Finite Group Databasebeta

← #20255421

Subgroups — #20255421

Order 6016.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689847C211yesmaximal, characteristic, complemented
2#15689768C211yesmaximal, characteristic
3#15689485C211yesmaximal, characteristic, complemented
4#15689467C211yesmaximal, characteristic, complemented
5#15689449C211yesmaximal, characteristic, complemented
6#15689382C211yesmaximal, characteristic, complemented
7#15689353C211yesmaximal, characteristic, complemented
8#15689346C211yesmaximal, characteristic, complemented
9#15689286C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12#15689193C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14#15689116C211yesmaximal, characteristic, complemented
15C47×#476C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×Dic188C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×#10625324C2211yescharacteristic
22C2×C8×D47C2211yescharacteristic, complemented
23#13094019—21no—
24#13094019—21no—
25#13094013—21no—
26#13094012C2211yescharacteristic
27#13094008—21no—
28#13094004C2211yescharacteristic
29#13094004C2211yescharacteristic
30#13094004C2211yescharacteristic, complemented
31#13093999C2211yescharacteristic
32#13093998—21no—
33#13093994—21no—
34Q8×Dic47—21no—
35C4×Dic94C2211yescharacteristic, complemented
36C4×D188C2211yescharacteristic
37#13093982C2211yescharacteristic
38#13093982C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4—21no—
40#13093957C2211yescharacteristic, complemented
41#13093949C2211yescharacteristic, complemented
42#13093947C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093935C2211yescharacteristic, complemented
52C4⋊Q8×C47C2211yescharacteristic, complemented
53C4×D4×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66#10625352—22no—
67#10625352—41no—
68D4×D47—22no—
69D4×D47—41no—
70C2×D188—21no—
71C2×D188D411yescharacteristic
72C2×D188C2311yescharacteristic
73C2×C4×D47C2311yescharacteristic
74C2×C4×D47C2311yescharacteristic
75C2×Dic94C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C42×C47C2311yescharacteristic
85#10625335—22no—
86(C2×D47)⋊C4—21no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89(C2×D47)⋊C4—21no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4D411yescharacteristic
95(C2×D47)⋊C4D411yescharacteristic
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47D411yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107Dic188—41no—
108#10625325—41no—
109#10625324—41no—
110C8×D47—41no—
111C23×C47—21no—
112C22×D47—21no—
113C22×D47—42no—
114C22×D47—42no—
115C22×D47—81no—
116C22×D47C2×D411yescharacteristic
117C22×D47C2×D411yescharacteristic
118Q8×C47—42no—
119D4×C47—21no—
120D4×C47#4112yes—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—81no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—42no—
129C22⋊D47—42no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—42no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136D188—21no—
137D188—21no—
138D188—41no—
139D188—81no—
140C4×D47—21no—
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—21no—
144Dic94—21no—
145Dic94—21no—
146Dic94—21no—
147Dic94—21no—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—22no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—84no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47C2×#4111yescharacteristic
172C4×C47H(5,𝔽2)11yescharacteristic
173Dic47—21no—
174Dic47—21no—
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178#3311—471nomaximal, Sylow
179C2×C47—42no—
180C2×C47#54611yescharacteristic
181C2×C47#57511yescharacteristic
182C2×C47#57711yescharacteristic
183D47—41no—
184D47—41no—
185D47—81no—
186#556—471no—
187#546—471no—
188#489—471no—
189#485—471no—
190#482—471no—
191#476D4711yescharacteristic, complemented
192#470—471no—
193#465—471no—
194#464—471no—
195#452—471no—
196#450—471no—
197#440—471no—
198#435—471no—
199#418—471no—
200#416—471no—
201C47#331111yescharacteristic, complemented, Sylow
202C2×#41—471no—
203C22×D4—471no—
204C2×Q16—471no—
205C2×SD16—471no—
206C2×SD16—471no—
207C2×M16—471no—
208C22×C8—471no—
209C4⋊Q8C2×D4711yescharacteristic, complemented
210#126—941no—
211#126—941no—
212#124—471no—
213#124—941no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8—471no—
218#121—471no—
219#121—941no—
220#120—941no—
221C4×Q8—471no—
222C4×Q8—941no—
223C4×D4—471no—
224C4×D4C2×D4711yescharacteristic
225#117—471no—
226#117—471no—
227C2×C22⋊C4—941no—
228#107—471no—
229#106C2×D4711yescharacteristic, complemented
230#106C2×D4711yescharacteristic, complemented
231C4⋊C8C2×D4711yescharacteristic, complemented
232#103—471no—
233#103—471no—
234#103—471no—
235#103—471no—
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102C2×D4711yescharacteristic
241#102C2×D4711yescharacteristic
242C22⋊C8—471no—
243C22⋊C8—471no—
244#97—471no—
245C24—941no—
246#41—942no—
247#41—1881no—
248C2×Q8—21no—
249C2×Q8—471no—
250C2×Q8—471no—
251C2×D4—471no—
252C2×D4—471no—
253C2×D4—941no—
254C2×D4—941no—
255C2×D4—942no—
256C2×D4—941no—
257C2×D4—1881no—
258C2×D4C22×D4711yescharacteristic
259C22×C4—21no—
260C22×C4—471no—
261C22×C4—471no—
262C22×C4—941no—
263Q16—1881no—
264SD16—942no—
265SD16—1881no—
266M16—1881no—
267C2×C8—471no—
268C2×C8—471no—
269C2×C8—1881no—
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—471no—
274C4⋊C4—471no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4C22×D4711yescharacteristic
280C4⋊C4C22×D4711yescharacteristic
281C4⋊C4C22×D4711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—471no—
284C22⋊C4—471no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C42—941no—
294C42—941no—
295C42—941no—
296C42C22×D4711yescharacteristic
297C23—21no—
298C23—471no—
299C23—471no—
300C23—941no—
301C23—3761no—
302C23—1882no—
303C23—1882no—
304Q8—42no—
305Q8—941no—
306Q8—941no—
307Q8—941no—
308Q8—941no—
309D4—21no—
310D4—941no—
311D4—941no—
312D4—3761no—
313D4—1881no—
314D4—1882no—
315D4—1882no—
316D4#1062535412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—471no—
322C2×C4—471no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—1882no—
331C2×C4D4×D4711yescharacteristic
332C2×C4D4×D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—21no—
335C8—21no—
336C8—941no—
337C8—941no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—941no—
342C22—941no—
343C22—941no—
344C22—941no—
345C22—941no—
346C22—941no—
347C22—3764no—
348C22—1881no—
349C22—1881no—
350C22—1881no—
351C22C2×D4×D4711yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—941no—
358C4—941no—
359C4—1881no—
360C4—1881no—
361C4—1881no—
362C4C2×#1062535411yescharacteristic
363C4#1309407011yescharacteristic
364C2—42no—
365C2—3761no—
366C2—1881no—
367C2—1881no—
368C2#1568976411yescharacteristic
369C2#1568991911yescharacteristic
370C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#476C2
socleC22×C47C22×D4
hypercenter#476D47
hypocenterC47#3311
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #15689847C2semidirect
3. #15689485C2semidirect
4. #15689467C2semidirect
5. #15689449C2semidirect
6. #15689382C2semidirect
7. #15689353C2semidirect
8. #15689346C2semidirect
9. #15689286C2semidirect
10. #15689275C2semidirect
11. #15689223C2semidirect
12. #15689193C2semidirect
13. #15689126C2semidirect
14. #15689116C2semidirect
15. C47×#476C2semidirect
18. C2×Dic188C22semidirect
22. C2×C8×D47C22semidirect
30. #13094004C22semidirect
35. C4×Dic94C22semidirect
38. #13093982C22semidirect
40. #13093957C22semidirect
41. #13093949C22semidirect
42. #13093947C22semidirect
43. #13093947C22semidirect
44. #13093947C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093935C22semidirect
52. C4⋊Q8×C47C22semidirect
54. #106×C47C22semidirect
55. #106×C47C22semidirect
56. C4⋊C8×C47C22semidirect
191. #476D47semidirect
201. C47#3311semidirect
209. C4⋊Q8C2×D47semidirect
229. #106C2×D47semidirect
230. #106C2×D47semidirect
231. C4⋊C8C2×D47semidirect