Finite Group Databasebeta

← #20264943

Subgroups — #20264943

Order 6464.

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⋊Dic101C211yesmaximal, characteristic
2C2×C22⋊Dic101C211yesmaximal, characteristic
3C2×C22⋊C4×C101C211yesmaximal, characteristic
4C22×Dic101—21no—
5C22×Dic101C412yescomplemented
6C22⋊Dic101—21no—
7C22⋊Dic101—21no—
8C22⋊Dic101—21no—
9C22⋊Dic101C412yescomplemented
10C24×C101C2211yescharacteristic
11C22×C4×C101—21no—
12C22⋊C4×C101—21no—
13C22⋊C4×C101C412yescomplemented
14C23×C101—42no—
15C23×C101C2×C411yescharacteristic
16C23×C101C2×C411yescharacteristic
17C23×C101C2×C411yescharacteristic
18C23×C101D411yescharacteristic
19C23×C101D411yescharacteristic
20C23×C101D411yescharacteristic
21C23×C101Q811yescharacteristic
22C2×C4×C101—22no—
23C2×C4×C101—42no—
24C2×Dic101—22no—
25C2×Dic101—22no—
26C2×Dic101—42no—
27C2×Dic101—42no—
28C22×C101—22no—
29C22×C101—22no—
30C22×C101—22no—
31C22×C101—41no—
32C22×C101—41no—
33C22×C101—41no—
34C22×C101—41no—
35C22×C101C4211yescharacteristic
36C22×C101C22⋊C411yescharacteristic
37C22×C101C22⋊C411yescharacteristic
38C22×C101C22⋊C411yescharacteristic
39C22×C101C4⋊C411yescharacteristic
40C22×C101C4⋊C411yescharacteristic
41C22×C101C4⋊C411yescharacteristic
42C4×C101—42no—
43Dic101—42no—
44Dic101—42no—
45C2×C101—21no—
46C2×C101—21no—
47C2×C101—21no—
48C2×C101—21no—
49C2×C101—21no—
50C2×C101—21no—
51C2×C101#9511yescharacteristic
52C2×C101#9912yes—
53C101#34211yescharacteristic, complemented, Sylow
54#342—1011nomaximal, Sylow
55C2×C22⋊C4—1011no—
56C2×C22⋊C4—1011no—
57C2×C22⋊C4D10111yescharacteristic
58C24C2×D10111yescharacteristic
59C22×C4—21no—
60C22×C4—1012no—
61C22×C4—2021no—
62C22⋊C4—21no—
63C22⋊C4—1012no—
64C22⋊C4—2021no—
65C22⋊C4—2021no—
66C22⋊C4—2021no—
67C22⋊C4Dic10112yescomplemented
68C23—42no—
69C23Dic20211yescharacteristic
70C23C4×D10111yescharacteristic
71C23C4×D10111yescharacteristic
72C23D40411yescharacteristic
73C23C2×Dic10111yescharacteristic
74C23C22⋊D10111yescharacteristic
75C23C22⋊D10111yescharacteristic
76C2×C4—22no—
77C2×C4—42no—
78C2×C4—4042no—
79C2×C4—4042no—
80C2×C4—2022no—
81C2×C4—2022no—
82C22—22no—
83C22—22no—
84C22—22no—
85C22—41no—
86C22—41no—
87C22—41no—
88C22—41no—
89C22C4×Dic10111yescharacteristic
90C22#1310805111yescharacteristic
91C22#1310805111yescharacteristic
92C22C22⋊Dic10111yescharacteristic
93C22#1310805311yescharacteristic
94C22#1310805311yescharacteristic
95C22C4⋊Dic10111yescharacteristic
96C4—42no—
97C4—4042no—
98C4—4042no—
99C2—21no—
100C2—21no—
101C2—21no—
102C2—21no—
103C2—21no—
104C2—21no—
105C2#1569216211yescharacteristic
106C2#1569216912yes—
subgroupG/H
centerC22#13108051
commutatorC22×C101C42
FrattiniC24C2×D101
FittingC2×C22⋊C4×C101C2
socleC22×C101C22⋊C4
hypercenterC2×C22⋊C4D101
hypocenterC101#342
LCSG ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C22×Dic101C4semidirect
9. C22⋊Dic101C4semidirect
13. C22⋊C4×C101C4semidirect
53. C101#342semidirect
67. C22⋊C4Dic101semidirect