Finite Group Databasebeta

← #20254184

Subgroups — #20254184

Order 6016.

514 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 113 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#121×D47C212yesmaximal, complemented
2#15689443C212yesmaximal, complemented
3#15689440C212yesmaximal, complemented
4#15689376C211yesmaximal, characteristic, complemented
5#15689374C212yesmaximal, complemented
6#15689258C212yesmaximal, complemented
7#15689255C212yesmaximal, complemented
8#15689086C211yesmaximal, characteristic, complemented
9C47×#469C211yesmaximal, characteristic, complemented
10C2×D4×D47—22no—
11C2×D4×D47C2212yescomplemented
12C22×C4×D47C2211yescharacteristic
13C2×D376C2211yescharacteristic, complemented
14C2×#10625334C2212yescomplemented
15C2×#10625329C2211yescharacteristic, complemented
16#13093999C2212yes—
17#13093998C2212yescomplemented
18#13093997—22no—
19#13093996—22no—
20#13093995C2212yes—
21C4⋊C4×D47C2212yescomplemented
22C22⋊C4×D47—22no—
23#13093956C2211yescharacteristic, complemented
24#13093955C2212yescomplemented
25#13093946C2212yescomplemented
26#13093945C2212yescomplemented
27#13093944C2212yescomplemented
28(C2×D47)⋊C8C2212yescomplemented
29(C2×D47)⋊C8C2212yescomplemented
30C2×D8×C47C2211yescharacteristic, complemented
31C2×M16×C47C2211yescharacteristic, complemented
32#121×C47C2212yescomplemented
33#106×C47C2211yescharacteristic, complemented
34#102×C47C2212yescomplemented
35C23×D47—22no—
36C23×D47D411yescharacteristic
37C2×D4×C47—22no—
38C2×D4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—22no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47—22no—
43C22×Dic47D411yescharacteristic
44D4×D47—42no—
45D4×D47—42no—
46D4×D47—48no—
47C2×D188—22no—
48C2×D188C2312yes—
49C2×C4×D47—22no—
50C2×C4×D47—41no—
51C2×C4×D47—41no—
52C2×C4×D47D412yes—
53C2×C4×D47C2312yes—
54D8×C47—41no—
55M16×C47—41no—
56C2×C8×C47C2311yescharacteristic
57C2×C8×C47C2311yescharacteristic
58C4⋊C4×C47C2312yes—
59C22⋊C4×C47—22no—
60C22⋊Dic47—22no—
61#10625334—42no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64C4⋊Dic47C2312yes—
65Dic47⋊C4—22no—
66#10625329—41no—
67C2×C47⋊C8C2312yes—
68D376—41no—
69C23×C47—22no—
70C23×C47C2×D411yescharacteristic
71C22×D47—24no—
72C22×D47—22no—
73C22×D47—41no—
74C22×D47—44no—
75C22×D47—44no—
76C22×D47—44no—
77C22×D47C2×D412yes—
78D4×C47—22no—
79D4×C47—22no—
80D4×C47—44no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2411yescharacteristic
86C22⋊D47—44no—
87C22⋊D47—44no—
88C22⋊D47—44no—
89C2×Dic47—22no—
90C2×Dic47—41no—
91C2×Dic47C2×D412yes—
92D188—22no—
93D188—22no—
94D188—44no—
95C4×D47—22no—
96C4×D47—22no—
97C4×D47—42no—
98C4×D47—44no—
99C8×C47—21no—
100C8×C47—21no—
101C47⋊C8—22no—
102C22×C47—21no—
103C22×C47—22no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—42no—
107C22×C47C22×D411yescharacteristic
108C2×D47—22no—
109C2×D47—22no—
110C2×D47—44no—
111C2×D47—42no—
112C2×D47—42no—
113C2×D47—42no—
114C2×D47—88no—
115C2×D47AGL(1,ℤ/8)14yes—
116C4×C47—21no—
117C4×C47—42no—
118C4×C47H(5,𝔽2)11yescharacteristic
119C4×C47H(5,𝔽2)11yescharacteristic
120Dic47—22no—
121Dic47—42no—
122#3192—471nomaximal, Sylow
123C2×C47—41no—
124C2×C47—82no—
125C2×C47#53411yescharacteristic
126C2×C47C2×AGL(1,ℤ/8)12yes—
127D47—24no—
128D47—82no—
129C2×#121—472no—
130#481—472no—
131#481—472no—
132#469—471no—
133#469—472no—
134#469D4711yescharacteristic, complemented
135#447—472no—
136#447—472no—
137#407—471no—
138C47#319211yescharacteristic, complemented, Sylow
139C22×D4—472no—
140C22×D4—942no—
141C23×C4—471no—
142C2×D8—472no—
143C2×D8—471no—
144C2×D8C2×D4711yescharacteristic, complemented
145C2×M16—471no—
146C2×M16C2×D4711yescharacteristic, complemented
147#121—472no—
148#121—472no—
149#121—472no—
150#121—942no—
151#121—942no—
152#121C2×D4712yescomplemented
153C2×C4⋊C4—472no—
154C2×C22⋊C4—942no—
155#106—471no—
156#106—472no—
157#106C2×D4711yescharacteristic, complemented
158#102—472no—
159#102—472no—
160#102—472no—
161#102C2×D4712yescomplemented
162C22⋊C8—472no—
163C22⋊C8—472no—
164C24—471no—
165C24—942no—
166C2×D4—22no—
167C2×D4—472no—
168C2×D4—942no—
169C2×D4—942no—
170C2×D4—942no—
171C2×D4—942no—
172C2×D4—1882no—
173C2×D4—1882no—
174C2×D4—1888no—
175C2×D4C22×D4712yes—
176C22×C4—471no—
177C22×C4—472no—
178C22×C4—472no—
179C22×C4—942no—
180C22×C4—1881no—
181C22×C4—1881no—
182C22×C4C22×D4711yescharacteristic
183D8—41no—
184D8—1881no—
185D8—1882no—
186M16—41no—
187M16—1881no—
188C2×C8—472no—
189C2×C8C22×D4711yescharacteristic
190C2×C8C22×D4711yescharacteristic
191C4⋊C4—472no—
192C4⋊C4—942no—
193C4⋊C4C22×D4712yes—
194C22⋊C4—22no—
195C22⋊C4—942no—
196C22⋊C4—942no—
197C22⋊C4—942no—
198C23—22no—
199C23—472no—
200C23—944no—
201C23—942no—
202C23—1881no—
203C23—1884no—
204C23—1884no—
205C23—1884no—
206C23D4×D4711yescharacteristic
207D4—22no—
208D4—22no—
209D4—44no—
210D4—942no—
211D4—942no—
212D4—1884no—
213D4—1884no—
214D4—1884no—
215D4—1884no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—472no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—1882no—
224C2×C4—1884no—
225C2×C4—1881no—
226C2×C4D4×D4711yescharacteristic
227C2×C4C23×D4711yescharacteristic
228C8—21no—
229C8—21no—
230C8—942no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—474no—
237C22—942no—
238C22—942no—
239C22—3768no—
240C22—1884no—
241C22—1882no—
242C22—1882no—
243C22—1882no—
244C22C2×D4×D4711yescharacteristic
245C4—21no—
246C4—42no—
247C4—942no—
248C4—1882no—
249C4#1309406911yescharacteristic
250C4#1309407011yescharacteristic
251C2—41no—
252C2—82no—
253C2—944no—
254C2—3762no—
255C2#1568968111yescharacteristic
256C2AGL(1,ℤ/8)×D4712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#469C2
socleC22×C47C22×D4
hypercenter#469D47
hypocenterC47#3192
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #121×D47C2semidirect
2. #15689443C2semidirect
3. #15689440C2semidirect
4. #15689376C2semidirect
5. #15689374C2semidirect
6. #15689258C2semidirect
7. #15689255C2semidirect
8. #15689086C2semidirect
9. C47×#469C2semidirect
11. C2×D4×D47C22semidirect
13. C2×D376C22semidirect
14. C2×#10625334C22semidirect
15. C2×#10625329C22semidirect
17. #13093998C22semidirect
21. C4⋊C4×D47C22semidirect
23. #13093956C22semidirect
24. #13093955C22semidirect
25. #13093946C22semidirect
26. #13093945C22semidirect
27. #13093944C22semidirect
28. (C2×D47)⋊C8C22semidirect
29. (C2×D47)⋊C8C22semidirect
30. C2×D8×C47C22semidirect
31. C2×M16×C47C22semidirect
32. #121×C47C22semidirect
33. #106×C47C22semidirect
34. #102×C47C22semidirect
134. #469D47semidirect
138. C47#3192semidirect
144. C2×D8C2×D47semidirect
146. C2×M16C2×D47semidirect
152. #121C2×D47semidirect
157. #106C2×D47semidirect
161. #102C2×D47semidirect