Finite Group Databasebeta

← #20255229

Subgroups — #20255229

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#15689815C211yesmaximal, characteristic, complemented
2#15689764C211yesmaximal, characteristic
3#15689479C211yesmaximal, characteristic, complemented
4#15689451C211yesmaximal, characteristic, complemented
5#15689450C211yesmaximal, characteristic, complemented
6#15689426C211yesmaximal, characteristic, complemented
7#15689355C211yesmaximal, characteristic, complemented
8#15689347C211yesmaximal, characteristic, complemented
9#15689284C211yesmaximal, characteristic, complemented
10#15689273C211yesmaximal, characteristic, complemented
11#15689208C211yesmaximal, characteristic, complemented
12C8×C22⋊D47C211yesmaximal, characteristic, complemented
13#15689118C211yesmaximal, characteristic, complemented
14C2×#13093946C211yesmaximal, characteristic, complemented
15C47×#467C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×#10625336C2211yescharacteristic
19C2×#10625336C2211yescharacteristic
20C2×C8×D47C2211yescharacteristic, complemented
21#13094019—21no—
22#13094015—21no—
23#13094015C2211yescharacteristic, complemented
24#13094013C2211yescharacteristic
25#13094009—21no—
26#13094008—21no—
27#13094000C2211yescharacteristic, complemented
28#13093999—21no—
29#13093999C2211yescharacteristic
30#13093994—21no—
31Q8×Dic47C2211yescharacteristic, complemented
32#13093986C2211yescharacteristic
33C4×C22⋊D47C2211yescharacteristic
34#13093982C2211yescharacteristic, complemented
35#13093980—21no—
36C2×C4⋊Dic47C2211yescharacteristic
37C22⋊C4×D47—21no—
38#13093955C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40Dic47⋊C8C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C8×Dic47C2211yescharacteristic, complemented
52C2×Q16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55C22⋊Q8×C47C2211yescharacteristic
56#107×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#103×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×Q8×C47C2311yescharacteristic
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47D411yescharacteristic
64C22×Dic47—21no—
65#10625354—22no—
66#10625354—41no—
67C2×D188—22no—
68C2×D188—21no—
69C2×D188—21no—
70C2×D188—21no—
71C2×D188—41no—
72C2×D188C2311yescharacteristic
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×C4×D47C2311yescharacteristic
77Q16×C47—41no—
78C2×C8×C47—41no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊Dic47D411yescharacteristic
88#10625336—22no—
89#10625336—41no—
90(C2×D47)⋊C4—21no—
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
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C8×D47—41no—
111C23×C47C2×D411yescharacteristic
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—42no—
115C22×D47—42no—
116C22×D47—81no—
117C22×D47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×C47—21no—
120Q8×C47—21no—
121Q8×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—22no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—42no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—21no—
138D188—21no—
139D188—21no—
140D188—42no—
141D188—42no—
142D188—81no—
143D188#4112yes—
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—42no—
147C4×D47—81no—
148C8×C47—21no—
149C8×C47—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47#13512yes—
155C22×C47C22×D411yescharacteristic
156C2×D47—21no—
157C2×D47—22no—
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—84no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47—41no—
170C4×C47—41no—
171C4×C47C2×#4111yescharacteristic
172C4×C47H(5,𝔽2)11yescharacteristic
173Dic47—21no—
174Dic47—21no—
175Dic47—21no—
176Dic47—41no—
177Dic47—41no—
178#3296—471nomaximal, Sylow
179C2×C47—22no—
180C2×C47#54611yescharacteristic
181C2×C47C2×#13511yescharacteristic
182C2×C47#57711yescharacteristic
183D47—41no—
184D47—42no—
185D47—81no—
186#552—471no—
187#546—471no—
188#488—471no—
189#483—471no—
190#482—471no—
191#478—471no—
192#467D4711yescharacteristic, complemented
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×Q16C2×D4711yescharacteristic, complemented
205C2×SD16—471no—
206C2×SD16—471no—
207C22×C8—471no—
208C22×C8C2×D4711yescharacteristic
209#126—941no—
210#125—471no—
211#125—941no—
212#124—471no—
213#123—941no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8C2×D4711yescharacteristic
217C22⋊Q8C2×D4711yescharacteristic
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#107C2×D4711yescharacteristic, complemented
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#102—471no—
241#102—471no—
242C22⋊C8—471no—
243C22⋊C8—471no—
244C4×C8—471no—
245C24—941no—
246#41—942no—
247#41—1881no—
248C2×Q8C22×D4711yescharacteristic
249C2×Q8C22×D4711yescharacteristic
250C2×D4—471no—
251C2×D4—471no—
252C2×D4—471no—
253C2×D4—942no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4—1881no—
258C22×C4—471no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4C22×D4711yescharacteristic
263Q16—41no—
264SD16—942no—
265SD16—1881no—
266C2×C8—41no—
267C2×C8—471no—
268C2×C8—471no—
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—471no—
295C42—941no—
296C42—941no—
297C23—471no—
298C23—941no—
299C23—941no—
300C23—3761no—
301C23—1882no—
302C23—1882no—
303C23D4×D4711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—472no—
309D4—942no—
310D4—941no—
311D4—941no—
312D4—941no—
313D4—3761no—
314D4—1882no—
315D4—1882no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—471no—
323C2×C4—471no—
324C2×C4—471no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—3761no—
330C2×C4—1882no—
331C2×C4—1882no—
332C2×C4D4×D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—21no—
335C8—21no—
336C8—941no—
337C8—941no—
338C22—21no—
339C22—21no—
340C22—941no—
341C22—942no—
342C22—941no—
343C22—941no—
344C22—3764no—
345C22—1881no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22—1881no—
350C22#1309404712yes—
351C22C2×D4×D4711yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—941no—
358C4—941no—
359C4—941no—
360C4—1881no—
361C4—1881no—
362C4#41×D4711yescharacteristic
363C4#1309406911yescharacteristic
364C2—22no—
365C2—3761no—
366C2—1881no—
367C2—1882no—
368C2#1568976211yescharacteristic
369C2C2×#1309404711yescharacteristic
370C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3296
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #15689815C2semidirect
3. #15689479C2semidirect
4. #15689451C2semidirect
5. #15689450C2semidirect
6. #15689426C2semidirect
7. #15689355C2semidirect
8. #15689347C2semidirect
9. #15689284C2semidirect
10. #15689273C2semidirect
11. #15689208C2semidirect
12. C8×C22⋊D47C2semidirect
13. #15689118C2semidirect
14. C2×#13093946C2semidirect
15. C47×#467C2semidirect
20. C2×C8×D47C22semidirect
23. #13094015C22semidirect
27. #13094000C22semidirect
31. Q8×Dic47C22semidirect
34. #13093982C22semidirect
38. #13093955C22semidirect
39. #13093955C22semidirect
40. Dic47⋊C8C22semidirect
41. #13093948C22semidirect
42. #13093948C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C8×Dic47C22semidirect
52. C2×Q16×C47C22semidirect
56. #107×C47C22semidirect
57. #103×C47C22semidirect
58. #103×C47C22semidirect
192. #467D47semidirect
201. C47#3296semidirect
204. C2×Q16C2×D47semidirect
228. #107C2×D47semidirect
234. #103C2×D47semidirect
235. #103C2×D47semidirect