Finite Group Databasebeta

← #20255418

Subgroups — #20255418

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#15689769C211yesmaximal, characteristic
2#15689485C211yesmaximal, characteristic, complemented
3#15689464C211yesmaximal, characteristic, complemented
4#15689447C211yesmaximal, characteristic, complemented
5#15689410C211yesmaximal, characteristic, complemented
6#15689379C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689345C211yesmaximal, characteristic, complemented
9#15689283C211yesmaximal, characteristic, complemented
10#15689273C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689127C211yesmaximal, characteristic, complemented
14#15689117C211yesmaximal, characteristic, complemented
15C47×#556C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C2×#10625329C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic, complemented
23#13094012C2211yescharacteristic
24#13094009—21no—
25#13094003C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093997—21no—
28#13093992—21no—
29C4×D188C2211yescharacteristic
30C22⋊C4×D47—21no—
31#13093957C2211yescharacteristic, complemented
32#13093955C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35#13093948C2211yescharacteristic, complemented
36#13093947C2211yescharacteristic, complemented
37#13093947C2211yescharacteristic, complemented
38#13093947C2211yescharacteristic, complemented
39#13093944C2211yescharacteristic
40#13093944C2211yescharacteristic
41#13093944C2211yescharacteristic
42#13093944C2211yescharacteristic
43#13093944C2211yescharacteristic
44#13093944C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47#13093935C2211yescharacteristic, complemented
48C4⋊Q8×C47C2211yescharacteristic, complemented
49#126×C47—21no—
50#126×C47—21no—
51#124×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic, complemented
54C4×Q8×C47—21no—
55C4×Q8×C47C2211yescharacteristic, complemented
56C4×D4×C47C2211yescharacteristic
57#117×C47C2211yescharacteristic
58#117×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47D411yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67#10625350—22no—
68#10625350—41no—
69C2×D188—22no—
70C2×D188—21no—
71C2×D188—41no—
72C2×D188C2311yescharacteristic
73C2×D188C2311yescharacteristic
74C2×C4×D47—21no—
75C2×C4×D47—21no—
76C2×Dic94C2311yescharacteristic
77C4⋊C4×C47—21no—
78C4⋊C4×C47—21no—
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47D411yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C4⋊C4×C47C2311yescharacteristic
84C4⋊C4×C47C2311yescharacteristic
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊C4×C47D411yescharacteristic
90C22⋊C4×C47D411yescharacteristic
91C42×C47—21no—
92C42×C47—21no—
93C42×C47—21no—
94C42×C47C2311yescharacteristic
95C22⋊Dic47—21no—
96#10625337—41no—
97#10625336—22no—
98#10625336—41no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47C2×D411yescharacteristic
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—81no—
118Q8×C47—21no—
119Q8×C47—21no—
120Q8×C47—42no—
121D4×C47—41no—
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×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2411yescharacteristic
135C22⋊D47—42no—
136C22⋊D47—81no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139D188—21no—
140D188—21no—
141D188—21no—
142D188—42no—
143D188#4112yes—
144C4×D47—42no—
145C4×D47—81no—
146Dic94—21no—
147Dic94—21no—
148C47⋊C8—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47C22×D411yescharacteristic
159C2×D47—22no—
160C2×D47—41no—
161C2×D47—41no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—84no—
166C4×C47—21no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—41no—
171C4×C47—41no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47C2×#4111yescharacteristic
175C4×C47H(5,𝔽2)11yescharacteristic
176Dic47—41no—
177Dic47—41no—
178#3311—471nomaximal, Sylow
179C2×C47—41no—
180C2×C47—41no—
181C2×C47#54611yescharacteristic
182C2×C47#57511yescharacteristic
183C2×C47#57711yescharacteristic
184D47—42no—
185D47—81no—
186#556D4711yescharacteristic, complemented
187#546—471no—
188#489—471no—
189#485—471no—
190#482—471no—
191#476—471no—
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—21no—
211#126—21no—
212#124—21no—
213#124—471no—
214#123—941no—
215C22⋊Q8—471no—
216C22⋊Q8C2×D4711yescharacteristic
217C22⋊Q8C2×D4711yescharacteristic, complemented
218#121—471no—
219#121—941no—
220#120—941no—
221C4×Q8—21no—
222C4×Q8C2×D4711yescharacteristic, complemented
223C4×D4—471no—
224C4×D4C2×D4711yescharacteristic
225#117C2×D4711yescharacteristic
226#117C2×D4711yescharacteristic, complemented
227C2×C22⋊C4—941no—
228#107—471no—
229#106—471no—
230#106—471no—
231C4⋊C8—471no—
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#102—471no—
241#102—471no—
242C22⋊C8—471no—
243C22⋊C8—471no—
244#97—471no—
245C24—941no—
246#41—942no—
247#41—1881no—
248C2×Q8—21no—
249C2×Q8—471no—
250C2×Q8C22×D4711yescharacteristic
251C2×D4—471no—
252C2×D4—471no—
253C2×D4—942no—
254C2×D4—941no—
255C2×D4—941no—
256C2×D4—941no—
257C2×D4—1881no—
258C2×D4C22⋊D4711yescharacteristic
259C22×C4—941no—
260C22×C4—941no—
261C22×C4C22×D4711yescharacteristic
262C22×C4C22×D4711yescharacteristic
263Q16—1881no—
264SD16—942no—
265SD16—1881no—
266M16—1881no—
267C2×C8—471no—
268C2×C8—471no—
269C2×C8—471no—
270C2×C8—471no—
271C2×C8—1881no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—471no—
277C4⋊C4—941no—
278C4⋊C4C22⋊D4711yescharacteristic
279C4⋊C4C22×D4711yescharacteristic
280C4⋊C4C22×D4711yescharacteristic
281C4⋊C4C22×D4711yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C22⋊C4—941no—
290C22⋊C4—941no—
291C22⋊C4C22⋊D4711yescharacteristic
292C22⋊C4C22⋊D4711yescharacteristic
293C42—21no—
294C42—21no—
295C42—21no—
296C42C22×D4711yescharacteristic
297C23—941no—
298C23—941no—
299C23—3761no—
300C23—1882no—
301C23—1882no—
302C23C2×C22⋊D4711yescharacteristic
303C23C2×C22⋊D4711yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—42no—
307Q8—941no—
308Q8—941no—
309D4—41no—
310D4—472no—
311D4—941no—
312D4—941no—
313D4—941no—
314D4—3761no—
315D4—1882no—
316D4—1882no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—941no—
326C2×C4—941no—
327C2×C4—3761no—
328C2×C4—1882no—
329C2×C4C2×C22⋊D4711yescharacteristic
330C2×C4C2×C22⋊D4711yescharacteristic
331C2×C4C2×C22⋊D4711yescharacteristic
332C2×C4C2×C22⋊D4711yescharacteristic
333C2×C4C23×D4711yescharacteristic
334C8—941no—
335C8—941no—
336C8—941no—
337C8—941no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—942no—
345C22—3764no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22—1881no—
350C22—1881no—
351C22C22×C22⋊D4711yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—1881no—
361C4—1881no—
362C4#41×D4711yescharacteristic
363C4#1309407011yescharacteristic
364C2—41no—
365C2—41no—
366C2—3761no—
367C2—1882no—
368C2#1568976111yescharacteristic
369C2#1568992111yescharacteristic
370C2#1568993111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#556C2
socleC22×C47C22×D4
hypercenter#556D47
hypocenterC47#3311
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #15689485C2semidirect
3. #15689464C2semidirect
4. #15689447C2semidirect
5. #15689410C2semidirect
6. #15689379C2semidirect
7. #15689354C2semidirect
8. #15689345C2semidirect
9. #15689283C2semidirect
10. #15689273C2semidirect
11. #15689221C2semidirect
12. #15689195C2semidirect
13. #15689127C2semidirect
14. #15689117C2semidirect
15. C47×#556C2semidirect
18. C2×#10625337C22semidirect
22. C22×C47⋊C8C22semidirect
31. #13093957C22semidirect
32. #13093955C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. #13093948C22semidirect
36. #13093947C22semidirect
37. #13093947C22semidirect
38. #13093947C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. #13093935C22semidirect
48. C4⋊Q8×C47C22semidirect
53. C22⋊Q8×C47C22semidirect
55. C4×Q8×C47C22semidirect
58. #117×C47C22semidirect
186. #556D47semidirect
201. C47#3311semidirect
209. C4⋊Q8C2×D47semidirect
217. C22⋊Q8C2×D47semidirect
222. C4×Q8C2×D47semidirect
226. #117C2×D47semidirect