Finite Group Databasebeta

← #20253303

Subgroups — #20253303

Order 6016.

420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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#15689634C211yesmaximal, characteristic
2C2×#13093983C211yesmaximal, characteristic, complemented
3#15689465C212yesmaximal, complemented
4#15689459C211yesmaximal, characteristic, complemented
5#15689454C211yesmaximal, characteristic, complemented
6#15689448C212yesmaximal, complemented
7#15689442C211yesmaximal, characteristic, complemented
8#15689437C211yesmaximal, characteristic, complemented
9#15689161C212yesmaximal, complemented
10#15689120C212yesmaximal, complemented
11C2×C22⋊C8×C47C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13#13094007—21no—
14#13094003C2211yescharacteristic
15#13094003C2211yescharacteristic
16#13093998C2211yescharacteristic
17#13093998C2211yescharacteristic
18#13093993—21no—
19C4×C22⋊D47—21no—
20C4×C22⋊D47—21no—
21#13093983—21no—
22#13093983—21no—
23#13093983C2212yes—
24#13093983C2212yes—
25#13093983C2211yescharacteristic
26C2×C4⋊Dic47C2211yescharacteristic
27C2×C4⋊Dic47C2211yescharacteristic
28C2×C22⋊Dic47—21no—
29C2×C4×Dic47—21no—
30#13093958C2212yescomplemented
31#13093958C2212yescomplemented
32#13093956C2212yescomplemented
33#13093956C2212yescomplemented
34#13093949C2212yescomplemented
35#13093949C2212yescomplemented
36#13093946C2212yescomplemented
37#13093946C2212yescomplemented
38C23×C4×C47C2211yescharacteristic
39C22×C8×C47C2212yes—
40C22⋊C8×C47C2211yescharacteristic
41C22⋊C8×C47C2211yescharacteristic
42C22⋊C8×C47C2212yes—
43C24×C47D411yescharacteristic
44C22×C4×C47—24no—
45C22×C4×C47D411yescharacteristic
46C22×C4×C47D411yescharacteristic
47C22×C4×C47D411yescharacteristic
48C22×C4×C47C2311yescharacteristic
49C22×C4×C47C2311yescharacteristic
50C22×C4×C47C2311yescharacteristic
51C2×C22⋊D47—21no—
52C2×C22⋊D47—21no—
53C2×C22⋊D47—21no—
54C22×Dic47—21no—
55C22×Dic47—21no—
56#10625350—24no—
57C2×D188C2311yescharacteristic
58C2×C4×D47—21no—
59C2×Dic94C2311yescharacteristic
60C2×C8×C47—24no—
61C2×C8×C47C2312yes—
62C2×C8×C47C2312yes—
63C22⋊Dic47—22no—
64C22⋊Dic47—22no—
65C22⋊Dic47—21no—
66C22⋊Dic47—21no—
67C22⋊Dic47—21no—
68(C2×D47)⋊C4—21no—
69(C2×D47)⋊C4—21no—
70C4⋊Dic47—21no—
71C4⋊Dic47—21no—
72C4⋊Dic47C2312yes—
73C4⋊Dic47C2312yes—
74C4⋊Dic47C2311yescharacteristic
75C4⋊Dic47C2311yescharacteristic
76Dic47⋊C4—21no—
77Dic47⋊C4—21no—
78C4×Dic47—22no—
79C4×Dic47—22no—
80C4×Dic47—21no—
81C23×C47—22no—
82C23×C47—22no—
83C23×C47—41no—
84C23×C47C2×D411yescharacteristic
85C23×C47C2×D411yescharacteristic
86C23×C47C2×D411yescharacteristic
87C22×D47—21no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—22no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47#4114yes—
97C2×C4×C47C2411yescharacteristic
98C22⋊D47—42no—
99C22⋊D47—42no—
100C22⋊D47—42no—
101C2×Dic47—22no—
102C2×Dic47—22no—
103C2×Dic47—21no—
104C2×Dic47—21no—
105C2×Dic47—21no—
106C2×Dic47—42no—
107C2×Dic47—42no—
108D188—22no—
109C4×D47—42no—
110Dic94—22no—
111C8×C47—22no—
112C8×C47—22no—
113C22×C47—21no—
114C22×C47—21no—
115C22×C47—21no—
116C22×C47—21no—
117C22×C47—21no—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47—44no—
121C22×C47#12312yes—
122C22×C47#13512yes—
123C22×C47C22×D411yescharacteristic
124C2×D47—41no—
125C2×D47—41no—
126C2×D47—41no—
127C4×C47—21no—
128C4×C47—21no—
129C4×C47#12312yes—
130C4×C47C2×#4112yes—
131Dic47—41no—
132Dic47—42no—
133Dic47—41no—
134Dic47—42no—
135Dic47—41no—
136#3091—471nomaximal, Sylow
137C2×C47—22no—
138C2×C47—22no—
139C2×C47—41no—
140C2×C47C2×#12311yescharacteristic
141C2×C47C2×#13511yescharacteristic
142C2×C47#57511yescharacteristic
143D47—81no—
144#525—471no—
145C2×#117—471no—
146#485—472no—
147#484—471no—
148#483—471no—
149#482—472no—
150#481—471no—
151#480—471no—
152#427—472no—
153#416—472no—
154C2×C22⋊C8D4711yescharacteristic, complemented
155C47#309111yescharacteristic, complemented, Sylow
156C2×#41—471no—
157C23×C4C2×D4711yescharacteristic
158C22×C8C2×D4712yes—
159#123—941no—
160C22⋊Q8—471no—
161C22⋊Q8—471no—
162#121—471no—
163#121—471no—
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⋊C4—471no—
174C2×C22⋊C4—941no—
175C2×C42—941no—
176#107—472no—
177#107—472no—
178#106—472no—
179#106—472no—
180#103—472no—
181#103—472no—
182#102—472no—
183#102—472no—
184C22⋊C8C2×D4711yescharacteristic
185C22⋊C8C2×D4711yescharacteristic
186C22⋊C8C2×D4712yes—
187C24D18811yescharacteristic
188#41—944no—
189C2×Q8—471no—
190C2×D4—471no—
191C2×D4—941no—
192C2×D4—941no—
193C2×D4—941no—
194C22×C4—24no—
195C22×C4—941no—
196C22×C4—941no—
197C22×C4—941no—
198C22×C4D18811yescharacteristic
199C22×C4D18811yescharacteristic
200C22×C4D18811yescharacteristic
201C22×C4C22×D4711yescharacteristic
202C22×C4C22×D4711yescharacteristic
203C22×C4C22×D4711yescharacteristic
204C2×C8—24no—
205C2×C8C22×D4712yes—
206C2×C8C22×D4712yes—
207C4⋊C4—472no—
208C4⋊C4—472no—
209C4⋊C4—471no—
210C4⋊C4—471no—
211C4⋊C4—941no—
212C4⋊C4—941no—
213C4⋊C4—941no—
214C4⋊C4—941no—
215C22⋊C4—942no—
216C22⋊C4—942no—
217C22⋊C4—941no—
218C22⋊C4—941no—
219C22⋊C4—941no—
220C22⋊C4—941no—
221C22⋊C4—941no—
222C42—942no—
223C42—942no—
224C42—941no—
225C23—22no—
226C23—22no—
227C23—41no—
228C23—941no—
229C23C2×D18811yescharacteristic
230C23C2×D18811yescharacteristic
231C23C2×D18811yescharacteristic
232Q8—942no—
233D4—942no—
234D4—1882no—
235D4—1882no—
236D4—1882no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—942no—
243C2×C4—942no—
244C2×C4—941no—
245C2×C4—941no—
246C2×C4—941no—
247C2×C4—1882no—
248C2×C4—1882no—
249C2×C4—1882no—
250C2×C4C2×D18811yescharacteristic
251C2×C4C2×D18811yescharacteristic
252C2×C4C2×D18811yescharacteristic
253C2×C4#1062535214yes—
254C2×C4C23×D4711yescharacteristic
255C8—22no—
256C8—22no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—44no—
265C22—1881no—
266C22—1881no—
267C22—1881no—
268C22#1309400812yes—
269C22#1309404612yes—
270C22C22×D18811yescharacteristic
271C4—21no—
272C4—21no—
273C4—1881no—
274C4—1882no—
275C4—1881no—
276C4—1882no—
277C4—1881no—
278C4#1309400812yes—
279C4C2×#1062535212yes—
280C2—22no—
281C2—22no—
282C2—41no—
283C2—3761no—
284C2C2×#1309400811yescharacteristic
285C2C2×#1309404611yescharacteristic
286C2#1568992311yescharacteristic
subgroupG/H
centerC2×C4C2×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C22⋊C8×C47C2
socleC22×C47C22×D4
hypercenterC2×C22⋊C8D47
hypocenterC47#3091
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#13093983C2semidirect
3. #15689465C2semidirect
4. #15689459C2semidirect
5. #15689454C2semidirect
6. #15689448C2semidirect
7. #15689442C2semidirect
8. #15689437C2semidirect
9. #15689161C2semidirect
10. #15689120C2semidirect
11. C2×C22⋊C8×C47C2semidirect
30. #13093958C22semidirect
31. #13093958C22semidirect
32. #13093956C22semidirect
33. #13093956C22semidirect
34. #13093949C22semidirect
35. #13093949C22semidirect
36. #13093946C22semidirect
37. #13093946C22semidirect
154. C2×C22⋊C8D47semidirect
155. C47#3091semidirect