Finite Group Databasebeta

← #20252780

Subgroups — #20252780

Order 6016.

766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 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#15689630C213yesmaximal, complemented
2#15689313C214yesmaximal, complemented
3#15689310C214yesmaximal, complemented
4#15689097C213yesmaximal, complemented
5C47×#585C211yesmaximal, characteristic, complemented
6C22×C4×D47C2211yescharacteristic, complemented
7#13094005C2216yescomplemented
8#13094000—23no—
9#13093995—23no—
10#13093992C2216yescomplemented
11C4×C22⋊D47—26no—
12#13093983C2213yescomplemented
13#13093939C22112yescomplemented
142−1+4×C47—23no—
15H(5,𝔽2)×C47—23no—
16H(5,𝔽2)×C47C2214yes—
17C2×#41×C47—26no—
18C2×#41×C47C2213yes—
19C23×D47C2311yescharacteristic
20#41×C47—24no—
21#41×C47—212no—
22#41×C47—26no—
23#41×C47—212no—
24#41×C47—26no—
25C2×Q8×C47—26no—
26C2×Q8×C47D413yescomplemented
27C2×D4×C47—26no—
28C2×D4×C47—212no—
29C2×D4×C47D413yescomplemented
30C2×D4×C47C2316yes—
31C22×C4×C47—24no—
32C22×C4×C47D416yescomplemented
33C22×C4×C47C2311yescharacteristic
34C2×C22⋊D47—26no—
35C22×Dic47C2311yescharacteristic
36C2×C4×D47—23no—
37C2×C4×D47—23no—
38C22⋊Dic47—26no—
39C22⋊Dic47C2316yes—
40(C2×D47)⋊C4—26no—
41C4⋊Dic47—23no—
42Dic47⋊C4—26no—
43C4×Dic47—23no—
44C23×C47—24no—
45C23×C47C2×D416yes—
46C23×C47C2411yescharacteristic
47C22×D47—23no—
48C22×D47—42no—
49Q8×C47—24no—
50Q8×C47—26no—
51D4×C47—212no—
52D4×C47—212no—
53D4×C47—26no—
54C2×C4×C47—212no—
55C2×C4×C47—26no—
56C2×C4×C47—26no—
57C2×C4×C47C2×D416yes—
58C2×C4×C47C2×D413yes—
59C2×C4×C47C2×D413yes—
60C22⋊D47—412no—
61C2×Dic47—26no—
62C2×Dic47—23no—
63C4×D47—43no—
64C4×D47—41no—
65C22×C47—26no—
66C22×C47—41no—
67C22×C47—46no—
68C22×C47—84no—
69C22×C47C22×D413yes—
70C2×D47—26no—
71C2×D47—43no—
72C2×D47—41no—
73C4×C47—26no—
74C4×C47#12013yes—
75C4×C47#12011yescharacteristic
76Dic47—46no—
77Dic47—41no—
78#3025—471nomaximal, Sylow
79C2×C47—23no—
80C2×C47—46no—
81C2×C47C2×#12011yescharacteristic
82D47—42no—
83#585D4711yescharacteristic, complemented
84#525—473no—
85#458—474no—
86B(4,𝔽2)—474no—
87#410—473no—
88C47#302511yescharacteristic, complemented, Sylow
892−1+4—23no—
90H(5,𝔽2)—23no—
91H(5,𝔽2)C2×D4714yes—
92C2×#41—26no—
93C2×#41C2×D4713yes—
94C23×C4—471no—
95#123—476no—
96C22⋊Q8—943no—
97#121—943no—
98#120—476no—
99C4×D4—946no—
100#117—473no—
101#99—4712no—
102C24—471no—
103#41—24no—
104#41—212no—
105#41—26no—
106#41—212no—
107#41—26no—
108C2×Q8—26no—
109C2×Q8C22⋊D4713yescomplemented
110C2×D4—26no—
111C2×D4—212no—
112C2×D4—946no—
113C2×D4C22⋊D4713yescomplemented
114C2×D4C22×D4716yes—
115C22×C4—24no—
116C22×C4—471no—
117C22×C4—943no—
118C22×C4—943no—
119C22×C4C22⋊D4716yescomplemented
120C22×C4C22×D4711yescharacteristic
121C4⋊C4—946no—
122C4⋊C4—943no—
123C22⋊C4—476no—
124C22⋊C4—946no—
125C22⋊C4—946no—
126C42—943no—
127C23—24no—
128C23—943no—
129C23—1882no—
130C23C2×C22⋊D4716yes—
131C23C23×D4711yescharacteristic
132Q8—24no—
133Q8—26no—
134D4—212no—
135D4—212no—
136D4—26no—
137D4—18812no—
138C2×C4—212no—
139C2×C4—26no—
140C2×C4—26no—
141C2×C4—946no—
142C2×C4—943no—
143C2×C4—1883no—
144C2×C4—1881no—
145C2×C4C2×C22⋊D4716yes—
146C2×C4C2×C22⋊D4713yes—
147C2×C4C2×C22⋊D4713yes—
148C22—26no—
149C22—41no—
150C22—46no—
151C22—84no—
152C22—946no—
153C22—1883no—
154C22—1881no—
155C22C22×C22⋊D4713yes—
156C4—26no—
157C4—1886no—
158C4—1881no—
159C4#1309399313yes—
160C4#1309399311yescharacteristic
161C2—23no—
162C2—46no—
163C2—1882no—
164C2C2×#1309399311yescharacteristic
subgroupG/H
centerC4#13093993
commutatorC23×C47C24
FrattiniC23C23×D47
FittingC47×#585C2
socleC2×C47C2×#120
hypercenter#585D47
hypocenterC47#3025
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #15689630C2semidirect
2. #15689313C2semidirect
3. #15689310C2semidirect
4. #15689097C2semidirect
5. C47×#585C2semidirect
6. C22×C4×D47C22semidirect
7. #13094005C22semidirect
10. #13093992C22semidirect
12. #13093983C22semidirect
13. #13093939C22semidirect
26. C2×Q8×C47D4semidirect
29. C2×D4×C47D4semidirect
32. C22×C4×C47D4semidirect
83. #585D47semidirect
88. C47#3025semidirect
109. C2×Q8C22⋊D47semidirect
113. C2×D4C22⋊D47semidirect
119. C22×C4C22⋊D47semidirect