Finite Group Databasebeta

← #20255469

Subgroups — #20255469

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#15689830C211yesmaximal, characteristic, complemented
2#15689482C211yesmaximal, characteristic, complemented
3#15689456C211yesmaximal, characteristic, complemented
4#15689434C211yesmaximal, characteristic, complemented
5#15689403C211yesmaximal, characteristic, complemented
6#15689367C211yesmaximal, characteristic, complemented
7#15689362C211yesmaximal, characteristic, complemented
8#15689342C211yesmaximal, characteristic, complemented
9#15689285C211yesmaximal, characteristic, complemented
10#15689274C211yesmaximal, characteristic, complemented
11#15689223C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14C2×#13093945C211yesmaximal, characteristic, complemented
15C47×#546C211yesmaximal, characteristic
16C2×#10625337C2211yescharacteristic, complemented
17C2×#10625335C2211yescharacteristic
18C2×#10625335C2211yescharacteristic
19C2×#10625329C2211yescharacteristic, complemented
20C22×C47⋊C8C2211yescharacteristic
21#13094024C2211yescharacteristic, complemented
22#13094015—21no—
23#13094003C2211yescharacteristic
24#13094003C2211yescharacteristic, complemented
25#13094001—21no—
26#13094001—21no—
27C4×Dic94C2211yescharacteristic, complemented
28D4×Dic47—21no—
29C2×C4⋊Dic47C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic, complemented
31#13093957C2211yescharacteristic, complemented
32#13093957C2211yescharacteristic, complemented
33#13093957C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35#13093948C2211yescharacteristic, complemented
36#13093948C2211yescharacteristic, complemented
37#13093948C2211yescharacteristic, complemented
38#13093947C2211yescharacteristic, complemented
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093945C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47#13093935C2211yescharacteristic, complemented
48C2×#41×C47C2211yescharacteristic
49C22×D4×C47C2211yescharacteristic
50#124×C47C2211yescharacteristic
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53#121×C47—21no—
54#121×C47C2211yescharacteristic
55#120×C47—21no—
56C4×D4×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58C2×C22⋊C4×C47—21no—
59C24×C47—21no—
60#41×C47—22no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—22no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—41no—
68C2×D4×C47D411yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C2×D4×C47C2311yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×Dic47—21no—
76C22×Dic47—21no—
77C2×Dic94—21no—
78C2×Dic94C2311yescharacteristic
79C4⋊C4×C47—21no—
80C4⋊C4×C47D411yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C22⋊C4×C47—21no—
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C22⋊C4×C47—21no—
86C22⋊C4×C47—21no—
87C22⋊C4×C47D411yescharacteristic
88C22⋊C4×C47D411yescharacteristic
89C42×C47C2311yescharacteristic
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92#10625337—41no—
93#10625335—22no—
94#10625335—41no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47C2311yescharacteristic
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105#10625329—41no—
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C23×C47—21no—
112C23×C47—21no—
113C23×C47—42no—
114C23×C47—42no—
115C23×C47—81no—
116C23×C47C2×D411yescharacteristic
117C23×C47C2×D411yescharacteristic
118Q8×C47—21no—
119Q8×C47—21no—
120D4×C47—22no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—42no—
125D4×C47—42no—
126D4×C47—81no—
127D4×C47#4112yes—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—42no—
135C2×C4×C47—81no—
136C2×C4×C47C2×D411yescharacteristic
137C2×C4×C47C2×D411yescharacteristic
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2411yescharacteristic
141C2×Dic47—21no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—81no—
146C2×Dic47—81no—
147Dic94—21no—
148Dic94—21no—
149Dic94—81no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47—22no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—84no—
166C22×C47#13712yes—
167C22×C47C22×D411yescharacteristic
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47—41no—
173C4×C47—41no—
174C4×C47C2×#4111yescharacteristic
175C4×C47H(5,𝔽2)11yescharacteristic
176Dic47—41no—
177Dic47—41no—
178Dic47—41no—
179Dic47—41no—
180#3314—471nomaximal, Sylow
181C2×C47—22no—
182C2×C47—41no—
183C2×C47—42no—
184C2×C47—81no—
185C2×C47#54611yescharacteristic
186C2×C47C2×#13711yescharacteristic
187C2×C47#57611yescharacteristic
188#554—471no—
189#546D4711yescharacteristic
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×#41C2×D4711yescharacteristic
205C22×D4C2×D4711yescharacteristic
206C2×Q16—471no—
207C2×SD16—471no—
208C2×SD16—471no—
209C2×M16—471no—
210C22×C8—471no—
211C4⋊Q8—471no—
212#125—941no—
213#124C2×D4711yescharacteristic
214#123—21no—
215C22⋊Q8—471no—
216C22⋊Q8—471no—
217C22⋊Q8—941no—
218C22⋊Q8—941no—
219C22⋊Q8C2×D4711yescharacteristic
220#121—21no—
221#121C2×D4711yescharacteristic
222#120—21no—
223C4×Q8—471no—
224C4×D4—941no—
225C4×D4C2×D4711yescharacteristic
226C4×D4C2×D4711yescharacteristic
227C2×C4⋊C4—471no—
228C2×C4⋊C4—471no—
229C2×C22⋊C4—21no—
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—21no—
248#41—22no—
249#41—41no—
250C2×Q8—471no—
251C2×Q8—941no—
252C2×Q8C22×D4711yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊D4711yescharacteristic
259C2×D4C22×D4711yescharacteristic
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—471no—
278C4⋊C4—471no—
279C4⋊C4—471no—
280C4⋊C4—941no—
281C4⋊C4—941no—
282C4⋊C4—941no—
283C4⋊C4—941no—
284C4⋊C4—941no—
285C4⋊C4—941no—
286C4⋊C4C22⋊D4711yescharacteristic
287C4⋊C4C22×D4711yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4C22⋊D4711yescharacteristic
296C22⋊C4C22⋊D4711yescharacteristic
297C42—941no—
298C42C22×D4711yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D4711yescharacteristic
305C23C2×C22⋊D4711yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—941no—
309Q8—941no—
310Q8—3761no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#1062535212yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—941no—
328C2×C4—941no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—3761no—
332C2×C4—3761no—
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—22no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#1309405412yes—
355C22C22×C22⋊D4711yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—1881no—
363C4—1881no—
364C4—1881no—
365C4—1881no—
366C4C2×#1062535211yescharacteristic
367C4#1309406911yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#1568976711yescharacteristic
373C2C2×#1309405411yescharacteristic
374C2#1568992611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#546C2
socleC22×C47C22×D4
hypercenter#546D47
hypocenterC47#3314
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #15689830C2semidirect
2. #15689482C2semidirect
3. #15689456C2semidirect
4. #15689434C2semidirect
5. #15689403C2semidirect
6. #15689367C2semidirect
7. #15689362C2semidirect
8. #15689342C2semidirect
9. #15689285C2semidirect
10. #15689274C2semidirect
11. #15689223C2semidirect
12. #15689195C2semidirect
13. #15689124C2semidirect
14. C2×#13093945C2semidirect
16. C2×#10625337C22semidirect
19. C2×#10625329C22semidirect
21. #13094024C22semidirect
24. #13094003C22semidirect
27. C4×Dic94C22semidirect
30. C2×C4⋊Dic47C22semidirect
31. #13093957C22semidirect
32. #13093957C22semidirect
33. #13093957C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. #13093948C22semidirect
36. #13093948C22semidirect
37. #13093948C22semidirect
38. #13093947C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. #13093935C22semidirect
203. C47#3314semidirect