Finite Group Databasebeta

← C4×#13110094 #20267881

Subgroups — C4×#13110094 #20267881

Order 6592.

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×#13110094C211yesmaximal, characteristic
2C4×Dic206C211yesmaximal, characteristic, complemented
3C4×D412C211yesmaximal, characteristic
4#15692953C211yesmaximal, characteristic, complemented
5#15692946C211yesmaximal, characteristic, complemented
6#15692943C211yesmaximal, characteristic
7C4×C8×C103C211yesmaximal, characteristic, complemented
8C2×Dic206C2211yescharacteristic
9C2×D412C2211yescharacteristic
10C2×C4×D103—21no—
11#13110094C414yesdirect product factor
12C4⋊Dic103C2211yescharacteristic
13C4⋊Dic103C2211yescharacteristic
14Dic103⋊C4—21no—
15(C2×D103)⋊C4—21no—
16C4×Dic103—21no—
17C2×C8×C103C2211yescharacteristic
18C2×C8×C103C2211yescharacteristic
19C42×C103C2211yescharacteristic
20C22×D103—21no—
21C2×C4×C103D411yescharacteristic
22C2×C4×C103D411yescharacteristic
23C2×C4×C103C2311yescharacteristic
24C2×Dic103—21no—
25C2×Dic103—21no—
26C2×Dic103—21no—
27D412—21no—
28D412C2×C412yes—
29C4×D103—42no—
30Dic206—21no—
31Dic206C2×C412yescomplemented
32C8×C103—21no—
33C8×C103C2×C412yescomplemented
34C22×C103C2×D411yescharacteristic
35C2×D103—22no—
36C2×D103—41no—
37C2×D103—41no—
38C4×C103—21no—
39C4×C103SD1612yescomplemented
40C4×C103C22×C411yescharacteristic
41C4×C103#4111yescharacteristic
42Dic103—22no—
43Dic103—41no—
44Dic103—41no—
45C2×C103C4×D411yescharacteristic
46C2×C103C2×SD1611yescharacteristic
47C2×C103#13511yescharacteristic
48D103—42no—
49C103C4×SD1611yescharacteristic, complemented, Sylow
50C4×SD16—1031nomaximal, Sylow
51C2×SD16—1031no—
52C4×Q8—1031no—
53C4×D4—1031no—
54#106—1031no—
55#103—1031no—
56#102—1031no—
57C4×C8D10311yescharacteristic, complemented
58C2×Q8—1031no—
59C2×D4—1031no—
60C22×C4—2061no—
61SD16—1034no—
62C2×C8C2×D10311yescharacteristic
63C2×C8C2×D10311yescharacteristic
64C4⋊C4—1031no—
65C4⋊C4—1031no—
66C4⋊C4—2061no—
67C22⋊C4—2061no—
68C42—2061no—
69C42C2×D10311yescharacteristic
70C23—2061no—
71Q8—1032no—
72Q8—2061no—
73D4—1032no—
74D4—2061no—
75C2×C4—4122no—
76C2×C4—2061no—
77C2×C4—2061no—
78C2×C4—2061no—
79C2×C4D41211yescharacteristic
80C2×C4D41211yescharacteristic
81C2×C4C22×D10311yescharacteristic
82C8—21no—
83C8C4×D10312yescomplemented
84C22—4121no—
85C22—4121no—
86C22—2062no—
87C22C2×D41211yescharacteristic
88C4—21no—
89C4—4121no—
90C4—4121no—
91C4—2062no—
92C4#1311009412yesdirect product factor
93C4C2×C4×D10311yescharacteristic
94C4#1311010511yescharacteristic
95C2—4122no—
96C2C4×D41211yescharacteristic
97C2C2×#1311009411yescharacteristic
98C2#1569304311yescharacteristic
subgroupG/H
centerC2×C4D412
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
FittingC4×C8×C103C2
socleC22×C103C2×D4
hypercenterC4×C8D103
hypocenterC103C4×SD16
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C4×Dic206C2semidirect
4. #15692953C2semidirect
5. #15692946C2semidirect
7. C4×C8×C103C2semidirect
11. #13110094C4direct (N × H)
31. Dic206C2×C4semidirect
33. C8×C103C2×C4semidirect
39. C4×C103SD16semidirect
49. C103C4×SD16semidirect
57. C4×C8D103semidirect
83. C8C4×D103semidirect
92. C4#13110094direct (N × H)