Finite Group Databasebeta

← #20255526

Subgroups — #20255526

Order 6016.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689826C211yesmaximal, characteristic, complemented
2D4×D188C211yesmaximal, characteristic, complemented
3#15689489C211yesmaximal, characteristic, complemented
4#15689450C211yesmaximal, characteristic, complemented
5#15689443C211yesmaximal, characteristic, complemented
6#15689377C211yesmaximal, characteristic, complemented
7#15689360C211yesmaximal, characteristic, complemented
8#15689319C211yesmaximal, characteristic, complemented
9#15689258C211yesmaximal, characteristic, complemented
10#15689258C211yesmaximal, characteristic, complemented
11#15689233C211yesmaximal, 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×D376C2211yescharacteristic, complemented
20C2×D376C2211yescharacteristic, complemented
21C2×#10625334C2211yescharacteristic
22C2×#10625324C2211yescharacteristic, complemented
23C2×C8×D47C2211yescharacteristic, complemented
24#13094021C2211yescharacteristic
25#13094019—21no—
26#13094009—21no—
27#13093999—21no—
28#13093999C2211yescharacteristic
29#13093999C2211yescharacteristic
30#13093999C2211yescharacteristic, complemented
31#13093999C2211yescharacteristic, complemented
32#13093998—21no—
33#13093994—21no—
34#13093994—21no—
35C4×D188C2211yescharacteristic
36C4×D188C2211yescharacteristic, complemented
37#13093986—21no—
38#13093982C2211yescharacteristic, complemented
39C4⋊C4×D47C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41#13093946C2211yescharacteristic, complemented
42#13093946C2211yescharacteristic, complemented
43#13093945C2211yescharacteristic
44#13093944C2211yescharacteristic, complemented
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—21no—
74C2×D188—21no—
75C2×D188—44no—
76C2×D188D411yescharacteristic
77C2×D188C2311yescharacteristic
78C2×D188C2311yescharacteristic
79C2×D188C2311yescharacteristic
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47C2311yescharacteristic
83C2×C4×D47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C4⋊C4×C47—21no—
87C4⋊C4×C47—21no—
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2311yescharacteristic
90C4⋊C4×C47C2311yescharacteristic
91C22⋊C4×C47—21no—
92C42×C47C2311yescharacteristic
93#10625334—22no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4D411yescharacteristic
101(C2×D47)⋊C4D411yescharacteristic
102C4⋊Dic47D411yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105C4×Dic47—21no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108D376—41no—
109D376—41no—
110#10625324—41no—
111C8×D47—41no—
112C23×C47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C22×D47—81no—
121C22×D47—81no—
122C22×D47C2×D411yescharacteristic
123C22×D47C2×D411yescharacteristic
124D4×C47—21no—
125D4×C47#4112yes—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—42no—
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C22⋊D47—42no—
134C22⋊D47—42no—
135C2×Dic47—21no—
136C2×Dic47C2×D411yescharacteristic
137C2×Dic47C2×D411yescharacteristic
138D188—22no—
139D188—21no—
140D188—21no—
141D188—21no—
142D188—21no—
143D188—21no—
144D188—21no—
145D188—42no—
146D188—42no—
147D188—42no—
148D188—42no—
149D188—81no—
150D188—81no—
151C4×D47—21no—
152C4×D47—21no—
153C4×D47—21no—
154C4×D47—21no—
155C4×D47—81no—
156C4×D47—81no—
157C8×C47—21no—
158C8×C47—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—22no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47C22×D411yescharacteristic
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—21no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C2×D47—41no—
179C2×D47—84no—
180C2×D47—84no—
181C2×D47AGL(1,ℤ/8)12yes—
182C4×C47—21no—
183C4×C47—21no—
184C4×C47—41no—
185C4×C47—41no—
186C4×C47—41no—
187C4×C47C2×#4111yescharacteristic
188C4×C47H(5,𝔽2)11yescharacteristic
189Dic47—21no—
190Dic47—21no—
191Dic47—41no—
192#3318—471nomaximal, Sylow
193C2×C47—42no—
194C2×C47#54611yescharacteristic
195C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C47#57611yescharacteristic
197D47—22no—
198D47—41no—
199D47—81no—
200D47—81no—
201D47—81no—
202#553—471no—
203D42—471no—
204#490—471no—
205#482—471no—
206#481—471no—
207#478D4711yescharacteristic, complemented
208#469—471no—
209#466—471no—
210#459—471no—
211#447—471no—
212#447—471no—
213#442—471no—
214#435—471no—
215#418—471no—
216C2×#102—471no—
217C47#331811yescharacteristic, complemented, Sylow
218C22×D4—471no—
219C22×D4—471no—
220C22×D4—941no—
221C2×D8—471no—
222C2×D8—471no—
223C2×D8—471no—
224C2×M16—471no—
225C22×C8—471no—
226#127—471no—
227#126—941no—
228#125C2×D4711yescharacteristic, complemented
229#123—941no—
230#121—471no—
231#121—471no—
232#121—471no—
233#121—471no—
234#121—941no—
235#121—941no—
236#120—941no—
237#120—941no—
238C4×D4—471no—
239C4×D4—471no—
240C4×D4—941no—
241C4×D4C2×D4711yescharacteristic
242#117—471no—
243C2×C4⋊C4—471no—
244#107C2×D4711yescharacteristic, complemented
245#106—471no—
246#106C2×D4711yescharacteristic, complemented
247C4⋊C8C2×D4711yescharacteristic, complemented
248#102—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252#102—471no—
253#102—471no—
254#102—471no—
255#102—471no—
256#102C2×D4711yescharacteristic
257#102C2×D4711yescharacteristic
258C22⋊C8—471no—
259C22⋊C8—471no—
260#97—471no—
261C24—941no—
262C24—941no—
263C2×D4—471no—
264C2×D4—471no—
265C2×D4—471no—
266C2×D4—471no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—941no—
270C2×D4—941no—
271C2×D4—941no—
272C2×D4—941no—
273C2×D4—942no—
274C2×D4—942no—
275C2×D4—941no—
276C2×D4—941no—
277C2×D4—1884no—
278C2×D4—1881no—
279C2×D4—1881no—
280C2×D4C22×D4711yescharacteristic
281C22×C4—21no—
282C22×C4—471no—
283C22×C4—471no—
284C22×C4—941no—
285C22×C4—941no—
286D8—942no—
287D8—1881no—
288D8—1881no—
289M16—1881no—
290C2×C8—471no—
291C2×C8—471no—
292C2×C8—1881no—
293C2×C8C22×D4711yescharacteristic
294C2×C8C22×D4711yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—471no—
298C4⋊C4—471no—
299C4⋊C4—941no—
300C4⋊C4C22×D4711yescharacteristic
301C4⋊C4C22×D4711yescharacteristic
302C4⋊C4C22×D4711yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—471no—
305C22⋊C4—471no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C22⋊C4—941no—
311C22⋊C4—941no—
312C42—941no—
313C42C22×D4711yescharacteristic
314C23—21no—
315C23—471no—
316C23—471no—
317C23—941no—
318C23—941no—
319C23—941no—
320C23—3761no—
321C23—3761no—
322C23—1882no—
323C23—1882no—
324C23—1882no—
325C23—1882no—
326D4—21no—
327D4—942no—
328D4—941no—
329D4—941no—
330D4—941no—
331D4—941no—
332D4—941no—
333D4—941no—
334D4—3761no—
335D4—3761no—
336D4—1882no—
337D4—1882no—
338D4—1882no—
339D4—1882no—
340D4—1882no—
341D4—1882no—
342D4#1062535412yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—471no—
348C2×C4—471no—
349C2×C4—941no—
350C2×C4—941no—
351C2×C4—941no—
352C2×C4—941no—
353C2×C4—941no—
354C2×C4—3761no—
355C2×C4—3761no—
356C2×C4D4×D4711yescharacteristic
357C2×C4D4×D4711yescharacteristic
358C2×C4C23×D4711yescharacteristic
359C8—21no—
360C8—21no—
361C8—941no—
362C8—941no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—472no—
367C22—941no—
368C22—941no—
369C22—941no—
370C22—941no—
371C22—941no—
372C22—3764no—
373C22—3764no—
374C22—1881no—
375C22—1881no—
376C22—1881no—
377C22—1881no—
378C22—1881no—
379C22—1881no—
380C22—1881no—
381C22—1881no—
382C22—1881no—
383C22C2×D4×D4711yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—941no—
390C4—941no—
391C4—1881no—
392C4C2×#1062535411yescharacteristic
393C4#1309407011yescharacteristic
394C2—42no—
395C2—942no—
396C2—3761no—
397C2—3761no—
398C2—3761no—
399C2—1881no—
400C2#1568976411yescharacteristic
401C2AGL(1,ℤ/8)×D4711yescharacteristic
402C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3318
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. #15689826C2semidirect
2. D4×D188C2semidirect
3. #15689489C2semidirect
4. #15689450C2semidirect
5. #15689443C2semidirect
6. #15689377C2semidirect
7. #15689360C2semidirect
8. #15689319C2semidirect
9. #15689258C2semidirect
10. #15689258C2semidirect
11. #15689233C2semidirect
12. #15689193C2semidirect
13. #15689126C2semidirect
14. #102×D47C2semidirect
15. C47×#478C2semidirect
19. C2×D376C22semidirect
20. C2×D376C22semidirect
22. C2×#10625324C22semidirect
23. C2×C8×D47C22semidirect
30. #13093999C22semidirect
31. #13093999C22semidirect
36. C4×D188C22semidirect
38. #13093982C22semidirect
39. C4⋊C4×D47C22semidirect
40. #13093955C22semidirect
41. #13093946C22semidirect
42. #13093946C22semidirect
44. #13093944C22semidirect
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
207. #478D47semidirect
217. C47#3318semidirect
228. #125C2×D47semidirect
244. #107C2×D47semidirect
246. #106C2×D47semidirect
247. C4⋊C8C2×D47semidirect