Finite Group Databasebeta

← #20252633

Subgroups — #20252633

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×#13094057C211yesmaximal, characteristic, complemented
3C2×#13094052C211yesmaximal, characteristic, complemented
4#15689634C211yesmaximal, characteristic, complemented
5#15689287C214yesmaximal, complemented
6#15689270C214yesmaximal, complemented
7#15689133C211yesmaximal, characteristic, complemented
8#15689129C211yesmaximal, characteristic, complemented
9C47×#407C211yesmaximal, characteristic, complemented
10C2×#10625350—22no—
11C2×#10625350—24no—
12C2×#10625350—24no—
13C2×#10625350C2214yes—
14C2×#10625350C2211yescharacteristic
15C22×Dic94C2211yescharacteristic
16C22×D188C2211yescharacteristic
17C22×C22⋊D47—21no—
18C22×C4×D47—21no—
19#13094057—24no—
20#13094052—24no—
21C2×Dic188C2212yescomplemented
22C2×#10625325C2212yescomplemented
23C2×#10625325C2212yescomplemented
24C2×D376C2212yescomplemented
25#13094007—21no—
26#13094003C2212yescomplemented
27#13093998C2212yescomplemented
28#13093993—21no—
29C4×C22⋊D47—22no—
30#13093983C2211yescharacteristic
31#13093949C2214yescomplemented
32#13093946C2214yescomplemented
33C23×C4×C47C2211yescharacteristic
34C2×M16×C47C2211yescharacteristic
35C2×M16×C47C2211yescharacteristic
36C22⋊C8×C47C2214yescomplemented
37C24×C47D411yescharacteristic
38C23×D47—21no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47D412yes—
42C22×C4×C47D411yescharacteristic
43C22×C4×C47C2312yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—28no—
46C2×C22⋊D47—24no—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—21no—
49C22×Dic47—21no—
50#10625350—216no—
51#10625350—28no—
52#10625350—22no—
53#10625350—22no—
54#10625350—28no—
55C2×D188—21no—
56C2×D188—22no—
57C2×D188D414yescomplemented
58C2×D188C2311yescharacteristic
59C2×D188C2312yes—
60C2×C4×D47—28no—
61C2×C4×D47—24no—
62C2×C4×D47—21no—
63C2×Dic94—21no—
64C2×Dic94—22no—
65C2×Dic94D414yescomplemented
66C2×Dic94C2311yescharacteristic
67C2×Dic94C2312yes—
68M16×C47—22no—
69M16×C47—22no—
70C2×C8×C47C2312yes—
71C2×C8×C47C2312yes—
72C22⋊Dic47—21no—
73C22⋊Dic47—22no—
74(C2×D47)⋊C4—22no—
75C4⋊Dic47C2312yes—
76Dic47⋊C4—22no—
77C4×Dic47—21no—
78Dic188—24no—
79D376—24no—
80#10625325—24no—
81#10625325—24no—
82C23×C47—22no—
83C23×C47—42no—
84C23×C47C2×D412yes—
85C23×C47C2×D411yescharacteristic
86C22×D47—24no—
87C22×D47—22no—
88C22×D47—21no—
89C22×D47—44no—
90C2×C4×C47—22no—
91C2×C4×C47—24no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47C2×D412yes—
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D412yes—
98C2×C4×C47C2411yescharacteristic
99C22⋊D47—216no—
100C22⋊D47—44no—
101C22⋊D47—42no—
102C2×Dic47—24no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—21no—
106D188—24no—
107D188—22no—
108D188—21no—
109D188—21no—
110D188C2×D414yes—
111C4×D47—216no—
112C4×D47—42no—
113Dic94—24no—
114Dic94—22no—
115Dic94—21no—
116Dic94—21no—
117Dic94C2×D414yes—
118C8×C47—22no—
119C8×C47—22no—
120C22×C47—22no—
121C22×C47—22no—
122C22×C47—22no—
123C22×C47—22no—
124C22×C47—44no—
125C22×C47#12012yes—
126C22×C47C22×D411yescharacteristic
127C2×D47—24no—
128C2×D47—48no—
129C2×D47—44no—
130C2×D47—41no—
131C2×D47—42no—
132C4×C47—22no—
133C4×C47#12012yes—
134C4×C47C22×D411yescharacteristic
135C4×C47C22×D411yescharacteristic
136Dic47—24no—
137Dic47—41no—
138Dic47—42no—
139#3005—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47—42no—
142C2×C47C2×#12011yescharacteristic
143C2×C47#57512yes—
144D47—44no—
145D47—81no—
146C22×#41—471no—
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#407D4711yescharacteristic, complemented
155C47#300511yescharacteristic, complemented, Sylow
156C2×#41—471no—
157C2×#41—474no—
158C2×#41—944no—
159C2×#41—944no—
160C2×#41—942no—
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×M16C2×D4711yescharacteristic
173C2×M16C2×D4711yescharacteristic
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⋊C8C2×D4714yescomplemented
183C24—941no—
184C24D18811yescharacteristic
185#41—948no—
186#41—948no—
187#41—9416no—
188#41—942no—
189#41—942no—
190C2×Q8—474no—
191C2×Q8—472no—
192C2×Q8—471no—
193C2×Q8—941no—
194C2×Q8—942no—
195C2×D4—474no—
196C2×D4—472no—
197C2×D4—471no—
198C2×D4—948no—
199C2×D4—944no—
200C2×D4—942no—
201C2×D4—941no—
202C2×D4—941no—
203C2×D4—942no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—948no—
207C22×C4—941no—
208C22×C4—944no—
209C22×C4—941no—
210C22×C4D18812yes—
211C22×C4D18811yescharacteristic
212C22×C4C22×D4712yes—
213C22×C4C22×D4711yescharacteristic
214Q16—944no—
215SD16—944no—
216SD16—944no—
217D8—944no—
218M16—22no—
219M16—22no—
220C2×C8C22×D4712yes—
221C2×C8C22×D4712yes—
222C4⋊C4—472no—
223C4⋊C4—942no—
224C22⋊C4—941no—
225C22⋊C4—942no—
226C22⋊C4—942no—
227C42—941no—
228C23—22no—
229C23—42no—
230C23—944no—
231C23—942no—
232C23—941no—
233C23—1884no—
234C23C2×D18812yes—
235C23C2×D18811yescharacteristic
236Q8—474no—
237Q8—944no—
238Q8—942no—
239Q8—941no—
240Q8—941no—
241D4—474no—
242D4—9416no—
243D4—944no—
244D4—942no—
245D4—941no—
246D4—941no—
247D4—1884no—
248D4—1882no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—9416no—
254C2×C4—944no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—941no—
258C2×C4—1882no—
259C2×C4C2×D18812yes—
260C2×C4C2×D18811yescharacteristic
261C2×C4D4×D4712yes—
262C2×C4D4×D4712yes—
263C2×C4C23×D4711yescharacteristic
264C8—22no—
265C8—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22—44no—
271C22—944no—
272C22—1888no—
273C22—1881no—
274C22—1882no—
275C22—1884no—
276C22#1309399412yes—
277C22C22×D18811yescharacteristic
278C4—22no—
279C4—944no—
280C4—1881no—
281C4—1882no—
282C4#1309399412yes—
283C4C2×D4×D4711yescharacteristic
284C4C2×D4×D4711yescharacteristic
285C2—22no—
286C2—42no—
287C2—3761no—
288C2—1884no—
289C2C2×#1309399411yescharacteristic
290C2#1568992312yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#407C2
socleC22×C47C22×D4
hypercenter#407D47
hypocenterC47#3005
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#10625350C2semidirect
2. C2×#13094057C2semidirect
3. C2×#13094052C2semidirect
4. #15689634C2semidirect
5. #15689287C2semidirect
6. #15689270C2semidirect
7. #15689133C2semidirect
8. #15689129C2semidirect
9. C47×#407C2semidirect
21. C2×Dic188C22semidirect
22. C2×#10625325C22semidirect
23. C2×#10625325C22semidirect
24. C2×D376C22semidirect
26. #13094003C22semidirect
27. #13093998C22semidirect
31. #13093949C22semidirect
32. #13093946C22semidirect
36. C22⋊C8×C47C22semidirect
57. C2×D188D4semidirect
65. C2×Dic94D4semidirect
154. #407D47semidirect
155. C47#3005semidirect
182. C22⋊C8C2×D47semidirect