Finite Group Databasebeta

← #20268117

Subgroups — #20268117

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#15692996C211yesmaximal, characteristic
2#15692979C211yesmaximal, characteristic, complemented
3#15692954C211yesmaximal, characteristic, complemented
4#15692943C211yesmaximal, characteristic, complemented
5#15692941C211yesmaximal, characteristic, complemented
6(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
7#106×C103C211yesmaximal, characteristic, complemented
8C2×D412—21no—
9C2×D412C2211yescharacteristic
10C2×C4×D103C2211yescharacteristic
11C2×C103⋊C8C2211yescharacteristic
12C4⋊Dic103C2211yescharacteristic
13(C2×D103)⋊C4—21no—
14(C2×D103)⋊C4—21no—
15C4×Dic103—21no—
16C2×C8×C103C2211yescharacteristic
17C4⋊C4×C103C2211yescharacteristic
18C4⋊C4×C103C2211yescharacteristic
19C22×D103—21no—
20C22×D103D411yescharacteristic
21C2×C4×C103—21no—
22C2×C4×C103—21no—
23C2×C4×C103C2311yescharacteristic
24C2×Dic103—21no—
25C2×Dic103D411yescharacteristic
26D412—21no—
27D412—21no—
28D412—42no—
29C4×D103—21no—
30C4×D103—21no—
31C8×C103—21no—
32C103⋊C8—21no—
33C22×C103C2×D411yescharacteristic
34C2×D103—21no—
35C2×D103—21no—
36C2×D103—21no—
37C2×D103—41no—
38C2×D103—41no—
39C2×D103—41no—
40C4×C103—41no—
41C4×C103—41no—
42C4×C103#4111yescharacteristic
43C4×C103#4111yescharacteristic
44Dic103—21no—
45Dic103—41no—
46C2×C103#12311yescharacteristic
47C2×C103#13511yescharacteristic
48C2×C103AGL(1,ℤ/8)11yescharacteristic
49D103—41no—
50D103—81no—
51C103#48211yescharacteristic, complemented, Sylow
52#482—1031nomaximal, Sylow
53#121—1031no—
54#117—1031no—
55#107—1031no—
56#106D10311yescharacteristic, complemented
57#102—1031no—
58#102—1031no—
59C22⋊C8—1031no—
60C2×D4—1031no—
61C2×D4—2061no—
62C22×C4—1031no—
63C2×C8—1031no—
64C2×C8C2×D10311yescharacteristic
65C4⋊C4—1031no—
66C4⋊C4C2×D10311yescharacteristic
67C4⋊C4C2×D10311yescharacteristic
68C22⋊C4—2061no—
69C22⋊C4—2061no—
70C42—2061no—
71C23—1031no—
72C23—2061no—
73D4—4122no—
74D4—2061no—
75D4—2061no—
76C2×C4—21no—
77C2×C4—21no—
78C2×C4—1031no—
79C2×C4—2061no—
80C2×C4—2061no—
81C2×C4—2061no—
82C2×C4C22×D10311yescharacteristic
83C8—21no—
84C8—2061no—
85C22—4121no—
86C22—4121no—
87C22—4121no—
88C22—2061no—
89C22—2061no—
90C22—2061no—
91C22D4×D10311yescharacteristic
92C4—41no—
93C4—41no—
94C4—4121no—
95C4—2061no—
96C4#1311010511yescharacteristic
97C4#1311010611yescharacteristic
98C2—8241no—
99C2—4121no—
100C2#1569300611yescharacteristic
101C2#1569304211yescharacteristic
102C2#1569304811yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#106×C103C2
socleC22×C103C2×D4
hypercenter#106D103
hypocenterC103#482
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #15692979C2semidirect
3. #15692954C2semidirect
4. #15692943C2semidirect
5. #15692941C2semidirect
6. (C2×D103)⋊C8C2semidirect
7. #106×C103C2semidirect
51. C103#482semidirect
56. #106D103semidirect