Finite Group Databasebeta

← #20241489

Subgroups — #20241489

Order 6016.

132 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#13093964C211yesmaximal, characteristic
2#15689161C211yesmaximal, characteristic
3C47×#427C211yesmaximal, characteristic
4#13093983—21no—
5#13093964—21no—
6#13093964—21no—
7C2×C47⋊C16C412yescomplemented
8#13093958—21no—
9#13093956C412yescomplemented
10C22×C8×C47C2211yescharacteristic
11#117×C47—21no—
12#107×C47—21no—
13#106×C47C412yescomplemented
14C22×C4×C47D411yescharacteristic
15C2×C8×C47C2×C411yescharacteristic
16C2×C8×C47C2×C411yescharacteristic
17C2×C8×C47C2×C411yescharacteristic
18C2×C8×C47D411yescharacteristic
19C2×C8×C47D411yescharacteristic
20C2×C8×C47Q811yescharacteristic
21C4⋊C4×C47—22no—
22C22⋊C4×C47—41no—
23C42×C47—41no—
24C22⋊Dic47—41no—
25C4⋊Dic47—22no—
26C4×Dic47—41no—
27C47⋊C16—22no—
28C23×C47D811yescharacteristic
29C2×C4×C47—42no—
30C2×C4×C47C22⋊C411yescharacteristic
31C2×C4×C47C22⋊C411yescharacteristic
32C2×C4×C47C4⋊C411yescharacteristic
33C2×C4×C47SD1611yescharacteristic
34C2×C4×C47SD1611yescharacteristic
35C2×C4×C47Q1611yescharacteristic
36C2×Dic47—42no—
37C8×C47C4211yescharacteristic
38C8×C47C22⋊C411yescharacteristic
39C8×C47C4⋊C411yescharacteristic
40C8×C47C4⋊C411yescharacteristic
41C22×C47—41no—
42C22×C47#10211yescharacteristic
43C22×C47#10211yescharacteristic
44C22×C47#10711yescharacteristic
45C4×C47—82no—
46C4×C47#9511yescharacteristic
47C4×C47#10311yescharacteristic
48C4×C47#10311yescharacteristic
49C4×C47#10611yescharacteristic
50Dic47—82no—
51#1384—471nomaximal, Sylow
52C2×C47—21no—
53C2×C47—21no—
54C2×C47—21no—
55C2×C47#34011yescharacteristic
56C2×M32—471no—
57#427—471no—
58#427D4711yescharacteristic
59C47#138411yescharacteristic, complemented, Sylow
60C22×C8C2×D4711yescharacteristic
61#117—21no—
62#117—941no—
63M32—941no—
64M32—941no—
65C2×C16—472no—
66#107—21no—
67#107—941no—
68#106—472no—
69#106Dic4712yescomplemented
70C22×C4C22⋊D4711yescharacteristic
71C2×C8Dic9411yescharacteristic
72C2×C8C4×D4711yescharacteristic
73C2×C8C4×D4711yescharacteristic
74C2×C8D18811yescharacteristic
75C2×C8C2×Dic4711yescharacteristic
76C2×C8C22⋊D4711yescharacteristic
77C4⋊C4—22no—
78C4⋊C4—942no—
79C22⋊C4—41no—
80C22⋊C4—1881no—
81C42—41no—
82C42—1881no—
83C16—942no—
84C23#1062533411yescharacteristic
85C2×C4—42no—
86C2×C4—1882no—
87C2×C4Dic47⋊C411yescharacteristic
88C2×C4(C2×D47)⋊C411yescharacteristic
89C2×C4#1062533511yescharacteristic
90C2×C4#1062533611yescharacteristic
91C2×C4#1062533711yescharacteristic
92C2×C4C22⋊Dic4711yescharacteristic
93C8C4×Dic4711yescharacteristic
94C8Dic47⋊C411yescharacteristic
95C8C4⋊Dic4711yescharacteristic
96C8(C2×D47)⋊C411yescharacteristic
97C22—41no—
98C22#1309394411yescharacteristic
99C22#1309394511yescharacteristic
100C22#1309395711yescharacteristic
101C4—82no—
102C4—3762no—
103C4C47⋊#9511yescharacteristic
104C4#1309394711yescharacteristic
105C4#1309394811yescharacteristic
106C4#1309395511yescharacteristic
107C2—21no—
108C2—21no—
109C2—21no—
110C2#1568888511yescharacteristic
subgroupG/H
centerC4#13093955
commutatorC8×C47C42
FrattiniC22×C8C2×D47
FittingC47×#427C2
socleC2×C47#340
hypercenter#427D47
hypocenterC47#1384
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
7. C2×C47⋊C16C4semidirect
9. #13093956C4semidirect
13. #106×C47C4semidirect
59. C47#1384semidirect
69. #106Dic47semidirect