Finite Group Databasebeta

← #20253522

Subgroups — #20253522

Order 6016.

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

normal subgroups only

This group has 450 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×C4×D188C211yesmaximal, characteristic, complemented
2#15689451C211yesmaximal, characteristic, complemented
3#15689434C211yesmaximal, characteristic, complemented
4#15689420C212yesmaximal, complemented
5#15689335C212yesmaximal, complemented
6#15689273C211yesmaximal, characteristic, complemented
7#15689256C211yesmaximal, characteristic
8#15689233C212yesmaximal, complemented
9#15689221C212yesmaximal, complemented
10#15689180C211yesmaximal, characteristic, complemented
11C47×#529C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13C22×C4×D47—21no—
14C2×#10625336C2212yes—
15C2×#10625334C2212yes—
16C4×D188—21no—
17C4×D188—21no—
18C4×D188C2212yes—
19C4×D188C2212yes—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×(C2×D47)⋊C4—21no—
22#13093957C2212yescomplemented
23#13093955C2212yescomplemented
24C4⋊(C47⋊C8)C2212yescomplemented
25#13093948C2212yescomplemented
26#13093945C2212yescomplemented
27#13093944C2212yes—
28#13093944C2212yes—
29C22⋊(C47⋊C8)C2211yescharacteristic
30C22⋊(C47⋊C8)C2211yescharacteristic
31#13093935C2212yescomplemented
32#126×C47—21no—
33#125×C47C2211yescharacteristic, complemented
34#124×C47C2211yescharacteristic, complemented
35#123×C47—21no—
36C22⋊Q8×C47C2211yescharacteristic
37#121×C47C2211yescharacteristic
38C4×Q8×C47C2211yescharacteristic, complemented
39C4×D4×C47—21no—
40C4×D4×C47C2211yescharacteristic, complemented
41#117×C47—21no—
42C2×C42×C47C2211yescharacteristic
43C23×D47—21no—
44C2×Q8×C47C2311yescharacteristic
45C2×D4×C47—21no—
46C2×D4×C47C2311yescharacteristic
47C22×C4×C47—21no—
48C22×C4×C47D411yescharacteristic
49C22×C4×C47D411yescharacteristic
50C22×C4×C47C2311yescharacteristic
51C22×Dic47—21no—
52C2×D188—21no—
53C2×D188—24no—
54C2×D188C2312yes—
55C2×C4×D47—22no—
56C2×C4×D47—22no—
57C2×C4×D47—44no—
58C4⋊C4×C47—21no—
59C4⋊C4×C47—21no—
60C4⋊C4×C47—21no—
61C4⋊C4×C47—21no—
62C4⋊C4×C47C2311yescharacteristic
63C4⋊C4×C47C2311yescharacteristic
64C22⋊C4×C47—21no—
65C22⋊C4×C47—21no—
66C22⋊C4×C47—21no—
67C22⋊C4×C47—21no—
68C22⋊C4×C47—21no—
69C42×C47—21no—
70C42×C47D411yescharacteristic
71C42×C47D411yescharacteristic
72C42×C47C2311yescharacteristic
73C42×C47C2311yescharacteristic
74#10625336—24no—
75#10625334—24no—
76(C2×D47)⋊C4—22no—
77(C2×D47)⋊C4—22no—
78C4⋊Dic47—21no—
79C4⋊Dic47C2312yes—
80C2×C47⋊C8C2312yes—
81C2×C47⋊C8C2312yes—
82C23×C47—21no—
83C23×C47C2×D411yescharacteristic
84C22×D47—24no—
85C22×D47—22no—
86C22×D47—42no—
87C22×D47—42no—
88Q8×C47—22no—
89D4×C47—22no—
90D4×C47—42no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—41no—
97C2×C4×C47—42no—
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2×D411yescharacteristic
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2411yescharacteristic
104C2×Dic47—22no—
105C2×Dic47—42no—
106D188—24no—
107D188—22no—
108D188#4114yes—
109C4×D47—44no—
110C4×D47—44no—
111C47⋊C8—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—21no—
126C4×C47—21no—
127C4×C47—21no—
128C4×C47—21no—
129C4×C47—41no—
130C4×C47—41no—
131C4×C47—41no—
132C4×C47C2×#4112yes—
133Dic47—42no—
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#529D4711yescharacteristic, complemented
142C2×C4×D4—471no—
143#483—471no—
144#480—471no—
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—21no—
158#125C2×D4711yescharacteristic, complemented
159#124C2×D4711yescharacteristic, complemented
160#123—21no—
161C22⋊Q8C2×D4711yescharacteristic
162#121C2×D4711yescharacteristic
163C4×Q8C2×D4711yescharacteristic, complemented
164C4×D4—21no—
165C4×D4—472no—
166C4×D4—472no—
167C4×D4—941no—
168C4×D4—941no—
169C4×D4C2×D4711yescharacteristic, complemented
170#117—21no—
171C2×C4⋊C4—471no—
172C2×C22⋊C4—941no—
173C2×C42C2×D4711yescharacteristic
174#107—472no—
175#106—472no—
176C4⋊C8—472no—
177#103—472no—
178#102—472no—
179#102—472no—
180#102—472no—
181C22⋊C8—471no—
182C22⋊C8—471no—
183#97—472no—
184C24—941no—
185C2×Q8C22×D4711yescharacteristic
186C2×D4—21no—
187C2×D4—472no—
188C2×D4—944no—
189C2×D4—941no—
190C2×D4C22×D4711yescharacteristic
191C22×C4—21no—
192C22×C4—941no—
193C22×C4—942no—
194C22×C4—942no—
195C22×C4—1884no—
196C22×C4C22⋊D4711yescharacteristic
197C22×C4C22⋊D4711yescharacteristic
198C22×C4C22×D4711yescharacteristic
199SD16—944no—
200D8—944no—
201C2×C8—472no—
202C2×C8—472no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—472no—
208C4⋊C4—941no—
209C4⋊C4C22×D4711yescharacteristic
210C4⋊C4C22×D4711yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—21no—
215C22⋊C4—21no—
216C22⋊C4—942no—
217C22⋊C4—942no—
218C42—21no—
219C42C22⋊D4711yescharacteristic
220C42C22⋊D4711yescharacteristic
221C42C22×D4711yescharacteristic
222C42C22×D4711yescharacteristic
223C23—21no—
224C23—944no—
225C23—942no—
226C23—1882no—
227C23—1882no—
228C23C2×C22⋊D4711yescharacteristic
229Q8—22no—
230D4—22no—
231D4—42no—
232D4—474no—
233D4—944no—
234D4—942no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—942no—
243C2×C4—1884no—
244C2×C4—1884no—
245C2×C4—1882no—
246C2×C4C2×C22⋊D4711yescharacteristic
247C2×C4C2×C22⋊D4711yescharacteristic
248C2×C4C2×C22⋊D4711yescharacteristic
249C2×C4C2×C22⋊D4711yescharacteristic
250C2×C4C2×C22⋊D4711yescharacteristic
251C2×C4C23×D4711yescharacteristic
252C8—942no—
253C8—942no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—944no—
260C22—1888no—
261C22—1882no—
262C22—1882no—
263C22#1309404912yes—
264C22C22×C22⋊D4711yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—1882no—
274C4#41×D4712yes—
275C2—22no—
276C2—81no—
277C2—1884no—
278C2#1568963011yescharacteristic
279C2C2×#1309404911yescharacteristic
280C2#1568992111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#529C2
socleC22×C47C22×D4
hypercenter#529D47
hypocenterC47#3114
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×C4×D188C2semidirect
2. #15689451C2semidirect
3. #15689434C2semidirect
4. #15689420C2semidirect
5. #15689335C2semidirect
6. #15689273C2semidirect
8. #15689233C2semidirect
9. #15689221C2semidirect
10. #15689180C2semidirect
11. C47×#529C2semidirect
22. #13093957C22semidirect
23. #13093955C22semidirect
24. C4⋊(C47⋊C8)C22semidirect
25. #13093948C22semidirect
26. #13093945C22semidirect
31. #13093935C22semidirect
33. #125×C47C22semidirect
34. #124×C47C22semidirect
38. C4×Q8×C47C22semidirect
40. C4×D4×C47C22semidirect
141. #529D47semidirect
152. C47#3114semidirect
158. #125C2×D47semidirect
159. #124C2×D47semidirect
163. C4×Q8C2×D47semidirect
169. C4×D4C2×D47semidirect