Finite Group Databasebeta

← #20261612

Subgroups — #20261612

Order 6208.

142 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 36 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⋊#87604C211yesmaximal, characteristic
2C2×C22⋊#87604C211yesmaximal, characteristic
3C22⋊C4×D97C211yesmaximal, characteristic
4C22×#87604—21no—
5C22×#87604C412yescomplemented
6C22⋊#87604—21no—
7C22⋊#87604—21no—
8C22⋊#87604—21no—
9C22⋊#87604C412yescomplemented
10C23×D97C2211yescharacteristic
11C2×C4×D97—21no—
12C22⋊Dic97C411yescharacteristic, complemented
13#13095488—21no—
14C22⋊C4×C97C411yescharacteristic, complemented
15C23×C97C2×C411yescharacteristic
16C22×D97—42no—
17C22×D97C2×C411yescharacteristic
18C22×D97C2×C411yescharacteristic
19C22×D97D411yescharacteristic
20C22×D97D411yescharacteristic
21C22×D97D411yescharacteristic
22C22×D97Q811yescharacteristic
23C2×#87604—22no—
24C2×#87604—22no—
25C2×#87604—42no—
26C2×#87604—42no—
27C2×C4×C97—21no—
28C2×Dic97—21no—
29C4×D97—42no—
30C22×C97—41no—
31C22×C97C4211yescharacteristic
32C22×C97C22⋊C411yescharacteristic
33C22×C97C4⋊C411yescharacteristic
34C2×D97—22no—
35C2×D97—22no—
36C2×D97—22no—
37C2×D97—41no—
38C2×D97—41no—
39C2×D97—41no—
40C2×D97C22⋊C411yescharacteristic
41C2×D97C22⋊C411yescharacteristic
42C2×D97C4⋊C411yescharacteristic
43C2×D97C4⋊C411yescharacteristic
44#87604—42no—
45#87604—42no—
46C4×C97—41no—
47Dic97—41no—
48C2×C97—21no—
49C2×C97—21no—
50C2×C97—21no—
51C2×C97#9511yescharacteristic
52D97—21no—
53D97—21no—
54D97—21no—
55D97#9912yes—
56C97#34211yescharacteristic, complemented, Sylow
57#342—971nomaximal, Sylow
58C2×C22⋊C4—971no—
59C2×C22⋊C4—971no—
60C2×C22⋊C4—971no—
61C24—971no—
62C22×C4—972no—
63C22×C4—1941no—
64C22×C4—1941no—
65C22⋊C4—972no—
66C22⋊C4—971no—
67C22⋊C4—1941no—
68C22⋊C4—1941no—
69C22⋊C4—1941no—
70C22⋊C4—1941no—
71C22⋊C4#8760411yescharacteristic, complemented
72C23—971no—
73C23—971no—
74C23—971no—
75C23—971no—
76C23—971no—
77C23—971no—
78C23—3882no—
79C23C2×#8760411yescharacteristic
80C2×C4—21no—
81C2×C4—3882no—
82C2×C4—3882no—
83C2×C4—3882no—
84C2×C4—1942no—
85C2×C4—1942no—
86C2×C4—1941no—
87C22—41no—
88C22—971no—
89C22—971no—
90C22—971no—
91C22—971no—
92C22—3881no—
93C22—3881no—
94C22—3881no—
95C22—1942no—
96C22—1942no—
97C22—1942no—
98C22C4×#8760411yescharacteristic
99C22C22⋊#8760411yescharacteristic
100C22C4⋊#8760411yescharacteristic
101C4—41no—
102C4—3881no—
103C4—3882no—
104C4—3882no—
105C2—21no—
106C2—21no—
107C2—21no—
108C2—972no—
109C2—1941no—
110C2—1941no—
111C2—1941no—
112C2(C2×#87604)⋊C411yescharacteristic
subgroupG/H
centerC2(C2×#87604)⋊C4
commutatorC22×C97C42
FrattiniC23C2×#87604
FittingC22⋊C4×C97C4
socleC2×C97#95
hypercenterC22⋊C4#87604
hypocenterC97#342
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C23 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C22×#87604C4semidirect
9. C22⋊#87604C4semidirect
12. C22⋊Dic97C4semidirect
14. C22⋊C4×C97C4semidirect
56. C97#342semidirect
71. C22⋊C4#87604semidirect