Finite Group Databasebeta

← #20267890

Subgroups — #20267890

Order 6592.

120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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
2#15692986C211yesmaximal, characteristic, complemented
3#15692983C211yesmaximal, characteristic
4#15692944C211yesmaximal, characteristic, complemented
5#15692941C211yesmaximal, characteristic
6#15692931C211yesmaximal, characteristic, complemented
7#107×C103C211yesmaximal, characteristic, complemented
8C2×Dic206C2211yescharacteristic
9C2×D412C2211yescharacteristic
10C2×C4×D103—21no—
11#13110094C414yescomplemented
12C2×C103⋊C8C2211yescharacteristic
13Dic103⋊C4—21no—
14(C2×D103)⋊C4—21no—
15C4×Dic103—21no—
16C4×Dic103C2211yescharacteristic
17C2×C8×C103C2211yescharacteristic
18C4⋊C4×C103C2211yescharacteristic
19C4⋊C4×C103C2211yescharacteristic
20C22×D103—21no—
21C2×C4×C103—21no—
22C2×C4×C103—21no—
23C2×C4×C103C2311yescharacteristic
24C2×Dic103—21no—
25C2×Dic103D411yescharacteristic
26C2×Dic103D411yescharacteristic
27D412—21no—
28D412C2×C412yes—
29C4×D103—42no—
30Dic206—21no—
31Dic206C2×C412yescomplemented
32C8×C103C2×C412yescomplemented
33C103⋊C8—21no—
34C22×C103C2×D411yescharacteristic
35C2×D103—22no—
36C2×D103—41no—
37C2×D103—41no—
38C4×C103—41no—
39C4×C103—41no—
40C4×C103C22×C411yescharacteristic
41C4×C103#4111yescharacteristic
42Dic103—22no—
43Dic103—21no—
44Dic103—21no—
45C2×C103C4×D411yescharacteristic
46C2×C103AGL(1,ℤ/8)11yescharacteristic
47C2×C103#13711yescharacteristic
48D103—42no—
49C103#44011yescharacteristic, complemented, Sylow
50#440—1031nomaximal, Sylow
51C2×SD16—1031no—
52C4×Q8—1031no—
53C4×D4—1031no—
54#107D10311yescharacteristic, complemented
55#103—1031no—
56#102—1031no—
57#97—1031no—
58C2×Q8—1031no—
59C2×D4—1031no—
60C22×C4—2061no—
61SD16—1034no—
62C2×C8—1031no—
63C2×C8C2×D10311yescharacteristic
64C4⋊C4—2061no—
65C4⋊C4C2×D10311yescharacteristic
66C4⋊C4C2×D10311yescharacteristic
67C22⋊C4—2061no—
68C42—1031no—
69C42—2061no—
70C23—2061no—
71Q8—1032no—
72Q8—2061no—
73D4—1032no—
74D4—2061no—
75C2×C4—21no—
76C2×C4—21no—
77C2×C4—1031no—
78C2×C4—1031no—
79C2×C4—4122no—
80C2×C4—2061no—
81C2×C4C22×D10311yescharacteristic
82C8—2061no—
83C8C4×D10312yescomplemented
84C22—4121no—
85C22—4121no—
86C22—2062no—
87C22D4×D10311yescharacteristic
88C4—41no—
89C4—41no—
90C4—2062no—
91C4—2061no—
92C4—2061no—
93C4C2×C4×D10311yescharacteristic
94C4#1311010611yescharacteristic
95C2—4122no—
96C2#1569298311yescharacteristic
97C2#1569304511yescharacteristic
98C2#1569305311yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#107×C103C2
socleC22×C103C2×D4
hypercenter#107D103
hypocenterC103#440
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #15692986C2semidirect
4. #15692944C2semidirect
6. #15692931C2semidirect
7. #107×C103C2semidirect
11. #13110094C4semidirect
31. Dic206C2×C4semidirect
32. C8×C103C2×C4semidirect
49. C103#440semidirect
54. #107D103semidirect
83. C8C4×D103semidirect