Finite Group Databasebeta

← #20247054

Subgroups — #20247054

Order 6016.

780 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13094001C212yesmaximal, complemented
2C22×C22⋊Dic47C212yesmaximal
3#15689059C211yesmaximal, characteristic, complemented
4#15689046C212yesmaximal, complemented
5#15689035C211yesmaximal, characteristic, complemented
6#15688998C212yesmaximal, complemented
7#15688995C212yesmaximal, complemented
8#15688981C212yesmaximal, complemented
9C47×#379C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic, complemented
11C23×Dic47C2212yes—
12C23×Dic47C2212yes—
13#13094001—28no—
14C2×C4⋊Dic47C2212yescomplemented
15C2×C4⋊Dic47C2211yescharacteristic, complemented
16C2×Dic47⋊C4C2212yescomplemented
17C2×Dic47⋊C4C2212yescomplemented
18C2×Dic47⋊C4C2212yescomplemented
19C2×C22⋊Dic47—28no—
20C2×C22⋊Dic47C2212yes—
21C2×C22⋊Dic47C2212yes—
22C2×C22⋊Dic47C2212yes—
23C2×C22⋊Dic47C2212yes—
24C47⋊#95C2211yescharacteristic, complemented
25C47⋊#95C2212yescomplemented
26C47⋊#95C2211yescharacteristic, complemented
27C47⋊#95C2212yescomplemented
28C25×C47C2211yescharacteristic
29C2×C22⋊C4×C47C2212yes—
30C2×C22⋊C4×C47C2212yes—
31C2×C22⋊C4×C47C2211yescharacteristic
32C2×C22⋊C4×C47C2211yescharacteristic
33C24×C47—24no—
34C24×C47—24no—
35C24×C47—41no—
36C24×C47—41no—
37C24×C47Q814yescomplemented
38C24×C47C2311yescharacteristic
39C24×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2311yescharacteristic
43C22×Dic47—24no—
44C22×Dic47—24no—
45C22×Dic47—24no—
46C22×Dic47—24no—
47C22×Dic47—42no—
48C22×Dic47—42no—
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C22×Dic47C2312yes—
52C22×Dic47C2312yes—
53C2×Dic94—24no—
54C2×Dic94—41no—
55C22⋊C4×C47—24no—
56C22⋊C4×C47—24no—
57C22⋊C4×C47—41no—
58C22⋊C4×C47—41no—
59C22⋊Dic47—24no—
60C22⋊Dic47—24no—
61C22⋊Dic47—24no—
62C22⋊Dic47D418yes—
63C4⋊Dic47—24no—
64C4⋊Dic47—41no—
65Dic47⋊C4—24no—
66Dic47⋊C4—24no—
67Dic47⋊C4—42no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—22no—
71C23×C47—22no—
72C23×C47—216no—
73C23×C47—22no—
74C23×C47—22no—
75C23×C47—21no—
76C23×C47—21no—
77C23×C47—44no—
78C23×C47—44no—
79C23×C47—48no—
80C23×C47—44no—
81C23×C47C2×D414yes—
82C23×C47C2×Q812yes—
83C23×C47C2×Q814yes—
84C23×C47#4114yes—
85C23×C47C2411yescharacteristic
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—48no—
104C2×Dic47—48no—
105C2×Dic47C2×D414yes—
106C2×Dic47C2×D414yes—
107Dic94—44no—
108C22×C47—24no—
109C22×C47—24no—
110C22×C47—24no—
111C22×C47—24no—
112C22×C47—24no—
113C22×C47—24no—
114C22×C47—24no—
115C22×C47—22no—
116C22×C47—416no—
117C22×C47—41no—
118C22×C47—42no—
119C22×C47—41no—
120C22×C47C22⋊Q818yescomplemented
121C22×C47C22×D412yes—
122C22×C47C22×Q811yescharacteristic
123C22×C47C2×#4112yes—
124C22×C47H(5,𝔽2)11yescharacteristic
125C22×C47H(5,𝔽2)11yescharacteristic
126C4×C47—41no—
127C4×C47—42no—
128C4×C47—41no—
129Dic47—24no—
130Dic47—24no—
131Dic47—42no—
132Dic47—42no—
133#2437—471nomaximal, Sylow
134C2×C47—28no—
135C2×C47—42no—
136C2×C47C2×C22⋊Q812yes—
137C2×C47#54311yescharacteristic
138C2×C47D4211yescharacteristic
139C2×C47#54612yes—
140C2×C47#55111yescharacteristic
141C2×C22⋊Q8—472no—
142C22×C22⋊C4—472no—
143#399—471no—
144#396—472no—
145#393—471no—
146#385—472no—
147#385—472no—
148#380—472no—
149#379D4711yescharacteristic
150C47#243711yescharacteristic, complemented, Sylow
151C25C2×D4711yescharacteristic
152C22×Q8—471no—
153C23×C4—472no—
154C23×C4—472no—
155C22⋊Q8—948no—
156C2×C4⋊C4—472no—
157C2×C4⋊C4—472no—
158C2×C4⋊C4—472no—
159C2×C4⋊C4—472no—
160C2×C4⋊C4—471no—
161C2×C22⋊C4—472no—
162C2×C22⋊C4—472no—
163C2×C22⋊C4—472no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4—948no—
166C2×C22⋊C4C2×D4712yes—
167C2×C22⋊C4C2×D4712yes—
168C2×C22⋊C4C2×D4711yescharacteristic
169C2×C22⋊C4C2×D4711yescharacteristic
170#95—471no—
171#95—472no—
172#95—472no—
173#95—471no—
174C24—24no—
175C24—24no—
176C24—41no—
177C24—41no—
178C24Dic9414yescomplemented
179C24C22×D4711yescharacteristic
180C24C22×D4712yes—
181C2×Q8—944no—
182C2×Q8—1881no—
183C22×C4—472no—
184C22×C4—472no—
185C22×C4—472no—
186C22×C4—472no—
187C22×C4—944no—
188C22×C4—944no—
189C22×C4—944no—
190C22×C4—944no—
191C22×C4—1882no—
192C22×C4—1882no—
193C22×C4C22×D4711yescharacteristic
194C22×C4C22×D4712yes—
195C22×C4C22×D4711yescharacteristic
196C4⋊C4—944no—
197C4⋊C4—944no—
198C4⋊C4—944no—
199C4⋊C4—1882no—
200C4⋊C4—1881no—
201C22⋊C4—24no—
202C22⋊C4—24no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C22⋊C4—478no—
206C22⋊C4—944no—
207C22⋊C4—944no—
208C22⋊C4—944no—
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—216no—
214C23—22no—
215C23—22no—
216C23—21no—
217C23—21no—
218C23—44no—
219C23—44no—
220C23—48no—
221C23—44no—
222C23C2×Dic9412yes—
223C23C2×Dic9414yes—
224C23D4×D4714yes—
225C23#1062535214yes—
226C23C23×D4711yescharacteristic
227Q8—1884no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—474no—
236C2×C4—474no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—1888no—
248C2×C4—1888no—
249C22—24no—
250C22—24no—
251C22—24no—
252C22—24no—
253C22—24no—
254C22—24no—
255C22—22no—
256C22—24no—
257C22—416no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22#1309400118yescomplemented
262C22C2×D4×D4712yes—
263C22C22×Dic9411yescharacteristic
264C22C2×#1062535212yes—
265C22#1309406911yescharacteristic
266C22#1309406911yescharacteristic
267C4—41no—
268C4—42no—
269C4—41no—
270C4—944no—
271C4—944no—
272C4—1882no—
273C4—1882no—
274C2—28no—
275C2—42no—
276C2C2×#1309400112yes—
277C2#1568974911yescharacteristic
278C2#1568975511yescharacteristic
279C2#1568976012yes—
280C2#1568980411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#379C2
hypercenter#379D47
hypocenterC47#2437
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#13094001C2semidirect
3. #15689059C2semidirect
4. #15689046C2semidirect
5. #15689035C2semidirect
6. #15688998C2semidirect
7. #15688995C2semidirect
8. #15688981C2semidirect
10. C22×Dic94C22semidirect
14. C2×C4⋊Dic47C22semidirect
15. C2×C4⋊Dic47C22semidirect
16. C2×Dic47⋊C4C22semidirect
17. C2×Dic47⋊C4C22semidirect
18. C2×Dic47⋊C4C22semidirect
24. C47⋊#95C22semidirect
25. C47⋊#95C22semidirect
26. C47⋊#95C22semidirect
27. C47⋊#95C22semidirect
37. C24×C47Q8semidirect
120. C22×C47C22⋊Q8semidirect
150. C47#2437semidirect
178. C24Dic94semidirect
261. C22#13094001semidirect