Finite Group Databasebeta

← C4×#13095499 #20260821

Subgroups — C4×#13095499 #20260821

Order 6208.

122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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×#13095499C211yesmaximal, characteristic
2C4×Dic194C211yesmaximal, characteristic, complemented
3#15690741C211yesmaximal, characteristic, complemented
4#15690733C211yesmaximal, characteristic, complemented
5#15690731C211yesmaximal, characteristic
6C4×#11715895C211yesmaximal, characteristic, complemented
7C4×D4×C97C211yesmaximal, characteristic
8C2×Dic194C2211yescharacteristic
9#13095499C414yesdirect product factor
10C2×#11715895C2211yescharacteristic
11C2×#11715895C2211yescharacteristic
12C4⋊Dic97C2211yescharacteristic
13#13095490—21no—
14C4×Dic97—21no—
15C2×D4×C97C2211yescharacteristic
16C22×C4×C97—21no—
17C4⋊C4×C97C2211yescharacteristic
18C22⋊C4×C97—21no—
19C42×C97C2211yescharacteristic
20C23×C97—21no—
21D4×C97—21no—
22D4×C97C2×C412yes—
23C2×C4×C97—21no—
24C2×C4×C97—42no—
25C2×C4×C97D411yescharacteristic
26C2×C4×C97D411yescharacteristic
27C2×C4×C97C2311yescharacteristic
28C2×Dic97—21no—
29C2×Dic97—21no—
30Dic194—21no—
31Dic194C2×C412yescomplemented
32#11715895—21no—
33#11715895C2×C412yescomplemented
34C22×C97—22no—
35C22×C97—41no—
36C22×C97—41no—
37C22×C97C2×D411yescharacteristic
38C4×C97—21no—
39C4×C97—41no—
40C4×C97SD1612yescomplemented
41C4×C97C22×C411yescharacteristic
42C4×C97#4111yescharacteristic
43Dic97—22no—
44Dic97—41no—
45C2×C97—42no—
46C2×C97C4×D411yescharacteristic
47C2×C97C2×SD1611yescharacteristic
48C2×C97#13511yescharacteristic
49C97C4×SD1611yescharacteristic, complemented, Sylow
50C4×SD16—971nomaximal, Sylow
51C2×SD16—971no—
52C4×Q8—971no—
53C4×D4D9711yescharacteristic
54#106—971no—
55#103—971no—
56#102—971no—
57C4×C8—971no—
58C2×Q8—971no—
59C2×D4C2×D9711yescharacteristic
60C22×C4—21no—
61SD16—974no—
62C2×C8—971no—
63C2×C8—971no—
64C4⋊C4—971no—
65C4⋊C4—1941no—
66C4⋊C4C2×D9711yescharacteristic
67C22⋊C4—21no—
68C42—1941no—
69C42C2×D9711yescharacteristic
70C23—21no—
71Q8—972no—
72Q8—1941no—
73D4—21no—
74D4C4×D9712yes—
75C2×C4—21no—
76C2×C4—42no—
77C2×C4—1941no—
78C2×C4—1941no—
79C2×C4C22⋊D9711yescharacteristic
80C2×C4C22⋊D9711yescharacteristic
81C2×C4C22×D9711yescharacteristic
82C8—972no—
83C8—1941no—
84C22—22no—
85C22—41no—
86C22—41no—
87C22C2×C22⋊D9711yescharacteristic
88C4—21no—
89C4—41no—
90C4—3881no—
91C4—1942no—
92C4#1309549912yesdirect product factor
93C4C2×C4×D9711yescharacteristic
94C4#1309551111yescharacteristic
95C2—42no—
96C2C4×C22⋊D9711yescharacteristic
97C2C2×#1309549911yescharacteristic
98C2#1569083011yescharacteristic
subgroupG/H
centerC2×C4C22⋊D97
commutatorC4×C97C22×C4
FrattiniC2×C4C22×D97
FittingC4×D4×C97C2
socleC22×C97C2×D4
hypercenterC4×D4D97
hypocenterC97C4×SD16
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×Dic194C2semidirect
3. #15690741C2semidirect
4. #15690733C2semidirect
6. C4×#11715895C2semidirect
9. #13095499C4direct (N × H)
31. Dic194C2×C4semidirect
33. #11715895C2×C4semidirect
40. C4×C97SD16semidirect
49. C97C4×SD16semidirect
92. C4#13095499direct (N × H)