Finite Group Databasebeta

← #20254224

Subgroups — #20254224

Order 6016.

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

normal subgroups only

This group has 418 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#15689633C212yesmaximal, complemented
2#15689467C212yesmaximal, complemented
3#15689446C212yesmaximal, complemented
4#15689381C211yesmaximal, characteristic, complemented
5#15689367C212yesmaximal, complemented
6#15689286C212yesmaximal, complemented
7#15689265C212yesmaximal, complemented
8#15689086C211yesmaximal, characteristic, complemented
9C47×#469C211yesmaximal, characteristic, complemented
10C2×#10625352C2212yes—
11C22×C4×D47C2211yescharacteristic
12C2×Dic188C2211yescharacteristic, complemented
13C2×#10625335C2212yescomplemented
14C2×#10625329C2211yescharacteristic
15#13094006—22no—
16#13094004C2212yes—
17#13094003C2212yes—
18#13093995C2212yes—
19#13093992—22no—
20D4×Dic47—22no—
21(C22⋊D47)⋊C4—22no—
22#13093982C2212yes—
23#13093957C2212yescomplemented
24#13093956C2211yescharacteristic, complemented
25#13093949C2212yescomplemented
26#13093947C2212yescomplemented
27#13093945C2212yescomplemented
28(C2×D47)⋊C8C2212yes—
29(C2×D47)⋊C8C2212yes—
30C2×D8×C47C2211yescharacteristic, complemented
31C2×M16×C47C2211yescharacteristic
32#121×C47C2212yes—
33#106×C47C2211yescharacteristic, complemented
34#102×C47C2212yescomplemented
35C23×D47D411yescharacteristic
36C2×D4×C47—22no—
37C2×D4×C47C2312yes—
38C22×C4×C47C2311yescharacteristic
39C2×C22⋊D47—22no—
40C2×C22⋊D47—22no—
41C22×Dic47—22no—
42C22×Dic47D411yescharacteristic
43#10625352—42no—
44#10625352—42no—
45C2×C4×D47—41no—
46C2×C4×D47—41no—
47C2×C4×D47D412yes—
48C2×C4×D47C2312yes—
49C2×Dic94C2312yes—
50D8×C47—41no—
51M16×C47—41no—
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2311yescharacteristic
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—22no—
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58#10625335—42no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47—22no—
62C4⋊Dic47C2312yes—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65#10625329—41no—
66C2×C47⋊C8C2312yes—
67Dic188—41no—
68C23×C47—22no—
69C23×C47C2×D411yescharacteristic
70C22×D47—41no—
71C22×D47—42no—
72C22×D47C2×D412yes—
73D4×C47—22no—
74D4×C47—22no—
75D4×C47—44no—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C22⋊D47—44no—
82C22⋊D47—44no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—41no—
86C2×Dic47—44no—
87C2×Dic47C2×D412yes—
88C4×D47—22no—
89C4×D47—22no—
90C4×D47—42no—
91Dic94—22no—
92Dic94—22no—
93C8×C47—21no—
94C8×C47—21no—
95C47⋊C8—22no—
96C22×C47—21no—
97C22×C47—22no—
98C22×C47—42no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47C22×D411yescharacteristic
102C2×D47—22no—
103C2×D47—22no—
104C2×D47—22no—
105C2×D47—44no—
106C4×C47—21no—
107C4×C47—42no—
108C4×C47H(5,𝔽2)11yescharacteristic
109C4×C47H(5,𝔽2)11yescharacteristic
110Dic47—22no—
111Dic47—42no—
112Dic47—42no—
113#3197—471nomaximal, Sylow
114C2×C47—41no—
115C2×C47—82no—
116C2×C47#53411yescharacteristic
117C2×C47#57512yes—
118D47—42no—
119#525—472no—
120#485—472no—
121#482—472no—
122#470—471no—
123#469D4711yescharacteristic, complemented
124#468—472no—
125#452—472no—
126#449—472no—
127#407—471no—
128C47#319711yescharacteristic, complemented, Sylow
129C2×#41—472no—
130C23×C4—471no—
131C2×Q16—471no—
132C2×SD16—472no—
133C2×D8C2×D4711yescharacteristic, complemented
134C2×M16—471no—
135C2×M16C2×D4711yescharacteristic
136#123—942no—
137C22⋊Q8—472no—
138C22⋊Q8—472no—
139#121—472no—
140#121C2×D4712yes—
141#120—942no—
142C4×D4—942no—
143C4×D4—942no—
144#117—472no—
145#107—472no—
146#106—471no—
147#106C2×D4711yescharacteristic, complemented
148#103—472no—
149#103—472no—
150#102—472no—
151#102C2×D4712yescomplemented
152C22⋊C8—472no—
153C22⋊C8—472no—
154C24—471no—
155#41—1882no—
156#41—1882no—
157C2×Q8—472no—
158C2×D4—22no—
159C2×D4—942no—
160C2×D4—942no—
161C2×D4C22×D4712yes—
162C22×C4—471no—
163C22×C4—472no—
164C22×C4—472no—
165C22×C4—942no—
166C22×C4—1881no—
167C22×C4—1881no—
168C22×C4C22×D4711yescharacteristic
169Q16—1881no—
170SD16—1882no—
171D8—41no—
172M16—41no—
173M16—1881no—
174C2×C8—472no—
175C2×C8C22×D4711yescharacteristic
176C2×C8C22×D4711yescharacteristic
177C4⋊C4—472no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4C22×D4712yes—
181C22⋊C4—22no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C42—942no—
187C23—22no—
188C23—472no—
189C23—1881no—
190C23—1882no—
191C23D4×D4711yescharacteristic
192Q8—942no—
193Q8—942no—
194D4—22no—
195D4—22no—
196D4—44no—
197D4—1884no—
198D4—1884no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—472no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—1882no—
208C2×C4—1881no—
209C2×C4—1884no—
210C2×C4D4×D4711yescharacteristic
211C2×C4C23×D4711yescharacteristic
212C8—21no—
213C8—21no—
214C8—942no—
215C22—22no—
216C22—21no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—942no—
221C22—942no—
222C22—942no—
223C22—1884no—
224C22C2×D4×D4711yescharacteristic
225C4—21no—
226C4—42no—
227C4—942no—
228C4—1882no—
229C4—1882no—
230C4#1309406911yescharacteristic
231C4#1309407011yescharacteristic
232C2—41no—
233C2—82no—
234C2—1882no—
235C2#1568968111yescharacteristic
236C2#1568991912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#469C2
socleC22×C47C22×D4
hypercenter#469D47
hypocenterC47#3197
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. #15689633C2semidirect
2. #15689467C2semidirect
3. #15689446C2semidirect
4. #15689381C2semidirect
5. #15689367C2semidirect
6. #15689286C2semidirect
7. #15689265C2semidirect
8. #15689086C2semidirect
9. C47×#469C2semidirect
12. C2×Dic188C22semidirect
13. C2×#10625335C22semidirect
23. #13093957C22semidirect
24. #13093956C22semidirect
25. #13093949C22semidirect
26. #13093947C22semidirect
27. #13093945C22semidirect
30. C2×D8×C47C22semidirect
33. #106×C47C22semidirect
34. #102×C47C22semidirect
123. #469D47semidirect
128. C47#3197semidirect
133. C2×D8C2×D47semidirect
147. #106C2×D47semidirect
151. #102C2×D47semidirect