Finite Group Databasebeta

← #20241333

Subgroups — #20241333

Order 6016.

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

normal subgroups only

This group has 134 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#15688992C211yesmaximal, characteristic
2#15688849C211yesmaximal, characteristic
3C47×#324C211yesmaximal, characteristic
4C2×C4⋊Dic47C411yescharacteristic
5C2×Dic47⋊C4—21no—
6C2×Dic47⋊C4—21no—
7C2×C4×Dic47C411yescharacteristic
8C22⋊(C47⋊C8)—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—
19Dic47⋊C4—42no—
20Dic47⋊C4—42no—
21C4×Dic47—21no—
22C4×Dic47C812yescomplemented
23C2×C47⋊C8—41no—
24C23×C47C22⋊C411yescharacteristic
25C2×C4×C47—21no—
26C2×C4×C47—21no—
27C2×C4×C47—21no—
28C2×C4×C47—21no—
29C2×C4×C47—41no—
30C2×C4×C47—41no—
31C2×C4×C47C2×C811yescharacteristic
32C2×C4×C47M1611yescharacteristic
33C2×Dic47—22no—
34C2×Dic47—22no—
35C2×Dic47—22no—
36C2×Dic47—41no—
37C2×Dic47—41no—
38C2×Dic47—41no—
39C8×C47—81no—
40C47⋊C8—81no—
41C22×C47—21no—
42C22×C47—21no—
43C22×C47C22⋊C811yescharacteristic
44C22×C47#9911yescharacteristic
45C22×C47#10111yescharacteristic
46C4×C47—21no—
47C4×C47—21no—
48C4×C47—41no—
49C4×C47—41no—
50Dic47—24no—
51Dic47—81no—
52#1325—471nomaximal, Sylow
53C2×C47—21no—
54C2×C47—21no—
55C2×C47#32411yescharacteristic
56C2×C47#35311yescharacteristic
57C2×C47#35611yescharacteristic
58#384—471no—
59#324—471no—
60#324D4711yescharacteristic
61C47#132511yescharacteristic, complemented, Sylow
62C2×C4⋊C4—471no—
63C2×C4⋊C4—941no—
64C2×C4⋊C4—941no—
65C2×C4⋊C4C2×D4711yescharacteristic
66C2×C42—471no—
67C22⋊C8—21no—
68C22⋊C8—941no—
69C22×C4—941no—
70C22×C4—941no—
71C22×C4C4×D4711yescharacteristic
72C22×C4D18811yescharacteristic
73C22×C4C22⋊D4711yescharacteristic
74C2×C8—41no—
75C2×C8—1881no—
76C4⋊C4—41no—
77C4⋊C4—1881no—
78C4⋊C4—1882no—
79C4⋊C4—1882no—
80C42—472no—
81C42—941no—
82C23(C2×D47)⋊C411yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—942no—
90C2×C4—942no—
91C2×C4—942no—
92C2×C4—1881no—
93C2×C4—1881no—
94C2×C4—1881no—
95C2×C4C8×D4711yescharacteristic
96C2×C4#1062532411yescharacteristic
97C8—81no—
98C8—3761no—
99C22—21no—
100C22—21no—
101C22(C2×D47)⋊C811yescharacteristic
102C22#1309393811yescharacteristic
103C22#1309394211yescharacteristic
104C4—21no—
105C4—21no—
106C4—41no—
107C4—41no—
108C4—944no—
109C4—3761no—
110C2—21no—
111C2—21no—
112C2#1568884811yescharacteristic
113C2#1568891511yescharacteristic
114C2#1568892111yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC2×C4×C47C2×C8
FrattiniC2×C4⋊C4C2×D47
FittingC47×#324C2
socleC22×C47#99
hypercenter#324D47
hypocenterC47#1325
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
22. C4×Dic47C8semidirect
61. C47#1325semidirect