Finite Group Databasebeta

← #20241331

Subgroups — #20241331

Order 6016.

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

normal subgroups only

This group has 118 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
1#15688988C211yesmaximal, characteristic
2#15688849C211yesmaximal, characteristic
3C47×#324C211yesmaximal, characteristic
4C2×C4⋊Dic47C411yescharacteristic
5C2×C4×Dic47C411yescharacteristic
6C22⋊(C47⋊C8)—21no—
7C47⋊#95—21no—
8C47⋊#95—21no—
9C2×C4⋊C4×C47C2211yescharacteristic
10C22⋊C8×C47—21no—
11C22×C4×C47C2×C411yescharacteristic
12C22×C4×C47D411yescharacteristic
13C22×C4×C47D411yescharacteristic
14C22×Dic47—21no—
15C22×Dic47—21no—
16C2×C8×C47—41no—
17C4⋊C4×C47—41no—
18C4⋊Dic47—41no—
19C4×Dic47—21no—
20C4×Dic47C812yescomplemented
21C2×C47⋊C8—41no—
22C23×C47C22⋊C411yescharacteristic
23C2×C4×C47—21no—
24C2×C4×C47—21no—
25C2×C4×C47—21no—
26C2×C4×C47—21no—
27C2×C4×C47—41no—
28C2×C4×C47—41no—
29C2×C4×C47C2×C811yescharacteristic
30C2×C4×C47M1611yescharacteristic
31C2×Dic47—22no—
32C2×Dic47—41no—
33C2×Dic47—41no—
34C2×Dic47—42no—
35C2×Dic47—41no—
36C8×C47—81no—
37C47⋊C8—81no—
38C22×C47—21no—
39C22×C47—21no—
40C22×C47C22⋊C811yescharacteristic
41C22×C47#9911yescharacteristic
42C22×C47#10111yescharacteristic
43C4×C47—21no—
44C4×C47—21no—
45C4×C47—41no—
46C4×C47—41no—
47Dic47—42no—
48Dic47—81no—
49#1324—471nomaximal, Sylow
50C2×C47—21no—
51C2×C47—21no—
52C2×C47#32411yescharacteristic
53C2×C47#35411yescharacteristic
54C2×C47#35511yescharacteristic
55#382—471no—
56#324—471no—
57#324D4711yescharacteristic
58C47#132411yescharacteristic, complemented, Sylow
59C2×C4⋊C4—471no—
60C2×C4⋊C4C2×D4711yescharacteristic
61C2×C42—471no—
62C22⋊C8—21no—
63C22⋊C8—941no—
64#95—941no—
65#95—941no—
66C22×C4—941no—
67C22×C4—941no—
68C22×C4C4×D4711yescharacteristic
69C22×C4D18811yescharacteristic
70C22×C4C22⋊D4711yescharacteristic
71C2×C8—41no—
72C2×C8—1881no—
73C4⋊C4—41no—
74C4⋊C4—1881no—
75C42—472no—
76C42—941no—
77C23(C2×D47)⋊C411yescharacteristic
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—41no—
83C2×C4—41no—
84C2×C4—942no—
85C2×C4—1882no—
86C2×C4—1881no—
87C2×C4—1881no—
88C2×C4—1881no—
89C2×C4C8×D4711yescharacteristic
90C2×C4#1062532411yescharacteristic
91C8—81no—
92C8—3761no—
93C22—21no—
94C22—21no—
95C22(C2×D47)⋊C811yescharacteristic
96C22#1309393811yescharacteristic
97C22#1309394211yescharacteristic
98C4—21no—
99C4—21no—
100C4—41no—
101C4—41no—
102C4—3761no—
103C4—1882no—
104C2—21no—
105C2—21no—
106C2#1568884811yescharacteristic
107C2#1568891711yescharacteristic
108C2#1568891911yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC2×C4×C47C2×C8
FrattiniC2×C4⋊C4C2×D47
FittingC47×#324C2
socleC22×C47#99
hypercenter#324D47
hypocenterC47#1324
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
20. C4×Dic47C8semidirect
58. C47#1324semidirect