Finite Group Databasebeta

← #20253523

Subgroups — #20253523

Order 6016.

450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#15689654C211yesmaximal, characteristic, complemented
2C2×#13093986C211yesmaximal, characteristic, complemented
3#15689453C211yesmaximal, characteristic, complemented
4#15689426C212yesmaximal, complemented
5#15689337C212yesmaximal, complemented
6#15689276C211yesmaximal, characteristic, complemented
7#15689256C211yesmaximal, characteristic
8#15689232C212yesmaximal, complemented
9#15689222C212yesmaximal, complemented
10#15689177C211yesmaximal, characteristic, complemented
11C47×#480C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C4×D47—21no—
14C2×#10625325C2212yes—
15C2×#10625334C2212yes—
16#13094017—21no—
17#13094015C2211yescharacteristic, complemented
18#13094011C2211yescharacteristic, complemented
19#13094005—21no—
20#13094003C2211yescharacteristic
21#13093989C2211yescharacteristic, complemented
22D4×Dic47—21no—
23D4×Dic47C2211yescharacteristic, complemented
24#13093986—21no—
25#13093986—21no—
26#13093986C2212yes—
27#13093986C2212yes—
28#13093980—21no—
29C2×(C2×D47)⋊C4—21no—
30C2×C4×Dic47C2211yescharacteristic
31#13093955C2212yescomplemented
32Dic47⋊C8C2212yescomplemented
33#13093947C2212yescomplemented
34#13093946C2212yes—
35#13093944C2212yes—
36C22⋊(C47⋊C8)C2211yescharacteristic
37#13093934C2212yescomplemented
38#121×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#107×C47C2212yescomplemented
41#102×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C23×D47—21no—
44C2×D4×C47—21no—
45C2×D4×C47C2311yescharacteristic
46C22×C4×C47—21no—
47C22×C4×C47C2311yescharacteristic
48C22×Dic47—21no—
49C22×Dic47D411yescharacteristic
50C22×Dic47D411yescharacteristic
51C2×D188—21no—
52C2×D188—24no—
53C2×D188C2312yes—
54C2×C4×D47—22no—
55C2×C4×D47—22no—
56C2×C4×D47—44no—
57C2×Dic94C2311yescharacteristic
58C2×C8×C47C2312yes—
59C4⋊C4×C47—21no—
60C4⋊C4×C47C2311yescharacteristic
61C4⋊C4×C47C2312yes—
62C22⋊C4×C47—21no—
63C22⋊Dic47—21no—
64C22⋊Dic47—21no—
65C22⋊Dic47—21no—
66C22⋊Dic47—21no—
67#10625334—24no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4—22no—
70C4⋊Dic47—21no—
71C4⋊Dic47C2311yescharacteristic
72Dic47⋊C4—21no—
73Dic47⋊C4—21no—
74Dic47⋊C4—21no—
75C4×Dic47—21no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C4×Dic47C2311yescharacteristic
80C2×C47⋊C8C2312yes—
81#10625325—24no—
82C23×C47—21no—
83C23×C47C2×D411yescharacteristic
84C22×D47—24no—
85C22×D47—22no—
86C22×D47—42no—
87C22×D47—42no—
88D4×C47—22no—
89D4×C47—42no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—42no—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2411yescharacteristic
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—41no—
100C2×Dic47—42no—
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D411yescharacteristic
104C2×Dic47C2×D411yescharacteristic
105D188—24no—
106D188—22no—
107D188#4114yes—
108C4×D47—44no—
109C4×D47—44no—
110Dic94—22no—
111C8×C47—22no—
112C47⋊C8—22no—
113C22×C47—21no—
114C22×C47—21no—
115C22×C47—41no—
116C22×C47—41no—
117C22×C47—41no—
118C22×C47AGL(1,ℤ/8)12yes—
119C22×C47C22×D411yescharacteristic
120C2×D47—24no—
121C2×D47—48no—
122C2×D47—42no—
123C2×D47—42no—
124C4×C47—21no—
125C4×C47—42no—
126C4×C47—41no—
127C4×C47C2×#4112yes—
128Dic47—21no—
129Dic47—21no—
130Dic47—21no—
131Dic47—21no—
132Dic47—41no—
133Dic47—41no—
134#3114—471nomaximal, Sylow
135C2×C47—22no—
136C2×C47—81no—
137C2×C47#52511yescharacteristic
138C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C47#57511yescharacteristic
140D47—44no—
141#529—471no—
142C2×C4×D4—471no—
143#483—471no—
144#480D4711yescharacteristic, complemented
145#478—472no—
146#463—472no—
147#450—471no—
148#447—471no—
149#442—472no—
150#440—472no—
151#432—471no—
152C47#311411yescharacteristic, complemented, Sylow
153C22×D4—471no—
154C23×C4—941no—
155C2×SD16—472no—
156C2×D8—472no—
157#126—941no—
158#125—471no—
159#124—471no—
160#123—941no—
161C22⋊Q8—471no—
162#121C2×D4711yescharacteristic
163C4×Q8—471no—
164C4×D4—471no—
165C4×D4—472no—
166C4×D4—472no—
167C4×D4—941no—
168C4×D4—941no—
169C4×D4—941no—
170#117—941no—
171C2×C4⋊C4C2×D4711yescharacteristic
172C2×C22⋊C4—941no—
173C2×C42—471no—
174#107C2×D4712yescomplemented
175#106—472no—
176C4⋊C8—472no—
177#103—472no—
178#102—472no—
179#102—472no—
180#102C2×D4712yescomplemented
181C22⋊C8—471no—
182C22⋊C8C2×D4711yescharacteristic
183#97—472no—
184C24—941no—
185C2×Q8—471no—
186C2×D4—21no—
187C2×D4—472no—
188C2×D4—944no—
189C2×D4—941no—
190C2×D4C22×D4711yescharacteristic
191C22×C4—21no—
192C22×C4—471no—
193C22×C4—471no—
194C22×C4—942no—
195C22×C4—942no—
196C22×C4—941no—
197C22×C4—1884no—
198C22×C4C22×D4711yescharacteristic
199SD16—944no—
200D8—944no—
201C2×C8—472no—
202C2×C8C22×D4712yes—
203C4⋊C4—21no—
204C4⋊C4—471no—
205C4⋊C4—941no—
206C4⋊C4—941no—
207C4⋊C4—941no—
208C4⋊C4—941no—
209C4⋊C4C22×D4711yescharacteristic
210C4⋊C4C22×D4712yes—
211C22⋊C4—21no—
212C22⋊C4—942no—
213C22⋊C4—942no—
214C22⋊C4—941no—
215C22⋊C4—941no—
216C22⋊C4—941no—
217C22⋊C4—941no—
218C42—471no—
219C42—471no—
220C42—471no—
221C42—471no—
222C42—941no—
223C23—21no—
224C23—944no—
225C23—942no—
226C23—1882no—
227C23—1882no—
228C23D4×D4711yescharacteristic
229Q8—942no—
230D4—22no—
231D4—42no—
232D4—474no—
233D4—944no—
234D4—942no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—471no—
240C2×C4—471no—
241C2×C4—471no—
242C2×C4—471no—
243C2×C4—942no—
244C2×C4—941no—
245C2×C4—941no—
246C2×C4—1884no—
247C2×C4—1884no—
248C2×C4—1881no—
249C2×C4—1882no—
250C2×C4D4×D4711yescharacteristic
251C2×C4C23×D4711yescharacteristic
252C8—22no—
253C8—942no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—944no—
260C22—1888no—
261C22—1882no—
262C22—1882no—
263C22#1309404812yes—
264C22C2×D4×D4711yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—941no—
269C4—941no—
270C4—941no—
271C4—941no—
272C4—1881no—
273C4—1881no—
274C4#41×D4712yes—
275C2—22no—
276C2—81no—
277C2—1884no—
278C2#1568963111yescharacteristic
279C2C2×#1309404811yescharacteristic
280C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#480C2
socleC22×C47C22×D4
hypercenter#480D47
hypocenterC47#3114
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #15689654C2semidirect
2. C2×#13093986C2semidirect
3. #15689453C2semidirect
4. #15689426C2semidirect
5. #15689337C2semidirect
6. #15689276C2semidirect
8. #15689232C2semidirect
9. #15689222C2semidirect
10. #15689177C2semidirect
11. C47×#480C2semidirect
17. #13094015C22semidirect
18. #13094011C22semidirect
21. #13093989C22semidirect
23. D4×Dic47C22semidirect
31. #13093955C22semidirect
32. Dic47⋊C8C22semidirect
33. #13093947C22semidirect
37. #13093934C22semidirect
40. #107×C47C22semidirect
41. #102×C47C22semidirect
144. #480D47semidirect
152. C47#3114semidirect
174. #107C2×D47semidirect
180. #102C2×D47semidirect