Finite Group Databasebeta

← #20256776

Subgroups — #20256776

Order 6016.

1040 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689746C212yesmaximal, complemented
2#15689740C212yesmaximal, complemented
3#15689733C212yesmaximal, complemented
4#15689726C212yesmaximal, complemented
5#15689717C214yesmaximal, complemented
6#15689708C214yesmaximal, complemented
7#15689676C211yesmaximal, characteristic, complemented
8#15689669C211yesmaximal, characteristic, complemented
9#15689655C214yesmaximal, complemented
10#15689653C214yesmaximal, complemented
11#15689634C211yesmaximal, characteristic, complemented
12#41×Dic47C211yesmaximal, characteristic, complemented
13#15689591C211yesmaximal, characteristic, complemented
14C2×#13093983C211yesmaximal, characteristic, complemented
15C47×#525C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17#13094023C2212yescomplemented
18#13094022C2211yescharacteristic, complemented
19#13094020C2211yescharacteristic, complemented
20#13094019C2214yescomplemented
21#13094017C2214yes—
22#13094017C2214yes—
23#13094017C2214yescomplemented
24#13094015C2214yescomplemented
25#13094015C2212yescomplemented
26#13094014C2214yescomplemented
27#13094013C2211yescharacteristic, complemented
28#13094011C2214yes—
29#13094011C2211yescharacteristic, complemented
30#13094010C2214yes—
31#13094008C2214yescomplemented
32#13094007C2212yes—
33#13094006C2214yes—
34#13094006C2214yescomplemented
35#13094005C2214yes—
36#13094004C2214yescomplemented
37#13094003C2212yes—
38#13094001C2214yes—
39#13094001C2214yescomplemented
40#13093998C2212yes—
41#13093996C2214yes—
42#13093996C2214yes—
43#13093995C2214yes—
44#13093993C2212yes—
45Q8×Dic47C2212yescomplemented
46C4×Dic94C2214yescomplemented
47#13093989C2212yescomplemented
48D4×Dic47C2214yes—
49D4×Dic47C2212yescomplemented
50#13093986C2212yescomplemented
51C4×C22⋊D47C2214yes—
52C4×C22⋊D47C2214yescomplemented
53(C22⋊D47)⋊C4C2214yes—
54#13093983C2212yes—
55#13093983C2212yes—
56#13093983C2212yes—
57#13093983C2212yes—
58#13093983C2211yescharacteristic
59#13093983C2212yescomplemented
60#13093981C2212yescomplemented
61C2×C4⋊Dic47C2212yes—
62C2×C22⋊Dic47C2212yes—
63C2×C4×Dic47C2211yescharacteristic
64C2×C4×Dic47C2211yescharacteristic
65C2×C4×Dic47C2212yescomplemented
66C42×D47C2212yescomplemented
67C2×#41×C47C2211yescharacteristic
68C23×C4×C47C2211yescharacteristic
69#123×C47C2212yes—
70C22⋊Q8×C47C2212yes—
71#121×C47C2212yes—
72#120×C47C2212yes—
73C4×D4×C47C2214yes—
74#117×C47C2211yescharacteristic
75C24×C47C2311yescharacteristic
76#41×C47—24no—
77C2×Q8×C47C2311yescharacteristic
78C2×D4×C47C2312yes—
79C2×D4×C47C2311yescharacteristic
80C2×D4×C47C2314yes—
81C22×C4×C47—24no—
82C22×C4×C47C2312yes—
83C22×C4×C47C2312yes—
84C22×C4×C47C2312yes—
85C22×C4×C47C2311yescharacteristic
86C22×C4×C47C2311yescharacteristic
87C2×C22⋊D47C2312yes—
88C2×C22⋊D47C2314yes—
89C2×C22⋊D47C2314yes—
90C22×Dic47C2312yes—
91C22×Dic47C2312yes—
92C22×Dic47C2314yes—
93#10625350—24no—
94C2×D188C2311yescharacteristic
95C2×C4×D47C2312yes—
96C2×C4×D47C2314yes—
97C2×Dic94C2311yescharacteristic
98C2×Dic94C2314yes—
99C4⋊C4×C47C2312yes—
100C4⋊C4×C47C2314yes—
101C22⋊C4×C47C2312yes—
102C22⋊C4×C47C2314yes—
103C22⋊C4×C47C2314yes—
104C42×C47C2312yes—
105C22⋊Dic47C2312yes—
106C22⋊Dic47C2312yes—
107C22⋊Dic47C2312yes—
108C22⋊Dic47C2312yes—
109C22⋊Dic47C2312yes—
110C22⋊Dic47C2314yes—
111C22⋊Dic47C2314yes—
112C22⋊Dic47C2314yes—
113(C2×D47)⋊C4C2314yes—
114(C2×D47)⋊C4C2314yes—
115(C2×D47)⋊C4C2314yes—
116C4⋊Dic47C2312yes—
117C4⋊Dic47C2312yes—
118C4⋊Dic47C2312yes—
119C4⋊Dic47C2312yes—
120C4⋊Dic47C2312yes—
121C4⋊Dic47C2314yes—
122C4⋊Dic47C2314yes—
123Dic47⋊C4C2314yes—
124Dic47⋊C4C2314yes—
125Dic47⋊C4C2314yes—
126Dic47⋊C4C2314yes—
127Dic47⋊C4C2314yes—
128C4×Dic47C2311yescharacteristic
129C4×Dic47C2314yes—
130C4×Dic47C2311yescharacteristic
131C4×Dic47C2312yes—
132C4×Dic47C2312yes—
133C4×Dic47C2311yescharacteristic
134C4×Dic47C2311yescharacteristic
135C4×Dic47C2312yes—
136C4×Dic47C2314yes—
137C23×C47—22no—
138C23×C47—42no—
139C23×C47C2412yes—
140C23×C47C2412yes—
141C23×C47C2411yescharacteristic
142C22×D47C2412yes—
143Q8×C47—22no—
144D4×C47—24no—
145D4×C47—22no—
146D4×C47—44no—
147C2×C4×C47—22no—
148C2×C4×C47—24no—
149C2×C4×C47—24no—
150C2×C4×C47—24no—
151C2×C4×C47#4114yes—
152C2×C4×C47C2412yes—
153C2×C4×C47C2414yes—
154C2×C4×C47C2412yes—
155C2×C4×C47C2411yescharacteristic
156C2×C4×C47C2411yescharacteristic
157C22⋊D47—24no—
158C22⋊D47—44no—
159C22⋊D47—44no—
160C2×Dic47—42no—
161C2×Dic47—44no—
162C2×Dic47—42no—
163C2×Dic47C2412yes—
164C2×Dic47C2412yes—
165C2×Dic47C2412yes—
166C2×Dic47C2412yes—
167C2×Dic47C2414yes—
168C2×Dic47C2412yes—
169D188—22no—
170C4×D47—24no—
171C4×D47—44no—
172Dic94—22no—
173Dic94—44no—
174C22×C47—22no—
175C22×C47—22no—
176C22×C47—22no—
177C22×C47—24no—
178C22×C47—22no—
179C22×C47—22no—
180C22×C47—44no—
181C22×C47C2×#4112yes—
182C22×C47C2511yescharacteristic
183C2×D47—22no—
184C2×D47—24no—
185C4×C47—22no—
186C4×C47—22no—
187C4×C47—24no—
188C4×C47C2×#4112yes—
189C4×C47C2×#4112yes—
190Dic47—22no—
191Dic47—22no—
192Dic47—24no—
193Dic47—22no—
194Dic47—22no—
195Dic47—22no—
196#3455—471nomaximal, Sylow
197C2×C47—22no—
198C2×C47—42no—
199C2×C47—42no—
200C2×C47C22×#4111yescharacteristic
201C2×C47#58512yes—
202D47—42no—
203#542—472no—
204#542—472no—
205#541—472no—
206#540—472no—
207#539—474no—
208#538—474no—
209#533—471no—
210#532—471no—
211#529—474no—
212#529—474no—
213#525—471no—
214#525D4711yescharacteristic, complemented
215C4×#41—471no—
216C4×#41—471no—
217C2×#117—471no—
218C47#345511yescharacteristic, complemented, Sylow
219C2×#41—471no—
220C2×#41C2×D4711yescharacteristic
221C23×C4C2×D4711yescharacteristic
222C4⋊Q8—471no—
223C4⋊Q8—472no—
224#127—471no—
225#126—474no—
226#126—474no—
227#126—474no—
228#126—474no—
229#125—474no—
230#125—474no—
231#125—472no—
232#124—471no—
233#124—474no—
234#124—471no—
235#124—474no—
236#123—474no—
237#123—472no—
238#123—474no—
239#123—474no—
240#123—474no—
241#123C2×D4712yes—
242C22⋊Q8—472no—
243C22⋊Q8—474no—
244C22⋊Q8—474no—
245C22⋊Q8—474no—
246C22⋊Q8C2×D4712yes—
247#121—474no—
248#121—474no—
249#121—474no—
250#121—472no—
251#121C2×D4712yes—
252#120—472no—
253#120C2×D4712yes—
254C4×Q8—472no—
255C4×Q8—472no—
256C4×Q8—474no—
257C4×D4—474no—
258C4×D4—472no—
259C4×D4—474no—
260C4×D4—474no—
261C4×D4—472no—
262C4×D4—474no—
263C4×D4C2×D4714yes—
264#117—472no—
265#117—472no—
266#117—472no—
267#117—472no—
268#117—471no—
269#117—472no—
270#117—472no—
271#117C2×D4711yescharacteristic
272C2×C4⋊C4—472no—
273C2×C22⋊C4—472no—
274C2×C42—471no—
275C2×C42—471no—
276C2×C42—472no—
277C2×C42—472no—
278C24C22×D4711yescharacteristic
279#41—24no—
280#41—944no—
281C2×Q8—471no—
282C2×Q8—474no—
283C2×Q8C22×D4711yescharacteristic
284C2×D4—472no—
285C2×D4—474no—
286C2×D4—474no—
287C2×D4—471no—
288C2×D4C22×D4712yes—
289C2×D4C22×D4711yescharacteristic
290C2×D4C22×D4714yes—
291C22×C4—24no—
292C22×C4—472no—
293C22×C4—472no—
294C22×C4—474no—
295C22×C4—472no—
296C22×C4—474no—
297C22×C4C22×D4711yescharacteristic
298C22×C4C22×D4712yes—
299C22×C4C22×D4712yes—
300C22×C4C22×D4712yes—
301C22×C4C22×D4711yescharacteristic
302C4⋊C4—474no—
303C4⋊C4—474no—
304C4⋊C4—474no—
305C4⋊C4—474no—
306C4⋊C4—474no—
307C4⋊C4—472no—
308C4⋊C4—472no—
309C4⋊C4—472no—
310C4⋊C4—472no—
311C4⋊C4—472no—
312C4⋊C4—474no—
313C4⋊C4—474no—
314C4⋊C4C22×D4712yes—
315C4⋊C4C22×D4714yes—
316C22⋊C4—472no—
317C22⋊C4—472no—
318C22⋊C4—472no—
319C22⋊C4—472no—
320C22⋊C4—472no—
321C22⋊C4—474no—
322C22⋊C4—474no—
323C22⋊C4—474no—
324C22⋊C4—474no—
325C22⋊C4—474no—
326C22⋊C4—474no—
327C22⋊C4C22×D4712yes—
328C22⋊C4C22×D4714yes—
329C22⋊C4C22×D4714yes—
330C42—472no—
331C42—471no—
332C42—471no—
333C42—474no—
334C42—474no—
335C42—471no—
336C42—471no—
337C42—472no—
338C42—472no—
339C42C22×D4712yes—
340C23—22no—
341C23—42no—
342C23—472no—
343C23C23×D4712yes—
344C23C23×D4712yes—
345C23C23×D4711yescharacteristic
346Q8—22no—
347Q8—942no—
348Q8—1884no—
349D4—24no—
350D4—22no—
351D4—44no—
352D4—944no—
353D4—942no—
354D4—1884no—
355D4—1884no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—472no—
361C2×C4—472no—
362C2×C4—472no—
363C2×C4—472no—
364C2×C4—474no—
365C2×C4—472no—
366C2×C4—944no—
367C2×C4—1884no—
368C2×C4—1882no—
369C2×C4—1884no—
370C2×C4—1882no—
371C2×C4#1062535214yes—
372C2×C4C23×D4712yes—
373C2×C4C23×D4714yes—
374C2×C4C23×D4712yes—
375C2×C4C23×D4711yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C22—22no—
378C22—22no—
379C22—22no—
380C22—24no—
381C22—22no—
382C22—22no—
383C22—44no—
384C22—942no—
385C22—944no—
386C22C2×#1062535212yes—
387C22C24×D4711yescharacteristic
388C4—22no—
389C4—22no—
390C4—24no—
391C4—942no—
392C4—942no—
393C4—942no—
394C4—942no—
395C4—944no—
396C4—942no—
397C4C2×#1062535212yes—
398C4C2×#1062535212yes—
399C2—22no—
400C2—42no—
401C2—42no—
402C2—1882no—
403C2C22×#1062535211yescharacteristic
404C2#1568995912yes—
subgroupG/H
centerC2×C4C23×D47
commutator, socleC22×C47C25
FrattiniC22C24×D47
FittingC47×#525C2
hypercenter#525D47
hypocenterC47#3455
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #15689746C2semidirect
2. #15689740C2semidirect
3. #15689733C2semidirect
4. #15689726C2semidirect
5. #15689717C2semidirect
6. #15689708C2semidirect
7. #15689676C2semidirect
8. #15689669C2semidirect
9. #15689655C2semidirect
10. #15689653C2semidirect
11. #15689634C2semidirect
12. #41×Dic47C2semidirect
13. #15689591C2semidirect
14. C2×#13093983C2semidirect
15. C47×#525C2semidirect
17. #13094023C22semidirect
18. #13094022C22semidirect
19. #13094020C22semidirect
20. #13094019C22semidirect
23. #13094017C22semidirect
24. #13094015C22semidirect
25. #13094015C22semidirect
26. #13094014C22semidirect
27. #13094013C22semidirect
29. #13094011C22semidirect
31. #13094008C22semidirect
34. #13094006C22semidirect
36. #13094004C22semidirect
39. #13094001C22semidirect
45. Q8×Dic47C22semidirect
46. C4×Dic94C22semidirect
47. #13093989C22semidirect
49. D4×Dic47C22semidirect
50. #13093986C22semidirect
52. C4×C22⋊D47C22semidirect
59. #13093983C22semidirect
60. #13093981C22semidirect
65. C2×C4×Dic47C22semidirect
66. C42×D47C22semidirect
214. #525D47semidirect
218. C47#3455semidirect