Finite Group Databasebeta

← #20252628

Subgroups — #20252628

Order 6016.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#10625350C211yesmaximal, characteristic, complemented
2C2×#13094054C211yesmaximal, characteristic, complemented
3C2×#13094049C211yesmaximal, characteristic, complemented
4#15689283C214yesmaximal, complemented
5#15689266C214yesmaximal, complemented
6#15689131C211yesmaximal, characteristic, complemented
7#15689127C211yesmaximal, characteristic, complemented
8#15689087C211yesmaximal, characteristic, complemented
9C47×#525C211yesmaximal, characteristic, complemented
10C2×#10625350—22no—
11C2×#10625350—24no—
12C2×#10625350—24no—
13C2×#10625350C2214yes—
14C22×Dic94C2211yescharacteristic
15C22×D188C2211yescharacteristic
16C22×C22⋊D47—21no—
17C22×C4×D47—21no—
18#13094054—24no—
19#13094049—24no—
20C2×#10625337C2212yescomplemented
21C2×#10625335C2212yescomplemented
22C2×#10625336C2212yescomplemented
23C2×#10625334C2212yescomplemented
24C2×#10625329C2211yescharacteristic
25C2×#10625329C2211yescharacteristic
26#13093947C2214yescomplemented
27#13093944C2214yescomplemented
28C22⋊(C47⋊C8)C2214yescomplemented
29C2×#41×C47C2211yescharacteristic
30C23×C4×C47C2211yescharacteristic
31#123×C47—21no—
32C22⋊Q8×C47C2212yescomplemented
33#121×C47C2212yescomplemented
34#120×C47—21no—
35C4×D4×C47—22no—
36#117×C47C2211yescharacteristic
37C24×C47D411yescharacteristic
38C23×D47—21no—
39#41×C47—22no—
40#41×C47—22no—
41C2×Q8×C47C2311yescharacteristic
42C2×D4×C47—22no—
43C2×D4×C47—21no—
44C2×D4×C47C2311yescharacteristic
45C22×C4×C47—22no—
46C22×C4×C47—22no—
47C22×C4×C47—21no—
48C22×C4×C47D412yes—
49C22×C4×C47D411yescharacteristic
50C22×C4×C47C2312yes—
51C22×C4×C47C2311yescharacteristic
52C2×C22⋊D47—28no—
53C2×C22⋊D47—24no—
54C22×Dic47—21no—
55#10625350—216no—
56#10625350—28no—
57#10625350—28no—
58C2×D188—21no—
59C2×D188—22no—
60C2×D188D414yescomplemented
61C2×D188C2312yes—
62C2×C4×D47—28no—
63C2×C4×D47—24no—
64C2×Dic94—21no—
65C2×Dic94—22no—
66C2×Dic94D414yescomplemented
67C2×Dic94C2312yes—
68C4⋊C4×C47—22no—
69C4⋊C4×C47C2312yes—
70C22⋊C4×C47—21no—
71C22⋊C4×C47—22no—
72C22⋊C4×C47—22no—
73C42×C47—21no—
74#10625337—24no—
75#10625336—24no—
76#10625335—24no—
77#10625334—24no—
78#10625329—22no—
79#10625329—22no—
80C2×C47⋊C8C2312yes—
81C2×C47⋊C8C2312yes—
82C23×C47—22no—
83C23×C47—21no—
84C23×C47—42no—
85C23×C47C2×D412yes—
86C23×C47C2×D411yescharacteristic
87C22×D47—24no—
88C22×D47—22no—
89C22×D47—44no—
90Q8×C47—21no—
91Q8×C47—21no—
92D4×C47—21no—
93D4×C47—21no—
94D4×C47—44no—
95D4×C47—42no—
96C2×C4×C47—22no—
97C2×C4×C47—24no—
98C2×C4×C47—22no—
99C2×C4×C47—22no—
100C2×C4×C47—22no—
101C2×C4×C47—21no—
102C2×C4×C47—42no—
103C2×C4×C47C2×D412yes—
104C2×C4×C47C2×D412yes—
105C2×C4×C47C2×D412yes—
106C2×C4×C47C2×D411yescharacteristic
107C2×C4×C47C2411yescharacteristic
108C22⋊D47—216no—
109C2×Dic47—24no—
110C2×Dic47—22no—
111D188—24no—
112D188—22no—
113D188C2×D414yes—
114C4×D47—216no—
115Dic94—24no—
116Dic94—22no—
117Dic94C2×D414yes—
118C47⋊C8—22no—
119C47⋊C8—22no—
120C22×C47—22no—
121C22×C47—22no—
122C22×C47—22no—
123C22×C47—22no—
124C22×C47—44no—
125C22×C47—41no—
126C22×C47—42no—
127C22×C47#12012yes—
128C22×C47C22×D411yescharacteristic
129C2×D47—24no—
130C2×D47—48no—
131C2×D47—44no—
132C4×C47—22no—
133C4×C47—41no—
134C4×C47—42no—
135C4×C47#12012yes—
136C4×C47C22×D411yescharacteristic
137C4×C47C22×D411yescharacteristic
138Dic47—24no—
139#3005—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47—42no—
142C2×C47—81no—
143C2×C47C2×#12011yescharacteristic
144C2×C47#57512yes—
145D47—44no—
146C22×#41—471no—
147C2×#137—471no—
148C2×AGL(1,ℤ/8)—471no—
149#525D4711yescharacteristic, complemented
150#452—474no—
151#449—474no—
152#419—471no—
153#418—471no—
154#407—471no—
155C47#300511yescharacteristic, complemented, Sylow
156C2×#41—474no—
157C2×#41—944no—
158C2×#41—944no—
159C2×#41—942no—
160C2×#41C2×D4711yescharacteristic
161C22×Q8—471no—
162C22×D4—471no—
163C22×D4—941no—
164C23×C4—941no—
165C23×C4C2×D4711yescharacteristic
166#137—944no—
167AGL(1,ℤ/8)—944no—
168C2×Q16—472no—
169C2×SD16—472no—
170C2×SD16—472no—
171C2×D8—472no—
172C2×M16—471no—
173C2×M16—471no—
174#123—21no—
175C22⋊Q8C2×D4712yescomplemented
176#121C2×D4712yescomplemented
177#120—21no—
178C4×D4—22no—
179#117C2×D4711yescharacteristic
180#103—474no—
181#102—474no—
182C22⋊C8—474no—
183C24—941no—
184C24C22⋊D4711yescharacteristic
185#41—22no—
186#41—22no—
187#41—948no—
188#41—948no—
189#41—9416no—
190C2×Q8—474no—
191C2×Q8—472no—
192C2×Q8—942no—
193C2×Q8—941no—
194C2×Q8C22×D4711yescharacteristic
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—474no—
198C2×D4—472no—
199C2×D4—948no—
200C2×D4—944no—
201C2×D4—942no—
202C2×D4—941no—
203C2×D4C22×D4711yescharacteristic
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—21no—
207C22×C4—948no—
208C22×C4—941no—
209C22×C4—944no—
210C22×C4C22⋊D4712yes—
211C22×C4C22⋊D4711yescharacteristic
212C22×C4C22×D4712yes—
213C22×C4C22×D4711yescharacteristic
214Q16—944no—
215SD16—944no—
216SD16—944no—
217D8—944no—
218M16—942no—
219M16—942no—
220C2×C8—472no—
221C2×C8—472no—
222C4⋊C4—22no—
223C4⋊C4C22×D4712yes—
224C22⋊C4—21no—
225C22⋊C4—22no—
226C22⋊C4—22no—
227C42—21no—
228C23—22no—
229C23—21no—
230C23—42no—
231C23—944no—
232C23—942no—
233C23—1884no—
234C23C2×C22⋊D4712yes—
235C23C2×C22⋊D4711yescharacteristic
236Q8—21no—
237Q8—21no—
238Q8—474no—
239Q8—944no—
240Q8—942no—
241D4—21no—
242D4—21no—
243D4—44no—
244D4—42no—
245D4—474no—
246D4—9416no—
247D4—944no—
248D4—942no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—9416no—
257C2×C4—944no—
258C2×C4—942no—
259C2×C4D4×D4712yes—
260C2×C4D4×D4712yes—
261C2×C4C2×C22⋊D4712yes—
262C2×C4C2×C22⋊D4711yescharacteristic
263C2×C4C23×D4711yescharacteristic
264C8—942no—
265C8—942no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—41no—
272C22—42no—
273C22—944no—
274C22—1888no—
275C22—1884no—
276C22#1309399212yes—
277C22C22×C22⋊D4711yescharacteristic
278C4—22no—
279C4—41no—
280C4—42no—
281C4—944no—
282C4#1309399212yes—
283C4C2×D4×D4711yescharacteristic
284C4C2×D4×D4711yescharacteristic
285C2—22no—
286C2—42no—
287C2—81no—
288C2—1884no—
289C2C2×#1309399211yescharacteristic
290C2#1568992112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#525C2
socleC22×C47C22×D4
hypercenter#525D47
hypocenterC47#3005
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. C22×#10625350C2semidirect
2. C2×#13094054C2semidirect
3. C2×#13094049C2semidirect
4. #15689283C2semidirect
5. #15689266C2semidirect
6. #15689131C2semidirect
7. #15689127C2semidirect
8. #15689087C2semidirect
9. C47×#525C2semidirect
20. C2×#10625337C22semidirect
21. C2×#10625335C22semidirect
22. C2×#10625336C22semidirect
23. C2×#10625334C22semidirect
26. #13093947C22semidirect
27. #13093944C22semidirect
28. C22⋊(C47⋊C8)C22semidirect
32. C22⋊Q8×C47C22semidirect
33. #121×C47C22semidirect
60. C2×D188D4semidirect
66. C2×Dic94D4semidirect
149. #525D47semidirect
155. C47#3005semidirect
175. C22⋊Q8C2×D47semidirect
176. #121C2×D47semidirect