Finite Group Databasebeta

← #20251653

Subgroups — #20251653

Order 6016.

548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689059C213yesmaximal, complemented
2#15689047C212yesmaximal, complemented
3#15689045C216yesmaximal, complemented
4#15688978C213yesmaximal
5C47×#399C211yesmaximal, characteristic, complemented
6C24×D47C2211yescharacteristic
7C2×C4⋊Dic47C2213yescomplemented
8C2×Dic47⋊C4C2216yescomplemented
9C2×C22⋊Dic47C2213yes—
10C2×(C2×D47)⋊C4C2216yes—
11C2×(C2×D47)⋊C4C2216yes—
12C47⋊#95C2213yescomplemented
13C2×C4⋊C4×C47C2213yescomplemented
14C2×C22⋊C4×C47C2213yes—
15#95×C47C2211yescharacteristic, complemented
16C24×C47C2311yescharacteristic
17C23×D47—43no—
18C23×D47—43no—
19C23×D47Q814yes—
20C23×D47C2312yes—
21C22×C4×C47C2313yes—
22C22×C4×C47C2313yes—
23C22×Dic47C2316yes—
24C4⋊C4×C47—43no—
25C22⋊C4×C47—43no—
26C22⋊Dic47—43no—
27(C2×D47)⋊C4—46no—
28(C2×D47)⋊C4—46no—
29C4⋊Dic47—43no—
30Dic47⋊C4—46no—
31C23×C47—23no—
32C23×C47—23no—
33C23×C47C2×Q812yes—
34C23×C47C2411yescharacteristic
35C22×D47—26no—
36C22×D47—26no—
37C22×D47—412no—
38C22×D47—44no—
39C22×D47—412no—
40C22×D47C2×Q814yes—
41C2×C4×C47—26no—
42C2×C4×C47—23no—
43C2×C4×C47—26no—
44C2×C4×C47—23no—
45C2×Dic47—26no—
46C2×Dic47—26no—
47C2×Dic47—26no—
48C22×C47—26no—
49C22×C47—41no—
50C22×C47—43no—
51C22×C47C22×Q811yescharacteristic
52C22×C47H(5,𝔽2)13yes—
53C22×C47H(5,𝔽2)13yes—
54C2×D47—212no—
55C2×D47—416no—
56C2×D47—42no—
57C2×D47—46no—
58C4×C47—43no—
59C4×C47—43no—
60Dic47—46no—
61#2842—471nomaximal, Sylow
62C2×C47—42no—
63C2×C47#54313yes—
64C2×C47#56011yescharacteristic
65C2×C47#56013yes—
66D47—44no—
67#399—473no—
68#399D4711yescharacteristic, complemented
69#396—476no—
70#396—472no—
71#379—473no—
72C47#284211yescharacteristic, complemented, Sylow
73C25—471no—
74C2×C4⋊C4—476no—
75C2×C4⋊C4—473no—
76C2×C4⋊C4C2×D4713yescomplemented
77C2×C22⋊C4—473no—
78C2×C22⋊C4—476no—
79C2×C22⋊C4—476no—
80C2×C22⋊C4C2×D4713yes—
81#95—473no—
82#95C2×D4711yescharacteristic, complemented
83C24—472no—
84C24—474no—
85C24—1883no—
86C24—1883no—
87C24C22×D4711yescharacteristic
88C22×C4—476no—
89C22×C4C22×D4713yes—
90C22×C4C22×D4713yes—
91C4⋊C4—43no—
92C4⋊C4—1886no—
93C4⋊C4—1883no—
94C22⋊C4—43no—
95C22⋊C4—1886no—
96C22⋊C4—1886no—
97C22⋊C4—1883no—
98C23—23no—
99C23—23no—
100C23—474no—
101C23—946no—
102C23—946no—
103C23—18812no—
104C23—1884no—
105C23—18812no—
106C23Q8×D4712yes—
107C23C23×D4711yescharacteristic
108C2×C4—23no—
109C2×C4—23no—
110C2×C4—26no—
111C2×C4—26no—
112C2×C4—946no—
113C2×C4—946no—
114C2×C4—946no—
115C22—26no—
116C22—41no—
117C22—43no—
118C22—9412no—
119C22—18816no—
120C22—1882no—
121C22—1886no—
122C22C2×Q8×D4711yescharacteristic
123C22#1309406913yes—
124C22#1309407013yes—
125C4—43no—
126C4—43no—
127C4—1886no—
128C2—42no—
129C2—1884no—
130C2#1568974813yes—
131C2#1568986011yescharacteristic
132C2#1568986313yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#399C2
hypercenter#399D47
hypocenterC47#2842
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. #15689059C2semidirect
2. #15689047C2semidirect
3. #15689045C2semidirect
5. C47×#399C2semidirect
7. C2×C4⋊Dic47C22semidirect
8. C2×Dic47⋊C4C22semidirect
12. C47⋊#95C22semidirect
13. C2×C4⋊C4×C47C22semidirect
15. #95×C47C22semidirect
68. #399D47semidirect
72. C47#2842semidirect
76. C2×C4⋊C4C2×D47semidirect
82. #95C2×D47semidirect