Finite Group Databasebeta

← #20253486

Subgroups — #20253486

Order 6016.

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

normal subgroups only

This group has 444 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#15689678C211yesmaximal, characteristic, complemented
2C4×D4×D47C211yesmaximal, characteristic
3#15689457C212yesmaximal, complemented
4#15689404C211yesmaximal, characteristic, complemented
5#15689403C211yesmaximal, characteristic, complemented
6#15689325C211yesmaximal, characteristic, complemented
7#15689272C212yesmaximal
8#15689226C212yesmaximal, complemented
9#15689224C212yesmaximal, complemented
10#15689179C211yesmaximal, characteristic, complemented
11C47×#461C211yesmaximal, characteristic, complemented
12C2×D4×D47C2211yescharacteristic
13C22×C4×D47—21no—
14C2×#10625336C2212yes—
15#13094024C2211yescharacteristic, complemented
16#13094015—21no—
17#13094004—21no—
18#13094000C2212yes—
19Q8×Dic47C2212yescomplemented
20#13093989—21no—
21C4×D188C2211yescharacteristic
22D4×Dic47C2211yescharacteristic
23#13093986C2211yescharacteristic
24C4×C22⋊D47—21no—
25(C22⋊D47)⋊C4—21no—
26#13093982—21no—
27C4⋊C4×D47C2211yescharacteristic
28C22⋊C4×D47—21no—
29C42×D47C2211yescharacteristic
30#13093958C2212yescomplemented
31#13093957C2212yescomplemented
32C4⋊(C47⋊C8)C2211yescharacteristic, complemented
33#13093948C2212yescomplemented
34#13093946C2212yes—
35#13093945C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093934C2212yescomplemented
38C2×SD16×C47C2212yes—
39C4⋊Q8×C47C2211yescharacteristic, complemented
40C4×D4×C47C2211yescharacteristic
41C4⋊C8×C47C2211yescharacteristic, complemented
42#103×C47C2212yescomplemented
43C23×D47—21no—
44C2×Q8×C47C2312yes—
45C2×D4×C47C2311yescharacteristic
46C22×C4×C47—21no—
47C2×C22⋊D47—21no—
48C22×Dic47—21no—
49D4×D47—22no—
50D4×D47—22no—
51C2×D188C2311yescharacteristic
52C2×C4×D47—21no—
53C2×C4×D47—21no—
54C2×C4×D47—21no—
55C2×C4×D47—44no—
56C2×C4×D47D411yescharacteristic
57C2×C4×D47D411yescharacteristic
58C2×C4×D47C2311yescharacteristic
59C2×Dic94—21no—
60SD16×C47—24no—
61C2×C8×C47C2312yes—
62C4⋊C4×C47—21no—
63C4⋊C4×C47—21no—
64C4⋊C4×C47C2311yescharacteristic
65C22⋊C4×C47—21no—
66C42×C47C2311yescharacteristic
67C22⋊Dic47—21no—
68#10625336—24no—
69(C2×D47)⋊C4—22no—
70(C2×D47)⋊C4—21no—
71(C2×D47)⋊C4—21no—
72C4⋊Dic47—21no—
73C4⋊Dic47—22no—
74C4⋊Dic47C2312yes—
75C4⋊Dic47C2311yescharacteristic
76Dic47⋊C4—21no—
77Dic47⋊C4—22no—
78C4×Dic47—22no—
79C4×Dic47D411yescharacteristic
80C4×Dic47D411yescharacteristic
81C4×Dic47C2311yescharacteristic
82C2×C47⋊C8C2312yes—
83C23×C47—21no—
84C22×D47—24no—
85C22×D47—21no—
86C22×D47—42no—
87C22×D47—42no—
88C22×D47C2×D411yescharacteristic
89Q8×C47—22no—
90Q8×C47—22no—
91D4×C47—21no—
92D4×C47#4112yes—
93C2×C4×C47—22no—
94C2×C4×C47—21no—
95C2×C4×C47—42no—
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2×D411yescharacteristic
98C2×C4×C47C2411yescharacteristic
99C22⋊D47—24no—
100C2×Dic47—22no—
101C2×Dic47—21no—
102C2×Dic47—42no—
103C2×Dic47C2×D411yescharacteristic
104C2×Dic47C2×D411yescharacteristic
105C2×Dic47C2×D411yescharacteristic
106D188—21no—
107D188#4112yes—
108C4×D47—22no—
109C4×D47—22no—
110C4×D47—21no—
111C4×D47—21no—
112C4×D47—42no—
113C4×D47—42no—
114C4×D47—42no—
115Dic94—42no—
116C8×C47—22no—
117C47⋊C8—22no—
118C22×C47—22no—
119C22×C47—41no—
120C22×C47—41no—
121C22×C47C22×D411yescharacteristic
122C2×D47—21no—
123C2×D47—21no—
124C2×D47—22no—
125C2×D47—48no—
126C2×D47—41no—
127C2×D47—41no—
128C2×D47#13712yes—
129C4×C47—21no—
130C4×C47—42no—
131C4×C47—41no—
132C4×C47AGL(1,ℤ/8)12yes—
133C4×C47C2×#4111yescharacteristic
134C4×C47C2×#4111yescharacteristic
135Dic47—21no—
136Dic47—21no—
137Dic47—21no—
138Dic47—42no—
139Dic47—41no—
140#3110—471nomaximal, Sylow
141C2×C47—42no—
142C2×C47#52511yescharacteristic
143C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C47C2×#13711yescharacteristic
145D47—22no—
146D47—42no—
147#533—471no—
148C2×C4×D4—471no—
149#484—472no—
150#474—471no—
151#474—471no—
152#461—471no—
153#461D4711yescharacteristic, complemented
154#450—472no—
155#440—472no—
156#440—472no—
157#432—471no—
158C47#311011yescharacteristic, complemented, Sylow
159C22×D4—471no—
160C23×C4—941no—
161C2×SD16—472no—
162C2×SD16C2×D4712yes—
163C4⋊Q8—471no—
164C4⋊Q8C2×D4711yescharacteristic, complemented
165#125—941no—
166C22⋊Q8—472no—
167C22⋊Q8—941no—
168C4×Q8—472no—
169C4×Q8—941no—
170C4×D4—471no—
171C4×D4—471no—
172C4×D4—471no—
173C4×D4—941no—
174C4×D4—941no—
175C4×D4C2×D4711yescharacteristic
176#117—941no—
177C2×C4⋊C4—471no—
178C2×C22⋊C4—941no—
179C2×C42—471no—
180#107—472no—
181#107—472no—
182C4⋊C8—471no—
183C4⋊C8C2×D4711yescharacteristic, complemented
184#103—472no—
185#103C2×D4712yescomplemented
186#102—472no—
187#102—472no—
188C22⋊C8—472no—
189#97—472no—
190C24—941no—
191C2×Q8—941no—
192C2×Q8C22×D4712yes—
193C2×D4—471no—
194C2×D4—941no—
195C2×D4—942no—
196C2×D4—942no—
197C2×D4C22×D4711yescharacteristic
198C22×C4—21no—
199C22×C4—471no—
200C22×C4—471no—
201C22×C4—471no—
202C22×C4—941no—
203C22×C4—941no—
204C22×C4—941no—
205C22×C4—941no—
206C22×C4—1884no—
207SD16—24no—
208SD16—944no—
209C2×C8—472no—
210C2×C8C22×D4712yes—
211C4⋊C4—21no—
212C4⋊C4—21no—
213C4⋊C4—472no—
214C4⋊C4—471no—
215C4⋊C4—941no—
216C4⋊C4—942no—
217C4⋊C4—942no—
218C4⋊C4—941no—
219C4⋊C4C22×D4711yescharacteristic
220C22⋊C4—21no—
221C22⋊C4—941no—
222C22⋊C4—942no—
223C22⋊C4—941no—
224C22⋊C4—941no—
225C42—471no—
226C42—471no—
227C42—471no—
228C42—942no—
229C42C22×D4711yescharacteristic
230C23—21no—
231C23—471no—
232C23—944no—
233C23—941no—
234C23—1882no—
235C23—1882no—
236Q8—22no—
237Q8—22no—
238Q8—1882no—
239D4—21no—
240D4—472no—
241D4—944no—
242D4—941no—
243D4#1062535212yes—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—471no—
248C2×C4—471no—
249C2×C4—471no—
250C2×C4—942no—
251C2×C4—942no—
252C2×C4—941no—
253C2×C4—941no—
254C2×C4—942no—
255C2×C4—941no—
256C2×C4—1882no—
257C2×C4—1882no—
258C2×C4—1882no—
259C2×C4—1882no—
260C2×C4D4×D4711yescharacteristic
261C2×C4D4×D4711yescharacteristic
262C2×C4C23×D4711yescharacteristic
263C8—22no—
264C8—942no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—472no—
269C22—941no—
270C22—941no—
271C22—942no—
272C22—1888no—
273C22—1881no—
274C22—1881no—
275C22C2×D4×D4711yescharacteristic
276C4—21no—
277C4—42no—
278C4—41no—
279C4—941no—
280C4—941no—
281C4—941no—
282C4—1881no—
283C4—1882no—
284C4#1309405112yes—
285C4#41×D4711yescharacteristic
286C4C2×#1062535211yescharacteristic
287C2—42no—
288C2—942no—
289C2—1882no—
290C2#1568963311yescharacteristic
291C2C2×#1309405111yescharacteristic
292C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3110
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689457C2semidirect
4. #15689404C2semidirect
5. #15689403C2semidirect
6. #15689325C2semidirect
8. #15689226C2semidirect
9. #15689224C2semidirect
10. #15689179C2semidirect
11. C47×#461C2semidirect
15. #13094024C22semidirect
19. Q8×Dic47C22semidirect
30. #13093958C22semidirect
31. #13093957C22semidirect
32. C4⋊(C47⋊C8)C22semidirect
33. #13093948C22semidirect
37. #13093934C22semidirect
39. C4⋊Q8×C47C22semidirect
41. C4⋊C8×C47C22semidirect
42. #103×C47C22semidirect
153. #461D47semidirect
158. C47#3110semidirect
164. C4⋊Q8C2×D47semidirect
183. C4⋊C8C2×D47semidirect
185. #103C2×D47semidirect