Finite Group Databasebeta

← #20255463

Subgroups — #20255463

Order 6016.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689769C211yesmaximal, characteristic
2#15689485C211yesmaximal, characteristic, complemented
3#15689458C211yesmaximal, characteristic, complemented
4#15689436C211yesmaximal, characteristic, complemented
5#15689400C211yesmaximal, characteristic, complemented
6#15689371C211yesmaximal, characteristic, complemented
7#15689362C211yesmaximal, characteristic, complemented
8#15689345C211yesmaximal, characteristic, complemented
9#15689283C211yesmaximal, characteristic, complemented
10#15689273C211yesmaximal, characteristic, complemented
11#15689221C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689122C211yesmaximal, characteristic, complemented
14C2×#13093944C211yesmaximal, characteristic, complemented
15C47×#554C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C22×D188C2211yescharacteristic
18C2×#10625337C2211yescharacteristic, complemented
19C2×#10625336C2211yescharacteristic
20C2×#10625336C2211yescharacteristic
21C2×#10625329C2211yescharacteristic, complemented
22C22×C47⋊C8C2211yescharacteristic
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#13093957C2211yescharacteristic, complemented
33#13093957C2211yescharacteristic, 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#125×C47—21no—
50C22⋊Q8×C47—21no—
51C22⋊Q8×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53C22⋊Q8×C47C2211yescharacteristic, complemented
54C4×Q8×C47C2211yescharacteristic, complemented
55C4×D4×C47—21no—
56C4×D4×C47C2211yescharacteristic
57C2×C4⋊C4×C47C2211yescharacteristic
58C2×C4⋊C4×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47D411yescharacteristic
63C22×C4×C47—21no—
64C22×C4×C47—21no—
65C22×C4×C47C2311yescharacteristic
66C22×C4×C47C2311yescharacteristic
67C2×C22⋊D47—21no—
68C2×C22⋊D47—21no—
69#10625350—22no—
70#10625350—41no—
71C2×D188—22no—
72C2×D188—21no—
73C2×D188—41no—
74C2×D188C2311yescharacteristic
75C2×D188C2311yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×Dic94C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47—21no—
81C4⋊C4×C47—21no—
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47—21no—
85C4⋊C4×C47D411yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊C4×C47D411yescharacteristic
92C22⋊C4×C47D411yescharacteristic
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—81no—
121D4×C47—22no—
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×C47—81no—
131C2×C4×C47—81no—
132C2×C4×C47C2×D411yescharacteristic
133C2×C4×C47C2×D411yescharacteristic
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2×D411yescharacteristic
136C2×C4×C47C2411yescharacteristic
137C22⋊D47—42no—
138C22⋊D47—81no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141D188—21no—
142D188—21no—
143D188—21no—
144D188—42no—
145D188#4112yes—
146C4×D47—42no—
147C4×D47—81no—
148Dic94—21no—
149Dic94—21no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—21no—
158C22×C47—21no—
159C22×C47#13712yes—
160C22×C47C22×D411yescharacteristic
161C2×D47—22no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—84no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47C2×#4111yescharacteristic
177C4×C47H(5,𝔽2)11yescharacteristic
178Dic47—41no—
179Dic47—41no—
180#3314—471nomaximal, Sylow
181C2×C47—22no—
182C2×C47—41no—
183C2×C47#54611yescharacteristic
184C2×C47C2×#13711yescharacteristic
185C2×C47#57611yescharacteristic
186D47—42no—
187D47—81no—
188#554D4711yescharacteristic, complemented
189#546—471no—
190#489—471no—
191#484—471no—
192#480—471no—
193#474—471no—
194#468—471no—
195#467—471no—
196#464—471no—
197#452—471no—
198#450—471no—
199#440—471no—
200#435—471no—
201#417—471no—
202C2×#102—471no—
203C47#331411yescharacteristic, complemented, Sylow
204C2×#41—471no—
205C22×D4—471no—
206C2×Q16—471no—
207C2×SD16—471no—
208C2×SD16—471no—
209C2×M16—471no—
210C22×C8—471no—
211C4⋊Q8C2×D4711yescharacteristic, complemented
212#125—21no—
213#124—471no—
214#123—941no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—471no—
218C22⋊Q8C2×D4711yescharacteristic
219C22⋊Q8C2×D4711yescharacteristic, complemented
220#121—471no—
221#121—941no—
222#120—941no—
223C4×Q8C2×D4711yescharacteristic, complemented
224C4×D4—21no—
225C4×D4—471no—
226C4×D4C2×D4711yescharacteristic
227C2×C4⋊C4C2×D4711yescharacteristic
228C2×C4⋊C4C2×D4711yescharacteristic, complemented
229C2×C22⋊C4—941no—
230#107—471no—
231#107—471no—
232#107—471no—
233C4⋊C8—471no—
234#103—471no—
235#103—471no—
236#103—471no—
237#103—471no—
238#102—471no—
239#102—471no—
240#102—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244C22⋊C8—471no—
245C22⋊C8—471no—
246#97—471no—
247C24—941no—
248#41—942no—
249#41—1881no—
250C2×Q8—21no—
251C2×Q8—471no—
252C2×Q8C22×D4711yescharacteristic
253C2×D4—471no—
254C2×D4—471no—
255C2×D4—942no—
256C2×D4—941no—
257C2×D4—941no—
258C2×D4—941no—
259C2×D4—1881no—
260C2×D4C22⋊D4711yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4C22×D4711yescharacteristic
266C22×C4C22×D4711yescharacteristic
267Q16—1881no—
268SD16—942no—
269SD16—1881no—
270M16—1881no—
271C2×C8—471no—
272C2×C8—471no—
273C2×C8—471no—
274C2×C8—471no—
275C2×C8—1881no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—471no—
283C4⋊C4—941no—
284C4⋊C4C22⋊D4711yescharacteristic
285C4⋊C4C22×D4711yescharacteristic
286C4⋊C4C22×D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4C22⋊D4711yescharacteristic
296C22⋊C4C22⋊D4711yescharacteristic
297C42—21no—
298C42C22×D4711yescharacteristic
299C23—941no—
300C23—941no—
301C23—3761no—
302C23—1882no—
303C23—1882no—
304C23C2×C22⋊D4711yescharacteristic
305C23C2×C22⋊D4711yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—81no—
309Q8—941no—
310Q8—941no—
311D4—22no—
312D4—472no—
313D4—941no—
314D4—941no—
315D4—941no—
316D4—3761no—
317D4—1882no—
318D4—1882no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—3761no—
332C2×C4—1882no—
333C2×C4C2×C22⋊D4711yescharacteristic
334C2×C4C2×C22⋊D4711yescharacteristic
335C2×C4C2×C22⋊D4711yescharacteristic
336C2×C4C2×C22⋊D4711yescharacteristic
337C2×C4C23×D4711yescharacteristic
338C8—941no—
339C8—941no—
340C8—941no—
341C8—941no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—942no—
348C22—3764no—
349C22—1881no—
350C22—1881no—
351C22—1881no—
352C22—1881no—
353C22—1881no—
354C22#1309405512yes—
355C22C22×C22⋊D4711yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—1881no—
365C4—1881no—
366C4#41×D4711yescharacteristic
367C4#1309407011yescharacteristic
368C2—22no—
369C2—41no—
370C2—3761no—
371C2—1882no—
372C2#1568976111yescharacteristic
373C2C2×#1309405511yescharacteristic
374C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#554C2
socleC22×C47C22×D4
hypercenter#554D47
hypocenterC47#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #15689485C2semidirect
3. #15689458C2semidirect
4. #15689436C2semidirect
5. #15689400C2semidirect
6. #15689371C2semidirect
7. #15689362C2semidirect
8. #15689345C2semidirect
9. #15689283C2semidirect
10. #15689273C2semidirect
11. #15689221C2semidirect
12. #15689195C2semidirect
13. #15689122C2semidirect
14. C2×#13093944C2semidirect
15. C47×#554C2semidirect
18. C2×#10625337C22semidirect
21. C2×#10625329C22semidirect
31. #13093957C22semidirect
32. #13093957C22semidirect
33. #13093957C22semidirect
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
54. C4×Q8×C47C22semidirect
58. C2×C4⋊C4×C47C22semidirect
188. #554D47semidirect
203. C47#3314semidirect
211. C4⋊Q8C2×D47semidirect
219. C22⋊Q8C2×D47semidirect
223. C4×Q8C2×D47semidirect
228. C2×C4⋊C4C2×D47semidirect