Finite Group Databasebeta

← #20253298

Subgroups — #20253298

Order 6016.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#15689633C211yesmaximal, characteristic
2C2×#13093982C211yesmaximal, characteristic, complemented
3#15689467C212yesmaximal, complemented
4#15689458C211yesmaximal, characteristic, complemented
5#15689454C211yesmaximal, characteristic, complemented
6#15689446C212yesmaximal, complemented
7#15689434C211yesmaximal, characteristic, complemented
8#15689158C212yesmaximal, complemented
9#15689116C212yesmaximal, complemented
10C22⋊C8×D47C211yesmaximal, characteristic, complemented
11C47×#481C211yesmaximal, characteristic, complemented
12C2×#10625352C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C2×C8×D47C2212yes—
15#13094006—21no—
16#13094004C2211yescharacteristic
17#13094003C2211yescharacteristic
18#13093995C2211yescharacteristic
19#13093992—21no—
20D4×Dic47—21no—
21(C22⋊D47)⋊C4—21no—
22#13093982—21no—
23#13093982—21no—
24#13093982C2212yes—
25#13093982C2212yes—
26#13093982C2211yescharacteristic
27C2×C4⋊Dic47C2211yescharacteristic
28C2×(C2×D47)⋊C4—21no—
29C2×C4×Dic47—21no—
30#13093957C2212yescomplemented
31#13093957C2212yescomplemented
32#13093956C2212yescomplemented
33#13093949C2212yescomplemented
34#13093947C2212yescomplemented
35#13093945C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic
37(C2×D47)⋊C8C2212yes—
38#121×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#106×C47C2212yescomplemented
41#102×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C23×D47D411yescharacteristic
44C2×D4×C47—21no—
45C2×D4×C47C2311yescharacteristic
46C22×C4×C47—21no—
47C22×C4×C47C2311yescharacteristic
48C2×C22⋊D47—21no—
49C2×C22⋊D47—21no—
50C22×Dic47—21no—
51C22×Dic47—21no—
52C22×Dic47D411yescharacteristic
53#10625352—24no—
54C2×C4×D47—24no—
55C2×C4×D47D411yescharacteristic
56C2×C4×D47D411yescharacteristic
57C2×C4×D47C2311yescharacteristic
58C2×C4×D47C2311yescharacteristic
59C2×Dic94C2311yescharacteristic
60C2×C8×C47C2312yes—
61C4⋊C4×C47—21no—
62C4⋊C4×C47C2311yescharacteristic
63C4⋊C4×C47C2312yes—
64C22⋊C4×C47—21no—
65C22⋊Dic47—21no—
66C22⋊Dic47—21no—
67(C2×D47)⋊C4—22no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4—21no—
70(C2×D47)⋊C4—21no—
71C4⋊Dic47—21no—
72C4⋊Dic47—21no—
73C4⋊Dic47C2312yes—
74C4⋊Dic47C2311yescharacteristic
75Dic47⋊C4—21no—
76C4×Dic47—22no—
77C4×Dic47—22no—
78C4×Dic47—21no—
79C2×C47⋊C8C2312yes—
80C8×D47—24no—
81C23×C47—21no—
82C23×C47C2×D411yescharacteristic
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—41no—
86C22×D47C2×D411yescharacteristic
87C22×D47C2×D411yescharacteristic
88D4×C47—22no—
89D4×C47—42no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47—42no—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2411yescharacteristic
96C22⋊D47—42no—
97C22⋊D47—42no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—21no—
101C2×Dic47—21no—
102C2×Dic47—42no—
103C2×Dic47—42no—
104C2×Dic47C2×D411yescharacteristic
105C2×Dic47C2×D411yescharacteristic
106C4×D47—22no—
107C4×D47—22no—
108C4×D47—22no—
109C4×D47#4114yes—
110Dic94—22no—
111C8×C47—22no—
112C47⋊C8—22no—
113C22×C47—21no—
114C22×C47—21no—
115C22×C47—41no—
116C22×C47—41no—
117C22×C47—41no—
118C22×C47#13512yes—
119C22×C47C22×D411yescharacteristic
120C2×D47—21no—
121C2×D47—21no—
122C2×D47—21no—
123C2×D47—21no—
124C2×D47—21no—
125C2×D47—44no—
126C2×D47#12312yes—
127C4×C47—21no—
128C4×C47—41no—
129C4×C47—42no—
130C4×C47C2×#4112yes—
131Dic47—21no—
132Dic47—41no—
133Dic47—42no—
134Dic47—41no—
135Dic47#12312yes—
136#3091—471nomaximal, Sylow
137C2×C47—22no—
138C2×C47—81no—
139C2×C47C2×#12311yescharacteristic
140C2×C47C2×#13511yescharacteristic
141C2×C47#57511yescharacteristic
142D47—22no—
143D47—41no—
144#525—471no—
145C2×#117—471no—
146#485—472no—
147#484—471no—
148#483—471no—
149#482—472no—
150#481D4711yescharacteristic, complemented
151#480—471no—
152#427—472no—
153#416—472no—
154C2×C22⋊C8—471no—
155C47#309111yescharacteristic, complemented, Sylow
156C2×#41—471no—
157C23×C4—471no—
158C22×C8—472no—
159#123—941no—
160C22⋊Q8—471no—
161C22⋊Q8—471no—
162#121—471no—
163#121C2×D4711yescharacteristic
164#120—941no—
165C4×D4—941no—
166C4×D4—941no—
167#117—472no—
168#117—472no—
169#117—471no—
170#117—941no—
171#117—941no—
172C2×C4⋊C4—471no—
173C2×C4⋊C4C2×D4711yescharacteristic
174C2×C22⋊C4—941no—
175C2×C42—941no—
176#107—472no—
177#107—472no—
178#106—472no—
179#106C2×D4712yescomplemented
180#103—472no—
181#103—472no—
182#102—472no—
183#102C2×D4712yescomplemented
184C22⋊C8—471no—
185C22⋊C8—472no—
186C22⋊C8C2×D4711yescharacteristic
187C24—471no—
188#41—944no—
189C2×Q8—471no—
190C2×D4—21no—
191C2×D4—941no—
192C2×D4—941no—
193C2×D4C22×D4711yescharacteristic
194C22×C4—21no—
195C22×C4—471no—
196C22×C4—471no—
197C22×C4—471no—
198C22×C4—471no—
199C22×C4—471no—
200C22×C4—944no—
201C22×C4—941no—
202C22×C4—941no—
203C22×C4C22×D4711yescharacteristic
204C2×C8—472no—
205C2×C8—944no—
206C2×C8C22×D4712yes—
207C4⋊C4—21no—
208C4⋊C4—472no—
209C4⋊C4—471no—
210C4⋊C4—941no—
211C4⋊C4—941no—
212C4⋊C4—941no—
213C4⋊C4C22×D4712yes—
214C4⋊C4C22×D4711yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—942no—
217C22⋊C4—942no—
218C22⋊C4—941no—
219C22⋊C4—941no—
220C22⋊C4—941no—
221C22⋊C4—941no—
222C42—942no—
223C42—942no—
224C42—941no—
225C23—21no—
226C23—471no—
227C23—471no—
228C23—942no—
229C23—942no—
230C23—1881no—
231C23D4×D4711yescharacteristic
232Q8—942no—
233D4—22no—
234D4—42no—
235D4—1882no—
236D4—1882no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—42no—
241C2×C4—471no—
242C2×C4—474no—
243C2×C4—471no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—941no—
250C2×C4—941no—
251C2×C4—1882no—
252C2×C4—1882no—
253C2×C4D4×D4711yescharacteristic
254C2×C4C23×D4711yescharacteristic
255C8—22no—
256C8—942no—
257C22—21no—
258C22—21no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—472no—
263C22—941no—
264C22—941no—
265C22—941no—
266C22—941no—
267C22—941no—
268C22—1884no—
269C22#1309404512yes—
270C22C2×D4×D4711yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—472no—
275C4—941no—
276C4—1881no—
277C4—1882no—
278C4—1881no—
279C4#41×D4712yes—
280C2—22no—
281C2—81no—
282C2—942no—
283C2—1881no—
284C2#123×D4711yescharacteristic
285C2C2×#1309404511yescharacteristic
286C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#481C2
socleC22×C47C22×D4
hypercenter#481D47
hypocenterC47#3091
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#13093982C2semidirect
3. #15689467C2semidirect
4. #15689458C2semidirect
5. #15689454C2semidirect
6. #15689446C2semidirect
7. #15689434C2semidirect
8. #15689158C2semidirect
9. #15689116C2semidirect
10. C22⋊C8×D47C2semidirect
11. C47×#481C2semidirect
30. #13093957C22semidirect
31. #13093957C22semidirect
32. #13093956C22semidirect
33. #13093949C22semidirect
34. #13093947C22semidirect
35. #13093945C22semidirect
40. #106×C47C22semidirect
41. #102×C47C22semidirect
150. #481D47semidirect
155. C47#3091semidirect
179. #106C2×D47semidirect
183. #102C2×D47semidirect