Finite Group Databasebeta

← #20254250

Subgroups — #20254250

Order 6016.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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#15689689C212yesmaximal, complemented
2#15689449C212yesmaximal, complemented
3#15689446C212yesmaximal, complemented
4#15689376C211yesmaximal, characteristic, complemented
5#15689357C212yesmaximal, complemented
6#15689258C212yesmaximal, complemented
7#15689255C212yesmaximal, complemented
8#15689091C211yesmaximal, characteristic, complemented
9C47×#469C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C2×D4×D47C2212yescomplemented
12C2×D376C2211yescharacteristic
13C2×#10625334C2212yes—
14C22×C47⋊C8C2211yescharacteristic, complemented
15#13094020—22no—
16#13094010—22no—
17#13093999C2212yes—
18#13093998C2212yescomplemented
19#13093995C2212yes—
20#13093994—22no—
21#13093992—22no—
22#13093982C2212yescomplemented
23#13093957C2212yescomplemented
24#13093956C2211yescharacteristic, complemented
25#13093946C2212yescomplemented
26#13093945C2212yescomplemented
27#13093944C2212yescomplemented
28(C2×D47)⋊C8C2212yescomplemented
29(C2×D47)⋊C8C2212yescomplemented
30C2×D8×C47C2211yescharacteristic
31C2×M16×C47C2211yescharacteristic, complemented
32#121×C47C2212yescomplemented
33#106×C47C2211yescharacteristic, complemented
34#102×C47C2212yescomplemented
35C23×D47—22no—
36C2×D4×C47—22no—
37C2×D4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C2×C22⋊D47—22no—
40C2×C22⋊D47—22no—
41C2×C22⋊D47—22no—
42C2×C22⋊D47D412yes—
43D4×D47—42no—
44D4×D47—42no—
45#10625350—41no—
46#10625350—41no—
47C2×D188—22no—
48C2×D188D411yescharacteristic
49C2×D188C2312yes—
50C2×C4×D47C2312yes—
51C2×Dic94D411yescharacteristic
52D8×C47—41no—
53M16×C47—41no—
54C2×C8×C47C2311yescharacteristic
55C2×C8×C47C2311yescharacteristic
56C4⋊C4×C47C2312yes—
57C22⋊C4×C47—22no—
58C22⋊Dic47—22no—
59#10625334—42no—
60(C2×D47)⋊C4—22no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—22no—
63C4⋊Dic47C2312yes—
64C4×Dic47—22no—
65C2×C47⋊C8—41no—
66C2×C47⋊C8C2312yes—
67D376—41no—
68C23×C47—22no—
69C23×C47C2×D411yescharacteristic
70C22×D47—22no—
71C22×D47—44no—
72C22×D47—82no—
73C22×D47—82no—
74C22×D47C2×D412yes—
75D4×C47—22no—
76D4×C47—22no—
77D4×C47—82no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C22⋊D47—42no—
84C22⋊D47—44no—
85C22⋊D47—82no—
86C22⋊D47—82no—
87C2×Dic47—22no—
88C2×Dic47C2×D412yes—
89D188—22no—
90D188—22no—
91D188—41no—
92D188—82no—
93C4×D47—22no—
94C4×D47—22no—
95Dic94—41no—
96C8×C47—21no—
97C8×C47—21no—
98C47⋊C8—22no—
99C22×C47—21no—
100C22×C47—22no—
101C22×C47—42no—
102C22×C47—42no—
103C22×C47—42no—
104C22×C47C22×D411yescharacteristic
105C2×D47—22no—
106C2×D47—22no—
107C2×D47—22no—
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—42no—
111C2×D47—88no—
112C4×C47—21no—
113C4×C47—42no—
114C4×C47H(5,𝔽2)11yescharacteristic
115C4×C47H(5,𝔽2)11yescharacteristic
116Dic47—22no—
117Dic47—42no—
118#3199—471nomaximal, Sylow
119C2×C47—41no—
120C2×C47—82no—
121C2×C47#53411yescharacteristic
122C2×C47#57612yes—
123D47—42no—
124D47—82no—
125#535—472no—
126#482—472no—
127#482—472no—
128#469—471no—
129#469D4711yescharacteristic, complemented
130#466—472no—
131#447—472no—
132#447—472no—
133#408—471no—
134C47#319911yescharacteristic, complemented, Sylow
135C2×#41—471no—
136C22×D4—472no—
137C2×D8—472no—
138C2×D8—471no—
139C2×D8C2×D4711yescharacteristic
140C2×M16C2×D4711yescharacteristic, complemented
141C22×C8—471no—
142#127—942no—
143#124—942no—
144#121—472no—
145#121—472no—
146#121—472no—
147#121C2×D4712yescomplemented
148#120—942no—
149#120—942no—
150#117—472no—
151#107—472no—
152#106—471no—
153#106C2×D4711yescharacteristic, complemented
154#102—472no—
155#102—472no—
156#102—472no—
157#102C2×D4712yescomplemented
158C22⋊C8—472no—
159C22⋊C8—472no—
160C24—942no—
161#41—1881no—
162#41—1881no—
163C2×Q8—471no—
164C2×D4—22no—
165C2×D4—472no—
166C2×D4—471no—
167C2×D4—472no—
168C2×D4—942no—
169C2×D4—942no—
170C2×D4—942no—
171C2×D4—942no—
172C2×D4—1882no—
173C2×D4—1882no—
174C2×D4C22×D4712yes—
175C22×C4—472no—
176C22×C4C22×D4711yescharacteristic
177D8—41no—
178D8—1881no—
179D8—1882no—
180M16—41no—
181C2×C8—472no—
182C2×C8—1881no—
183C2×C8C22×D4711yescharacteristic
184C2×C8C22×D4711yescharacteristic
185C4⋊C4—472no—
186C4⋊C4C22×D4712yes—
187C22⋊C4—22no—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C22⋊C4—942no—
192C42—942no—
193C23—22no—
194C23—472no—
195C23—942no—
196C23—3762no—
197C23—3762no—
198C23—1884no—
199C23D4×D4711yescharacteristic
200Q8—1881no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—942no—
205D4—942no—
206D4—3762no—
207D4—3762no—
208D4—3762no—
209D4—1881no—
210D4—1882no—
211D4—1884no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—472no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4D4×D4711yescharacteristic
220C2×C4C23×D4711yescharacteristic
221C8—21no—
222C8—21no—
223C8—942no—
224C22—22no—
225C22—21no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—942no—
230C22—942no—
231C22—942no—
232C22—3768no—
233C22—1882no—
234C22—1882no—
235C22—1882no—
236C22C2×D4×D4711yescharacteristic
237C4—21no—
238C4—42no—
239C4—942no—
240C4—1882no—
241C4#1309406911yescharacteristic
242C4#1309407011yescharacteristic
243C2—41no—
244C2—82no—
245C2—3762no—
246C2—1882no—
247C2#1568968111yescharacteristic
248C2#1568992712yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#469C2
socleC22×C47C22×D4
hypercenter#469D47
hypocenterC47#3199
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. #15689689C2semidirect
2. #15689449C2semidirect
3. #15689446C2semidirect
4. #15689376C2semidirect
5. #15689357C2semidirect
6. #15689258C2semidirect
7. #15689255C2semidirect
8. #15689091C2semidirect
9. C47×#469C2semidirect
11. C2×D4×D47C22semidirect
14. C22×C47⋊C8C22semidirect
18. #13093998C22semidirect
22. #13093982C22semidirect
23. #13093957C22semidirect
24. #13093956C22semidirect
25. #13093946C22semidirect
26. #13093945C22semidirect
27. #13093944C22semidirect
28. (C2×D47)⋊C8C22semidirect
29. (C2×D47)⋊C8C22semidirect
31. C2×M16×C47C22semidirect
32. #121×C47C22semidirect
33. #106×C47C22semidirect
34. #102×C47C22semidirect
129. #469D47semidirect
134. C47#3199semidirect
140. C2×M16C2×D47semidirect
147. #121C2×D47semidirect
153. #106C2×D47semidirect
157. #102C2×D47semidirect