Finite Group Databasebeta

← #20268106

Subgroups — #20268106

Order 6592.

114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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
2C4⋊C4×D103C211yesmaximal, characteristic, complemented
3#15692954C211yesmaximal, characteristic, complemented
4#15692943C211yesmaximal, characteristic, complemented
5#15692941C211yesmaximal, characteristic, complemented
6(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
7#107×C103C211yesmaximal, characteristic, complemented
8C2×D412—21no—
9C2×D412C2211yescharacteristic
10C2×C4×D103—21no—
11C2×C4×D103C2211yescharacteristic
12C2×C103⋊C8C2211yescharacteristic
13C4⋊Dic103C2211yescharacteristic
14Dic103⋊C4—21no—
15(C2×D103)⋊C4—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—
31C4×D103—42no—
32C8×C103—21no—
33C103⋊C8—21no—
34C22×C103C2×D411yescharacteristic
35C2×D103—21no—
36C2×D103—21no—
37C2×D103—41no—
38C2×D103—41no—
39C2×D103—41no—
40C2×D103D812yes—
41C4×C103—41no—
42C4×C103—41no—
43C4×C103#4111yescharacteristic
44C4×C103#4111yescharacteristic
45Dic103—21no—
46Dic103—41no—
47C2×C103#12311yescharacteristic
48C2×C103C2×D811yescharacteristic
49C2×C103#13711yescharacteristic
50D103—22no—
51D103—81no—
52C103#48011yescharacteristic, complemented, Sylow
53#480—1031nomaximal, Sylow
54#121—1031no—
55C2×C4⋊C4—1031no—
56#107—1031no—
57#107D10311yescharacteristic, complemented
58#102—1031no—
59#102—1031no—
60C22⋊C8—1031no—
61C2×D4—1031no—
62C2×D4—2061no—
63C22×C4—1031no—
64C22×C4—2061no—
65C2×C8—1031no—
66C2×C8C2×D10311yescharacteristic
67C4⋊C4—1031no—
68C4⋊C4—2061no—
69C4⋊C4C2×D10311yescharacteristic
70C4⋊C4C2×D10311yescharacteristic
71C22⋊C4—2061no—
72C23—1031no—
73C23—2061no—
74D4—4122no—
75D4—2061no—
76D4—2061no—
77C2×C4—21no—
78C2×C4—21no—
79C2×C4—1031no—
80C2×C4—4122no—
81C2×C4—2061no—
82C2×C4—2061no—
83C2×C4—2061no—
84C2×C4C22×D10311yescharacteristic
85C8—21no—
86C8—2061no—
87C22—1032no—
88C22—4121no—
89C22—4121no—
90C22—4121no—
91C22—2061no—
92C22—2061no—
93C22D4×D10311yescharacteristic
94C4—41no—
95C4—41no—
96C4—4121no—
97C4—2061no—
98C4#1311010511yescharacteristic
99C4#1311010611yescharacteristic
100C2—8241no—
101C2—2062no—
102C2#1569300611yescharacteristic
103C2D8×D10311yescharacteristic
104C2#1569305311yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#107×C103C2
socleC22×C103C2×D4
hypercenter#107D103
hypocenterC103#480
LCSG ▷ C2×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. C4⋊C4×D103C2semidirect
3. #15692954C2semidirect
4. #15692943C2semidirect
5. #15692941C2semidirect
6. (C2×D103)⋊C8C2semidirect
7. #107×C103C2semidirect
52. C103#480semidirect
57. #107D103semidirect