Finite Group Databasebeta

← #24918339

Subgroups — #24918339

Order 10624.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19128272C211yesmaximal, characteristic, complemented
2#19128039C211yesmaximal, characteristic, complemented
3#19128036C211yesmaximal, characteristic, complemented
4#19128031C211yesmaximal, characteristic, complemented
5#19128022C211yesmaximal, characteristic, complemented
6#19127957C211yesmaximal, characteristic, complemented
7#19127945C211yesmaximal, characteristic, complemented
8#19127940C211yesmaximal, characteristic, complemented
9#19127928C211yesmaximal, characteristic, complemented
10#19127863C211yesmaximal, characteristic, complemented
11#19127863C211yesmaximal, characteristic, complemented
12#19127856C211yesmaximal, characteristic, complemented
13#19127839C211yesmaximal, characteristic, complemented
14#19127668C211yesmaximal, characteristic, complemented
15#537×C83C211yesmaximal, characteristic
16C22×Dic166C2211yescharacteristic
17C2×#13050580C2211yescharacteristic
18C2×#13050580C2211yescharacteristic
19C2×#13050578C2211yescharacteristic
20C2×#13050578C2211yescharacteristic
21C2×#13050574C2211yescharacteristic
22C22×C83⋊C8C2211yescharacteristic
23#14581790—21no—
24#14581779—21no—
25#14581773—21no—
26#14581773—21no—
27#14581771C2211yescharacteristic
28#14581771C2211yescharacteristic
29#14581771C2211yescharacteristic
30#14581771C2211yescharacteristic
31#14581751C2211yescharacteristic
32#14581725C2211yescharacteristic
33#14581725C2211yescharacteristic
34#14581723C2211yescharacteristic
35#14581723C2211yescharacteristic
36#14581716C2211yescharacteristic
37#14581716C2211yescharacteristic
38#14581715C2211yescharacteristic
39#14581715C2211yescharacteristic
40#14581715C2211yescharacteristic
41#14581715C2211yescharacteristic
42#14581713C2211yescharacteristic
43#14581713C2211yescharacteristic
44C22⋊(C83⋊C8)C2211yescharacteristic
45C22⋊(C83⋊C8)C2211yescharacteristic
46C22⋊(C83⋊C8)C2211yescharacteristic
47C22⋊(C83⋊C8)C2211yescharacteristic
48C2×#41×C83C2211yescharacteristic
49C2×#41×C83C2211yescharacteristic
50C22⋊Q8×C83—21no—
51C22⋊Q8×C83C2211yescharacteristic
52C22⋊Q8×C83C2211yescharacteristic
53#121×C83—21no—
54#121×C83—21no—
55#121×C83—21no—
56#121×C83C2211yescharacteristic
57#121×C83C2211yescharacteristic
58C2×C4⋊C4×C83C2211yescharacteristic
59C2×Dic166—21no—
60C2×Dic166—41no—
61C2×Dic166—41no—
62C2×Dic166C2311yescharacteristic
63C2×Dic166C2311yescharacteristic
64C22×Dic83—21no—
65#13050580—41no—
66#13050580—41no—
67#13050578—41no—
68#13050578—41no—
69#13050574—41no—
70C2×C83⋊C8—41no—
71C2×C83⋊C8C2311yescharacteristic
72C2×C83⋊C8C2311yescharacteristic
73C2×C83⋊C8C2311yescharacteristic
74C2×C83⋊C8C2311yescharacteristic
75C4⋊Dic83C2311yescharacteristic
76C4⋊Dic83C2311yescharacteristic
77Dic83⋊C4—21no—
78Dic83⋊C4—21no—
79Dic83⋊C4—21no—
80Dic83⋊C4—21no—
81C22⋊Dic83—21no—
82C22⋊Dic83—21no—
83C22⋊Dic83—21no—
84C22⋊Dic83—21no—
85C22⋊Dic83—21no—
86C4×Dic83—21no—
87#41×C83—41no—
88#41×C83—41no—
89#41×C83—41no—
90#41×C83—41no—
91C2×Q8×C83D411yescharacteristic
92C2×Q8×C83C2311yescharacteristic
93C2×D4×C83—21no—
94C2×D4×C83—21no—
95C2×D4×C83—21no—
96C2×D4×C83D411yescharacteristic
97C2×D4×C83D411yescharacteristic
98C2×D4×C83D411yescharacteristic
99C2×D4×C83C2311yescharacteristic
100C22×C4×C83—21no—
101C22×C4×C83—21no—
102C22×C4×C83C2311yescharacteristic
103C22×C4×C83C2311yescharacteristic
104C22×C4×C83C2311yescharacteristic
105C4⋊C4×C83—21no—
106C4⋊C4×C83—21no—
107C4⋊C4×C83—21no—
108C4⋊C4×C83C2311yescharacteristic
109C4⋊C4×C83C2311yescharacteristic
110C22⋊C4×C83—21no—
111C22⋊C4×C83—21no—
112C22⋊C4×C83—21no—
113C22⋊C4×C83—21no—
114C23×C83—21no—
115C23×C83C2×D411yescharacteristic
116C23×C83C2×D411yescharacteristic
117C23×C83C2×D411yescharacteristic
118Q8×C83—21no—
119Q8×C83—21no—
120Q8×C83—41no—
121D4×C83—21no—
122D4×C83—21no—
123D4×C83—41no—
124D4×C83—41no—
125D4×C83—41no—
126D4×C83—42no—
127D4×C83—81no—
128D4×C83—81no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—42no—
139C2×C4×C83—81no—
140C2×C4×C83C2×D411yescharacteristic
141C2×C4×C83C2×D411yescharacteristic
142C2×C4×C83C2×D411yescharacteristic
143C2×C4×C83C2411yescharacteristic
144C2×Dic83—21no—
145C2×Dic83—21no—
146C2×Dic83—21no—
147C2×Dic83—21no—
148C2×Dic83—42no—
149Dic166—21no—
150Dic166—21no—
151Dic166—21no—
152Dic166—21no—
153Dic166—42no—
154C83⋊C8—21no—
155C83⋊C8—21no—
156C83⋊C8—21no—
157C83⋊C8—21no—
158C22×C83—21no—
159C22×C83—21no—
160C22×C83—21no—
161C22×C83—21no—
162C22×C83—21no—
163C22×C83—21no—
164C22×C83—21no—
165C22×C83—21no—
166C22×C83—21no—
167C22×C83—41no—
168C22×C83—41no—
169C22×C83—41no—
170C22×C83C22×D411yescharacteristic
171C4×C83—21no—
172C4×C83—21no—
173C4×C83—21no—
174C4×C83—41no—
175C4×C83—41no—
176C4×C83—41no—
177C4×C83H(5,𝔽2)11yescharacteristic
178C4×C83H(5,𝔽2)11yescharacteristic
179Dic83—41no—
180Dic83—41no—
181Dic83—41no—
182Dic83—41no—
183C2×C83—41no—
184C2×C83—41no—
185C2×C83—41no—
186C2×C83—81no—
187C2×C83#53411yescharacteristic
188C2×C83#57711yescharacteristic
189C2×C83#57811yescharacteristic
190#3201—831nomaximal, Sylow
191C83#320111yescharacteristic, complemented, Sylow
192#537D8311yescharacteristic
193#536—831no—
194#485—831no—
195#484—831no—
196#483—831no—
197#482—831no—
198#470—831no—
199#468—831no—
200#467—831no—
201#465—831no—
202#452—831no—
203#452—831no—
204#451—831no—
205#448—831no—
206#408—831no—
207C2×#41C2×D8311yescharacteristic
208C2×#41C2×D8311yescharacteristic
209C22×Q8—831no—
210C2×Q16—831no—
211C2×Q16—831no—
212C2×SD16—831no—
213C2×SD16—831no—
214C2×M16—831no—
215C22×C8—831no—
216C4⋊Q8—1661no—
217#124—1661no—
218#123—1661no—
219#123—1661no—
220C22⋊Q8—21no—
221C22⋊Q8—831no—
222C22⋊Q8—831no—
223C22⋊Q8—831no—
224C22⋊Q8—831no—
225C22⋊Q8C2×D8311yescharacteristic
226C22⋊Q8C2×D8311yescharacteristic
227#121—21no—
228#121—21no—
229#121—21no—
230#121C2×D8311yescharacteristic
231#121C2×D8311yescharacteristic
232#117—831no—
233C2×C4⋊C4C2×D8311yescharacteristic
234#107—831no—
235#107—831no—
236#106—831no—
237#106—831no—
238#103—831no—
239#103—831no—
240#103—831no—
241#103—831no—
242#103—831no—
243#103—831no—
244#102—831no—
245#102—831no—
246C22⋊C8—831no—
247C22⋊C8—831no—
248C22⋊C8—831no—
249C22⋊C8—831no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—3321no—
255C2×Q8—3321no—
256C2×Q8—831no—
257C2×Q8—831no—
258C2×Q8—1661no—
259C2×Q8C22⋊D8311yescharacteristic
260C2×Q8C22×D8311yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C22⋊D8311yescharacteristic
265C2×D4C22⋊D8311yescharacteristic
266C2×D4C22⋊D8311yescharacteristic
267C2×D4C22×D8311yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—1661no—
271C22×C4C22×D8311yescharacteristic
272C22×C4C22×D8311yescharacteristic
273C22×C4C22×D8311yescharacteristic
274Q16—3321no—
275Q16—3321no—
276SD16—3321no—
277SD16—3321no—
278M16—3321no—
279C2×C8—3321no—
280C2×C8—831no—
281C2×C8—831no—
282C2×C8—831no—
283C2×C8—831no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—831no—
288C4⋊C4—831no—
289C4⋊C4—1661no—
290C4⋊C4—1661no—
291C4⋊C4—1661no—
292C4⋊C4—1661no—
293C4⋊C4C22×D8311yescharacteristic
294C4⋊C4C22×D8311yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—1661no—
300C22⋊C4—1661no—
301C22⋊C4—1661no—
302C22⋊C4—1661no—
303C22⋊C4—1661no—
304C42—1661no—
305C23—21no—
306C23C2×C22⋊D8311yescharacteristic
307C23C2×C22⋊D8311yescharacteristic
308C23C2×C22⋊D8311yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—41no—
312Q8—3322no—
313Q8—1661no—
314Q8—1661no—
315Q8—1661no—
316Q8—1661no—
317D4—21no—
318D4—21no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—3322no—
337C2×C4—1661no—
338C2×C4—1661no—
339C2×C4—1661no—
340C2×C4—1661no—
341C2×C4C2×C22⋊D8311yescharacteristic
342C2×C4C2×C22⋊D8311yescharacteristic
343C2×C4C2×C22⋊D8311yescharacteristic
344C2×C4C23×D8311yescharacteristic
345C8—1661no—
346C8—1661no—
347C8—1661no—
348C8—1661no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×C22⋊D8311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3321no—
369C4—3321no—
370C4—3321no—
371C4—3321no—
372C4#1458183711yescharacteristic
373C4#1458183711yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—81no—
378C2#1912826011yescharacteristic
379C2#1912851211yescharacteristic
380C2#1912851611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting, prime radical#537×C83C2
socleC22×C83C22×D4
hypercenter#537D83
hypocenterC83#3201
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #19128272C2semidirect
2. #19128039C2semidirect
3. #19128036C2semidirect
4. #19128031C2semidirect
5. #19128022C2semidirect
6. #19127957C2semidirect
7. #19127945C2semidirect
8. #19127940C2semidirect
9. #19127928C2semidirect
10. #19127863C2semidirect
11. #19127863C2semidirect
12. #19127856C2semidirect
13. #19127839C2semidirect
14. #19127668C2semidirect
191. C83#3201semidirect

Maximal subgroups

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

subgroupindex
#191282722
#191280392
#191280362
#191280312
#191280222
#191279572
#191279452
#191279402
#191279282
#191278632
#191278562
#191278392
#191276682
#537×C832
#320183