Finite Group Databasebeta

← #20247048

Subgroups — #20247048

Order 6016.

780 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 161 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×#13094000C212yesmaximal, complemented
2C2×C22⋊C4×D47C212yesmaximal
3#15689059C211yesmaximal, characteristic, complemented
4#15689046C212yesmaximal, complemented
5#15688997C212yesmaximal, complemented
6#15688997C212yesmaximal, complemented
7#15688982C212yesmaximal, complemented
8#15688978C211yesmaximal, characteristic
9C47×#393C211yesmaximal, characteristic, complemented
10C24×D47C2211yescharacteristic
11C22×C4×D47C2212yes—
12C22×C4×D47C2212yes—
13#13094000—28no—
14C2×C4⋊Dic47C2212yescomplemented
15C2×C4⋊Dic47C2211yescharacteristic, complemented
16C2×Dic47⋊C4C2212yescomplemented
17C2×Dic47⋊C4C2212yescomplemented
18C2×Dic47⋊C4C2212yescomplemented
19C2×C22⋊Dic47C2212yes—
20C2×C22⋊Dic47C2211yescharacteristic
21C2×(C2×D47)⋊C4C2212yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×(C2×D47)⋊C4C2212yes—
24C2×(C2×D47)⋊C4C2212yes—
25C22⋊C4×D47—28no—
26C47⋊#95C2212yescomplemented
27C47⋊#95C2211yescharacteristic, complemented
28C22×Q8×C47C2211yescharacteristic, complemented
29C2×C22⋊C4×C47C2212yes—
30C2×C22⋊C4×C47C2211yescharacteristic
31#95×C47C2211yescharacteristic, complemented
32#95×C47C2212yescomplemented
33C24×C47C2311yescharacteristic
34C23×D47—24no—
35C23×D47—24no—
36C23×D47—41no—
37C23×D47—41no—
38C23×D47Q814yescomplemented
39C23×D47C2312yes—
40C2×Q8×C47—24no—
41C2×Q8×C47—41no—
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2312yes—
45C22×C4×C47C2312yes—
46C22×Dic47C2312yes—
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C2×C4×D47—24no—
50C2×C4×D47—24no—
51C2×C4×D47—24no—
52C2×C4×D47—24no—
53C2×C4×D47—42no—
54C2×C4×D47—42no—
55C22⋊C4×C47—24no—
56C22⋊C4×C47—41no—
57C22⋊Dic47—24no—
58C22⋊Dic47—41no—
59(C2×D47)⋊C4—24no—
60(C2×D47)⋊C4—24no—
61(C2×D47)⋊C4—24no—
62(C2×D47)⋊C4D418yes—
63C4⋊Dic47—24no—
64C4⋊Dic47—41no—
65Dic47⋊C4—24no—
66Dic47⋊C4—24no—
67Dic47⋊C4—42no—
68C23×C47—22no—
69C23×C47—22no—
70C23×C47—21no—
71C23×C47—21no—
72C23×C47C2×Q812yes—
73C23×C47C2411yescharacteristic
74C22×D47—22no—
75C22×D47—22no—
76C22×D47—22no—
77C22×D47—22no—
78C22×D47—216no—
79C22×D47—44no—
80C22×D47—44no—
81C22×D47—48no—
82C22×D47—44no—
83C22×D47C2×D414yes—
84C22×D47C2×Q814yes—
85C22×D47#4114yes—
86Q8×C47—44no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47C2×D414yes—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47C2×D414yes—
106C4×D47—48no—
107C4×D47—48no—
108C22×C47—24no—
109C22×C47—22no—
110C22×C47—41no—
111C22×C47—42no—
112C22×C47—41no—
113C22×C47C22×D412yes—
114C22×C47C22×Q811yescharacteristic
115C22×C47C2×#4112yes—
116C22×C47H(5,𝔽2)11yescharacteristic
117C22×C47H(5,𝔽2)11yescharacteristic
118C2×D47—24no—
119C2×D47—24no—
120C2×D47—24no—
121C2×D47—24no—
122C2×D47—24no—
123C2×D47—24no—
124C2×D47—416no—
125C2×D47C22⋊Q818yescomplemented
126C4×C47—24no—
127C4×C47—41no—
128C4×C47—42no—
129C4×C47—41no—
130Dic47—24no—
131Dic47—42no—
132Dic47—42no—
133#2437—471nomaximal, Sylow
134C2×C47—42no—
135C2×C47C2×C22⋊Q812yes—
136C2×C47#54311yescharacteristic
137C2×C47D4211yescharacteristic
138C2×C47#54612yes—
139C2×C47#55111yescharacteristic
140D47—28no—
141C2×C22⋊Q8—472no—
142C22×C22⋊C4—472no—
143#399—471no—
144#396—472no—
145#393D4711yescharacteristic, complemented
146#385—472no—
147#385—472no—
148#380—472no—
149#379—471no—
150C47#243711yescharacteristic, complemented, Sylow
151C25—471no—
152C22×Q8C2×D4711yescharacteristic, complemented
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—472no—
166C2×C22⋊C4—471no—
167C2×C22⋊C4—948no—
168C2×C22⋊C4C2×D4712yes—
169C2×C22⋊C4C2×D4711yescharacteristic
170#95—472no—
171#95—471no—
172#95C2×D4711yescharacteristic, complemented
173#95C2×D4712yescomplemented
174C24—472no—
175C24—474no—
176C24—944no—
177C24—944no—
178C24—1881no—
179C24—1881no—
180C24C22×D4711yescharacteristic
181C2×Q8—24no—
182C2×Q8—41no—
183C22×C4—472no—
184C22×C4—472no—
185C22×C4—472no—
186C22×C4—944no—
187C22×C4—944no—
188C22×C4—944no—
189C22×C4—944no—
190C22×C4—1882no—
191C22×C4—1882no—
192C22×C4C22×D4711yescharacteristic
193C22×C4C22×D4712yes—
194C22×C4C22×D4711yescharacteristic
195C22×C4C22×D4712yes—
196C4⋊C4—944no—
197C4⋊C4—944no—
198C4⋊C4—944no—
199C4⋊C4—1882no—
200C4⋊C4—1881no—
201C22⋊C4—24no—
202C22⋊C4—41no—
203C22⋊C4—478no—
204C22⋊C4—944no—
205C22⋊C4—944no—
206C22⋊C4—944no—
207C22⋊C4—944no—
208C22⋊C4—1881no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—21no—
213C23—474no—
214C23—474no—
215C23—474no—
216C23—9416no—
217C23—942no—
218C23—942no—
219C23—942no—
220C23—942no—
221C23—1884no—
222C23—1884no—
223C23—1888no—
224C23—1884no—
225C23Q8×D4712yes—
226C23C23×D4711yescharacteristic
227Q8—44no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—474no—
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—1888no—
247C2×C4—1888no—
248C2×C4D4×D4714yes—
249C22—22no—
250C22—24no—
251C22—41no—
252C22—42no—
253C22—41no—
254C22—478no—
255C22—944no—
256C22—944no—
257C22—944no—
258C22—944no—
259C22—944no—
260C22—944no—
261C22—18816no—
262C22C2×D4×D4712yes—
263C22C2×Q8×D4711yescharacteristic
264C22#41×D4712yes—
265C22#1309406911yescharacteristic
266C22#1309407011yescharacteristic
267C4—24no—
268C4—41no—
269C4—42no—
270C4—41no—
271C4—944no—
272C4—1882no—
273C4—1882no—
274C2—42no—
275C2—948no—
276C2C22⋊Q8×D4712yes—
277C2#1568974811yescharacteristic
278C2#1568975511yescharacteristic
279C2#1568976612yes—
280C2#1568980311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#393C2
hypercenter#393D47
hypocenterC47#2437
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13094000C2semidirect
3. #15689059C2semidirect
4. #15689046C2semidirect
5. #15688997C2semidirect
6. #15688997C2semidirect
7. #15688982C2semidirect
9. C47×#393C2semidirect
14. C2×C4⋊Dic47C22semidirect
15. C2×C4⋊Dic47C22semidirect
16. C2×Dic47⋊C4C22semidirect
17. C2×Dic47⋊C4C22semidirect
18. C2×Dic47⋊C4C22semidirect
26. C47⋊#95C22semidirect
27. C47⋊#95C22semidirect
28. C22×Q8×C47C22semidirect
31. #95×C47C22semidirect
32. #95×C47C22semidirect
38. C23×D47Q8semidirect
125. C2×D47C22⋊Q8semidirect
145. #393D47semidirect
150. C47#2437semidirect
152. C22×Q8C2×D47semidirect
172. #95C2×D47semidirect
173. #95C2×D47semidirect