Finite Group Databasebeta

← #20254176

Subgroups — #20254176

Order 6016.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689634C211yesmaximal, characteristic, complemented
2#15689464C211yesmaximal, characteristic, complemented
3#15689461C211yesmaximal, characteristic, complemented
4#15689447C211yesmaximal, characteristic, complemented
5#15689444C211yesmaximal, characteristic, complemented
6#15689362C211yesmaximal, characteristic, complemented
7#15689357C211yesmaximal, characteristic, complemented
8#15689354C211yesmaximal, characteristic, complemented
9#15689350C211yesmaximal, characteristic, complemented
10#15689285C211yesmaximal, characteristic, complemented
11#15689283C211yesmaximal, characteristic, complemented
12#15689268C211yesmaximal, characteristic, complemented
13#15689266C211yesmaximal, characteristic, complemented
14C2×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
15C47×#525C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625337C2211yescharacteristic, complemented
18C2×#10625335C2211yescharacteristic, complemented
19C2×#10625336C2211yescharacteristic, complemented
20C2×#10625334C2211yescharacteristic, complemented
21C22×C47⋊C8C2211yescharacteristic
22C22×C47⋊C8C2211yescharacteristic
23#13094007—21no—
24#13094003C2211yescharacteristic
25#13094003C2211yescharacteristic
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic
28#13093993—21no—
29C4×C22⋊D47—21no—
30C4×C22⋊D47—21no—
31#13093983C2211yescharacteristic
32#13093957C2211yescharacteristic, complemented
33#13093957C2211yescharacteristic, complemented
34#13093955C2211yescharacteristic, complemented
35#13093955C2211yescharacteristic, complemented
36#13093948C2211yescharacteristic, complemented
37#13093948C2211yescharacteristic, complemented
38#13093947C2211yescharacteristic, complemented
39#13093947C2211yescharacteristic, complemented
40#13093945C2211yescharacteristic, complemented
41#13093945C2211yescharacteristic, complemented
42#13093944C2211yescharacteristic, complemented
43#13093944C2211yescharacteristic, complemented
44C22⋊(C47⋊C8)C2211yescharacteristic
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic
47C22⋊(C47⋊C8)C2211yescharacteristic
48C2×#41×C47C2211yescharacteristic
49C23×C4×C47C2211yescharacteristic
50#123×C47—21no—
51C22⋊Q8×C47C2211yescharacteristic
52C22⋊Q8×C47C2211yescharacteristic
53#121×C47C2211yescharacteristic
54#121×C47C2211yescharacteristic
55#120×C47—21no—
56C4×D4×C47—21no—
57C4×D4×C47—21no—
58#117×C47C2211yescharacteristic
59C24×C47D411yescharacteristic
60#41×C47—41no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47—21no—
68C22×C4×C47—41no—
69C22×C4×C47—41no—
70C22×C4×C47D411yescharacteristic
71C22×C4×C47D411yescharacteristic
72C22×C4×C47D411yescharacteristic
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C22×C4×C47C2311yescharacteristic
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79#10625350—41no—
80#10625350—41no—
81C2×D188C2311yescharacteristic
82C2×C4×D47—21no—
83C2×Dic94C2311yescharacteristic
84C4⋊C4×C47—21no—
85C4⋊C4×C47—21no—
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C22⋊C4×C47—21no—
93C42×C47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97#10625337—41no—
98#10625336—41no—
99#10625335—41no—
100#10625334—41no—
101(C2×D47)⋊C4—21no—
102(C2×D47)⋊C4—21no—
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107C4×Dic47—21no—
108C2×C47⋊C8—41no—
109C2×C47⋊C8—41no—
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C2×C47⋊C8C2311yescharacteristic
113C2×C47⋊C8C2311yescharacteristic
114C23×C47—22no—
115C23×C47—21no—
116C23×C47—41no—
117C23×C47—41no—
118C23×C47C2×D411yescharacteristic
119C23×C47C2×D411yescharacteristic
120C23×C47C2×D411yescharacteristic
121C22×D47—21no—
122Q8×C47—21no—
123Q8×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—42no—
127D4×C47—42no—
128D4×C47—42no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—21no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—41no—
141C2×C4×C47—42no—
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2×D411yescharacteristic
144C2×C4×C47C2×D411yescharacteristic
145C2×C4×C47C2411yescharacteristic
146C22⋊D47—42no—
147C22⋊D47—42no—
148C22⋊D47—42no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152D188—21no—
153D188—21no—
154C4×D47—42no—
155Dic94—21no—
156Dic94—21no—
157C47⋊C8—21no—
158C47⋊C8—21no—
159C47⋊C8—21no—
160C47⋊C8—21no—
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—21no—
167C22×C47—21no—
168C22×C47—21no—
169C22×C47—44no—
170C22×C47—41no—
171C22×C47—41no—
172C22×C47—41no—
173C22×C47#13512yes—
174C22×C47C22×D411yescharacteristic
175C2×D47—41no—
176C2×D47—41no—
177C2×D47—41no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—41no—
182C4×C47—41no—
183C4×C47—41no—
184C4×C47H(5,𝔽2)11yescharacteristic
185C4×C47H(5,𝔽2)11yescharacteristic
186Dic47—41no—
187Dic47—41no—
188Dic47—41no—
189#3191—471nomaximal, Sylow
190C2×C47—22no—
191C2×C47—41no—
192C2×C47—41no—
193C2×C47—81no—
194C2×C47#53411yescharacteristic
195C2×C47C2×#13511yescharacteristic
196C2×C47#57511yescharacteristic
197D47—81no—
198#525—471no—
199#525D4711yescharacteristic, complemented
200#485—471no—
201#485—471no—
202#482—471no—
203#482—471no—
204#467—471no—
205#466—471no—
206#465—471no—
207#465—471no—
208#452—471no—
209#452—471no—
210#449—471no—
211#449—471no—
212C2×C22⋊C8—471no—
213C47#319111yescharacteristic, complemented, Sylow
214C2×#41—471no—
215C2×#41C2×D4711yescharacteristic
216C23×C4C2×D4711yescharacteristic
217C2×Q16—471no—
218C2×SD16—471no—
219C2×SD16—471no—
220C2×D8—471no—
221C22×C8—471no—
222C22×C8—471no—
223#123—21no—
224#123—941no—
225C22⋊Q8—471no—
226C22⋊Q8—471no—
227C22⋊Q8C2×D4711yescharacteristic
228C22⋊Q8C2×D4711yescharacteristic
229#121—471no—
230#121—471no—
231#121C2×D4711yescharacteristic
232#121C2×D4711yescharacteristic
233#120—21no—
234#120—941no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—941no—
238C4×D4—941no—
239#117—471no—
240#117C2×D4711yescharacteristic
241#107—471no—
242#107—471no—
243#106—471no—
244#106—471no—
245#103—471no—
246#103—471no—
247#103—471no—
248#103—471no—
249#102—471no—
250#102—471no—
251#102—471no—
252#102—471no—
253C22⋊C8—471no—
254C22⋊C8—471no—
255C22⋊C8—471no—
256C22⋊C8—471no—
257C24C22⋊D4711yescharacteristic
258#41—41no—
259#41—41no—
260#41—1881no—
261#41—1881no—
262C2×Q8—471no—
263C2×Q8C22×D4711yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—471no—
268C2×D4—941no—
269C2×D4—941no—
270C2×D4—941no—
271C2×D4C22×D4711yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—941no—
276C22×C4C22⋊D4711yescharacteristic
277C22×C4C22⋊D4711yescharacteristic
278C22×C4C22⋊D4711yescharacteristic
279C22×C4C22×D4711yescharacteristic
280C22×C4C22×D4711yescharacteristic
281C22×C4C22×D4711yescharacteristic
282Q16—1881no—
283SD16—1881no—
284SD16—1881no—
285D8—1881no—
286C2×C8—471no—
287C2×C8—471no—
288C2×C8—471no—
289C2×C8—471no—
290C2×C8—1881no—
291C2×C8—1881no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—471no—
295C4⋊C4—471no—
296C4⋊C4—941no—
297C4⋊C4—941no—
298C4⋊C4C22×D4711yescharacteristic
299C4⋊C4C22×D4711yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—941no—
306C22⋊C4—941no—
307C22⋊C4—941no—
308C22⋊C4—941no—
309C22⋊C4—941no—
310C42—21no—
311C42—941no—
312C23—22no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—941no—
317C23C2×C22⋊D4711yescharacteristic
318C23C2×C22⋊D4711yescharacteristic
319C23C2×C22⋊D4711yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—941no—
323Q8—941no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—941no—
330D4—941no—
331D4—1882no—
332D4—1882no—
333D4—1882no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—941no—
348C2×C4—941no—
349C2×C4—941no—
350C2×C4—1882no—
351C2×C4C2×C22⋊D4711yescharacteristic
352C2×C4C2×C22⋊D4711yescharacteristic
353C2×C4C2×C22⋊D4711yescharacteristic
354C2×C4C23×D4711yescharacteristic
355C8—941no—
356C8—941no—
357C8—941no—
358C8—941no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—44no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—1881no—
372C22—1881no—
373C22—1881no—
374C22#1309404412yes—
375C22C22×C22⋊D4711yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—1881no—
383C4—1881no—
384C4—1881no—
385C4#1309406911yescharacteristic
386C4#1309406911yescharacteristic
387C2—22no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—3761no—
392C2#1568968211yescharacteristic
393C2C2×#1309404411yescharacteristic
394C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#525C2
socleC22×C47C22×D4
hypercenter#525D47
hypocenterC47#3191
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #15689634C2semidirect
2. #15689464C2semidirect
3. #15689461C2semidirect
4. #15689447C2semidirect
5. #15689444C2semidirect
6. #15689362C2semidirect
7. #15689357C2semidirect
8. #15689354C2semidirect
9. #15689350C2semidirect
10. #15689285C2semidirect
11. #15689283C2semidirect
12. #15689268C2semidirect
13. #15689266C2semidirect
14. C2×C22⋊(C47⋊C8)C2semidirect
15. C47×#525C2semidirect
17. C2×#10625337C22semidirect
18. C2×#10625335C22semidirect
19. C2×#10625336C22semidirect
20. C2×#10625334C22semidirect
32. #13093957C22semidirect
33. #13093957C22semidirect
34. #13093955C22semidirect
35. #13093955C22semidirect
36. #13093948C22semidirect
37. #13093948C22semidirect
38. #13093947C22semidirect
39. #13093947C22semidirect
40. #13093945C22semidirect
41. #13093945C22semidirect
42. #13093944C22semidirect
43. #13093944C22semidirect
199. #525D47semidirect
213. C47#3191semidirect