Finite Group Databasebeta

← #20254248

Subgroups — #20254248

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#15689450C212yesmaximal, complemented
3#15689445C212yesmaximal, complemented
4#15689374C212yesmaximal, complemented
5#15689359C211yesmaximal, characteristic, complemented
6#15689258C212yesmaximal, complemented
7#15689255C212yesmaximal, complemented
8#15689089C211yesmaximal, characteristic, complemented
9C47×#466C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C2×D4×D47C2212yescomplemented
12C2×D376C2211yescharacteristic
13C2×#10625334C2212yes—
14C2×#10625329C2211yescharacteristic, complemented
15#13094020—22no—
16#13094010—22no—
17#13093999C2212yes—
18#13093998C2212yescomplemented
19#13093995C2212yes—
20#13093994—22no—
21#13093992—22no—
22#13093982C2212yescomplemented
23#13093958C2211yescharacteristic, complemented
24#13093955C2212yescomplemented
25#13093946C2212yescomplemented
26#13093945C2212yescomplemented
27#13093944C2212yescomplemented
28(C2×D47)⋊C8C2212yescomplemented
29(C2×D47)⋊C8C2212yescomplemented
30C2×D8×C47C2211yescharacteristic
31C22×C8×C47C2211yescharacteristic, complemented
32#121×C47C2212yescomplemented
33#107×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—
53C2×C8×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—
65#10625329—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—21no—
101C22×C47—21no—
102C22×C47—42no—
103C22×C47—42no—
104C22×C47—42no—
105C22×C47C22×D411yescharacteristic
106C2×D47—22no—
107C2×D47—22no—
108C2×D47—22no—
109C2×D47—42no—
110C2×D47—42no—
111C2×D47—42no—
112C2×D47—88no—
113C4×C47—21no—
114C4×C47—42no—
115C4×C47H(5,𝔽2)11yescharacteristic
116C4×C47H(5,𝔽2)11yescharacteristic
117Dic47—22no—
118Dic47—42no—
119#3199—471nomaximal, Sylow
120C2×C47—41no—
121C2×C47—82no—
122C2×C47#53411yescharacteristic
123C2×C47#57611yescharacteristic
124C2×C47#57611yescharacteristic
125D47—42no—
126D47—82no—
127#535—472no—
128#482—472no—
129#482—472no—
130#469—472no—
131#466—471no—
132#466D4711yescharacteristic, complemented
133#447—472no—
134#447—472no—
135#408—471no—
136C47#319911yescharacteristic, complemented, Sylow
137C2×#41—471no—
138C22×D4—472no—
139C2×D8—472no—
140C2×D8—471no—
141C2×D8C2×D4711yescharacteristic
142C2×M16—471no—
143C22×C8C2×D4711yescharacteristic, complemented
144#127—942no—
145#124—942no—
146#121—472no—
147#121—472no—
148#121—472no—
149#121C2×D4712yescomplemented
150#120—942no—
151#120—942no—
152#117—472no—
153#107—471no—
154#107C2×D4711yescharacteristic, complemented
155#106—472no—
156#102—472no—
157#102—472no—
158#102—472no—
159#102C2×D4712yescomplemented
160C22⋊C8—472no—
161C22⋊C8—472no—
162C24—942no—
163#41—1881no—
164#41—1881no—
165C2×Q8—471no—
166C2×D4—22no—
167C2×D4—472no—
168C2×D4—471no—
169C2×D4—472no—
170C2×D4—942no—
171C2×D4—942no—
172C2×D4—942no—
173C2×D4—942no—
174C2×D4—1882no—
175C2×D4—1882no—
176C2×D4C22×D4712yes—
177C22×C4—472no—
178C22×C4C22×D4711yescharacteristic
179D8—41no—
180D8—1881no—
181D8—1882no—
182M16—1881no—
183C2×C8—41no—
184C2×C8—472no—
185C2×C8C22×D4711yescharacteristic
186C2×C8C22×D4711yescharacteristic
187C4⋊C4—472no—
188C4⋊C4C22×D4712yes—
189C22⋊C4—22no—
190C22⋊C4—942no—
191C22⋊C4—942no—
192C22⋊C4—942no—
193C22⋊C4—942no—
194C42—942no—
195C23—22no—
196C23—472no—
197C23—942no—
198C23—3762no—
199C23—3762no—
200C23—1884no—
201C23D4×D4711yescharacteristic
202Q8—1881no—
203D4—22no—
204D4—22no—
205D4—82no—
206D4—942no—
207D4—942no—
208D4—3762no—
209D4—3762no—
210D4—3762no—
211D4—1881no—
212D4—1882no—
213D4—1884no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—472no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4D4×D4711yescharacteristic
222C2×C4C23×D4711yescharacteristic
223C8—21no—
224C8—21no—
225C8—942no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—942no—
233C22—942no—
234C22—942no—
235C22—3768no—
236C22—1882no—
237C22—1882no—
238C22—1882no—
239C22C2×D4×D4711yescharacteristic
240C4—21no—
241C4—42no—
242C4—942no—
243C4—1882no—
244C4#1309406911yescharacteristic
245C4#1309407011yescharacteristic
246C2—41no—
247C2—82no—
248C2—3762no—
249C2—1882no—
250C2#1568968111yescharacteristic
251C2#1568992411yescharacteristic
252C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#466C2
socleC22×C47C22×D4
hypercenter#466D47
hypocenterC47#3199
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #15689689C2semidirect
2. #15689450C2semidirect
3. #15689445C2semidirect
4. #15689374C2semidirect
5. #15689359C2semidirect
6. #15689258C2semidirect
7. #15689255C2semidirect
8. #15689089C2semidirect
9. C47×#466C2semidirect
11. C2×D4×D47C22semidirect
14. C2×#10625329C22semidirect
18. #13093998C22semidirect
22. #13093982C22semidirect
23. #13093958C22semidirect
24. #13093955C22semidirect
25. #13093946C22semidirect
26. #13093945C22semidirect
27. #13093944C22semidirect
28. (C2×D47)⋊C8C22semidirect
29. (C2×D47)⋊C8C22semidirect
31. C22×C8×C47C22semidirect
32. #121×C47C22semidirect
33. #107×C47C22semidirect
34. #102×C47C22semidirect
132. #466D47semidirect
136. C47#3199semidirect
143. C22×C8C2×D47semidirect
149. #121C2×D47semidirect
154. #107C2×D47semidirect
159. #102C2×D47semidirect