Finite Group Databasebeta

← #20261608

Subgroups — #20261608

Order 6208.

114 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 46 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×#13095519C211yesmaximal, characteristic
2C2×C4⋊#87604C211yesmaximal, characteristic
3C4⋊C4×D97C211yesmaximal, characteristic
4C22×#87604—21no—
5#13095519—21no—
6#13095519C412yescomplemented
7C2×#11715897—21no—
8C4⋊#87604—21no—
9C4⋊#87604C412yescomplemented
10C2×C4×D97—21no—
11C2×C4×D97C2211yescharacteristic
12C4⋊Dic97C411yescharacteristic, complemented
13#13095490—21no—
14C4⋊C4×C97C411yescharacteristic, complemented
15C22×D97D411yescharacteristic
16C2×#87604—22no—
17C2×#87604—41no—
18C2×#87604—41no—
19C2×C4×C97—21no—
20C2×C4×C97C2×C411yescharacteristic
21C2×Dic97—21no—
22C2×Dic97D411yescharacteristic
23C4×D97—41no—
24C4×D97—41no—
25C4×D97C2×C411yescharacteristic
26C4×D97C2×C411yescharacteristic
27C4×D97D411yescharacteristic
28C4×D97Q811yescharacteristic
29#11715897—22no—
30C22×C97C22⋊C411yescharacteristic
31C2×D97C22⋊C411yescharacteristic
32C2×D97C4⋊C411yescharacteristic
33C2×D97D811yescharacteristic
34C2×D97SD1611yescharacteristic
35C2×D97SD1611yescharacteristic
36C2×D97Q1611yescharacteristic
37#87604—42no—
38C4×C97—41no—
39C4×C97C4211yescharacteristic
40C4×C97C4⋊C411yescharacteristic
41Dic97—41no—
42Dic97C22⋊C411yescharacteristic
43Dic97C4⋊C411yescharacteristic
44C2×C97#9511yescharacteristic
45C2×C97#10211yescharacteristic
46C2×C97#10311yescharacteristic
47D97#10211yescharacteristic
48D97#10311yescharacteristic
49D97#10611yescharacteristic
50D97#10711yescharacteristic
51C97#34011yescharacteristic, complemented, Sylow
52#340—971nomaximal, Sylow
53C22×C8—971no—
54C2×C4⋊C4—971no—
55C2×C4⋊C4—971no—
56C22×C4—971no—
57C22×C4—1941no—
58C22×C4—1941no—
59C2×C8—972no—
60C2×C8—1941no—
61C2×C8—1941no—
62C4⋊C4—972no—
63C4⋊C4—971no—
64C4⋊C4—1941no—
65C4⋊C4—1941no—
66C4⋊C4#8760411yescharacteristic, complemented
67C23—971no—
68C2×C4—21no—
69C2×C4—971no—
70C2×C4—971no—
71C2×C4—971no—
72C2×C4—971no—
73C2×C4—971no—
74C2×C4—3881no—
75C2×C4—3881no—
76C2×C4—3881no—
77C2×C4—3881no—
78C2×C4—1942no—
79C2×C4—1941no—
80C2×C4C2×#8760411yescharacteristic
81C8—1942no—
82C22—971no—
83C22—971no—
84C22—971no—
85C22—971no—
86C22—971no—
87C22—971no—
88C22C22⋊#8760411yescharacteristic
89C4—41no—
90C4—971no—
91C4—971no—
92C4—3882no—
93C4—3881no—
94C4C4×#8760411yescharacteristic
95C4C4⋊#8760411yescharacteristic
96C2—971no—
97C2—971no—
98C2—971no—
99C2—971no—
100C2(C2×#87604)⋊C411yescharacteristic
101C2#1569087211yescharacteristic
102C2#1569087311yescharacteristic
subgroupG/H
centerC22C22⋊#87604
commutatorC4×C97C42
FrattiniC2×C4C2×#87604
FittingC4⋊C4×C97C4
socleC22×C97C22⋊C4
hypercenterC4⋊C4#87604
hypocenterC97#340
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #13095519C4semidirect
9. C4⋊#87604C4semidirect
12. C4⋊Dic97C4semidirect
14. C4⋊C4×C97C4semidirect
51. C97#340semidirect
66. C4⋊C4#87604semidirect