—
158Dic83—22no—
159Dic83—41no—
160Dic83—41no—
161Dic83—41no—
162Dic83—41no—
163Dic83—41no—
164Dic83—41no—
165Dic83—41no—
166C2×C83—42no—
167C2×C83#53911yescharacteristic
168C2×C83#54011yescharacteristic
169C2×C83#54211yescharacteristic
170C2×C83#55111yescharacteristic
171C2×C83#55211yescharacteristic
172C2×C83#55211yescharacteristic
173C2×C83#56311yescharacteristic
174#2738—831nomaximal, Sylow
175C83#273811yescharacteristic, complemented, Sylow
176#400—831no—
177#400—831no—
178#399—831no—
179#398—831no—
180#398—831no—
181#397—831no—
182#389—831no—
183#388—831no—
184#388D8311yescharacteristic
185#387—831no—
186#387—831no—
187#385—831no—
188#383—831no—
189#381—831no—
190#380—831no—
191C23×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⋊C4—831no—
201C2×C4⋊C4C2×D8311yescharacteristic
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×C42C2×D8311yescharacteristic
210#95—831no—
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#95—831no—
224#95C2×D8311yescharacteristic
225#95C2×D8311yescharacteristic
226C24C22×D8311yescharacteristic
227C22×C4—3321no—
228C22×C4—831no—
229C22×C4—831no—
230C22×C4—831no—
231C22×C4—831no—
232C22×C4—831no—
233C22×C4—831no—
234C22×C4—831no—
235C22×C4—831no—
236C22×C4—1662no—
237C22×C4—1662no—
238C22×C4C22×D8311yescharacteristic
239C22×C4C22×D8311yescharacteristic
240C22×C4C22×D8311yescharacteristic
241C22×C4C22×D8311yescharacteristic
242C22×C4C22×D8311yescharacteristic
243C22×C4C22×D8311yescharacteristic
244C4⋊C4—41no—
245C4⋊C4—3321no—
246C4⋊C4—3321no—
247C4⋊C4—3321no—
248C4⋊C4—3321no—
249C4⋊C4—3321no—
250C4⋊C4—3321no—
251C4⋊C4—1662no—
252C4⋊C4—1662no—
253C4⋊C4—1662no—
254C22⋊C4—22no—
255C22⋊C4—22no—
256C22⋊C4—41no—
257C22⋊C4—3321no—
258C22⋊C4—3321no—
259C22⋊C4—1662no—
260C42—22no—
261C42—3321no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#1305059012yes—
269C23C23×D8311yescharacteristic
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—21no—
287C2×C4—3324no—
288C2×C4—832no—
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—1661no—
311C2×C4—1661no—
312C2×C4#1305058912yes—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#41×D8311yescharacteristic
321C22C2×#1305058911yescharacteristic
322C22C2×#1305059011yescharacteristic
323C22#1458183711yescharacteristic
324C22#1458183811yescharacteristic
325C22#1458183911yescharacteristic
326C22#1458183911yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—3321no—
334C4—3321no—
335C4—3321no—
336C4—3321no—
337C4—3321no—
338C4—3321no—
339C4—3321no—
340C4—1662no—
341C2—42no—
342C2#1912829311yescharacteristic
343C2#1912830411yescharacteristic
344C2#1912831511yescharacteristic
345C2#1912837511yescharacteristic
346C2#1912838811yescharacteristic
347C2#1912839111yescharacteristic
348C2#1912845311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#388×C83C2
prime radicalC24×C83C23
hypercenter#388D83
hypocenterC83#2738
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #19127643C2semidirect
2. #19127641C2semidirect
4. #19127634C2semidirect
5. #19127632C2semidirect
7. #19127599C2semidirect
9. #19127584C2semidirect
10. #19127583C2semidirect
12. #19127569C2semidirect
175. C83#2738semidirect

Maximal subgroups

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

subgroupindex
#191276432
#191276412
#191276372
#191276342
#191276322
#191276292
#191275992
#191275892
#191275842
#191275832
#191275762
#191275692
#191275622
#191275592
#388×C832
#273883