Finite Group Databasebeta

← #20253334

Subgroups — #20253334

Order 6016.

410 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 127 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×#13094000C211yesmaximal, characteristic
2#117×D47C211yesmaximal, characteristic
3#15689463C212yesmaximal, complemented
4#15689462C212yesmaximal, complemented
5#15689457C212yesmaximal, complemented
6#15689452C212yesmaximal, complemented
7#15689166C211yesmaximal, characteristic, complemented
8#15689165C211yesmaximal, characteristic, complemented
9#15689132C211yesmaximal, characteristic, complemented
10#15689086C211yesmaximal, characteristic
11C47×#419C211yesmaximal, characteristic, complemented
12C22×C4×D47C2211yescharacteristic
13C2×#10625329C2211yescharacteristic
14#13094000—21no—
15#13094000—21no—
16#13094000C2212yes—
17#13094000C2212yes—
18#13093983C2211yescharacteristic
19#13093982C2211yescharacteristic
20#13093982C2211yescharacteristic
21#13093981—21no—
22#13093980—21no—
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4—21no—
25C4⋊C4×D47C2211yescharacteristic
26C4⋊C4×D47C2211yescharacteristic
27C2×(C2×D47)⋊C4—21no—
28C22⋊C4×D47—21no—
29C42×D47—21no—
30#13093958C2212yescomplemented
31#13093957C2212yescomplemented
32#13093956C2212yescomplemented
33#13093955C2212yescomplemented
34#13093948C2212yescomplemented
35#13093948C2212yescomplemented
36(C2×D47)⋊C8C2212yes—
37(C2×D47)⋊C8C2212yes—
38C22×Q8×C47C2211yescharacteristic
39C2×M16×C47C2211yescharacteristic
40#117×C47C2211yescharacteristic
41#103×C47C2212yescomplemented
42#103×C47C2212yescomplemented
43C23×D47D411yescharacteristic
44C2×Q8×C47—21no—
45C2×Q8×C47—22no—
46C2×Q8×C47—22no—
47C2×Q8×C47C2312yes—
48C22×C4×C47—21no—
49C22×C4×C47C2311yescharacteristic
50C22×Dic47—21no—
51C22×Dic47D411yescharacteristic
52C2×C4×D47—22no—
53C2×C4×D47—22no—
54C2×C4×D47—21no—
55C2×C4×D47—21no—
56C2×C4×D47D411yescharacteristic
57C2×C4×D47D411yescharacteristic
58C2×C4×D47C2311yescharacteristic
59C2×C4×D47C2311yescharacteristic
60M16×C47—22no—
61C2×C8×C47C2312yes—
62C4⋊C4×C47C2311yescharacteristic
63C4⋊C4×C47C2311yescharacteristic
64C22⋊C4×C47—21no—
65C42×C47—21no—
66C22⋊Dic47—21no—
67(C2×D47)⋊C4—21no—
68(C2×D47)⋊C4—21no—
69(C2×D47)⋊C4—22no—
70(C2×D47)⋊C4—22no—
71C4⋊Dic47—21no—
72C4⋊Dic47C2311yescharacteristic
73C4⋊Dic47C2311yescharacteristic
74C4⋊Dic47C2312yes—
75Dic47⋊C4—21no—
76Dic47⋊C4—21no—
77Dic47⋊C4—22no—
78Dic47⋊C4—22no—
79C4×Dic47—21no—
80C4×Dic47—21no—
81C4×Dic47—21no—
82#10625329—22no—
83C2×C47⋊C8C2312yes—
84C23×C47C2×D411yescharacteristic
85C22×D47—22no—
86C22×D47—22no—
87C22×D47—41no—
88C22×D47C2×D411yescharacteristic
89C22×D47C2×D411yescharacteristic
90Q8×C47—22no—
91Q8×C47—22no—
92Q8×C47—42no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—22no—
96C2×C4×C47—42no—
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47#4112yes—
99C2×C4×C47#4112yes—
100C2×C4×C47C2411yescharacteristic
101C2×Dic47—22no—
102C2×Dic47—21no—
103C2×Dic47—21no—
104C2×Dic47—22no—
105C2×Dic47—42no—
106C2×Dic47C2×D411yescharacteristic
107C2×Dic47C2×D411yescharacteristic
108C4×D47—22no—
109C4×D47—22no—
110C4×D47—21no—
111C4×D47—21no—
112C4×D47—21no—
113C4×D47—21no—
114C4×D47—42no—
115C4×D47—42no—
116C8×C47—22no—
117C47⋊C8—22no—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47#12312yes—
121C22×C47C22×D411yescharacteristic
122C2×D47—21no—
123C2×D47—21no—
124C2×D47—21no—
125C2×D47—21no—
126C2×D47—21no—
127C2×D47—44no—
128C2×D47#13712yes—
129C4×C47—42no—
130C4×C47—41no—
131C4×C47—41no—
132C4×C47#12312yes—
133C4×C47C2×#4111yescharacteristic
134C4×C47C2×#4111yescharacteristic
135Dic47—21no—
136Dic47—21no—
137Dic47—41no—
138Dic47—41no—
139Dic47—42no—
140#3095—471nomaximal, Sylow
141C2×C47—22no—
142C2×C47C2×#12311yescharacteristic
143C2×C47C2×#13711yescharacteristic
144C2×C47#57511yescharacteristic
145D47—22no—
146D47—41no—
147C2×C22⋊Q8—471no—
148C2×#117—471no—
149#485—472no—
150#485—472no—
151#484—472no—
152#483—472no—
153#428—471no—
154#428—471no—
155#419—471no—
156#419D4711yescharacteristic, complemented
157#407—471no—
158C47#309511yescharacteristic, complemented, Sylow
159C22×Q8C2×D4711yescharacteristic
160C23×C4—471no—
161C2×M16—471no—
162C2×M16C2×D4711yescharacteristic
163C22⋊Q8—472no—
164C22⋊Q8—472no—
165C22⋊Q8—941no—
166C22⋊Q8—941no—
167#117—471no—
168#117—471no—
169#117—471no—
170#117—941no—
171#117—941no—
172#117C2×D4711yescharacteristic
173C2×C4⋊C4—471no—
174C2×C4⋊C4—471no—
175C2×C4⋊C4—471no—
176C2×C4⋊C4—941no—
177C2×C22⋊C4—941no—
178C2×C22⋊C4—941no—
179C2×C42—941no—
180#107—472no—
181#107—472no—
182#106—472no—
183#106—472no—
184#103—472no—
185#103—472no—
186#103C2×D4712yescomplemented
187#103C2×D4712yescomplemented
188C22⋊C8—472no—
189C22⋊C8—472no—
190C24—471no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8C22×D4712yes—
195C22×C4—21no—
196C22×C4—471no—
197C22×C4—471no—
198C22×C4—471no—
199C22×C4—471no—
200C22×C4—471no—
201C22×C4—941no—
202C22×C4—941no—
203C22×C4—942no—
204C22×C4—942no—
205C22×C4—941no—
206C22×C4C22×D4711yescharacteristic
207M16—22no—
208M16—942no—
209C2×C8—472no—
210C2×C8C22×D4712yes—
211C4⋊C4—471no—
212C4⋊C4—471no—
213C4⋊C4—472no—
214C4⋊C4—941no—
215C4⋊C4—941no—
216C4⋊C4—942no—
217C4⋊C4—942no—
218C4⋊C4—941no—
219C4⋊C4C22×D4711yescharacteristic
220C4⋊C4C22×D4711yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—941no—
223C22⋊C4—941no—
224C22⋊C4—942no—
225C22⋊C4—942no—
226C22⋊C4—941no—
227C42—21no—
228C42—941no—
229C42—941no—
230C42—941no—
231C23—471no—
232C23—471no—
233C23—942no—
234C23—942no—
235C23—1881no—
236C23D4×D4711yescharacteristic
237Q8—22no—
238Q8—22no—
239Q8—42no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—471no—
245C2×C4—471no—
246C2×C4—942no—
247C2×C4—942no—
248C2×C4—942no—
249C2×C4—941no—
250C2×C4—941no—
251C2×C4—941no—
252C2×C4—941no—
253C2×C4—941no—
254C2×C4—941no—
255C2×C4—942no—
256C2×C4—1882no—
257C2×C4—1882no—
258C2×C4—1882no—
259C2×C4#1062535012yes—
260C2×C4D4×D4711yescharacteristic
261C2×C4#1062535212yes—
262C2×C4C23×D4711yescharacteristic
263C8—22no—
264C8—942no—
265C22—21no—
266C22—21no—
267C22—472no—
268C22—941no—
269C22—941no—
270C22—941no—
271C22—941no—
272C22—941no—
273C22—1884no—
274C22#1309400612yes—
275C22C2×D4×D4711yescharacteristic
276C4—42no—
277C4—41no—
278C4—41no—
279C4—941no—
280C4—941no—
281C4—1881no—
282C4—1881no—
283C4—1882no—
284C4#1309400612yes—
285C4C2×#1062535211yescharacteristic
286C4C2×#1062535011yescharacteristic
287C2—22no—
288C2—942no—
289C2—1881no—
290C2C2×#1309400611yescharacteristic
291C2#137×D4711yescharacteristic
292C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#419C2
socleC22×C47C22×D4
hypercenter#419D47
hypocenterC47#3095
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #15689463C2semidirect
4. #15689462C2semidirect
5. #15689457C2semidirect
6. #15689452C2semidirect
7. #15689166C2semidirect
8. #15689165C2semidirect
9. #15689132C2semidirect
11. C47×#419C2semidirect
30. #13093958C22semidirect
31. #13093957C22semidirect
32. #13093956C22semidirect
33. #13093955C22semidirect
34. #13093948C22semidirect
35. #13093948C22semidirect
41. #103×C47C22semidirect
42. #103×C47C22semidirect
156. #419D47semidirect
158. C47#3095semidirect
186. #103C2×D47semidirect
187. #103C2×D47semidirect