Finite Group Databasebeta

← #24913490

Subgroups — #24913490

Order 10624.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127636C211yesmaximal, characteristic, complemented
2#19127635C211yesmaximal, characteristic, complemented
3#19127634C211yesmaximal, characteristic, complemented
4#19127630C211yesmaximal, characteristic, complemented
5#19127627C211yesmaximal, characteristic, complemented
6#19127625C211yesmaximal, characteristic, complemented
7#19127619C211yesmaximal, characteristic
8#19127618C211yesmaximal, characteristic
9#19127603C211yesmaximal, characteristic
10#19127592C211yesmaximal, characteristic, complemented
11#19127592C211yesmaximal, characteristic, complemented
12#19127592C211yesmaximal, characteristic, complemented
13#19127592C211yesmaximal, characteristic, complemented
14#19127585C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
16C22×D332C2211yescharacteristic
17C2×C4⋊Dic83C2211yescharacteristic
18C2×Dic83⋊C4C2211yescharacteristic
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×(C2×D83)⋊C4C2211yescharacteristic
25C2×(C2×D83)⋊C4C2211yescharacteristic
26C2×(C2×D83)⋊C4C2211yescharacteristic
27C2×(C2×D83)⋊C4C2211yescharacteristic
28C2×(C2×D83)⋊C4C2211yescharacteristic
29C2×(C2×D83)⋊C4C2211yescharacteristic
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×(C2×D83)⋊C4C2211yescharacteristic
33C2×(C2×D83)⋊C4C2211yescharacteristic
34C2×(C2×D83)⋊C4C2211yescharacteristic
35C2×(C2×D83)⋊C4C2211yescharacteristic
36C83⋊#95C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44C2×C4⋊C4×C83C2211yescharacteristic
45C2×C4⋊C4×C83C2211yescharacteristic
46C2×C42×C83C2211yescharacteristic
47C2×C42×C83C2211yescharacteristic
48C2×C42×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51C23×D83C2311yescharacteristic
52C23×D83C2311yescharacteristic
53C2×D332—22no—
54C2×D332—41no—
55C2×D332—41no—
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C22×Dic83C2311yescharacteristic
60C22×Dic83C2311yescharacteristic
61C22×Dic83C2311yescharacteristic
62C4⋊Dic83—41no—
63Dic83⋊C4—22no—
64Dic83⋊C4—41no—
65Dic83⋊C4—41no—
66Dic83⋊C4—41no—
67Dic83⋊C4—41no—
68Dic83⋊C4—41no—
69(C2×D83)⋊C4—22no—
70(C2×D83)⋊C4—22no—
71(C2×D83)⋊C4—22no—
72(C2×D83)⋊C4—22no—
73(C2×D83)⋊C4—41no—
74(C2×D83)⋊C4—41no—
75(C2×D83)⋊C4—41no—
76(C2×D83)⋊C4—41no—
77(C2×D83)⋊C4—41no—
78(C2×D83)⋊C4—41no—
79(C2×D83)⋊C4—41no—
80(C2×D83)⋊C4—41no—
81C22×C4×C83C2311yescharacteristic
82C22×C4×C83C2311yescharacteristic
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C22×C4×C83C2311yescharacteristic
88C4⋊C4×C83—22no—
89C4⋊C4×C83—22no—
90C42×C83—22no—
91C42×C83—41no—
92C42×C83—41no—
93C23×C83C2411yescharacteristic
94C22×D83—21no—
95C22×D83—21no—
96C22×D83—21no—
97C22×D83—21no—
98C22×D83—21no—
99C22×D83—21no—
100C22×D83—21no—
101C22×D83—21no—
102C22×D83—21no—
103C22×D83—21no—
104C22×D83—21no—
105C22×D83—21no—
106C22×D83—21no—
107C22×D83—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—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—
127C2×C4×C83#4112yes—
128C2×C4×C83#4112yes—
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—
147D332—44no—
148C22×C83C2×#4111yescharacteristic
149C22×C83C2×#4111yescharacteristic
150C22×C83C2×#4111yescharacteristic
151C22×C83H(5,𝔽2)11yescharacteristic
152C22×C83H(5,𝔽2)11yescharacteristic
153C22×C83H(5,𝔽2)11yescharacteristic
154C22×C832−1+411yescharacteristic
155C2×D83—41no—
156C2×D83—41no—
157C2×D83—41no—
158C2×D83—41no—
159C2×D83—41no—
160C2×D83—41no—
161C2×D83—41no—
162C2×D83—41no—
163C2×D83—41no—
164C2×D83—41no—
165C2×D83—41no—
166C2×D83—41no—
167C2×D83—41no—
168C2×D83—41no—
169C4×C83—22no—
170C4×C83—22no—
171C4×C83—22no—
172C4×C83—41no—
173C4×C83—41no—
174C4×C83—41no—
175C4×C83—41no—
176Dic83—41no—
177Dic83—41no—
178Dic83—41no—
179Dic83—41no—
180Dic83—41no—
181Dic83—41no—
182C2×C83#52911yescharacteristic
183C2×C83#53811yescharacteristic
184C2×C83#53911yescharacteristic
185C2×C83#54011yescharacteristic
186C2×C83#54011yescharacteristic
187C2×C83#54211yescharacteristic
188C2×C83#54211yescharacteristic
189D83—81no—
190D83—81no—
191#2651—831nomaximal, Sylow
192C83#265111yescharacteristic, complemented, Sylow
193#399—831no—
194#398—831no—
195#398—831no—
196#397—831no—
197#397—831no—
198#396—831no—
199#394—831no—
200#394—831no—
201#390—831no—
202#388—831no—
203#388—831no—
204#388—831no—
205#388—831no—
206#387—831no—
207C4×C4⋊C4D8311yescharacteristic, complemented
208C22×D4—831no—
209C2×C4⋊C4—831no—
210C2×C4⋊C4—831no—
211C2×C4⋊C4—831no—
212C2×C4⋊C4—831no—
213C2×C4⋊C4—831no—
214C2×C4⋊C4—831no—
215C2×C4⋊C4—831no—
216C2×C4⋊C4C2×D8311yescharacteristic
217C2×C4⋊C4C2×D8311yescharacteristic
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⋊C4—831no—
225C2×C22⋊C4—831no—
226C2×C22⋊C4—831no—
227C2×C22⋊C4—831no—
228C2×C22⋊C4—831no—
229C2×C22⋊C4—831no—
230C2×C42C2×D8311yescharacteristic
231C2×C42C2×D8311yescharacteristic
232C2×C42C2×D8311yescharacteristic
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#95C2×D8311yescharacteristic
242#95C2×D8311yescharacteristic
243C24—831no—
244C24—831no—
245C2×D4—3321no—
246C2×D4—3321no—
247C2×D4—1662no—
248C22×C4—831no—
249C22×C4—831no—
250C22×C4—831no—
251C22×C4—831no—
252C22×C4—831no—
253C22×C4—831no—
254C22×C4C22×D8311yescharacteristic
255C22×C4C22×D8311yescharacteristic
256C22×C4C22×D8311yescharacteristic
257C22×C4C22×D8311yescharacteristic
258C22×C4C22×D8311yescharacteristic
259C22×C4C22×D8311yescharacteristic
260C22×C4C22×D8311yescharacteristic
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—3321no—
264C4⋊C4—3321no—
265C4⋊C4—3321no—
266C4⋊C4—3321no—
267C4⋊C4—3321no—
268C4⋊C4—3321no—
269C4⋊C4—1662no—
270C22⋊C4—3321no—
271C22⋊C4—3321no—
272C22⋊C4—3321no—
273C22⋊C4—3321no—
274C22⋊C4—3321no—
275C22⋊C4—3321no—
276C22⋊C4—3321no—
277C22⋊C4—3321no—
278C22⋊C4—1662no—
279C22⋊C4—1662no—
280C22⋊C4—1662no—
281C22⋊C4—1662no—
282C42—22no—
283C42—41no—
284C42—41no—
285C23—1661no—
286C23—1661no—
287C23—1661no—
288C23—1661no—
289C23—1661no—
290C23—1661no—
291C23—1661no—
292C23—1661no—
293C23—1661no—
294C23—1661no—
295C23—1661no—
296C23—1661no—
297C23—1661no—
298C23—1661no—
299C23C23×D8311yescharacteristic
300D4—3324no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
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—1661no—
320C2×C4—1661no—
321C2×C4—1661no—
322C2×C4—1661no—
323C2×C4—1661no—
324C2×C4—1661no—
325C2×C4—1661no—
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#1305059012yes—
338C2×C4#1305059012yes—
339C2×C4#1305059012yes—
340C22—3321no—
341C22—3321no—
342C22—3321no—
343C22—3321no—
344C22—3321no—
345C22—3321no—
346C22—3321no—
347C22—3321no—
348C22—3321no—
349C22—3321no—
350C22—3321no—
351C22—3321no—
352C22—3321no—
353C22—3321no—
354C22C2×#1305059011yescharacteristic
355C22C2×#1305059011yescharacteristic
356C22C2×#1305059011yescharacteristic
357C22#1458183711yescharacteristic
358C22#1458183811yescharacteristic
359C22#1458183811yescharacteristic
360C22#1458184011yescharacteristic
361C4—22no—
362C4—22no—
363C4—22no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3321no—
369C4—3321no—
370C4—3321no—
371C4—3321no—
372C4—3321no—
373C4—3321no—
374C2—6641no—
375C2—6641no—
376C2#1912823511yescharacteristic
377C2#1912828411yescharacteristic
378C2#1912829811yescharacteristic
379C2#1912830211yescharacteristic
380C2#1912830611yescharacteristic
381C2#1912832311yescharacteristic
382C2#1912832311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
FittingC4×C4⋊C4×C83C2
prime radicalC22×D332C22
hypercenterC4×C4⋊C4D83
hypocenterC83#2651
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #19127636C2semidirect
2. #19127635C2semidirect
3. #19127634C2semidirect
4. #19127630C2semidirect
5. #19127627C2semidirect
6. #19127625C2semidirect
10. #19127592C2semidirect
11. #19127592C2semidirect
12. #19127592C2semidirect
13. #19127592C2semidirect
14. #19127585C2semidirect
15. C4×C4⋊C4×C83C2semidirect
192. C83#2651semidirect
207. C4×C4⋊C4D83semidirect

Maximal subgroups

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

subgroupindex
#191276362
#191276352
#191276342
#191276302
#191276272
#191276252
#191276192
#191276182
#191276032
#191275922
#191275852
C4×C4⋊C4×C832
#265183