Finite Group Databasebeta

← #20255003

Subgroups — #20255003

Order 6016.

556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094051C212yesmaximal, complemented
2#15689795C211yesmaximal, characteristic, complemented
3#15689758C211yesmaximal, characteristic, complemented
4#15689499C211yesmaximal, characteristic, complemented
5#15689375C212yesmaximal, complemented
6#15689319C211yesmaximal, characteristic, complemented
7#15689267C212yesmaximal, complemented
8#15689258C212yesmaximal, complemented
9C4×#10625336C211yesmaximal, characteristic, complemented
10#15689200C211yesmaximal, characteristic, complemented
11C47×#460C211yesmaximal, characteristic, complemented
12C2×#10625354C2212yescomplemented
13C2×D4×D47—21no—
14C2×D4×D47C2212yes—
15#13094051—28no—
16C2×#10625336C2211yescharacteristic
17C2×D376C2212yes—
18C2×#10625334C2212yescomplemented
19C2×#10625334C2212yescomplemented
20C2×#10625324C2212yescomplemented
21#13094021—21no—
22#13094021C2211yescharacteristic, complemented
23#13093999—22no—
24#13093999C2212yescomplemented
25#13093995—21no—
26#13093995C2212yes—
27#13093992—22no—
28C4×D188—21no—
29C4×D188C2211yescharacteristic
30C4×D188C2211yescharacteristic
31#13093955C2211yescharacteristic, complemented
32#13093948C2211yescharacteristic, complemented
33#13093946C2212yescomplemented
34#13093944C2211yescharacteristic
35(C2×D47)⋊C8C2212yescomplemented
36C4×C47⋊C8C2211yescharacteristic, complemented
37C2×SD16×C47C2212yescomplemented
38#127×C47C2211yescharacteristic
39C4×Q8×C47C2211yescharacteristic, complemented
40C4⋊C8×C47C2211yescharacteristic, complemented
41#102×C47C2212yescomplemented
42C23×D47—22no—
43C2×Q8×C47C2311yescharacteristic
44C2×D4×C47—21no—
45C2×D4×C47—21no—
46C2×D4×C47C2312yes—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49#10625354—24no—
50#10625354—42no—
51D4×D47—24no—
52D4×D47—42no—
53D4×D47—44no—
54C2×D188—22no—
55C2×D188—21no—
56C2×D188—22no—
57C2×D188—21no—
58C2×D188D411yescharacteristic
59C2×D188C2312yes—
60C2×D188C2311yescharacteristic
61C2×C4×D47—21no—
62C2×C4×D47—22no—
63C2×C4×D47C2312yes—
64SD16×C47—24no—
65C2×C8×C47C2312yes—
66C4⋊C4×C47—21no—
67C4⋊C4×C47C2311yescharacteristic
68C42×C47—21no—
69C42×C47C2311yescharacteristic
70C22⋊Dic47—22no—
71#10625336D414yescomplemented
72#10625334—24no—
73#10625334—42no—
74(C2×D47)⋊C4—21no—
75(C2×D47)⋊C4—22no—
76(C2×D47)⋊C4D412yes—
77C4⋊Dic47D411yescharacteristic
78C4⋊Dic47C2311yescharacteristic
79C2×C47⋊C8C2311yescharacteristic
80C2×C47⋊C8C2311yescharacteristic
81D376—24no—
82#10625324—24no—
83C23×C47—22no—
84C22×D47—21no—
85C22×D47—22no—
86C22×D47—44no—
87C22×D47—44no—
88C22×D47—82no—
89C22×D47C2×D412yes—
90Q8×C47—21no—
91Q8×C47C2×D412yescomplemented
92D4×C47—22no—
93D4×C47—22no—
94D4×C47—42no—
95D4×C47—81no—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2411yescharacteristic
101C22⋊D47—44no—
102C22⋊D47—44no—
103C2×Dic47—21no—
104C2×Dic47C2×D412yes—
105D188—22no—
106D188—22no—
107D188—21no—
108D188—22no—
109D188—44no—
110D188—42no—
111D188—81no—
112D188—82no—
113D188C2×D412yes—
114C4×D47—22no—
115C4×D47—22no—
116C4×D47—44no—
117C4×D47—42no—
118C8×C47—22no—
119C47⋊C8—21no—
120C47⋊C8C2×D412yescomplemented
121C22×C47—42no—
122C22×C47—42no—
123C22×C47—42no—
124C22×C47C22×D411yescharacteristic
125C2×D47—22no—
126C2×D47—22no—
127C2×D47—22no—
128C2×D47—22no—
129C2×D47—41no—
130C2×D47—41no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—42no—
134C2×D47—88no—
135C4×C47—22no—
136C4×C47—21no—
137C4×C47—41no—
138C4×C47AGL(1,ℤ/8)12yescomplemented
139C4×C47C22×D411yescharacteristic
140C4×C47H(5,𝔽2)11yescharacteristic
141Dic47—22no—
142Dic47—41no—
143#3274—471nomaximal, Sylow
144C2×C47—82no—
145C2×C47D4211yescharacteristic
146C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C47#57611yescharacteristic
148D47—42no—
149D47—42no—
150D47—82no—
151C2×AGL(1,ℤ/8)—472no—
152#550—471no—
153D42—471no—
154#493—471no—
155#469—472no—
156#460D4711yescharacteristic, complemented
157#459—471no—
158#449—472no—
159#447—472no—
160C4×SD16—471no—
161#436—471no—
162C47#327411yescharacteristic, complemented, Sylow
163C2×#41—472no—
164C22×D4—472no—
165C22×D4—941no—
166AGL(1,ℤ/8)—948no—
167C2×SD16—471no—
168C2×SD16C2×D4712yescomplemented
169C2×D8—472no—
170C2×D8—472no—
171C2×D8—472no—
172C2×M16—472no—
173#127—471no—
174#127—941no—
175#127C2×D4711yescharacteristic
176#121—472no—
177#121—472no—
178#121—942no—
179#121—941no—
180#120—942no—
181C4×Q8C2×D4711yescharacteristic, complemented
182C4×D4—471no—
183C4×D4—471no—
184C4×D4—941no—
185#106—471no—
186C4⋊C8C2×D4711yescharacteristic, complemented
187#103—471no—
188#102—472no—
189#102—471no—
190#102C2×D4712yescomplemented
191C22⋊C8—472no—
192C4×C8—471no—
193C24—942no—
194#41—944no—
195#41—1882no—
196C2×Q8C22×D4711yescharacteristic
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—471no—
200C2×D4—471no—
201C2×D4—472no—
202C2×D4—942no—
203C2×D4—942no—
204C2×D4—942no—
205C2×D4—944no—
206C2×D4—942no—
207C2×D4—941no—
208C2×D4—941no—
209C2×D4—1882no—
210C2×D4—1884no—
211C2×D4C22×D4712yes—
212C22×C4—472no—
213C22×C4—942no—
214C22×C4—941no—
215SD16—24no—
216SD16—474no—
217D8—944no—
218D8—944no—
219D8—1882no—
220M16—944no—
221C2×C8—471no—
222C2×C8—471no—
223C2×C8C22×D4712yes—
224C4⋊C4—21no—
225C4⋊C4—471no—
226C4⋊C4—471no—
227C4⋊C4C22×D4711yescharacteristic
228C22⋊C4—472no—
229C22⋊C4—942no—
230C22⋊C4—942no—
231C22⋊C4—941no—
232C42—21no—
233C42C22×D4711yescharacteristic
234C23—22no—
235C23—472no—
236C23—941no—
237C23—942no—
238C23—3762no—
239C23—1884no—
240C23—1884no—
241Q8—21no—
242Q8D4×D4712yescomplemented
243D4—22no—
244D4—22no—
245D4—42no—
246D4—81no—
247D4—472no—
248D4—942no—
249D4—942no—
250D4—941no—
251D4—942no—
252D4—3761no—
253D4—3762no—
254D4—1884no—
255D4—1884no—
256D4—1884no—
257D4—1882no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—472no—
261C2×C4—942no—
262C2×C4—942no—
263C2×C4—941no—
264C2×C4—1884no—
265C2×C4—1882no—
266C2×C4D4×D4711yescharacteristic
267C2×C4D4×D4711yescharacteristic
268C2×C4C23×D4711yescharacteristic
269C8—22no—
270C8—472no—
271C8—941no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—942no—
276C22—942no—
277C22—942no—
278C22—942no—
279C22—3768no—
280C22—1882no—
281C22—1882no—
282C22—1882no—
283C22—1881no—
284C22—1881no—
285C22C2×D4×D4711yescharacteristic
286C4—22no—
287C4—21no—
288C4—41no—
289C4—942no—
290C4—1881no—
291C4#1309405112yescomplemented
292C4C2×D4×D4711yescharacteristic
293C4#1309407011yescharacteristic
294C2—82no—
295C2—3762no—
296C2—1882no—
297C2—1882no—
298C2#1568975711yescharacteristic
299C2C2×#1309405111yescharacteristic
300C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3274
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#13094051C2semidirect
2. #15689795C2semidirect
3. #15689758C2semidirect
4. #15689499C2semidirect
5. #15689375C2semidirect
6. #15689319C2semidirect
7. #15689267C2semidirect
8. #15689258C2semidirect
9. C4×#10625336C2semidirect
10. #15689200C2semidirect
11. C47×#460C2semidirect
12. C2×#10625354C22semidirect
18. C2×#10625334C22semidirect
19. C2×#10625334C22semidirect
20. C2×#10625324C22semidirect
22. #13094021C22semidirect
24. #13093999C22semidirect
31. #13093955C22semidirect
32. #13093948C22semidirect
33. #13093946C22semidirect
35. (C2×D47)⋊C8C22semidirect
36. C4×C47⋊C8C22semidirect
37. C2×SD16×C47C22semidirect
39. C4×Q8×C47C22semidirect
40. C4⋊C8×C47C22semidirect
41. #102×C47C22semidirect
71. #10625336D4semidirect
91. Q8×C47C2×D4semidirect
120. C47⋊C8C2×D4semidirect
138. C4×C47AGL(1,ℤ/8)semidirect
156. #460D47semidirect
162. C47#3274semidirect
168. C2×SD16C2×D47semidirect
181. C4×Q8C2×D47semidirect
186. C4⋊C8C2×D47semidirect
190. #102C2×D47semidirect
242. Q8D4×D47semidirect
291. C4#13094051semidirect