Finite Group Databasebeta

← #20241394

Subgroups — #20241394

Order 6016.

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

normal subgroups only

This group has 124 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#15688892C211yesmaximal, characteristic
2#15688849C211yesmaximal, characteristic
3C47×#398C211yesmaximal, characteristic
4C2×#10625329—21no—
5C22⋊(C47⋊C8)—21no—
6C2×C4⋊C4×C47—21no—
7C2×C4⋊C4×C47C411yescharacteristic
8C2×C4⋊C4×C47C2211yescharacteristic
9#95×C47—21no—
10#95×C47C411yescharacteristic
11C22×C4×C47—21no—
12C22×C4×C47—21no—
13C22×C4×C47C2×C411yescharacteristic
14C22×C4×C47D411yescharacteristic
15C22×C4×C47D411yescharacteristic
16C4⋊C4×C47—41no—
17C4⋊C4×C47—41no—
18C4⋊C4×C47—41no—
19C4⋊C4×C47—41no—
20#10625329—22no—
21#10625329—41no—
22C2×C47⋊C8—41no—
23C2×C47⋊C8—41no—
24C23×C47C22⋊C411yescharacteristic
25C2×C4×C47—21no—
26C2×C4×C47—21no—
27C2×C4×C47—22no—
28C2×C4×C47—21no—
29C2×C4×C47—21no—
30C2×C4×C47—41no—
31C2×C4×C47—41no—
32C2×C4×C47—41no—
33C2×C4×C47—41no—
34C2×C4×C47—41no—
35C2×C4×C47—41no—
36C2×C4×C47—41no—
37C2×C4×C47D811yescharacteristic
38C2×C4×C47SD1611yescharacteristic
39C47⋊C8—42no—
40C47⋊C8—81no—
41C22×C47—21no—
42C22×C47—21no—
43C22×C47#9911yescharacteristic
44C22×C47#10211yescharacteristic
45C22×C47#10411yescharacteristic
46C4×C47—21no—
47C4×C47—21no—
48C4×C47—42no—
49C4×C47—41no—
50C4×C47—41no—
51C4×C47—81no—
52#1346—471nomaximal, Sylow
53C2×C47—21no—
54C2×C47—21no—
55C2×C47#32711yescharacteristic
56C2×C47#35211yescharacteristic
57C2×C47#35611yescharacteristic
58#398D4711yescharacteristic
59#343—471no—
60#324—471no—
61C47#134611yescharacteristic, complemented, Sylow
62C2×M16—941no—
63C2×C4⋊C4—21no—
64C2×C4⋊C4Dic4711yescharacteristic
65C2×C4⋊C4C2×D4711yescharacteristic
66C22⋊C8—941no—
67#95—21no—
68#95Dic4711yescharacteristic
69C22×C4—21no—
70C22×C4—21no—
71C22×C4C2×Dic4711yescharacteristic
72C22×C4C22⋊D4711yescharacteristic
73C22×C4C22⋊D4711yescharacteristic
74M16—942no—
75M16—1881no—
76C2×C8—1881no—
77C2×C8—1881no—
78C4⋊C4—41no—
79C4⋊C4—41no—
80C4⋊C4—41no—
81C4⋊C4—41no—
82C23C22⋊Dic4711yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—41no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—41no—
92C2×C4—41no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4#1062533411yescharacteristic
96C2×C4#1062533511yescharacteristic
97C8—3761no—
98C8—1882no—
99C22—21no—
100C22—21no—
101C22#1309393911yescharacteristic
102C22#1309394511yescharacteristic
103C22#1309395111yescharacteristic
104C4—21no—
105C4—21no—
106C4—42no—
107C4—41no—
108C4—41no—
109C4—81no—
110C2—21no—
111C2—21no—
112C2#1568885711yescharacteristic
113C2#1568891311yescharacteristic
114C2#1568892211yescharacteristic
subgroupG/H
centerC22#13093939
commutatorC22×C4×C47C2×C4
FrattiniC2×C4⋊C4C2×D47
FittingC47×#398C2
socleC22×C47#99
hypercenter#398D47
hypocenterC47#1346
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
61. C47#1346semidirect