Finite Group Databasebeta

← #21460739

Subgroups — #21460739

Order 7808.

140 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 44 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⋊#11758187C212yesmaximal, complemented
2C2×C22⋊#92418C211yesmaximal, characteristic
3C2×#11758187—22no—
4C22×#92418C411yescharacteristic
5C22×#92418C2211yescharacteristic
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
15C2×#92418—21no—
16C2×#92418—41no—
17C2×#92418—41no—
18C2×#92418D412yes—
19#11758187—42no—
20C23×C61—21no—
21C23×C61—21no—
22C23×C61—41no—
23C23×C61—41no—
24C23×C61C1612yescomplemented
25C23×C61C2×C811yescharacteristic
26C2×C4×C61—21no—
27C2×C4×C61—21no—
28C2×C4×C61—21no—
29C2×C4×C61—42no—
30C2×C4×C61—41no—
31C2×C4×C61—41no—
32C2×C4×C61—41no—
33C2×C4×C61C22⋊C411yescharacteristic
34C2×C4×C61M1611yescharacteristic
35#92418—22no—
36#92418—41no—
37C22×C61—21no—
38C22×C61—21no—
39C22×C61—22no—
40C22×C61—42no—
41C22×C61—42no—
42C22×C61—41no—
43C22×C61—41no—
44C22×C61C22⋊C811yescharacteristic
45C22×C61C2×C1611yescharacteristic
46C22×C61M3211yescharacteristic
47C4×C61—21no—
48C4×C61—41no—
49C4×C61#9911yescharacteristic
50C4×C61#10011yescharacteristic
51#1314—611nomaximal, Sylow
52C2×C61—21no—
53C2×C61—21no—
54C2×C61—42no—
55C2×C61#32311yescharacteristic
56C2×C61C22⋊C1611yescharacteristic
57C2×C61#34911yescharacteristic
58C2×C22⋊C8—611no—
59C22⋊C16—612no—
60C61#131411yescharacteristic, complemented, Sylow
61C23×C4#692311yescharacteristic
62C22×C8—611no—
63C22×C8—611no—
64C2×C16—1222no—
65C22⋊C8—1222no—
66C24#9242011yescharacteristic
67C22×C4—21no—
68C22×C4—21no—
69C22×C4—41no—
70C22×C4—41no—
71C22×C4#9242011yescharacteristic
72C22×C4C2×#692311yescharacteristic
73C2×C8—612no—
74C2×C8—1221no—
75C2×C8—2441no—
76C2×C8—2441no—
77C16—2442no—
78C23—21no—
79C23—21no—
80C23—41no—
81C23—41no—
82C23#1175818712yescomplemented
83C23C2×#9242011yescharacteristic
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—42no—
88C2×C4—41no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4#1175821711yescharacteristic
92C2×C4C22⋊#692311yescharacteristic
93C8—1222no—
94C8—2441no—
95C22—21no—
96C22—21no—
97C22—22no—
98C22—42no—
99C22—42no—
100C22—41no—
101C22—41no—
102C22C22⋊#9242011yescharacteristic
103C22C2×#1175818711yescharacteristic
104C22#1451985111yescharacteristic
105C4—21no—
106C4—41no—
107C4#1451983511yescharacteristic
108C4#1451983711yescharacteristic
109C2—21no—
110C2—21no—
111C2—42no—
112C2#1684060511yescharacteristic
113C2C22⋊#1175818711yescharacteristic
114C2#1684065811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC22×C61C2×C16
FrattiniC22×C4C2×#6923
FittingC23×C4×C61C4
socleC22×C61C22⋊C8
hypercenterC23×C4#6923
hypocenterC61#1314
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22⋊#11758187C2semidirect
24. C23×C61C16semidirect
60. C61#1314semidirect
82. C23#11758187semidirect