Finite Group Databasebeta

← #20241405

Subgroups — #20241405

Order 6016.

104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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#15689364C211yesmaximal, characteristic
2C22⋊(C47⋊C16)C211yesmaximal, characteristic
3C47×#341C211yesmaximal, characteristic
4C2×Dic188C411yescharacteristic
5#13094003—21no—
6C2×C47⋊C16—21no—
7#13093958C411yescharacteristic
8#13093949—21no—
9C2×M16×C47—21no—
10C22×C8×C47C2211yescharacteristic
11C22×C4×C47D411yescharacteristic
12C2×Dic94—21no—
13M16×C47—22no—
14M16×C47—41no—
15C2×C8×C47—41no—
16C2×C8×C47—41no—
17C2×C8×C47C2×C411yescharacteristic
18C2×C8×C47D411yescharacteristic
19C22⋊Dic47—41no—
20C4⋊Dic47—21no—
21Dic47⋊C4—41no—
22Dic188—41no—
23C47⋊C16—41no—
24C23×C47SD1611yescharacteristic
25C2×C4×C47—21no—
26C2×C4×C47—21no—
27C2×C4×C47C22⋊C411yescharacteristic
28C2×C4×C47D811yescharacteristic
29C2×Dic47—41no—
30C2×Dic47—41no—
31Dic94—41no—
32Dic94—41no—
33C8×C47—21no—
34C8×C47—21no—
35C8×C47—42no—
36C22×C47—21no—
37C22×C47—21no—
38C22×C47—21no—
39C22×C47#10211yescharacteristic
40C4×C47—21no—
41C4×C47#9911yescharacteristic
42C4×C47#10411yescharacteristic
43Dic47—81no—
44Dic47—81no—
45#1350—471nomaximal, Sylow
46C2×C47—41no—
47C2×C47#32711yescharacteristic
48C2×C47#35911yescharacteristic
49C2×C47#36211yescharacteristic
50#467—471no—
51C22⋊C16—471no—
52#341D4711yescharacteristic
53C47#135011yescharacteristic, complemented, Sylow
54C2×Q16—471no—
55C2×M16—21no—
56C22×C8C2×D4711yescharacteristic
57C22⋊Q8—941no—
58C2×C16—941no—
59#107—471no—
60#103—941no—
61C2×Q8—941no—
62C22×C4C22⋊D4711yescharacteristic
63Q16—1881no—
64M16—22no—
65M16—41no—
66C2×C8—41no—
67C2×C8—41no—
68C2×C8C4×D4711yescharacteristic
69C2×C8D18811yescharacteristic
70C4⋊C4—941no—
71C4⋊C4—1881no—
72C22⋊C4—1881no—
73C16—1881no—
74C23#1062533611yescharacteristic
75Q8—1881no—
76Q8—1881no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—1881no—
80C2×C4—1881no—
81C2×C4(C2×D47)⋊C411yescharacteristic
82C2×C4#1062533411yescharacteristic
83C8—21no—
84C8—21no—
85C8—42no—
86C22—21no—
87C22—21no—
88C22—21no—
89C22#1309394411yescharacteristic
90C4—21no—
91C4—3761no—
92C4—3761no—
93C4#1309393811yescharacteristic
94C4#1309395211yescharacteristic
95C2—41no—
96C2#1568885611yescharacteristic
97C2#1568892911yescharacteristic
98C2#1568893811yescharacteristic
subgroupG/H
centerC22#13093944
commutatorC2×C8×C47C2×C4
FrattiniC22×C8C2×D47
FittingC47×#341C2
socleC22×C47#102
hypercenter#341D47
hypocenterC47#1350
LCSG ▷ C2×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
53. C47#1350semidirect