Finite Group Databasebeta

← #20253338

Subgroups — #20253338

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×#13094004C211yesmaximal, characteristic
2#117×D47C211yesmaximal, characteristic
3#15689467C212yesmaximal, complemented
4#15689466C212yesmaximal, complemented
5#15689460C212yesmaximal, complemented
6#15689455C212yesmaximal, complemented
7#15689163C211yesmaximal, characteristic, complemented
8#15689133C211yesmaximal, characteristic, complemented
9#15689131C211yesmaximal, characteristic, complemented
10#15689086C211yesmaximal, characteristic
11C47×#428C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C22×C4×D47C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15#13094004—21no—
16#13094004—21no—
17#13094004C2212yes—
18#13094004C2212yes—
19#13093983C2211yescharacteristic
20#13093982C2211yescharacteristic
21#13093982C2211yescharacteristic
22#13093981—21no—
23#13093980—21no—
24C2×C4⋊Dic47—21no—
25C4⋊C4×D47C2211yescharacteristic
26C4⋊C4×D47C2211yescharacteristic
27C2×(C2×D47)⋊C4—21no—
28C22⋊C4×D47—21no—
29C42×D47—21no—
30#13093957C2212yescomplemented
31#13093955C2212yescomplemented
32#13093949C2212yescomplemented
33#13093949C2212yescomplemented
34#13093947C2212yescomplemented
35#13093947C2212yescomplemented
36(C2×D47)⋊C8C2212yes—
37(C2×D47)⋊C8C2212yes—
38C2×M16×C47C2211yescharacteristic
39#117×C47C2211yescharacteristic
40C2×C4⋊C4×C47C2211yescharacteristic
41#107×C47C2212yescomplemented
42#106×C47C2212yescomplemented
43C23×D47D411yescharacteristic
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C22×Dic47—21no—
47C22×Dic47D411yescharacteristic
48C2×C4×D47—22no—
49C2×C4×D47—22no—
50C2×C4×D47—21no—
51C2×C4×D47—21no—
52C2×C4×D47D411yescharacteristic
53C2×C4×D47D411yescharacteristic
54C2×C4×D47C2311yescharacteristic
55C2×C4×D47C2311yescharacteristic
56C2×Dic94—22no—
57C2×Dic94—22no—
58C2×Dic94—21no—
59C2×Dic94C2312yes—
60M16×C47—22no—
61C2×C8×C47C2312yes—
62C4⋊C4×C47—21no—
63C4⋊C4×C47C2311yescharacteristic
64C4⋊C4×C47C2312yes—
65C4⋊C4×C47C2311yescharacteristic
66C22⋊C4×C47—21no—
67C42×C47—21no—
68C22⋊Dic47—21no—
69(C2×D47)⋊C4—21no—
70(C2×D47)⋊C4—21no—
71(C2×D47)⋊C4—22no—
72(C2×D47)⋊C4—22no—
73C4⋊Dic47—22no—
74C4⋊Dic47—22no—
75C4⋊Dic47C2311yescharacteristic
76C4⋊Dic47C2311yescharacteristic
77Dic47⋊C4—21no—
78Dic47⋊C4—21no—
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
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—42no—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47#4112yes—
96C2×C4×C47#4112yes—
97C2×C4×C47C2411yescharacteristic
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—21no—
101C2×Dic47—22no—
102C2×Dic47—42no—
103C2×Dic47C2×D411yescharacteristic
104C2×Dic47C2×D411yescharacteristic
105C4×D47—22no—
106C4×D47—22no—
107C4×D47—21no—
108C4×D47—21no—
109C4×D47—21no—
110C4×D47—21no—
111C4×D47—42no—
112C4×D47—42no—
113Dic94—22no—
114Dic94—22no—
115Dic94—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—41no—
130C4×C47—41no—
131C4×C47—42no—
132C4×C47#12312yes—
133C4×C47C2×#4111yescharacteristic
134C4×C47C2×#4111yescharacteristic
135Dic47—21no—
136Dic47—21no—
137Dic47—42no—
138Dic47—41no—
139Dic47—41no—
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#428D4711yescharacteristic, complemented
155#419—471no—
156#419—471no—
157#407—471no—
158C47#309511yescharacteristic, complemented, Sylow
159C22×Q8—471no—
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—941no—
176C2×C4⋊C4C2×D4711yescharacteristic
177C2×C22⋊C4—941no—
178C2×C22⋊C4—941no—
179C2×C42—941no—
180#107—472no—
181#107C2×D4712yescomplemented
182#106—472no—
183#106C2×D4712yescomplemented
184#103—472no—
185#103—472no—
186#103—472no—
187#103—472no—
188C22⋊C8—472no—
189C22⋊C8—472no—
190C24—471no—
191C2×Q8—472no—
192C2×Q8—941no—
193C2×Q8—942no—
194C2×Q8—942no—
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—21no—
212C4⋊C4—471no—
213C4⋊C4—471no—
214C4⋊C4—941no—
215C4⋊C4—941no—
216C4⋊C4—942no—
217C4⋊C4—942no—
218C4⋊C4C22×D4711yescharacteristic
219C4⋊C4C22×D4711yescharacteristic
220C4⋊C4C22×D4712yes—
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—942no—
238Q8—942no—
239Q8—1882no—
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#1062535412yes—
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#1309400912yes—
275C22C2×D4×D4711yescharacteristic
276C4—41no—
277C4—42no—
278C4—41no—
279C4—941no—
280C4—941no—
281C4—1882no—
282C4—1881no—
283C4—1881no—
284C4#1309400912yes—
285C4C2×#1062535011yescharacteristic
286C4C2×#1062535411yescharacteristic
287C2—22no—
288C2—942no—
289C2—1881no—
290C2C2×#1309400911yescharacteristic
291C2#137×D4711yescharacteristic
292C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#428C2
socleC22×C47C22×D4
hypercenter#428D47
hypocenterC47#3095
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #15689467C2semidirect
4. #15689466C2semidirect
5. #15689460C2semidirect
6. #15689455C2semidirect
7. #15689163C2semidirect
8. #15689133C2semidirect
9. #15689131C2semidirect
11. C47×#428C2semidirect
30. #13093957C22semidirect
31. #13093955C22semidirect
32. #13093949C22semidirect
33. #13093949C22semidirect
34. #13093947C22semidirect
35. #13093947C22semidirect
41. #107×C47C22semidirect
42. #106×C47C22semidirect
154. #428D47semidirect
158. C47#3095semidirect
181. #107C2×D47semidirect
183. #106C2×D47semidirect