Finite Group Databasebeta

← #20241400

Subgroups — #20241400

Order 6016.

116 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 41 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
1C22⋊(C47⋊C16)C211yesmaximal, characteristic
2#15688886C211yesmaximal, characteristic
3C47×#467C211yesmaximal, characteristic
4C2×C4⋊Dic47—21no—
5C2×C47⋊C16—21no—
6C2×Q16×C47C411yescharacteristic, complemented
7C22×C8×C47C2211yescharacteristic
8C22⋊Q8×C47—21no—
9#107×C47C411yescharacteristic, complemented
10#103×C47—21no—
11C2×Q8×C47—21no—
12C22×C4×C47D411yescharacteristic
13C22×Dic47—41no—
14Q16×C47—41no—
15C2×C8×C47—41no—
16C2×C8×C47C2×C411yescharacteristic
17C2×C8×C47D411yescharacteristic
18C4⋊C4×C47—21no—
19C4⋊C4×C47—41no—
20C22⋊C4×C47—41no—
21C4⋊Dic47—22no—
22C4⋊Dic47—41no—
23C47⋊C16—41no—
24C23×C47D811yescharacteristic
25Q8×C47—41no—
26Q8×C47—41no—
27C2×C4×C47—21no—
28C2×C4×C47—21no—
29C2×C4×C47—41no—
30C2×C4×C47—41no—
31C2×C4×C47C22⋊C411yescharacteristic
32C2×C4×C47SD1611yescharacteristic
33C2×Dic47—42no—
34C2×Dic47—81no—
35C2×Dic47—81no—
36C8×C47—21no—
37C8×C47—21no—
38C22×C47—21no—
39C22×C47—21no—
40C22×C47#10211yescharacteristic
41C22×C47SD3211yescharacteristic
42C22×C47Q3211yescharacteristic
43C4×C47—21no—
44C4×C47—81no—
45C4×C47—81no—
46C4×C47#9911yescharacteristic
47C4×C47#10411yescharacteristic
48Dic47—82no—
49#1348—471nomaximal, Sylow
50C2×C47—21no—
51C2×C47—21no—
52C2×C47#32711yescharacteristic
53C2×C47#35811yescharacteristic
54C2×C47#36011yescharacteristic
55#467D4711yescharacteristic
56C22⋊C16—471no—
57#340—471no—
58C47#134811yescharacteristic, complemented, Sylow
59C2×Q16Dic4711yescharacteristic, complemented
60C22×C8C2×D4711yescharacteristic
61C22⋊Q8—21no—
62C2×C4⋊C4—941no—
63C2×C16—941no—
64#107Dic4711yescharacteristic, complemented
65#103—21no—
66C2×Q8—21no—
67C22×C4—1881no—
68C22×C4C22⋊D4711yescharacteristic
69Q16—41no—
70C2×C8—41no—
71C2×C8C2×Dic4711yescharacteristic
72C2×C8C22⋊D4711yescharacteristic
73C4⋊C4—21no—
74C4⋊C4—41no—
75C4⋊C4—942no—
76C4⋊C4—1881no—
77C22⋊C4—41no—
78C16—1881no—
79C23#1062533411yescharacteristic
80Q8—41no—
81Q8—41no—
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—41no—
86C2×C4—3761no—
87C2×C4—3761no—
88C2×C4—1882no—
89C2×C4#1062533511yescharacteristic
90C2×C4C22⋊Dic4711yescharacteristic
91C8—21no—
92C8—21no—
93C22—21no—
94C22—21no—
95C22#1309394511yescharacteristic
96C22#1309396711yescharacteristic
97C22#1309397011yescharacteristic
98C4—21no—
99C4—81no—
100C4—81no—
101C4—3762no—
102C4#1309393911yescharacteristic
103C4#1309395111yescharacteristic
104C2—21no—
105C2—21no—
106C2#1568885711yescharacteristic
107C2#1568892711yescharacteristic
108C2#1568893311yescharacteristic
subgroupG/H
centerC22#13093945
commutatorC2×C8×C47C2×C4
FrattiniC22×C8C2×D47
FittingC47×#467C2
socleC22×C47#102
hypercenter#467D47
hypocenterC47#1348
LCSG ▷ C2×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
6. C2×Q16×C47C4semidirect
9. #107×C47C4semidirect
58. C47#1348semidirect
59. C2×Q16Dic47semidirect
64. #107Dic47semidirect