Finite Group Databasebeta

← #20241479

Subgroups — #20241479

Order 6016.

152 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 89 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⋊C16C211yesmaximal, characteristic
2C2×#13093958C211yesmaximal, characteristic
3C2×#107×C47C211yesmaximal, characteristic
4C2×C4⋊Dic47—21no—
5C2×C47⋊C16—21no—
6C2×C47⋊C16—21no—
7C2×C47⋊C16C412yescomplemented
8#13093958—21no—
9#13093958C412yescomplemented
10C22×C8×C47C2211yescharacteristic
11C2×C4⋊C4×C47—21no—
12#107×C47—21no—
13#107×C47C412yescomplemented
14C22×C4×C47—41no—
15C22×C4×C47D411yescharacteristic
16C22×Dic47—41no—
17C2×C8×C47C2×C411yescharacteristic
18C2×C8×C47C2×C411yescharacteristic
19C2×C8×C47C2×C411yescharacteristic
20C2×C8×C47D411yescharacteristic
21C2×C8×C47D411yescharacteristic
22C2×C8×C47Q811yescharacteristic
23C4⋊C4×C47—22no—
24C4⋊C4×C47—41no—
25C4⋊Dic47—22no—
26C4⋊Dic47—41no—
27C47⋊C16—22no—
28C23×C47D811yescharacteristic
29C2×C4×C47—42no—
30C2×C4×C47—81no—
31C2×C4×C47—81no—
32C2×C4×C47C22⋊C411yescharacteristic
33C2×C4×C47C22⋊C411yescharacteristic
34C2×C4×C47C4⋊C411yescharacteristic
35C2×C4×C47SD1611yescharacteristic
36C2×C4×C47SD1611yescharacteristic
37C2×C4×C47Q1611yescharacteristic
38C2×Dic47—42no—
39C2×Dic47—81no—
40C2×Dic47—81no—
41C8×C47C4211yescharacteristic
42C8×C47C22⋊C411yescharacteristic
43C8×C47C4⋊C411yescharacteristic
44C8×C47C4⋊C411yescharacteristic
45C22×C47#10211yescharacteristic
46C22×C47#10211yescharacteristic
47C22×C47#10711yescharacteristic
48C22×C47D1611yescharacteristic
49C22×C47SD3211yescharacteristic
50C22×C47SD3211yescharacteristic
51C22×C47Q3211yescharacteristic
52C4×C47—82no—
53C4×C47#9511yescharacteristic
54C4×C47#10311yescharacteristic
55C4×C47#10311yescharacteristic
56C4×C47#10611yescharacteristic
57Dic47—82no—
58#1380—471nomaximal, Sylow
59C2×C47#34011yescharacteristic
60C2×C47#35711yescharacteristic
61C2×C47#35711yescharacteristic
62C2×C47#35811yescharacteristic
63C2×C47#35811yescharacteristic
64C2×C47#36611yescharacteristic
65C2×C47#36711yescharacteristic
66C22×C16—471no—
67C2×#107—471no—
68C2×#107D4711yescharacteristic
69C47#138011yescharacteristic, complemented, Sylow
70C22×C8C2×D4711yescharacteristic
71C2×C4⋊C4—21no—
72C2×C4⋊C4—941no—
73C2×C16—472no—
74C2×C16—941no—
75C2×C16—941no—
76#107—21no—
77#107—472no—
78#107—941no—
79#107Dic4712yescomplemented
80C22×C4—41no—
81C22×C4—1881no—
82C22×C4C22⋊D4711yescharacteristic
83C2×C8Dic9411yescharacteristic
84C2×C8C4×D4711yescharacteristic
85C2×C8C4×D4711yescharacteristic
86C2×C8D18811yescharacteristic
87C2×C8C2×Dic4711yescharacteristic
88C2×C8C22⋊D4711yescharacteristic
89C4⋊C4—22no—
90C4⋊C4—41no—
91C4⋊C4—942no—
92C4⋊C4—1881no—
93C16—942no—
94C23#1062533411yescharacteristic
95C2×C4—42no—
96C2×C4—81no—
97C2×C4—81no—
98C2×C4—3761no—
99C2×C4—3761no—
100C2×C4—1882no—
101C2×C4Dic47⋊C411yescharacteristic
102C2×C4(C2×D47)⋊C411yescharacteristic
103C2×C4#1062533511yescharacteristic
104C2×C4#1062533611yescharacteristic
105C2×C4#1062533711yescharacteristic
106C2×C4C22⋊Dic4711yescharacteristic
107C8C4×Dic4711yescharacteristic
108C8Dic47⋊C411yescharacteristic
109C8C4⋊Dic4711yescharacteristic
110C8(C2×D47)⋊C411yescharacteristic
111C22#1309394411yescharacteristic
112C22#1309394511yescharacteristic
113C22#1309395711yescharacteristic
114C22#1309396511yescharacteristic
115C22#1309396711yescharacteristic
116C22#1309396811yescharacteristic
117C22#1309397011yescharacteristic
118C4—82no—
119C4—3762no—
120C4C47⋊#9511yescharacteristic
121C4#1309394711yescharacteristic
122C4#1309394811yescharacteristic
123C4#1309395511yescharacteristic
124C2#1568888511yescharacteristic
125C2#1568892311yescharacteristic
126C2#1568892411yescharacteristic
127C2#1568892611yescharacteristic
128C2#1568892711yescharacteristic
129C2#1568894811yescharacteristic
130C2#1568895011yescharacteristic
subgroupG/H
centerC23#10625334
commutatorC8×C47C42
FrattiniC22×C8C2×D47
FittingC2×#107×C47C2
socleC23×C47D8
hypercenterC2×#107D47
hypocenterC47#1380
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
7. C2×C47⋊C16C4semidirect
9. #13093958C4semidirect
13. #107×C47C4semidirect
69. C47#1380semidirect
79. #107Dic47semidirect