Finite Group Databasebeta

← #20255222

Subgroups — #20255222

Order 6016.

408 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#15689811C211yesmaximal, characteristic, complemented
2#15689766C211yesmaximal, characteristic
3#15689452C211yesmaximal, characteristic, complemented
4#15689446C211yesmaximal, characteristic, complemented
5#15689420C211yesmaximal, characteristic, complemented
6#15689363C211yesmaximal, characteristic, complemented
7#15689351C211yesmaximal, characteristic, complemented
8#15689342C211yesmaximal, characteristic, complemented
9#15689288C211yesmaximal, characteristic, complemented
10#15689275C211yesmaximal, characteristic, complemented
11C4×#10625325C211yesmaximal, characteristic, complemented
12C8×D188C211yesmaximal, characteristic, complemented
13#15689118C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#488C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625325C2211yescharacteristic
20C2×#10625335C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22C2×C8×D47C2211yescharacteristic, complemented
23#13094019—21no—
24#13094015—21no—
25#13094009—21no—
26#13094006—21no—
27#13094004C2211yescharacteristic
28#13094004C2211yescharacteristic, complemented
29#13094000C2211yescharacteristic
30#13093997—21no—
31#13093995C2211yescharacteristic
32#13093994—21no—
33C4×Dic94C2211yescharacteristic, complemented
34C4×D188C2211yescharacteristic
35C4×D188C2211yescharacteristic
36#13093982—21no—
37#13093982C2211yescharacteristic, complemented
38C4⋊C4×D47C2211yescharacteristic
39C22⋊C4×D47—21no—
40#13093957C2211yescharacteristic, complemented
41#13093956C2211yescharacteristic, complemented
42#13093955C2211yescharacteristic, complemented
43C4⋊(C47⋊C8)C2211yescharacteristic, complemented
44#13093949C2211yescharacteristic, complemented
45#13093948C2211yescharacteristic, complemented
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52#125×C47C2211yescharacteristic, complemented
53#124×C47C2211yescharacteristic
54#103×C47C2211yescharacteristic, complemented
55#103×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C4×C8×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64#10625354—22no—
65#10625354—41no—
66D4×D47—22no—
67D4×D47—41no—
68C2×D188—21no—
69C2×D188D411yescharacteristic
70C2×D188C2311yescharacteristic
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—21no—
74C2×C4×D47C2311yescharacteristic
75C2×C4×D47C2311yescharacteristic
76C2×Dic94C2311yescharacteristic
77C2×C8×C47C2311yescharacteristic
78C2×C8×C47C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47C2311yescharacteristic
86C22⋊Dic47—21no—
87#10625337—41no—
88#10625335—41no—
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⋊Dic47D411yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105C4×Dic47—21no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108#10625325—22no—
109C8×D47—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—21no—
119Q8×C47—21no—
120D4×C47—21no—
121D4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—42no—
129C22⋊D47—81no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135D188—22no—
136D188—21no—
137D188—42no—
138D188#4112yes—
139C4×D47—21no—
140C4×D47—21no—
141C4×D47—21no—
142C4×D47—21no—
143C4×D47—42no—
144C4×D47—42no—
145C4×D47—81no—
146Dic94—21no—
147Dic94—21no—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—21no—
158C2×D47—21no—
159C2×D47—22no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—84no—
165C2×D47#13512yes—
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#3296—471nomaximal, Sylow
179C2×C47—81no—
180C2×C47#54611yescharacteristic
181C2×C47C2×#13511yescharacteristic
182C2×C47#57711yescharacteristic
183D47—22no—
184D47—41no—
185D47—42no—
186#552—471no—
187#546—471no—
188#488D4711yescharacteristic, complemented
189#483—471no—
190#482—471no—
191#478—471no—
192#467—471no—
193#465—471no—
194#464—471no—
195#452—471no—
196#450—471no—
197C4×SD16—471no—
198C8×D4—471no—
199#416—471no—
200C2×#102—471no—
201C47#329611yescharacteristic, complemented, Sylow
202C2×#41—471no—
203C22×D4—471no—
204C2×Q16—471no—
205C2×SD16—471no—
206C2×SD16—471no—
207C22×C8—471no—
208C22×C8—471no—
209#126—941no—
210#125—941no—
211#125C2×D4711yescharacteristic, complemented
212#124C2×D4711yescharacteristic
213#123—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×D4—471no—
223C4×D4—471no—
224#117—471no—
225#117—941no—
226C2×C4⋊C4—471no—
227C2×C22⋊C4—941no—
228#107—471no—
229#106—471no—
230#106—471no—
231C4⋊C8—471no—
232#103—471no—
233#103—471no—
234#103C2×D4711yescharacteristic, complemented
235#103C2×D4711yescharacteristic, complemented
236#102—471no—
237#102—471no—
238#102—471no—
239#102—471no—
240#102C2×D4711yescharacteristic
241#102C2×D4711yescharacteristic
242C22⋊C8—471no—
243C22⋊C8—471no—
244C4×C8C2×D4711yescharacteristic, complemented
245C24—941no—
246#41—942no—
247#41—1881no—
248C2×Q8—471no—
249C2×Q8C22×D4711yescharacteristic
250C2×D4—471no—
251C2×D4—471no—
252C2×D4—941no—
253C2×D4—941no—
254C2×D4—942no—
255C2×D4—941no—
256C2×D4—1881no—
257C2×D4C22×D4711yescharacteristic
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263Q16—1881no—
264SD16—942no—
265SD16—1881no—
266C2×C8—471no—
267C2×C8—471no—
268C2×C8—1881no—
269C2×C8—1881no—
270C2×C8C22×D4711yescharacteristic
271C2×C8C22×D4711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—471no—
275C4⋊C4—471no—
276C4⋊C4—471no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4C22×D4711yescharacteristic
283C4⋊C4C22×D4711yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—471no—
287C22⋊C4—471no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C42—941no—
295C42—941no—
296C42C22×D4711yescharacteristic
297C23—21no—
298C23—471no—
299C23—471no—
300C23—941no—
301C23—3761no—
302C23—1882no—
303C23—1882no—
304Q8—21no—
305Q8—21no—
306Q8—941no—
307Q8—941no—
308D4—21no—
309D4—21no—
310D4—472no—
311D4—942no—
312D4—941no—
313D4—3761no—
314D4—1882no—
315D4—1882no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—471no—
320C2×C4—471no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—941no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—3761no—
329C2×C4—1882no—
330C2×C4—1882no—
331C2×C4D4×D4711yescharacteristic
332C2×C4D4×D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—21no—
335C8—21no—
336C8—941no—
337C8—941no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—472no—
342C22—941no—
343C22—941no—
344C22—941no—
345C22—942no—
346C22—941no—
347C22—941no—
348C22—3764no—
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—
362C4#41×D4711yescharacteristic
363C4#1309407011yescharacteristic
364C2—81no—
365C2—942no—
366C2—1881no—
367C2—1882no—
368C2#1568976611yescharacteristic
369C2#135×D4711yescharacteristic
370C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#488C2
socleC22×C47C22×D4
hypercenter#488D47
hypocenterC47#3296
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #15689811C2semidirect
3. #15689452C2semidirect
4. #15689446C2semidirect
5. #15689420C2semidirect
6. #15689363C2semidirect
7. #15689351C2semidirect
8. #15689342C2semidirect
9. #15689288C2semidirect
10. #15689275C2semidirect
11. C4×#10625325C2semidirect
12. C8×D188C2semidirect
13. #15689118C2semidirect
14. #102×D47C2semidirect
15. C47×#488C2semidirect
18. C2×#10625337C22semidirect
22. C2×C8×D47C22semidirect
28. #13094004C22semidirect
33. C4×Dic94C22semidirect
37. #13093982C22semidirect
40. #13093957C22semidirect
41. #13093956C22semidirect
42. #13093955C22semidirect
43. C4⋊(C47⋊C8)C22semidirect
44. #13093949C22semidirect
45. #13093948C22semidirect
51. (C2×D47)⋊C8C22semidirect
52. #125×C47C22semidirect
54. #103×C47C22semidirect
55. #103×C47C22semidirect
58. C4×C8×C47C22semidirect
188. #488D47semidirect
201. C47#3296semidirect
211. #125C2×D47semidirect
234. #103C2×D47semidirect
235. #103C2×D47semidirect
244. C4×C8C2×D47semidirect