Finite Group Databasebeta

← #20268114

Subgroups — #20268114

Order 6592.

106 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 37 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
1#15692992C211yesmaximal, characteristic
2#15692979C211yesmaximal, characteristic, complemented
3#15692954C211yesmaximal, characteristic, complemented
4#15692953C211yesmaximal, characteristic, complemented
5#15692942C211yesmaximal, characteristic, complemented
6(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
7#102×C103C211yesmaximal, characteristic, complemented
8C2×C22⋊D103—21no—
9C2×C4×D103C2211yescharacteristic
10C2×C103⋊C8C2211yescharacteristic
11C4⋊Dic103C2211yescharacteristic
12C4⋊Dic103C2211yescharacteristic
13C22⋊Dic103—21no—
14(C2×D103)⋊C4—21no—
15C4×Dic103—21no—
16C2×D4×C103C2211yescharacteristic
17C2×C8×C103C2211yescharacteristic
18C4⋊C4×C103C2211yescharacteristic
19C23×C103—21no—
20C22×D103D411yescharacteristic
21D4×C103—21no—
22D4×C103—21no—
23C2×C4×C103—21no—
24C2×C4×C103C2311yescharacteristic
25C22⋊D103—42no—
26C2×Dic103—21no—
27C2×Dic103—21no—
28C2×Dic103D411yescharacteristic
29C4×D103—21no—
30C4×D103—21no—
31C8×C103—21no—
32C103⋊C8—21no—
33C22×C103—41no—
34C22×C103—41no—
35C22×C103—41no—
36C22×C103C2×D411yescharacteristic
37C2×D103—21no—
38C2×D103—21no—
39C2×D103—21no—
40C4×C103—41no—
41C4×C103#4111yescharacteristic
42C4×C103#4111yescharacteristic
43Dic103—21no—
44Dic103—41no—
45Dic103—41no—
46C2×C103—81no—
47C2×C103#12311yescharacteristic
48C2×C103#13511yescharacteristic
49C2×C103AGL(1,ℤ/8)11yescharacteristic
50D103—41no—
51C103#48211yescharacteristic, complemented, Sylow
52#482—1031nomaximal, Sylow
53#121—1031no—
54#117—1031no—
55#107—1031no—
56#106—1031no—
57#102—1031no—
58#102D10311yescharacteristic, complemented
59C22⋊C8—1031no—
60C2×D4—2061no—
61C2×D4C2×D10311yescharacteristic
62C22×C4—1031no—
63C2×C8—1031no—
64C2×C8C2×D10311yescharacteristic
65C4⋊C4—1031no—
66C4⋊C4—1031no—
67C4⋊C4C2×D10311yescharacteristic
68C22⋊C4—2061no—
69C22⋊C4—2061no—
70C42—2061no—
71C23—21no—
72C23—1031no—
73D4—21no—
74D4—21no—
75D4—4122no—
76C2×C4—21no—
77C2×C4—1031no—
78C2×C4—2061no—
79C2×C4—2061no—
80C2×C4—2061no—
81C2×C4—2061no—
82C2×C4C22×D10311yescharacteristic
83C8—21no—
84C8—2061no—
85C22—41no—
86C22—41no—
87C22—41no—
88C22—2061no—
89C22—2061no—
90C22—2061no—
91C22D4×D10311yescharacteristic
92C4—41no—
93C4—4121no—
94C4—4121no—
95C4—2061no—
96C4#1311010411yescharacteristic
97C4#1311010511yescharacteristic
98C2—81no—
99C2—4121no—
100C2#1569300311yescharacteristic
101C2#1569304211yescharacteristic
102C2#1569304511yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#102×C103C2
socleC22×C103C2×D4
hypercenter#102D103
hypocenterC103#482
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #15692979C2semidirect
3. #15692954C2semidirect
4. #15692953C2semidirect
5. #15692942C2semidirect
6. (C2×D103)⋊C8C2semidirect
7. #102×C103C2semidirect
51. C103#482semidirect
58. #102D103semidirect