Finite Group Databasebeta

← #20267892

Subgroups — #20267892

Order 6592.

120 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 57 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
1Q8×Dic103C211yesmaximal, characteristic, complemented
2D4×Dic103C211yesmaximal, characteristic
3#15692955C211yesmaximal, characteristic, complemented
4#15692945C211yesmaximal, characteristic, complemented
5#15692942C211yesmaximal, characteristic
6#15692931C211yesmaximal, characteristic, complemented
7C2×SD16×C103C211yesmaximal, characteristic
8C22×Dic103—21no—
9C2×C103⋊C8C2211yescharacteristic
10C4⋊Dic103—21no—
11C4⋊Dic103C2211yescharacteristic
12C4⋊Dic103C2211yescharacteristic
13C22⋊Dic103—21no—
14C4×Dic103—21no—
15C4×Dic103C2211yescharacteristic
16C2×Q8×C103C2211yescharacteristic
17C2×D4×C103C2211yescharacteristic
18SD16×C103C414yescomplemented
19C2×C8×C103C2211yescharacteristic
20C23×C103—21no—
21Q8×C103—21no—
22Q8×C103C2×C412yescomplemented
23D4×C103—21no—
24D4×C103C2×C412yes—
25C2×C4×C103—21no—
26C2×C4×C103C2311yescharacteristic
27C2×Dic103—21no—
28C2×Dic103—21no—
29C2×Dic103—42no—
30C2×Dic103D411yescharacteristic
31C2×Dic103D411yescharacteristic
32C8×C103C2×C412yescomplemented
33C103⋊C8—21no—
34C22×C103—22no—
35C22×C103—41no—
36C22×C103—41no—
37C22×C103C2×D411yescharacteristic
38C4×C103—22no—
39C4×C103C22×C411yescharacteristic
40C4×C103#4111yescharacteristic
41Dic103—21no—
42Dic103—21no—
43Dic103—41no—
44Dic103—41no—
45C2×C103—42no—
46C2×C103C4×D411yescharacteristic
47C2×C103AGL(1,ℤ/8)11yescharacteristic
48C2×C103#13711yescharacteristic
49C103#44011yescharacteristic, complemented, Sylow
50#440—1031nomaximal, Sylow
51C2×SD16D10311yescharacteristic
52C4×Q8—1031no—
53C4×D4—1031no—
54#107—1031no—
55#103—1031no—
56#102—1031no—
57#97—1031no—
58C2×Q8C2×D10311yescharacteristic
59C2×D4C2×D10311yescharacteristic
60C22×C4—2061no—
61SD16Dic10314yescomplemented
62C2×C8—1031no—
63C2×C8C2×D10311yescharacteristic
64C4⋊C4—1031no—
65C4⋊C4—1031no—
66C4⋊C4—2061no—
67C22⋊C4—2061no—
68C42—1031no—
69C42—2061no—
70C23—21no—
71Q8—21no—
72Q8C2×Dic10312yescomplemented
73D4—21no—
74D4C2×Dic10312yes—
75C2×C4—21no—
76C2×C4—1031no—
77C2×C4—1031no—
78C2×C4—4122no—
79C2×C4—2061no—
80C2×C4—2061no—
81C2×C4C22×D10311yescharacteristic
82C8—2061no—
83C8C2×Dic10312yescomplemented
84C22—22no—
85C22—41no—
86C22—41no—
87C22D4×D10311yescharacteristic
88C4—22no—
89C4—4121no—
90C4—4121no—
91C4—2061no—
92C4—2061no—
93C4C22×Dic10311yescharacteristic
94C4#1311010411yescharacteristic
95C2—42no—
96C2D4×Dic10311yescharacteristic
97C2#1569304811yescharacteristic
98C2#1569305011yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
FittingC2×SD16×C103C2
socleC22×C103C2×D4
hypercenterC2×SD16D103
hypocenterC103#440
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×Dic103C2semidirect
3. #15692955C2semidirect
4. #15692945C2semidirect
6. #15692931C2semidirect
18. SD16×C103C4semidirect
22. Q8×C103C2×C4semidirect
32. C8×C103C2×C4semidirect
49. C103#440semidirect
61. SD16Dic103semidirect
72. Q8C2×Dic103semidirect
83. C8C2×Dic103semidirect