Finite Group Databasebeta

← #442×D47 #20252177

Subgroups — #442×D47 #20252177

Order 6016.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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×D8×D47C211yesmaximal, characteristic
2C4×D4×D47C212yesmaximal, complemented
3#15689236C211yesmaximal, characteristic, complemented
4#15689235C211yesmaximal, characteristic, complemented
5#15689234C211yesmaximal, characteristic, complemented
6#15689233C212yesmaximal, complemented
7#15689232C212yesmaximal, complemented
8#106×D47C211yesmaximal, characteristic, complemented
9#102×D47C212yesmaximal, complemented
10#97×D47C211yesmaximal, characteristic, complemented
11C47×#442C211yesmaximal, characteristic, complemented
12C2×D4×D47C2212yes—
13C22×C4×D47—22no—
14C2×D376C2211yescharacteristic
15C2×#10625334C2212yes—
16D8×D47C418yescomplemented
17C2×C8×D47C2211yescharacteristic
18C2×C8×D47C2211yescharacteristic
19C4×D188C2212yescomplemented
20D4×Dic47C2212yescomplemented
21#13093986C2212yescomplemented
22C4×C22⋊D47—22no—
23(C22⋊D47)⋊C4—22no—
24C4⋊C4×D47C2212yes—
25C22⋊C4×D47—22no—
26C42×D47C2211yescharacteristic
27#13093956C2211yescharacteristic, complemented
28#13093955C2212yescomplemented
29#13093946C2212yescomplemented
30#13093945C2212yescomplemented
31#13093944C2212yescomplemented
32#13093935C2211yescharacteristic, complemented
33#13093934C2211yescharacteristic, complemented
34#13093934C2211yescharacteristic, complemented
35C2×D8×C47C2211yescharacteristic
36C4×D4×C47C2212yescomplemented
37#106×C47C2211yescharacteristic, complemented
38#102×C47C2212yescomplemented
39#97×C47C2211yescharacteristic, complemented
40C23×D47—22no—
41C2×D4×C47C2312yes—
42C22×C4×C47—22no—
43C2×C22⋊D47—22no—
44C22×Dic47—22no—
45D4×D47—24no—
46D4×D47C2×C418yescomplemented
47C2×D188C2312yes—
48C2×C4×D47—22no—
49C2×C4×D47—22no—
50C2×C4×D47—22no—
51C2×C4×D47—48no—
52C2×C4×D47D412yes—
53C2×C4×D47C2311yescharacteristic
54D8×C47C2×C414yescomplemented
55C2×C8×C47C2311yescharacteristic
56C2×C8×C47C2311yescharacteristic
57C4⋊C4×C47C2312yes—
58C22⋊C4×C47—22no—
59C42×C47C2311yescharacteristic
60C22⋊Dic47—22no—
61#10625334C2×C418yescomplemented
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64C4⋊Dic47C2312yes—
65Dic47⋊C4—22no—
66C4×Dic47D412yes—
67C4×Dic47C2311yescharacteristic
68C2×C47⋊C8C2311yescharacteristic
69C2×C47⋊C8C2311yescharacteristic
70D376C2×C414yescomplemented
71C8×D47—22no—
72C8×D47C2×C414yescomplemented
73C23×C47—22no—
74C22×D47—22no—
75C22×D47—28no—
76C22×D47—44no—
77C22×D47—44no—
78C22×D47C2×D411yescharacteristic
79D4×C47—22no—
80D4×C47C22×C414yescomplemented
81C2×C4×C47—22no—
82C2×C4×C47—44no—
83C2×C4×C47C2×D412yes—
84C2×C4×C47C2411yescharacteristic
85C22⋊D47—28no—
86C2×Dic47—22no—
87C2×Dic47—44no—
88C2×Dic47C2×D412yes—
89C2×Dic47C2×D411yescharacteristic
90D188—22no—
91D188C22×C414yescomplemented
92C4×D47—24no—
93C4×D47—44no—
94C4×D47—44no—
95C4×D47—44no—
96C4×D47C22×C412yes—
97C4×D47#4112yes—
98C8×C47—21no—
99C8×C47C22×C412yescomplemented
100C47⋊C8—21no—
101C47⋊C8C22×C412yescomplemented
102C22×C47—24no—
103C22×C47—42no—
104C22×C47—42no—
105C22×C47C22×D411yescharacteristic
106C2×D47—24no—
107C2×D47—42no—
108C2×D47—42no—
109C2×D47—416no—
110C2×D47C4×D412yes—
111C2×D47AGL(1,ℤ/8)14yes—
112C4×C47—22no—
113C4×C47—42no—
114C4×C47C23×C411yescharacteristic
115C4×C47C2×#4111yescharacteristic
116Dic47—22no—
117Dic47—42no—
118Dic47C4×D412yes—
119C2×#442—471nomaximal, Sylow
120C2×C47—44no—
121C2×C47C2×C4×D411yescharacteristic
122C2×C47C2×AGL(1,ℤ/8)12yes—
123D47—44no—
124D47#44214yesdirect product factor
125C22×D8—471no—
126C2×C4×D4—472no—
127#442—471no—
128#442—472no—
129#442—471no—
130#442—472no—
131#442—471no—
132#442D4711yescharacteristic, direct product factor
133C2×#106—471no—
134C2×#102—472no—
135C2×#97—471no—
136C47C2×#44211yescharacteristic, complemented, Sylow
137C22×D4—472no—
138C23×C4—942no—
139C2×D8—472no—
140C2×D8—478no—
141C2×D8—471no—
142C2×D8C2×D4711yescharacteristic
143C22×C8—471no—
144C22×C8—471no—
145C4×D4—472no—
146C4×D4—472no—
147C4×D4—472no—
148C4×D4—942no—
149C4×D4—942no—
150C4×D4C2×D4712yescomplemented
151C2×C4⋊C4—472no—
152C2×C22⋊C4—942no—
153C2×C42—471no—
154#106—471no—
155#106—472no—
156#106C2×D4711yescharacteristic, complemented
157#102—472no—
158#102—472no—
159#102—472no—
160#102C2×D4712yescomplemented
161#97—471no—
162#97—471no—
163#97—471no—
164#97C2×D4711yescharacteristic, complemented
165C24—942no—
166C2×D4—478no—
167C2×D4—472no—
168C2×D4—944no—
169C2×D4—942no—
170C2×D4C22×D4712yes—
171C22×C4—22no—
172C22×C4—471no—
173C22×C4—472no—
174C22×C4—942no—
175C22×C4—942no—
176C22×C4—942no—
177C22×C4—942no—
178C22×C4—1888no—
179D8—478no—
180D8—474no—
181D8C4×D4714yescomplemented
182C2×C8—471no—
183C2×C8—474no—
184C2×C8—471no—
185C2×C8—942no—
186C2×C8C22×D4711yescharacteristic
187C2×C8C22×D4711yescharacteristic
188C4⋊C4—472no—
189C4⋊C4—942no—
190C4⋊C4C22×D4712yes—
191C22⋊C4—22no—
192C22⋊C4—942no—
193C22⋊C4—942no—
194C22⋊C4—942no—
195C42—472no—
196C42—471no—
197C42C22×D4711yescharacteristic
198C23—22no—
199C23—471no—
200C23—948no—
201C23—942no—
202C23—1884no—
203C23—1884no—
204D4—22no—
205D4—474no—
206D4—948no—
207D4—942no—
208D4C2×C4×D4714yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—471no—
212C2×C4—472no—
213C2×C4—472no—
214C2×C4—472no—
215C2×C4—944no—
216C2×C4—942no—
217C2×C4—1884no—
218C2×C4—1884no—
219C2×C4—1884no—
220C2×C4—1884no—
221C2×C4D4×D4712yes—
222C2×C4C23×D4711yescharacteristic
223C8—21no—
224C8—472no—
225C8—941no—
226C8C2×C4×D4712yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—472no—
231C22—474no—
232C22—944no—
233C22—18816no—
234C22—1882no—
235C22—1882no—
236C22C2×D4×D4711yescharacteristic
237C4—22no—
238C4—42no—
239C4—472no—
240C4—942no—
241C4—1882no—
242C4C22×C4×D4711yescharacteristic
243C4#41×D4711yescharacteristic
244C2—44no—
245C2—474no—
246C2—1884no—
247C2C4×D4×D4711yescharacteristic
248C2AGL(1,ℤ/8)×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47C2×#442
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D47C2semidirect
3. #15689236C2semidirect
4. #15689235C2semidirect
5. #15689234C2semidirect
6. #15689233C2semidirect
7. #15689232C2semidirect
8. #106×D47C2semidirect
9. #102×D47C2semidirect
10. #97×D47C2semidirect
11. C47×#442C2semidirect
16. D8×D47C4semidirect
19. C4×D188C22semidirect
20. D4×Dic47C22semidirect
21. #13093986C22semidirect
27. #13093956C22semidirect
28. #13093955C22semidirect
29. #13093946C22semidirect
30. #13093945C22semidirect
31. #13093944C22semidirect
32. #13093935C22semidirect
33. #13093934C22semidirect
34. #13093934C22semidirect
36. C4×D4×C47C22semidirect
37. #106×C47C22semidirect
38. #102×C47C22semidirect
39. #97×C47C22semidirect
46. D4×D47C2×C4semidirect
54. D8×C47C2×C4semidirect
61. #10625334C2×C4semidirect
70. D376C2×C4semidirect
72. C8×D47C2×C4semidirect
80. D4×C47C22×C4semidirect
91. D188C22×C4semidirect
99. C8×C47C22×C4semidirect
101. C47⋊C8C22×C4semidirect
124. D47#442direct (N × H)
132. #442D47direct (N × H)
136. C47C2×#442semidirect
150. C4×D4C2×D47semidirect
156. #106C2×D47semidirect
160. #102C2×D47semidirect
164. #97C2×D47semidirect
181. D8C4×D47semidirect
208. D4C2×C4×D47semidirect
226. C8C2×C4×D47semidirect