Finite Group Databasebeta

← #20241406

Subgroups — #20241406

Order 6016.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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#15688888C211yesmaximal, characteristic
3C47×#467C211yesmaximal, characteristic
4C2×#10625329—21no—
5C2×C47⋊C16—21no—
6C2×Q16×C47C411yescharacteristic
7C22×C8×C47C2211yescharacteristic
8C22⋊Q8×C47—21no—
9#107×C47C411yescharacteristic
10#103×C47—21no—
11C2×Q8×C47—21no—
12C22×C4×C47D411yescharacteristic
13Q16×C47—41no—
14C2×C8×C47—41no—
15C2×C8×C47C2×C411yescharacteristic
16C2×C8×C47D411yescharacteristic
17C4⋊C4×C47—21no—
18C4⋊C4×C47—41no—
19C22⋊C4×C47—41no—
20#10625329—22no—
21#10625329—41no—
22C2×C47⋊C8—41no—
23C47⋊C16—41no—
24C23×C47SD1611yescharacteristic
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×C47D811yescharacteristic
33C8×C47—21no—
34C8×C47—21no—
35C47⋊C8—42no—
36C22×C47—21no—
37C22×C47—21no—
38C22×C47—21no—
39C22×C47#10211yescharacteristic
40C4×C47—21no—
41C4×C47—81no—
42C4×C47—81no—
43C4×C47#9911yescharacteristic
44C4×C47#10411yescharacteristic
45#1350—471nomaximal, Sylow
46C2×C47—41no—
47C2×C47#32711yescharacteristic
48C2×C47#35911yescharacteristic
49C2×C47#36211yescharacteristic
50#467D4711yescharacteristic
51C22⋊C16—471no—
52#341—471no—
53C47#135011yescharacteristic, complemented, Sylow
54C2×Q16Dic4711yescharacteristic
55C2×M16—941no—
56C22×C8C2×D4711yescharacteristic
57C22⋊Q8—21no—
58C2×C16—941no—
59#107Dic4711yescharacteristic
60#103—21no—
61C2×Q8—21no—
62C22×C4C22⋊D4711yescharacteristic
63Q16—41no—
64M16—942no—
65M16—1881no—
66C2×C8—41no—
67C2×C8—1881no—
68C2×C8C2×Dic4711yescharacteristic
69C2×C8C22⋊D4711yescharacteristic
70C4⋊C4—21no—
71C4⋊C4—41no—
72C22⋊C4—41no—
73C16—1881no—
74C23#1062533511yescharacteristic
75Q8—41no—
76Q8—41no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—41no—
80C2×C4—41no—
81C2×C4#1062533411yescharacteristic
82C2×C4C22⋊Dic4711yescharacteristic
83C8—21no—
84C8—21no—
85C8—1882no—
86C22—21no—
87C22—21no—
88C22—21no—
89C22#1309394511yescharacteristic
90C4—21no—
91C4—81no—
92C4—81no—
93C4#1309393911yescharacteristic
94C4#1309395111yescharacteristic
95C2—41no—
96C2#1568885711yescharacteristic
97C2#1568893011yescharacteristic
98C2#1568893911yescharacteristic
subgroupG/H
centerC22#13093945
commutatorC2×C8×C47C2×C4
FrattiniC22×C8C2×D47
FittingC47×#467C2
socleC22×C47#102
hypercenter#467D47
hypocenterC47#1350
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
53. C47#1350semidirect