Finite Group Databasebeta

← #20252630

Subgroups — #20252630

Order 6016.

758 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13094055C211yesmaximal, characteristic, complemented
2C2×#13094050C211yesmaximal, characteristic, complemented
3#15689634C211yesmaximal, characteristic, complemented
4#15689285C214yesmaximal, complemented
5#15689268C214yesmaximal, complemented
6#15689132C211yesmaximal, characteristic, complemented
7#15689128C211yesmaximal, characteristic, complemented
8#15689087C211yesmaximal, characteristic, complemented
9C22×#41×C47C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11#13094055—24no—
12#13094050—24no—
13C2×#10625337C2212yescomplemented
14C2×#10625335C2212yescomplemented
15C2×#10625336C2212yescomplemented
16C2×#10625334C2212yescomplemented
17C2×#10625329C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19#13094007—21no—
20#13094003C2212yescomplemented
21#13093998C2212yescomplemented
22#13093993—21no—
23C4×C22⋊D47—22no—
24#13093983C2211yescharacteristic
25#13093948C2214yescomplemented
26#13093945C2214yescomplemented
27C22⋊(C47⋊C8)C2214yescomplemented
28C2×#41×C47—24no—
29C2×#41×C47—24no—
30C2×#41×C47—22no—
31C2×#41×C47C2214yes—
32C22×Q8×C47C2211yescharacteristic
33C22×D4×C47—21no—
34C22×D4×C47C2211yescharacteristic
35C23×C4×C47—21no—
36C23×C4×C47C2211yescharacteristic
37C24×C47—21no—
38C24×C47D411yescharacteristic
39#41×C47—216no—
40#41×C47—28no—
41#41×C47—28no—
42C2×Q8×C47—22no—
43C2×Q8×C47—21no—
44C2×Q8×C47D414yescomplemented
45C2×Q8×C47C2312yes—
46C2×D4×C47—28no—
47C2×D4×C47—24no—
48C2×D4×C47—21no—
49C2×D4×C47—22no—
50C2×D4×C47D414yescomplemented
51C2×D4×C47C2312yes—
52C22×C4×C47—28no—
53C22×C4×C47—21no—
54C22×C4×C47—24no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
57C22×C4×C47D411yescharacteristic
58C22×C4×C47D412yes—
59C22×C4×C47C2312yes—
60C22×C4×C47C2311yescharacteristic
61C2×C22⋊D47—22no—
62C2×C22⋊D47—21no—
63#10625350—22no—
64#10625350—22no—
65C2×D188C2311yescharacteristic
66C2×C4×D47—21no—
67C2×Dic94C2311yescharacteristic
68C22⋊Dic47—21no—
69C22⋊Dic47—22no—
70#10625337—24no—
71#10625336—24no—
72#10625335—24no—
73#10625334—24no—
74(C2×D47)⋊C4—22no—
75C4⋊Dic47C2312yes—
76Dic47⋊C4—22no—
77C4×Dic47—21no—
78#10625329—22no—
79#10625329—22no—
80C2×C47⋊C8C2312yes—
81C2×C47⋊C8C2312yes—
82C23×C47—22no—
83C23×C47—24no—
84C23×C47—22no—
85C23×C47—42no—
86C23×C47—44no—
87C23×C47C2×D412yes—
88C23×C47C2×D411yescharacteristic
89C22×D47—21no—
90Q8×C47—24no—
91Q8×C47—22no—
92Q8×C47C2×D414yes—
93D4×C47—216no—
94D4×C47—24no—
95D4×C47—22no—
96D4×C47C2×D414yes—
97C2×C4×C47—216no—
98C2×C4×C47—22no—
99C2×C4×C47—24no—
100C2×C4×C47—22no—
101C2×C4×C47—24no—
102C2×C4×C47—22no—
103C2×C4×C47—22no—
104C2×C4×C47C2×D412yes—
105C2×C4×C47C2×D411yescharacteristic
106C2×C4×C47C2×D412yes—
107C2×C4×C47C2×D412yes—
108C2×C4×C47C2411yescharacteristic
109C22⋊D47—44no—
110C22⋊D47—42no—
111C2×Dic47—22no—
112C2×Dic47—21no—
113D188—21no—
114D188—21no—
115C4×D47—42no—
116Dic94—21no—
117Dic94—21no—
118C47⋊C8—22no—
119C47⋊C8—22no—
120C22×C47—22no—
121C22×C47—22no—
122C22×C47—24no—
123C22×C47—22no—
124C22×C47—22no—
125C22×C47—44no—
126C22×C47—48no—
127C22×C47—44no—
128C22×C47#12012yes—
129C22×C47C22×D411yescharacteristic
130C2×D47—41no—
131C2×D47—42no—
132C4×C47—22no—
133C4×C47—24no—
134C4×C47#12012yes—
135C4×C47C22×D411yescharacteristic
136C4×C47C22×D411yescharacteristic
137Dic47—41no—
138Dic47—42no—
139#3005—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47—42no—
142C2×C47—44no—
143C2×C47C2×#12011yescharacteristic
144C2×C47#57512yes—
145D47—81no—
146C22×#41D4711yescharacteristic, complemented
147C2×#137—471no—
148C2×AGL(1,ℤ/8)—471no—
149#525—471no—
150#452—474no—
151#449—474no—
152#419—471no—
153#418—471no—
154#407—471no—
155C47#300511yescharacteristic, complemented, Sylow
156C2×#41—24no—
157C2×#41—24no—
158C2×#41—22no—
159C2×#41—471no—
160C2×#41C2×D4714yes—
161C22×Q8C2×D4711yescharacteristic
162C22×D4—21no—
163C22×D4C2×D4711yescharacteristic
164C23×C4—21no—
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—941no—
175C22⋊Q8—472no—
176#121—472no—
177#120—941no—
178C4×D4—942no—
179#117—471no—
180#103—474no—
181#102—474no—
182C22⋊C8—474no—
183C24—21no—
184C24C22⋊D4711yescharacteristic
185#41—216no—
186#41—28no—
187#41—28no—
188#41—942no—
189#41—942no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8—471no—
193C2×Q8C22⋊D4714yescomplemented
194C2×Q8C22×D4712yes—
195C2×D4—28no—
196C2×D4—24no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—471no—
200C2×D4—942no—
201C2×D4—941no—
202C2×D4C22⋊D4714yescomplemented
203C2×D4C22×D4712yes—
204C22×C4—28no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—941no—
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—472no—
223C4⋊C4—942no—
224C22⋊C4—941no—
225C22⋊C4—942no—
226C22⋊C4—942no—
227C42—941no—
228C23—22no—
229C23—24no—
230C23—22no—
231C23—42no—
232C23—44no—
233C23—941no—
234C23C2×C22⋊D4712yes—
235C23C2×C22⋊D4711yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—941no—
239Q8—941no—
240Q8C2×C22⋊D4714yes—
241D4—216no—
242D4—24no—
243D4—22no—
244D4—941no—
245D4—941no—
246D4—1884no—
247D4—1882no—
248D4C2×C22⋊D4714yes—
249C2×C4—216no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—24no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—942no—
257C2×C4—941no—
258C2×C4—1882no—
259C2×C4C2×C22⋊D4712yes—
260C2×C4C2×C22⋊D4711yescharacteristic
261C2×C4C2×C22⋊D4712yes—
262C2×C4C2×C22⋊D4712yes—
263C2×C4C23×D4711yescharacteristic
264C8—942no—
265C8—942no—
266C22—22no—
267C22—22no—
268C22—24no—
269C22—22no—
270C22—22no—
271C22—44no—
272C22—48no—
273C22—44no—
274C22—1881no—
275C22—1882no—
276C22#1309399312yes—
277C22C22×C22⋊D4711yescharacteristic
278C4—22no—
279C4—24no—
280C4—1881no—
281C4—1882no—
282C4#1309399312yes—
283C4C22×C22⋊D4711yescharacteristic
284C4C22×C22⋊D4711yescharacteristic
285C2—22no—
286C2—42no—
287C2—44no—
288C2—3761no—
289C2C2×#1309399311yescharacteristic
290C2#1568992112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC22×#41×C47C2
socleC22×C47C22×D4
hypercenterC22×#41D47
hypocenterC47#3005
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
2. C2×#13094050C2semidirect
3. #15689634C2semidirect
4. #15689285C2semidirect
5. #15689268C2semidirect
6. #15689132C2semidirect
7. #15689128C2semidirect
8. #15689087C2semidirect
9. C22×#41×C47C2semidirect
13. C2×#10625337C22semidirect
14. C2×#10625335C22semidirect
15. C2×#10625336C22semidirect
16. C2×#10625334C22semidirect
20. #13094003C22semidirect
21. #13093998C22semidirect
25. #13093948C22semidirect
26. #13093945C22semidirect
27. C22⋊(C47⋊C8)C22semidirect
44. C2×Q8×C47D4semidirect
50. C2×D4×C47D4semidirect
146. C22×#41D47semidirect
155. C47#3005semidirect
193. C2×Q8C22⋊D47semidirect
202. C2×D4C22⋊D47semidirect