Finite Group Databasebeta

← #20255406

Subgroups — #20255406

Order 6016.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689811C211yesmaximal, characteristic, complemented
2D4×D188C211yesmaximal, characteristic
3#15689489C211yesmaximal, characteristic, complemented
4#15689449C211yesmaximal, characteristic, complemented
5#15689438C211yesmaximal, characteristic, complemented
6#15689370C211yesmaximal, characteristic, complemented
7#15689353C211yesmaximal, characteristic, complemented
8#15689324C211yesmaximal, characteristic, complemented
9#15689275C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12#15689193C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#478C211yesmaximal, characteristic, complemented
16C22×D188—21no—
17C2×D4×D47C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19C2×#10625325C2211yescharacteristic, complemented
20C2×#10625325C2211yescharacteristic, complemented
21C2×#10625335C2211yescharacteristic
22C2×#10625324C2211yescharacteristic, complemented
23C2×C8×D47C2211yescharacteristic, complemented
24#13094021C2211yescharacteristic
25#13094019—21no—
26#13094015—21no—
27#13094009—21no—
28#13094004C2211yescharacteristic, complemented
29#13094004C2211yescharacteristic, complemented
30#13093999C2211yescharacteristic
31#13093999C2211yescharacteristic
32#13093998—21no—
33#13093994—21no—
34#13093994—21no—
35C4×Dic94C2211yescharacteristic, complemented
36C4×D188C2211yescharacteristic
37#13093982—21no—
38#13093982C2211yescharacteristic, complemented
39C4⋊C4×D47C2211yescharacteristic, complemented
40#13093957C2211yescharacteristic, complemented
41#13093947C2211yescharacteristic, complemented
42#13093946C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic, complemented
44#13093945C2211yescharacteristic
45#13093944C2211yescharacteristic, complemented
46#13093944C2211yescharacteristic, complemented
47#13093944C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic, complemented
49(C2×D47)⋊C8C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093935C2211yescharacteristic, complemented
52#125×C47C2211yescharacteristic, complemented
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C23×D47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65D4×D47—22no—
66D4×D47—22no—
67D4×D47—41no—
68D4×D47—41no—
69C2×D188—21no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188—44no—
74C2×D188D411yescharacteristic
75C2×D188C2311yescharacteristic
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47C2311yescharacteristic
79C2×C4×D47C2311yescharacteristic
80C2×Dic94C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C2×C8×C47C2311yescharacteristic
83C4⋊C4×C47—21no—
84C4⋊C4×C47—21no—
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47—21no—
89C42×C47C2311yescharacteristic
90#10625335—22no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4D411yescharacteristic
97(C2×D47)⋊C4D411yescharacteristic
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47D411yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108#10625325—41no—
109#10625325—41no—
110#10625324—41no—
111C8×D47—41no—
112C23×C47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—81no—
120C22×D47—81no—
121C22×D47C2×D411yescharacteristic
122C22×D47C2×D411yescharacteristic
123D4×C47—21no—
124D4×C47#4112yes—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—42no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—42no—
133C22⋊D47—42no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138D188—22no—
139D188—21no—
140D188—21no—
141D188—21no—
142D188—21no—
143D188—42no—
144D188—42no—
145D188—42no—
146D188—81no—
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—21no—
150C4×D47—21no—
151C4×D47—42no—
152Dic94—21no—
153Dic94—21no—
154C8×C47—21no—
155C8×C47—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—22no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47C22×D411yescharacteristic
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—21no—
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—84no—
174C2×D47—84no—
175C2×D47AGL(1,ℤ/8)12yes—
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—41no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47C2×#4111yescharacteristic
182C4×C47H(5,𝔽2)11yescharacteristic
183Dic47—21no—
184Dic47—21no—
185Dic47—41no—
186Dic47—41no—
187#3310—471nomaximal, Sylow
188C2×C47—42no—
189C2×C47#54611yescharacteristic
190C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C47#57711yescharacteristic
192D47—22no—
193D47—41no—
194D47—81no—
195D47—81no—
196#552—471no—
197D42—471no—
198#490—471no—
199#482—471no—
200#480—471no—
201#478D4711yescharacteristic, complemented
202#468—471no—
203#465—471no—
204#460—471no—
205#450—471no—
206#450—471no—
207#440—471no—
208#435—471no—
209#418—471no—
210C2×#102—471no—
211C47#331011yescharacteristic, complemented, Sylow
212C22×D4—471no—
213C22×D4—471no—
214C22×D4—941no—
215C2×SD16—471no—
216C2×SD16—471no—
217C2×SD16—471no—
218C2×M16—471no—
219C22×C8—471no—
220#127—471no—
221#126—941no—
222#125—941no—
223#125C2×D4711yescharacteristic, complemented
224#123—941no—
225C22⋊Q8—471no—
226C22⋊Q8—471no—
227#121—471no—
228#121—471no—
229#121—941no—
230#120—941no—
231#120—941no—
232C4×Q8—471no—
233C4×D4—471no—
234C4×D4C2×D4711yescharacteristic
235#117—471no—
236#117—941no—
237C2×C4⋊C4—471no—
238#107—471no—
239#107C2×D4711yescharacteristic, complemented
240#106C2×D4711yescharacteristic, complemented
241C4⋊C8C2×D4711yescharacteristic, complemented
242#103—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102C2×D4711yescharacteristic
251#102C2×D4711yescharacteristic
252C22⋊C8—471no—
253C22⋊C8—471no—
254#97—471no—
255C24—941no—
256C24—941no—
257C2×Q8—471no—
258C2×D4—471no—
259C2×D4—471no—
260C2×D4—471no—
261C2×D4—941no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—941no—
265C2×D4—942no—
266C2×D4—942no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—1884no—
270C2×D4—1881no—
271C2×D4—1881no—
272C2×D4C22×D4711yescharacteristic
273C22×C4—21no—
274C22×C4—471no—
275C22×C4—471no—
276C22×C4—941no—
277SD16—942no—
278SD16—1881no—
279SD16—1881no—
280M16—1881no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8—1881no—
284C2×C8C22×D4711yescharacteristic
285C2×C8C22×D4711yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—471no—
289C4⋊C4—471no—
290C4⋊C4—941no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4C22×D4711yescharacteristic
295C4⋊C4C22×D4711yescharacteristic
296C4⋊C4C22×D4711yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—471no—
299C22⋊C4—471no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C42—941no—
306C42—941no—
307C42C22×D4711yescharacteristic
308C23—21no—
309C23—471no—
310C23—471no—
311C23—941no—
312C23—941no—
313C23—3761no—
314C23—3761no—
315C23—1882no—
316C23—1882no—
317C23—1882no—
318C23—1882no—
319Q8—941no—
320Q8—941no—
321D4—21no—
322D4—942no—
323D4—941no—
324D4—941no—
325D4—941no—
326D4—941no—
327D4—3761no—
328D4—1882no—
329D4—1882no—
330D4—1882no—
331D4—1882no—
332D4—1882no—
333D4#1062535412yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—471no—
339C2×C4—471no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—1882no—
347C2×C4D4×D4711yescharacteristic
348C2×C4D4×D4711yescharacteristic
349C2×C4C23×D4711yescharacteristic
350C8—21no—
351C8—21no—
352C8—941no—
353C8—941no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—472no—
358C22—941no—
359C22—941no—
360C22—941no—
361C22—941no—
362C22—941no—
363C22—3764no—
364C22—3764no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22—1881no—
371C22C2×D4×D4711yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—941no—
378C4—941no—
379C4—1881no—
380C4—1881no—
381C4C2×#1062535411yescharacteristic
382C4#1309407011yescharacteristic
383C2—42no—
384C2—942no—
385C2—3761no—
386C2—3761no—
387C2—1881no—
388C2#1568976411yescharacteristic
389C2AGL(1,ℤ/8)×D4711yescharacteristic
390C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3310
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #15689811C2semidirect
3. #15689489C2semidirect
4. #15689449C2semidirect
5. #15689438C2semidirect
6. #15689370C2semidirect
7. #15689353C2semidirect
8. #15689324C2semidirect
9. #15689275C2semidirect
10. #15689275C2semidirect
11. #15689223C2semidirect
12. #15689193C2semidirect
13. #15689126C2semidirect
14. #102×D47C2semidirect
15. C47×#478C2semidirect
19. C2×#10625325C22semidirect
20. C2×#10625325C22semidirect
22. C2×#10625324C22semidirect
23. C2×C8×D47C22semidirect
28. #13094004C22semidirect
29. #13094004C22semidirect
35. C4×Dic94C22semidirect
38. #13093982C22semidirect
39. C4⋊C4×D47C22semidirect
40. #13093957C22semidirect
41. #13093947C22semidirect
42. #13093946C22semidirect
43. #13093946C22semidirect
45. #13093944C22semidirect
46. #13093944C22semidirect
47. #13093944C22semidirect
48. #13093944C22semidirect
49. (C2×D47)⋊C8C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093935C22semidirect
52. #125×C47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. C4⋊C8×C47C22semidirect
201. #478D47semidirect
211. C47#3310semidirect
223. #125C2×D47semidirect
239. #107C2×D47semidirect
240. #106C2×D47semidirect
241. C4⋊C8C2×D47semidirect