Finite Group Databasebeta

← C2×#15690870 #20261717

Subgroups — C2×#15690870 #20261717

Order 6208.

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

normal subgroups only

This group has 186 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×#13095520C212yesmaximal, complemented
2#15690870C214yesmaximal, direct product factor
3C22×C22⋊D97C211yesmaximal, characteristic
4#13095520—22no—
5#13095520C2214yescomplemented
6C2×#11715897—22no—
7C23×D97C411yescharacteristic
8C2×C22⋊D97—22no—
9C2×C22⋊D97—22no—
10C2×C22⋊D97C412yes—
11C2×C22⋊D97C2212yes—
12C22×Dic97C2211yescharacteristic
13C24×C97C411yescharacteristic
14C23×C97—21no—
15C23×C97—21no—
16C23×C97—42no—
17C23×C97C2×C412yes—
18C23×C97C2×C411yescharacteristic
19C22×D97—21no—
20C22×D97—21no—
21C22×D97—42no—
22C22×D97C2×C412yes—
23C22⋊D97—24no—
24C22⋊D97—24no—
25C2×Dic97C2×C411yescharacteristic
26C2×Dic97D412yes—
27C2×Dic97D412yes—
28C2×Dic97C2311yescharacteristic
29#11715897—24no—
30C22×C97—22no—
31C22×C97—22no—
32C22×C97—42no—
33C22×C97—42no—
34C22×C97—42no—
35C22×C97C22⋊C411yescharacteristic
36C22×C97C22⋊C411yescharacteristic
37C22×C97C22×C411yescharacteristic
38C2×D97—22no—
39C2×D97—42no—
40C2×D97—42no—
41C2×D97—42no—
42Dic97C22⋊C412yes—
43Dic97C2×D412yes—
44C2×C97—21no—
45C2×C97—21no—
46C2×C97—42no—
47C2×C97#10012yescomplemented
48C2×C97C2×C22⋊C411yescharacteristic
49D97—42no—
50C97C2×#10011yescharacteristic, complemented, Sylow
51C2×#100—971nomaximal, Sylow
52C22×D4—971no—
53C2×M16—972no—
54#100—974no—
55C24—971no—
56C24#8760411yescharacteristic
57C2×D4—972no—
58C2×D4—972no—
59C2×D4—1942no—
60C2×D4—1942no—
61C22×C4—971no—
62M16—974no—
63M16—1942no—
64C2×C8—1942no—
65C23—21no—
66C23—21no—
67C23—42no—
68C23—972no—
69C23—3882no—
70C23—1941no—
71C23—1941no—
72C23C2×#8760412yes—
73C23C2×#8760411yescharacteristic
74D4—1944no—
75D4—1944no—
76C2×C4—972no—
77C2×C4—972no—
78C2×C4—971no—
79C2×C4—971no—
80C8—1944no—
81C22—22no—
82C22—22no—
83C22—42no—
84C22—42no—
85C22—42no—
86C22—3882no—
87C22—3882no—
88C22—3882no—
89C22—1942no—
90C22C22⋊#8760411yescharacteristic
91C22C22⋊#8760411yescharacteristic
92C22C22×#8760411yescharacteristic
93C4—972no—
94C4—972no—
95C2—21no—
96C2—21no—
97C2—42no—
98C2—3882no—
99C2#1569087012yesdirect product factor
100C2C2×C22⋊#8760411yescharacteristic
subgroupG/H
centerC22C22⋊#87604
commutatorC22×C97C22×C4
FrattiniC22C22×#87604
FittingC24×C97C4
socleC22×C97C22⋊C4
hypercenterC24#87604
hypocenterC97C2×#100
LCSG ▷ C22×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C2×#13095520C2semidirect
2. #15690870C2direct (N × H)
5. #13095520C22semidirect
47. C2×C97#100semidirect
50. C97C2×#100semidirect
99. C2#15690870direct (N × H)