Finite Group Databasebeta

← #20267876

Subgroups — #20267876

Order 6592.

122 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 51 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×#13110092C211yesmaximal, characteristic
2Q8×Dic103C211yesmaximal, characteristic, complemented
3#15692983C211yesmaximal, characteristic
4#15692952C211yesmaximal, characteristic, complemented
5#15692943C211yesmaximal, characteristic
6C8×Dic103C211yesmaximal, characteristic, complemented
7#103×C103C211yesmaximal, characteristic, complemented
8C2×D412C2211yescharacteristic
9C2×C4×D103—21no—
10#13110092C414yescomplemented
11C2×C103⋊C8C2211yescharacteristic
12C4⋊Dic103—21no—
13C4⋊Dic103C2211yescharacteristic
14(C2×D103)⋊C4—21no—
15C4×Dic103—21no—
16C4×Dic103C2211yescharacteristic
17C2×Q8×C103C2211yescharacteristic
18C2×C8×C103C2211yescharacteristic
19C4⋊C4×C103C2211yescharacteristic
20C22×D103—21no—
21Q8×C103—21no—
22Q8×C103C2×C412yescomplemented
23C2×C4×C103—21no—
24C2×C4×C103—21no—
25C2×C4×C103C2311yescharacteristic
26C2×Dic103—21no—
27C2×Dic103D411yescharacteristic
28C2×Dic103D411yescharacteristic
29D412—21no—
30D412C2×C412yes—
31C4×D103—42no—
32C8×C103—21no—
33C103⋊C8C2×C412yescomplemented
34C22×C103C2×D411yescharacteristic
35C2×D103—22no—
36C2×D103—41no—
37C2×D103—41no—
38C4×C103—22no—
39C4×C103—41no—
40C4×C103C22×C411yescharacteristic
41C4×C103#4111yescharacteristic
42Dic103—21no—
43Dic103—41no—
44Dic103SD1612yescomplemented
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#103D10311yescharacteristic, complemented
56#102—1031no—
57C4×C8—1031no—
58C2×Q8C2×D10311yescharacteristic
59C2×D4—1031no—
60C22×C4—2061no—
61SD16—1034no—
62C2×C8—1031no—
63C2×C8C2×D10311yescharacteristic
64C4⋊C4—1031no—
65C4⋊C4—2061no—
66C4⋊C4C2×D10311yescharacteristic
67C22⋊C4—2061no—
68C42—1031no—
69C42—2061no—
70C23—2061no—
71Q8—21no—
72Q8C4×D10312yescomplemented
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—21no—
83C8—1032no—
84C22—4121no—
85C22—4121no—
86C22—2062no—
87C22D4×D10311yescharacteristic
88C4—22no—
89C4—41no—
90C4—1032no—
91C4—4121no—
92C4—2061no—
93C4C2×C4×D10311yescharacteristic
94C4#1311010411yescharacteristic
95C2—4122no—
96C2(C22⋊D103)⋊C411yescharacteristic
97C2SD16×D10311yescharacteristic
98C2#1569304411yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#103×C103C2
socleC22×C103C2×D4
hypercenter#103D103
hypocenterC103C4×SD16
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. Q8×Dic103C2semidirect
4. #15692952C2semidirect
6. C8×Dic103C2semidirect
7. #103×C103C2semidirect
10. #13110092C4semidirect
22. Q8×C103C2×C4semidirect
33. C103⋊C8C2×C4semidirect
44. Dic103SD16semidirect
49. C103C4×SD16semidirect
55. #103D103semidirect
72. Q8C4×D103semidirect