Finite Group Databasebeta

← #20241373

Subgroups — #20241373

Order 6016.

114 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 33 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#15688905C211yesmaximal, characteristic, complemented
2#15688880C211yesmaximal, characteristic, complemented
3C47×#469C211yesmaximal, characteristic
4#13093983—21no—
5#13093964—21no—
6C2×D8×C47C411yescharacteristic, complemented
7C2×M16×C47C2211yescharacteristic
8#121×C47—21no—
9#106×C47C411yescharacteristic, complemented
10#102×C47—21no—
11C2×D4×C47—21no—
12C2×D4×C47—41no—
13C22×C4×C47D411yescharacteristic
14D8×C47—41no—
15M16×C47—41no—
16C2×C8×C47C2×C411yescharacteristic
17C2×C8×C47D411yescharacteristic
18C4⋊C4×C47—21no—
19C22⋊C4×C47—41no—
20C22⋊Dic47—41no—
21C4⋊Dic47—41no—
22C4×Dic47—22no—
23C47⋊C16—41no—
24C23×C47—41no—
25C23×C47D811yescharacteristic
26D4×C47—41no—
27D4×C47—41no—
28D4×C47—82no—
29C2×C4×C47—21no—
30C2×C4×C47—21no—
31C2×C4×C47—41no—
32C2×C4×C47C22⋊C411yescharacteristic
33C2×C4×C47SD1611yescharacteristic
34C2×Dic47—42no—
35C8×C47—21no—
36C8×C47—21no—
37C22×C47—21no—
38C22×C47—41no—
39C22×C47—81no—
40C22×C47—81no—
41C22×C47—81no—
42C22×C47#10211yescharacteristic
43C4×C47—21no—
44C4×C47—81no—
45C4×C47#9911yescharacteristic
46C4×C47#10411yescharacteristic
47Dic47—82no—
48#1339—471nomaximal, Sylow
49C2×C47—21no—
50C2×C47—41no—
51C2×C47—161no—
52C2×C47#32711yescharacteristic
53#469D4711yescharacteristic
54#349—471no—
55H(3,ℤ/4)—471no—
56C47#133911yescharacteristic, complemented, Sylow
57C2×D8Dic4711yescharacteristic, complemented
58C2×M16C2×D4711yescharacteristic
59#121—21no—
60#117—941no—
61M32—941no—
62#106Dic4711yescharacteristic, complemented
63#102—21no—
64C2×D4—21no—
65C2×D4—41no—
66C22×C4C22⋊D4711yescharacteristic
67D8—41no—
68M16—41no—
69C2×C8C2×Dic4711yescharacteristic
70C2×C8C22⋊D4711yescharacteristic
71C4⋊C4—21no—
72C4⋊C4—1881no—
73C22⋊C4—41no—
74C22⋊C4—1881no—
75C42—942no—
76C16—1881no—
77C23—41no—
78C23#1062533411yescharacteristic
79D4—41no—
80D4—41no—
81D4—82no—
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—1882no—
86C2×C4#1062533511yescharacteristic
87C2×C4C22⋊Dic4711yescharacteristic
88C8—21no—
89C8—21no—
90C22—21no—
91C22—41no—
92C22—81no—
93C22—81no—
94C22—81no—
95C22#1309394511yescharacteristic
96C4—21no—
97C4—81no—
98C4—3762no—
99C4#1309393911yescharacteristic
100C4#1309395111yescharacteristic
101C2—21no—
102C2—41no—
103C2—161no—
104C2#1568885711yescharacteristic
subgroupG/H
centerC2#15688857
commutatorC2×C8×C47C2×C4
FrattiniC2×M16C2×D47
FittingC47×#469C2
socleC2×C47#327
hypercenter#469D47
hypocenterC47#1339
LCSG ▷ C2×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #15688905C2semidirect
2. #15688880C2semidirect
6. C2×D8×C47C4semidirect
9. #106×C47C4semidirect
56. C47#1339semidirect
57. C2×D8Dic47semidirect
62. #106Dic47semidirect