Finite Group Databasebeta

← #20253333

Subgroups — #20253333

Order 6016.

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

normal subgroups only

This group has 410 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
1C22⋊Q8×D47C211yesmaximal, characteristic
2C2×#13093982C211yesmaximal, characteristic
3#15689466C212yesmaximal, complemented
4#15689462C212yesmaximal, complemented
5#15689458C211yesmaximal, characteristic, complemented
6#15689454C211yesmaximal, characteristic, complemented
7#15689451C211yesmaximal, characteristic, complemented
8#15689164C212yesmaximal, complemented
9#15689130C212yesmaximal, complemented
10#15689085C211yesmaximal, characteristic
11C47×#484C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C2×#10625324C2212yes—
15#13094004C2211yescharacteristic
16#13094003C2211yescharacteristic
17#13094002—21no—
18#13094001—21no—
19#13094000C2211yescharacteristic
20#13093982—21no—
21#13093982—21no—
22#13093982C2212yes—
23#13093982C2212yes—
24C2×C4⋊Dic47C2211yescharacteristic
25C4⋊C4×D47—21no—
26C4⋊C4×D47C2211yescharacteristic
27C2×(C2×D47)⋊C4—21no—
28C22⋊C4×D47—21no—
29C2×C4×Dic47—21no—
30#13093957C2212yescomplemented
31#13093956C2212yescomplemented
32#13093955C2212yescomplemented
33#13093949C2212yescomplemented
34#13093948C2212yescomplemented
35#13093947C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic
37(C2×D47)⋊C8C2212yes—
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#107×C47C2212yescomplemented
41#103×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C23×D47D411yescharacteristic
44C2×Q8×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C22×C4×C47C2311yescharacteristic
47C22×Dic47—21no—
48C22×Dic47D411yescharacteristic
49Q8×D47—24no—
50C2×C4×D47—24no—
51C2×C4×D47—21no—
52C2×C4×D47—21no—
53C2×C4×D47D411yescharacteristic
54C2×C4×D47D411yescharacteristic
55C2×C4×D47C2311yescharacteristic
56C2×C4×D47C2311yescharacteristic
57C2×Dic94—21no—
58C2×Dic94C2311yescharacteristic
59C2×C8×C47C2312yes—
60C4⋊C4×C47—21no—
61C4⋊C4×C47—21no—
62C4⋊C4×C47C2312yes—
63C4⋊C4×C47C2311yescharacteristic
64C22⋊C4×C47—21no—
65C22⋊Dic47—21no—
66(C2×D47)⋊C4—21no—
67(C2×D47)⋊C4—21no—
68(C2×D47)⋊C4—22no—
69(C2×D47)⋊C4—22no—
70C4⋊Dic47—21no—
71C4⋊Dic47—21no—
72C4⋊Dic47C2312yes—
73C4⋊Dic47C2311yescharacteristic
74Dic47⋊C4—21no—
75Dic47⋊C4—21no—
76Dic47⋊C4—21no—
77C4×Dic47—22no—
78C4×Dic47—22no—
79C2×C47⋊C8C2312yes—
80#10625324—24no—
81C23×C47C2×D411yescharacteristic
82C22×D47—22no—
83C22×D47—22no—
84C22×D47—41no—
85C22×D47C2×D411yescharacteristic
86C22×D47C2×D411yescharacteristic
87Q8×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—42no—
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2411yescharacteristic
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—42no—
100C2×Dic47C2×D411yescharacteristic
101C2×Dic47C2×D411yescharacteristic
102C4×D47—22no—
103C4×D47—22no—
104C4×D47—22no—
105C4×D47—42no—
106C4×D47—42no—
107C4×D47#4114yes—
108Dic94—22no—
109Dic94—42no—
110C8×C47—22no—
111C47⋊C8—22no—
112C22×C47—21no—
113C22×C47—21no—
114C22×C47#13712yes—
115C22×C47C22×D411yescharacteristic
116C2×D47—21no—
117C2×D47—21no—
118C2×D47—21no—
119C2×D47—21no—
120C2×D47—21no—
121C2×D47—44no—
122C2×D47#12312yes—
123C4×C47—21no—
124C4×C47—41no—
125C4×C47—41no—
126C4×C47—42no—
127C4×C47C2×#4112yes—
128Dic47—21no—
129Dic47—41no—
130Dic47—42no—
131Dic47—41no—
132Dic47#12312yes—
133#3095—471nomaximal, Sylow
134C2×C47—22no—
135C2×C47C2×#12311yescharacteristic
136C2×C47C2×#13711yescharacteristic
137C2×C47#57511yescharacteristic
138D47—22no—
139D47—41no—
140C2×C22⋊Q8—471no—
141C2×#117—471no—
142#485—472no—
143#485—472no—
144#484—471no—
145#484D4711yescharacteristic, complemented
146#483—471no—
147#483—471no—
148#428—472no—
149#419—472no—
150#407—471no—
151C47#309511yescharacteristic, complemented, Sylow
152C22×Q8—471no—
153C23×C4—471no—
154C2×M16—472no—
155C22⋊Q8—471no—
156C22⋊Q8—471no—
157C22⋊Q8—471no—
158C22⋊Q8—941no—
159C22⋊Q8—941no—
160C22⋊Q8C2×D4711yescharacteristic
161#117—472no—
162#117—472no—
163#117—941no—
164#117—941no—
165C2×C4⋊C4—471no—
166C2×C4⋊C4—471no—
167C2×C4⋊C4—941no—
168C2×C4⋊C4C2×D4711yescharacteristic
169C2×C22⋊C4—941no—
170C2×C22⋊C4—941no—
171C2×C42—941no—
172#107—472no—
173#107C2×D4712yescomplemented
174#106—472no—
175#106—472no—
176#103—472no—
177#103—472no—
178#103—472no—
179#103C2×D4712yescomplemented
180C22⋊C8—471no—
181C22⋊C8—472no—
182C22⋊C8C2×D4711yescharacteristic
183C24—471no—
184C2×Q8—471no—
185C2×Q8—941no—
186C2×Q8—944no—
187C2×Q8C22×D4711yescharacteristic
188C22×C4—21no—
189C22×C4—471no—
190C22×C4—471no—
191C22×C4—471no—
192C22×C4—471no—
193C22×C4—471no—
194C22×C4—944no—
195C22×C4—941no—
196C22×C4—941no—
197C22×C4—941no—
198C22×C4C22×D4711yescharacteristic
199M16—944no—
200C2×C8—472no—
201C2×C8C22×D4712yes—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—472no—
205C4⋊C4—471no—
206C4⋊C4—941no—
207C4⋊C4—941no—
208C4⋊C4—941no—
209C4⋊C4—941no—
210C4⋊C4—941no—
211C4⋊C4C22×D4712yes—
212C4⋊C4C22×D4711yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—942no—
215C22⋊C4—942no—
216C22⋊C4—941no—
217C22⋊C4—941no—
218C22⋊C4—941no—
219C42—942no—
220C42—942no—
221C23—471no—
222C23—471no—
223C23—942no—
224C23—942no—
225C23—1881no—
226C23D4×D4711yescharacteristic
227Q8—22no—
228Q8—942no—
229Q8—1882no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—471no—
236C2×C4—474no—
237C2×C4—471no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4—942no—
241C2×C4—942no—
242C2×C4—942no—
243C2×C4—941no—
244C2×C4—941no—
245C2×C4—1882no—
246C2×C4—1882no—
247C2×C4—1882no—
248C2×C4D4×D4711yescharacteristic
249C2×C4C23×D4711yescharacteristic
250C8—22no—
251C8—942no—
252C22—21no—
253C22—21no—
254C22—472no—
255C22—941no—
256C22—941no—
257C22—941no—
258C22—941no—
259C22—941no—
260C22—1884no—
261C22#1309405612yes—
262C22C2×D4×D4711yescharacteristic
263C4—21no—
264C4—41no—
265C4—42no—
266C4—41no—
267C4—472no—
268C4—941no—
269C4—1881no—
270C4—1882no—
271C4—1881no—
272C4#41×D4712yes—
273C2—22no—
274C2—942no—
275C2—1881no—
276C2#123×D4711yescharacteristic
277C2C2×#1309405611yescharacteristic
278C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#484C2
socleC22×C47C22×D4
hypercenter#484D47
hypocenterC47#3095
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #15689466C2semidirect
4. #15689462C2semidirect
5. #15689458C2semidirect
6. #15689454C2semidirect
7. #15689451C2semidirect
8. #15689164C2semidirect
9. #15689130C2semidirect
11. C47×#484C2semidirect
30. #13093957C22semidirect
31. #13093956C22semidirect
32. #13093955C22semidirect
33. #13093949C22semidirect
34. #13093948C22semidirect
35. #13093947C22semidirect
40. #107×C47C22semidirect
41. #103×C47C22semidirect
145. #484D47semidirect
151. C47#3095semidirect
173. #107C2×D47semidirect
179. #103C2×D47semidirect