Finite Group Databasebeta

← #20267557

Subgroups — #20267557

Order 6592.

142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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×C22⋊Dic103C211yesmaximal, characteristic
2C2×C22⋊Dic103C211yesmaximal, characteristic
3C2×C22⋊C4×C103C211yesmaximal, characteristic
4C22×Dic103—21no—
5C22×Dic103C412yescomplemented
6C22⋊Dic103—21no—
7C22⋊Dic103—21no—
8C22⋊Dic103—21no—
9C22⋊Dic103C412yescomplemented
10C24×C103C2211yescharacteristic
11C22×C4×C103—21no—
12C22⋊C4×C103—21no—
13C22⋊C4×C103C412yescomplemented
14C23×C103—42no—
15C23×C103C2×C411yescharacteristic
16C23×C103C2×C411yescharacteristic
17C23×C103C2×C411yescharacteristic
18C23×C103D411yescharacteristic
19C23×C103D411yescharacteristic
20C23×C103D411yescharacteristic
21C23×C103Q811yescharacteristic
22C2×C4×C103—22no—
23C2×C4×C103—42no—
24C2×Dic103—22no—
25C2×Dic103—22no—
26C2×Dic103—42no—
27C2×Dic103—42no—
28C22×C103—22no—
29C22×C103—22no—
30C22×C103—22no—
31C22×C103—41no—
32C22×C103—41no—
33C22×C103—41no—
34C22×C103—41no—
35C22×C103C4211yescharacteristic
36C22×C103C22⋊C411yescharacteristic
37C22×C103C22⋊C411yescharacteristic
38C22×C103C22⋊C411yescharacteristic
39C22×C103C4⋊C411yescharacteristic
40C22×C103C4⋊C411yescharacteristic
41C22×C103C4⋊C411yescharacteristic
42C4×C103—42no—
43Dic103—42no—
44Dic103—42no—
45C2×C103—21no—
46C2×C103—21no—
47C2×C103—21no—
48C2×C103—21no—
49C2×C103—21no—
50C2×C103—21no—
51C2×C103#9511yescharacteristic
52C2×C103#9912yes—
53C103#34211yescharacteristic, complemented, Sylow
54#342—1031nomaximal, Sylow
55C2×C22⋊C4—1031no—
56C2×C22⋊C4—1031no—
57C2×C22⋊C4D10311yescharacteristic
58C24C2×D10311yescharacteristic
59C22×C4—21no—
60C22×C4—1032no—
61C22×C4—2061no—
62C22⋊C4—21no—
63C22⋊C4—1032no—
64C22⋊C4—2061no—
65C22⋊C4—2061no—
66C22⋊C4—2061no—
67C22⋊C4Dic10312yescomplemented
68C23—42no—
69C23Dic20611yescharacteristic
70C23C4×D10311yescharacteristic
71C23C4×D10311yescharacteristic
72C23D41211yescharacteristic
73C23C2×Dic10311yescharacteristic
74C23C22⋊D10311yescharacteristic
75C23C22⋊D10311yescharacteristic
76C2×C4—22no—
77C2×C4—42no—
78C2×C4—4122no—
79C2×C4—4122no—
80C2×C4—2062no—
81C2×C4—2062no—
82C22—22no—
83C22—22no—
84C22—22no—
85C22—41no—
86C22—41no—
87C22—41no—
88C22—41no—
89C22C4×Dic10311yescharacteristic
90C22(C2×D103)⋊C411yescharacteristic
91C22(C2×D103)⋊C411yescharacteristic
92C22C22⋊Dic10311yescharacteristic
93C22Dic103⋊C411yescharacteristic
94C22Dic103⋊C411yescharacteristic
95C22C4⋊Dic10311yescharacteristic
96C4—42no—
97C4—4122no—
98C4—4122no—
99C2—21no—
100C2—21no—
101C2—21no—
102C2—21no—
103C2—21no—
104C2—21no—
105C2C103⋊#9511yescharacteristic
106C2#1569293512yes—
subgroupG/H
centerC22(C2×D103)⋊C4
commutatorC22×C103C42
FrattiniC24C2×D103
FittingC2×C22⋊C4×C103C2
socleC22×C103C22⋊C4
hypercenterC2×C22⋊C4D103
hypocenterC103#342
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C22×Dic103C4semidirect
9. C22⋊Dic103C4semidirect
13. C22⋊C4×C103C4semidirect
53. C103#342semidirect
67. C22⋊C4Dic103semidirect