Finite Group Databasebeta

← #20241327

Subgroups — #20241327

Order 6016.

108 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×Dic47⋊C8C211yesmaximal, characteristic
2C22⋊(C47⋊C16)C211yesmaximal, characteristic
3C47×C22⋊C16C211yesmaximal, characteristic
4C22×C47⋊C8C411yescharacteristic
5C2×C4×Dic47C411yescharacteristic
6C2×C47⋊C16—21no—
7Dic47⋊C8—21no—
8Dic47⋊C8—21no—
9C22×C8×C47C2211yescharacteristic
10C2×C16×C47—21no—
11C22×C4×C47C2×C411yescharacteristic
12C22×Dic47C811yescharacteristic
13C22×Dic47C811yescharacteristic
14C2×C8×C47—41no—
15C2×C8×C47D411yescharacteristic
16C2×C8×C47D411yescharacteristic
17C4×Dic47—21no—
18C4×Dic47—21no—
19C2×C47⋊C8—21no—
20C2×C47⋊C8—41no—
21C16×C47—41no—
22C47⋊C16—41no—
23C23×C47C2×C811yescharacteristic
24C2×C4×C47—21no—
25C2×C4×C47—21no—
26C2×C4×C47C22⋊C411yescharacteristic
27C2×C4×C47M1611yescharacteristic
28C2×Dic47—21no—
29C2×Dic47—21no—
30C2×Dic47—21no—
31C2×Dic47—41no—
32C2×Dic47C1612yescomplemented
33C8×C47—21no—
34C8×C47—21no—
35C47⋊C8—41no—
36C22×C47—21no—
37C22×C47—21no—
38C22×C47C22⋊C811yescharacteristic
39C22×C47C2×C1611yescharacteristic
40C22×C47M3211yescharacteristic
41C4×C47—21no—
42C4×C47#9911yescharacteristic
43C4×C47#10111yescharacteristic
44Dic47—22no—
45Dic47—41no—
46#1322—471nomaximal, Sylow
47C2×C47—21no—
48C2×C47—21no—
49C2×C47#32411yescharacteristic
50C2×C47C22⋊C1611yescharacteristic
51C2×C47#34911yescharacteristic
52C2×C4⋊C8—471no—
53C22⋊C16—471no—
54C22⋊C16D4711yescharacteristic
55C47#132211yescharacteristic, complemented, Sylow
56C22×C8—471no—
57C22×C8C2×D4711yescharacteristic
58C2×C42—471no—
59C2×C16—21no—
60C2×C16—941no—
61C4⋊C8—941no—
62C4⋊C8—941no—
63C22×C4—471no—
64C22×C4—471no—
65C22×C4C4×D4711yescharacteristic
66C2×C8—41no—
67C2×C8—941no—
68C2×C8—1881no—
69C2×C8D18811yescharacteristic
70C2×C8C22⋊D4711yescharacteristic
71C42—941no—
72C42—941no—
73C16—41no—
74C16—1881no—
75C23C8×D4711yescharacteristic
76C2×C4—21no—
77C2×C4—21no—
78C2×C4—472no—
79C2×C4—941no—
80C2×C4—941no—
81C2×C4—941no—
82C2×C4—1881no—
83C2×C4#1062532411yescharacteristic
84C2×C4(C2×D47)⋊C411yescharacteristic
85C8—21no—
86C8—21no—
87C8—1881no—
88C22—21no—
89C22—21no—
90C22(C2×D47)⋊C811yescharacteristic
91C22C16×D4711yescharacteristic
92C22#1309396311yescharacteristic
93C4—21no—
94C4—942no—
95C4—1881no—
96C4#1309393811yescharacteristic
97C4#1309394211yescharacteristic
98C2—21no—
99C2—21no—
100C2#1568884811yescharacteristic
101C2(C2×D47)⋊C1611yescharacteristic
102C2#1568890411yescharacteristic
subgroupG/H
centerC2×C4(C2×D47)⋊C4
commutatorC22×C47C2×C16
FrattiniC22×C8C2×D47
FittingC47×C22⋊C16C2
socleC22×C47C22⋊C8
hypercenterC22⋊C16D47
hypocenterC47#1322
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
32. C2×Dic47C16semidirect
55. C47#1322semidirect