Finite Group Databasebeta

← #21460751

Subgroups — #21460751

Order 7808.

128 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 32 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#16840658C212yesmaximal, complemented
2#16839726C211yesmaximal, characteristic
3#14519851—22no—
4C2×#11758194C411yescharacteristic
5C2×#11758194C2211yescharacteristic
6C22⋊#92418—22no—
7C23×C4×C61C411yescharacteristic
8C24×C61C811yescharacteristic
9C22×C4×C61—21no—
10C22×C4×C61—21no—
11C22×C4×C61—41no—
12C22×C4×C61—41no—
13C22×C4×C61C811yescharacteristic
14C22×C4×C61C2×C411yescharacteristic
15#11758194—41no—
16#11758194—41no—
17C2×#92418—21no—
18C2×#92418D412yes—
19#11758187—42no—
20C23×C61—21no—
21C23×C61—41no—
22C23×C61—42no—
23C23×C61C2×C811yescharacteristic
24C2×C4×C61—21no—
25C2×C4×C61—21no—
26C2×C4×C61—21no—
27C2×C4×C61—42no—
28C2×C4×C61—41no—
29C2×C4×C61—41no—
30C2×C4×C61—41no—
31C2×C4×C61C22⋊C411yescharacteristic
32C2×C4×C61M1611yescharacteristic
33#92418—22no—
34#92418—41no—
35C22×C61—22no—
36C22×C61—21no—
37C22×C61—41no—
38C22×C61—41no—
39C22×C61—42no—
40C22×C61—42no—
41C22×C61—41no—
42C22×C61C22⋊C811yescharacteristic
43C4×C61—21no—
44C4×C61—41no—
45C4×C61#9911yescharacteristic
46C4×C61#10011yescharacteristic
47#1320—611nomaximal, Sylow
48C2×C61—21no—
49C2×C61—42no—
50C2×C61—41no—
51C2×C61#32311yescharacteristic
52#407—611no—
53#349—612no—
54C61#132011yescharacteristic, complemented, Sylow
55C23×C4#692311yescharacteristic
56C2×M16—611no—
57C2×M16—611no—
58M32—1222no—
59C22⋊C8—1222no—
60C24#9242011yescharacteristic
61C22×C4—21no—
62C22×C4—21no—
63C22×C4—41no—
64C22×C4—41no—
65C22×C4#9242011yescharacteristic
66C22×C4C2×#692311yescharacteristic
67M16—2441no—
68M16—2441no—
69C2×C8—612no—
70C2×C8—1221no—
71C16—2442no—
72C23—21no—
73C23—41no—
74C23—42no—
75C23C2×#9242011yescharacteristic
76C2×C4—21no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—42no—
80C2×C4—41no—
81C2×C4—41no—
82C2×C4—41no—
83C2×C4#1175821711yescharacteristic
84C2×C4C22⋊#692311yescharacteristic
85C8—1222no—
86C8—2441no—
87C22—22no—
88C22—21no—
89C22—41no—
90C22—41no—
91C22—42no—
92C22—42no—
93C22—41no—
94C22C22⋊#9242011yescharacteristic
95C4—21no—
96C4—41no—
97C4#1451983511yescharacteristic
98C4#1451983711yescharacteristic
99C2—21no—
100C2—42no—
101C2—41no—
102C2#1684060511yescharacteristic
subgroupG/H
centerC4#14519835
commutatorC23×C61C2×C8
FrattiniC22×C4C2×#6923
FittingC23×C4×C61C4
socleC2×C61#323
hypercenterC23×C4#6923
hypocenterC61#1320
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #16840658C2semidirect
54. C61#1320semidirect