Finite Group Databasebeta

← #20241416

Subgroups — #20241416

Order 6016.

116 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 35 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#15689062C211yesmaximal, characteristic
2#15688892C211yesmaximal, characteristic
3C47×#324C211yesmaximal, characteristic
4C2×#10625329—21no—
5C2×C4⋊Dic47C411yescharacteristic
6C47⋊#95—21no—
7C47⋊#95—21no—
8C47⋊#95C411yescharacteristic
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—
19#10625329—22no—
20#10625329—41no—
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×C47SD1611yescharacteristic
30C2×C4×C47Q1611yescharacteristic
31C2×Dic47—41no—
32C2×Dic47—41no—
33C2×Dic47—42no—
34C2×Dic47—41no—
35C2×Dic47—41no—
36C8×C47—81no—
37C47⋊C8—42no—
38C22×C47—21no—
39C22×C47—21no—
40C22×C47#9911yescharacteristic
41C22×C47#10311yescharacteristic
42C22×C47#10411yescharacteristic
43C4×C47—21no—
44C4×C47—21no—
45C4×C47—41no—
46C4×C47—41no—
47Dic47—81no—
48Dic47—81no—
49#1353—471nomaximal, Sylow
50C2×C47—21no—
51C2×C47—21no—
52C2×C47#32811yescharacteristic
53C2×C47#35211yescharacteristic
54C2×C47#35511yescharacteristic
55#400—471no—
56#343—471no—
57#324D4711yescharacteristic
58C47#135311yescharacteristic, complemented, Sylow
59C2×M16—941no—
60C2×C4⋊C4—471no—
61C2×C4⋊C4C2×D4711yescharacteristic
62C22⋊C8—21no—
63#95—471no—
64#95—941no—
65#95—941no—
66C22×C4—941no—
67C22×C4—941no—
68C22×C4C4×D4711yescharacteristic
69C22×C4D18811yescharacteristic
70C22×C4C22⋊D4711yescharacteristic
71M16—942no—
72M16—1881no—
73C2×C8—41no—
74C2×C8—1881no—
75C4⋊C4—41no—
76C4⋊C4—1881no—
77C23(C2×D47)⋊C411yescharacteristic
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—41no—
83C2×C4—41no—
84C2×C4—1881no—
85C2×C4—1881no—
86C2×C4—1882no—
87C2×C4—1881no—
88C2×C4—1881no—
89C2×C4#1062532511yescharacteristic
90C2×C4Dic18811yescharacteristic
91C8—81no—
92C8—1882no—
93C22—21no—
94C22—21no—
95C22#1309393811yescharacteristic
96C22#1309394911yescharacteristic
97C22#1309395011yescharacteristic
98C4—21no—
99C4—21no—
100C4—41no—
101C4—41no—
102C4—3761no—
103C4—3761no—
104C2—21no—
105C2—21no—
106C2#1568886111yescharacteristic
107C2#1568891211yescharacteristic
108C2#1568891911yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC22×C4×C47C2×C4
FrattiniC2×C4⋊C4C2×D47
FittingC47×#324C2
socleC22×C47#99
hypercenter#324D47
hypocenterC47#1353
LCSG ▷ C22×C4×C47 ▷ C23×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
58. C47#1353semidirect