Finite Group Databasebeta

← #24912883

Subgroups — #24912883

Order 10624.

428 conjugacy classes of subgroups.

The subgroup lattice has 358 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#19127624C211yesmaximal, characteristic
4#19127624C211yesmaximal, characteristic
5#19127598C211yesmaximal, characteristic, complemented
6#19127597C211yesmaximal, characteristic, complemented
7#19127596C211yesmaximal, characteristic, complemented
8#19127595C211yesmaximal, characteristic
9#19127595C211yesmaximal, characteristic
10#19127587C211yesmaximal, characteristic, complemented
11#19127583C211yesmaximal, characteristic, complemented
12#19127574C211yesmaximal, characteristic
13#19127552C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic83C211yesmaximal, characteristic
15#385×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
32C2×C4×Dic83C2211yescharacteristic
33C2×C4×Dic83C2211yescharacteristic
34C83⋊#95C2211yescharacteristic
35C83⋊#95C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C23×C4×C83C2211yescharacteristic
45C2×C4⋊C4×C83C2211yescharacteristic
46C2×C4⋊C4×C83C2211yescharacteristic
47C2×C22⋊C4×C83C2211yescharacteristic
48C2×C22⋊C4×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—22no—
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⋊Dic83Q814yes—
73C4×Dic83—22no—
74C4×Dic83—41no—
75C4×Dic83—41no—
76C4×Dic83—41no—
77C24×C83C2311yescharacteristic
78C22×C4×C83—22no—
79C22×C4×C83—41no—
80C22×C4×C83—41no—
81C22×C4×C83C2311yescharacteristic
82C22×C4×C83C2311yescharacteristic
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C4⋊C4×C83—22no—
88C4⋊C4×C83—41no—
89C22⋊C4×C83—22no—
90C22⋊C4×C83—41no—
91C23×C83—21no—
92C23×C83—21no—
93C23×C83—21no—
94C23×C83—21no—
95C23×C83—21no—
96C23×C83—21no—
97C23×C83C2×Q812yes—
98C23×C83C2411yescharacteristic
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—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—44no—
116C2×C4×C83#4112yes—
117C2×C4×C83#4112yes—
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—21no—
137C2×Dic83—21no—
138C2×Dic83C2×Q812yes—
139C2×Dic83C2×Q812yes—
140C2×Dic83#4112yes—
141C2×Dic83#4112yes—
142C22×C83—22no—
143C22×C83—22no—
144C22×C83—22no—
145C22×C83—41no—
146C22×C83—41no—
147C22×C83—41no—
148C22×C83—41no—
149C22×C83C22×Q811yescharacteristic
150C22×C83C2×#4111yescharacteristic
151C22×C83C2×#4111yescharacteristic
152C22×C83C2×#4111yescharacteristic
153C22×C83C2×#4111yescharacteristic
154C22×C83H(5,𝔽2)11yescharacteristic
155C22×C83H(5,𝔽2)11yescharacteristic
156C4×C83—22no—
157C4×C83—22no—
158C4×C83—41no—
159C4×C83—41no—
160C4×C83—41no—
161C4×C83—41no—
162Dic83—22no—
163Dic83—22no—
164Dic83—22no—
165Dic83—22no—
166Dic83—41no—
167Dic83—41no—
168Dic83—41no—
169Dic83—41no—
170C2×C83—42no—
171C2×C83#52911yescharacteristic
172C2×C83#53311yescharacteristic
173C2×C83#53811yescharacteristic
174C2×C83#55311yescharacteristic
175C2×C83#55311yescharacteristic
176C2×C83#55411yescharacteristic
177C2×C83#55411yescharacteristic
178#2587—831nomaximal, Sylow
179C83#258711yescharacteristic, complemented, Sylow
180#400—831no—
181#398—831no—
182#396—831no—
183#396—831no—
184#389—831no—
185#389—831no—
186#389—831no—
187#388—831no—
188#388—831no—
189#387—831no—
190#387—831no—
191#385—831no—
192#385D8311yescharacteristic
193C4×C4⋊C4—831no—
194C4×C22⋊C4—831no—
195C23×C4C2×D8311yescharacteristic
196C2×C4⋊C4—831no—
197C2×C4⋊C4—831no—
198C2×C4⋊C4—831no—
199C2×C4⋊C4—831no—
200C2×C4⋊C4—831no—
201C2×C4⋊C4—831no—
202C2×C4⋊C4—831no—
203C2×C4⋊C4—831no—
204C2×C4⋊C4—831no—
205C2×C4⋊C4—831no—
206C2×C4⋊C4C2×D8311yescharacteristic
207C2×C4⋊C4C2×D8311yescharacteristic
208C2×C22⋊C4—831no—
209C2×C22⋊C4—831no—
210C2×C22⋊C4—831no—
211C2×C22⋊C4—831no—
212C2×C22⋊C4C2×D8311yescharacteristic
213C2×C22⋊C4C2×D8311yescharacteristic
214C2×C42—831no—
215C2×C42—831no—
216C2×C42—831no—
217C2×C42—831no—
218#95—831no—
219#95—831no—
220#95—831no—
221#95—831no—
222#95—831no—
223#95—831no—
224#95—831no—
225#95—831no—
226#95—831no—
227#95—831no—
228#95C2×D8311yescharacteristic
229#95C2×D8311yescharacteristic
230C24C22×D8311yescharacteristic
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—831no—
235C22×C4—831no—
236C22×C4—831no—
237C22×C4—831no—
238C22×C4—831no—
239C22×C4—831no—
240C22×C4—831no—
241C22×C4—831no—
242C22×C4C22×D8311yescharacteristic
243C22×C4C22×D8311yescharacteristic
244C22×C4C22×D8311yescharacteristic
245C22×C4C22×D8311yescharacteristic
246C22×C4C22×D8311yescharacteristic
247C22×C4C22×D8311yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—3321no—
251C4⋊C4—3321no—
252C4⋊C4—3321no—
253C4⋊C4—3321no—
254C4⋊C4—1662no—
255C4⋊C4—1662no—
256C4⋊C4—1662no—
257C4⋊C4—1662no—
258C4⋊C4—1662no—
259C4⋊C4—1662no—
260C22⋊C4—22no—
261C22⋊C4—41no—
262C22⋊C4—3321no—
263C22⋊C4—834no—
264C22⋊C4—1662no—
265C22⋊C4—1662no—
266C42—3321no—
267C42—3321no—
268C42—3321no—
269C42—1662no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23Q8×D8312yes—
277C23C23×D8311yescharacteristic
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—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—44no—
295C2×C4—832no—
296C2×C4—832no—
297C2×C4—832no—
298C2×C4—832no—
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—1661no—
313C2×C4—1661no—
314C2×C4—1661no—
315C2×C4—1661no—
316C2×C4—1661no—
317C2×C4—1661no—
318C2×C4—1661no—
319C2×C4#1305058912yes—
320C2×C4#1305059012yes—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22C2×Q8×D8311yescharacteristic
329C22#41×D8311yescharacteristic
330C22#41×D8311yescharacteristic
331C22C2×#1305058911yescharacteristic
332C22C2×#1305059011yescharacteristic
333C22#1458183711yescharacteristic
334C22#1458183711yescharacteristic
335C4—22no—
336C4—22no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—3321no—
342C4—3321no—
343C4—3321no—
344C4—3321no—
345C4—1662no—
346C4—1662no—
347C4—1662no—
348C4—1662no—
349C2—42no—
350C2#1912823311yescharacteristic
351C2#1912825311yescharacteristic
352C2#1912828611yescharacteristic
353C2#1912839611yescharacteristic
354C2#1912840011yescharacteristic
355C2#1912840511yescharacteristic
356C2#1912840611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#385×C83C2
prime radicalC24×C83C23
hypercenter#385D83
hypocenterC83#2587
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #19127642C2semidirect
2. #19127631C2semidirect
5. #19127598C2semidirect
6. #19127597C2semidirect
7. #19127596C2semidirect
10. #19127587C2semidirect
11. #19127583C2semidirect
13. #19127552C2semidirect
179. C83#2587semidirect

Maximal subgroups

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

subgroupindex
#191276422
#191276312
#191276242
#191275982
#191275972
#191275962
#191275952
#191275872
#191275832
#191275742
#191275522
C4×C22⋊Dic832
#385×C832
#258783