Finite Group Databasebeta

← #483×D47 #20253262

Subgroups — #483×D47 #20253262

Order 6016.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 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×C4⋊C4×D47C211yesmaximal, characteristic
3#15689455C212yesmaximal, complemented
4#15689454C211yesmaximal, characteristic, complemented
5#15689453C211yesmaximal, characteristic, complemented
6#15689452C212yesmaximal, complemented
7#15689451C211yesmaximal, characteristic, complemented
8#106×D47C212yesmaximal, complemented
9#103×D47C212yesmaximal, complemented
10C22⋊C8×D47C211yesmaximal, characteristic
11C47×#483C211yesmaximal, characteristic, complemented
12C2×Q8×D47C2211yescharacteristic
13C22×C4×D47—21no—
14C22×C4×D47C2211yescharacteristic
15C2×C8×D47C2212yes—
16#13094004C2211yescharacteristic
17#13094003C2211yescharacteristic
18#13094002—21no—
19#13094001—21no—
20#13094000C2211yescharacteristic
21C2×C4⋊Dic47C2211yescharacteristic
22C2×Dic47⋊C4—21no—
23C4⋊C4×D47—21no—
24C4⋊C4×D47—21no—
25C4⋊C4×D47—21no—
26C4⋊C4×D47C2212yes—
27C4⋊C4×D47C2212yes—
28C4⋊C4×D47C2211yescharacteristic
29C22⋊C4×D47—21no—
30#13093956C2212yescomplemented
31#13093955C2212yescomplemented
32#13093955C2212yescomplemented
33#13093949C2212yescomplemented
34#13093948C2212yescomplemented
35#13093947C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic
37(C2×D47)⋊C8C2212yes—
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#106×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×D47—22no—
54C2×C4×D47—22no—
55C2×C4×D47—44no—
56C2×C4×D47D411yescharacteristic
57C2×C4×D47D411yescharacteristic
58C2×C4×D47C2311yescharacteristic
59C2×C4×D47C2311yescharacteristic
60C2×Dic94—21no—
61C2×Dic94C2311yescharacteristic
62C2×C8×C47C2312yes—
63C4⋊C4×C47—21no—
64C4⋊C4×C47—21no—
65C4⋊C4×C47C2312yes—
66C4⋊C4×C47C2311yescharacteristic
67C22⋊C4×C47—21no—
68C22⋊Dic47—21no—
69(C2×D47)⋊C4—21no—
70(C2×D47)⋊C4—21no—
71C4⋊Dic47—21no—
72C4⋊Dic47—21no—
73C4⋊Dic47C2312yes—
74C4⋊Dic47C2311yescharacteristic
75Dic47⋊C4—21no—
76Dic47⋊C4—22no—
77Dic47⋊C4—22no—
78Dic47⋊C4—21no—
79Dic47⋊C4—21no—
80C2×C47⋊C8C2312yes—
81C8×D47—24no—
82C23×C47C2×D411yescharacteristic
83C22×D47—22no—
84C22×D47—22no—
85C22×D47SD1614yes—
86C22×D47C2×D411yescharacteristic
87C22×D47C2×D411yescharacteristic
88Q8×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—42no—
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2411yescharacteristic
96C2×Dic47—22no—
97C2×Dic47—21no—
98C2×Dic47—22no—
99C2×Dic47—21no—
100C2×Dic47—42no—
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103C4×D47—22no—
104C4×D47—22no—
105C4×D47—22no—
106C4×D47—42no—
107C4×D47—44no—
108C4×D47—44no—
109C4×D47—42no—
110C4×D47#4114yes—
111Dic94—22no—
112Dic94—42no—
113C8×C47—22no—
114C47⋊C8—22no—
115C22×C47—21no—
116C22×C47—21no—
117C22×C47C2×SD1612yes—
118C22×C47C22×D411yescharacteristic
119C2×D47—21no—
120C2×D47—21no—
121C2×D47—28no—
122C2×D47#12312yes—
123C2×D47C2×SD1612yes—
124C2×D47C2×SD1612yes—
125C2×D47#13712yes—
126C4×C47—21no—
127C4×C47—41no—
128C4×C47—42no—
129C4×C47—41no—
130C4×C47C2×#4112yes—
131Dic47—21no—
132Dic47—41no—
133Dic47—42no—
134Dic47—41no—
135Dic47#12312yes—
136C2×#483—471nomaximal, Sylow
137C2×C47—22no—
138C2×C47C2×#12311yescharacteristic
139C2×C47C22×SD1611yescharacteristic
140C2×C47C2×#13711yescharacteristic
141D47—22no—
142D47#48314yesdirect product factor
143C2×C22⋊Q8—471no—
144C22×C4⋊C4—471no—
145#483—471no—
146#483—471no—
147#483—472no—
148#483—472no—
149#483—471no—
150#483D4711yescharacteristic, direct product factor
151C2×#106—472no—
152C2×#103—472no—
153C2×C22⋊C8—471no—
154C47C2×#48311yescharacteristic, complemented, Sylow
155C22×Q8—471no—
156C23×C4—471no—
157C23×C4—941no—
158C22×C8—472no—
159C22⋊Q8—471no—
160C22⋊Q8—471no—
161C22⋊Q8—471no—
162C22⋊Q8—941no—
163C22⋊Q8—941no—
164C22⋊Q8C2×D4711yescharacteristic
165C2×C4⋊C4—471no—
166C2×C4⋊C4—472no—
167C2×C4⋊C4—472no—
168C2×C4⋊C4—471no—
169C2×C4⋊C4—941no—
170C2×C4⋊C4—941no—
171C2×C4⋊C4—941no—
172C2×C4⋊C4—941no—
173C2×C4⋊C4C2×D4711yescharacteristic
174C2×C22⋊C4—941no—
175#106—472no—
176#106—472no—
177#106—472no—
178#106C2×D4712yescomplemented
179#103—472no—
180#103—472no—
181#103—472no—
182#103C2×D4712yescomplemented
183C22⋊C8—471no—
184C22⋊C8—472no—
185C22⋊C8C2×D4711yescharacteristic
186C24—471no—
187C2×Q8—471no—
188C2×Q8—941no—
189C2×Q8—944no—
190C2×Q8C22×D4711yescharacteristic
191C22×C4—21no—
192C22×C4—471no—
193C22×C4—471no—
194C22×C4—471no—
195C22×C4—471no—
196C22×C4—471no—
197C22×C4—944no—
198C22×C4—941no—
199C22×C4—941no—
200C22×C4—942no—
201C22×C4—942no—
202C22×C4—941no—
203C22×C4—1884no—
204C22×C4C22×D4711yescharacteristic
205C2×C8—472no—
206C2×C8—944no—
207C2×C8C22×D4712yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—472no—
211C4⋊C4—471no—
212C4⋊C4—942no—
213C4⋊C4—942no—
214C4⋊C4—941no—
215C4⋊C4—941no—
216C4⋊C4—941no—
217C4⋊C4—941no—
218C4⋊C4—941no—
219C4⋊C4C22×D4712yes—
220C4⋊C4C22×D4711yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—941no—
223C22⋊C4—941no—
224C22⋊C4—941no—
225C23—471no—
226C23—474no—
227C23—471no—
228C23—942no—
229C23—942no—
230C23D4×D4711yescharacteristic
231Q8—22no—
232Q8—942no—
233Q8—1882no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—471no—
240C2×C4—474no—
241C2×C4—471no—
242C2×C4—942no—
243C2×C4—942no—
244C2×C4—942no—
245C2×C4—942no—
246C2×C4—941no—
247C2×C4—941no—
248C2×C4—942no—
249C2×C4—1882no—
250C2×C4—1884no—
251C2×C4—1884no—
252C2×C4—1882no—
253C2×C4—1882no—
254C2×C4D4×D4711yescharacteristic
255C2×C4C23×D4711yescharacteristic
256C8—22no—
257C8—942no—
258C22—21no—
259C22—21no—
260C22—472no—
261C22—472no—
262C22—472no—
263C22—472no—
264C22—948no—
265C22—941no—
266C22—941no—
267C22SD16×D4712yes—
268C22C2×D4×D4711yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—472no—
274C4—941no—
275C4—1881no—
276C4—1882no—
277C4—1881no—
278C4#41×D4712yes—
279C2—22no—
280C2—474no—
281C2—942no—
282C2#123×D4711yescharacteristic
283C2C2×SD16×D4711yescharacteristic
284C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47C2×#483
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #15689455C2semidirect
4. #15689454C2semidirect
5. #15689453C2semidirect
6. #15689452C2semidirect
7. #15689451C2semidirect
8. #106×D47C2semidirect
9. #103×D47C2semidirect
11. C47×#483C2semidirect
30. #13093956C22semidirect
31. #13093955C22semidirect
32. #13093955C22semidirect
33. #13093949C22semidirect
34. #13093948C22semidirect
35. #13093947C22semidirect
40. #106×C47C22semidirect
41. #103×C47C22semidirect
142. D47#483direct (N × H)
150. #483D47direct (N × H)
154. C47C2×#483semidirect
178. #106C2×D47semidirect
182. #103C2×D47semidirect