Finite Group Databasebeta

← C2×#15690869 #20261713

Subgroups — C2×#15690869 #20261713

Order 6208.

210 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 52 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⋊#87604C212yesmaximal, complemented
2#15690869C214yesmaximal, direct product factor
3C22×D388C211yesmaximal, characteristic
4C22×#87604—22no—
5C22⋊#87604—22no—
6C22⋊#87604C2214yescomplemented
7C23×D97C411yescharacteristic, complemented
8C23×D97C2211yescharacteristic
9C2×D388—22no—
10C2×D388—22no—
11C2×D388C412yescomplemented
12C2×D388C2212yes—
13C22×C4×C97C411yescharacteristic, complemented
14C23×C97C2×C411yescharacteristic
15C22×D97—21no—
16C22×D97—21no—
17C22×D97—42no—
18C22×D97—42no—
19C22×D97C2×C411yescharacteristic
20C22×D97C2×C412yescomplemented
21C22×D97D412yes—
22C22×D97D412yes—
23C22×D97C2311yescharacteristic
24C2×#87604—24no—
25C2×#87604—44no—
26C2×C4×C97—21no—
27C2×C4×C97—21no—
28C2×C4×C97C2×C412yescomplemented
29D388—24no—
30D388—24no—
31C22×C97—22no—
32C22×C97C22⋊C411yescharacteristic
33C22×C97C22⋊C411yescharacteristic
34C22×C97C22×C411yescharacteristic
35C2×D97—24no—
36C2×D97—22no—
37C2×D97—41no—
38C2×D97—42no—
39C2×D97—41no—
40C2×D97—42no—
41C2×D97—42no—
42C2×D97—42no—
43C2×D97C22⋊C412yes—
44C2×D97C2×D412yes—
45#87604—44no—
46C4×C97—22no—
47C2×C97—21no—
48C2×C97—21no—
49C2×C97#9912yescomplemented
50C2×C97C2×C22⋊C411yescharacteristic
51D97—22no—
52D97—22no—
53D97—42no—
54C97C2×#9911yescharacteristic, complemented, Sylow
55C2×#99—971nomaximal, Sylow
56C22×D4—971no—
57C2×C22⋊C4—972no—
58#99—974no—
59C24—971no—
60C24—971no—
61C2×D4—972no—
62C2×D4—972no—
63C2×D4—1942no—
64C2×D4—1942no—
65C22×C4—1942no—
66C22×C4#8760411yescharacteristic, complemented
67C22⋊C4—974no—
68C22⋊C4—1942no—
69C23—972no—
70C23—971no—
71C23—971no—
72C23—972no—
73C23—972no—
74C23—3882no—
75C23—3882no—
76C23—1941no—
77C23—1941no—
78C23C2×#8760411yescharacteristic
79D4—1944no—
80D4—1944no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—3884no—
84C2×C4—1944no—
85C2×C4C2×#8760412yescomplemented
86C22—22no—
87C22—972no—
88C22—972no—
89C22—3882no—
90C22—3882no—
91C22—3882no—
92C22—3881no—
93C22—3881no—
94C22—3882no—
95C22—1942no—
96C22—1944no—
97C22C22⋊#8760411yescharacteristic
98C22C22⋊#8760411yescharacteristic
99C22C22×#8760411yescharacteristic
100C4—22no—
101C4—3884no—
102C2—21no—
103C2—21no—
104C2—3882no—
105C2—1942no—
106C2—1942no—
107C2#1569086912yesdirect product factor
108C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC22C22⋊#87604
commutatorC22×C97C22×C4
FrattiniC22C22×#87604
FittingC22×C4×C97C4
socleC22×C97C22⋊C4
hypercenterC22×C4#87604
hypocenterC97C2×#99
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊#87604C2semidirect
2. #15690869C2direct (N × H)
6. C22⋊#87604C22semidirect
7. C23×D97C4semidirect
11. C2×D388C4semidirect
13. C22×C4×C97C4semidirect
20. C22×D97C2×C4semidirect
28. C2×C4×C97C2×C4semidirect
49. C2×C97#99semidirect
54. C97C2×#99semidirect
66. C22×C4#87604semidirect
85. C2×C4C2×#87604semidirect
107. C2#15690869direct (N × H)