Finite Group Databasebeta

← #20268035

Subgroups — #20268035

Order 6592.

120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#13110093C211yesmaximal, characteristic, complemented
2C2×#13110089C211yesmaximal, characteristic, complemented
3#15693000C211yesmaximal, characteristic, complemented
4#15692954C211yesmaximal, characteristic, complemented
5#15692944C211yesmaximal, characteristic, complemented
6#15692942C211yesmaximal, characteristic, complemented
7#121×C103C211yesmaximal, characteristic
8C2×Dic206C2211yescharacteristic
9#13110093—22no—
10#13110089—22no—
11C2×C103⋊C8C2211yescharacteristic
12C2×C103⋊C8C2211yescharacteristic
13C4⋊Dic103C2211yescharacteristic
14Dic103⋊C4—21no—
15C22⋊Dic103—21no—
16C2×D4×C103—21no—
17C2×D4×C103C2211yescharacteristic
18C22×C4×C103C2211yescharacteristic
19C4⋊C4×C103C2211yescharacteristic
20C22⋊C4×C103—21no—
21C23×C103—21no—
22C23×C103D411yescharacteristic
23D4×C103—21no—
24D4×C103—21no—
25D4×C103—42no—
26C2×C4×C103—21no—
27C2×C4×C103—21no—
28C2×C4×C103—21no—
29C2×C4×C103D411yescharacteristic
30C2×C4×C103C2311yescharacteristic
31C2×Dic103—21no—
32C2×Dic103—21no—
33Dic206—21no—
34Dic206—21no—
35C103⋊C8—21no—
36C103⋊C8D412yescomplemented
37C22×C103—21no—
38C22×C103—21no—
39C22×C103—21no—
40C22×C103—41no—
41C22×C103—41no—
42C22×C103—41no—
43C22×C103C2×D411yescharacteristic
44C4×C103—21no—
45C4×C103—41no—
46C4×C103C2×D411yescharacteristic
47C4×C103#4111yescharacteristic
48Dic103—41no—
49Dic103—41no—
50C2×C103—41no—
51C2×C103—81no—
52C2×C103#12111yescharacteristic
53C2×C103AGL(1,ℤ/8)11yescharacteristic
54C2×C103#13711yescharacteristic
55C103#46811yescharacteristic, complemented, Sylow
56#468—1031nomaximal, Sylow
57C2×SD16—1031no—
58C2×M16—1031no—
59C22⋊Q8—1031no—
60#121D10311yescharacteristic
61#107—1031no—
62#103—1031no—
63#102—1031no—
64C2×Q8—1031no—
65C2×D4—21no—
66C2×D4C2×D10311yescharacteristic
67C22×C4C2×D10311yescharacteristic
68SD16—2062no—
69M16—2062no—
70C2×C8—1031no—
71C2×C8—1031no—
72C4⋊C4—1031no—
73C4⋊C4—2061no—
74C4⋊C4C2×D10311yescharacteristic
75C22⋊C4—21no—
76C22⋊C4—2061no—
77C23—21no—
78C23C22⋊D10311yescharacteristic
79Q8—2061no—
80Q8—2061no—
81D4—21no—
82D4—21no—
83D4—42no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—2061no—
88C2×C4—2061no—
89C2×C4C22⋊D10311yescharacteristic
90C2×C4C22×D10311yescharacteristic
91C8—1032no—
92C8—2061no—
93C22—21no—
94C22—21no—
95C22—21no—
96C22—41no—
97C22—41no—
98C22—41no—
99C22C2×C22⋊D10311yescharacteristic
100C4—21no—
101C4—41no—
102C4—4121no—
103C4—4121no—
104C4D4×D10311yescharacteristic
105C4#1311010411yescharacteristic
106C2—41no—
107C2—81no—
108C2#1569299311yescharacteristic
109C2#1569304711yescharacteristic
110C2#1569305111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#121×C103C2
socleC22×C103C2×D4
hypercenter#121D103
hypocenterC103#468
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#13110093C2semidirect
2. C2×#13110089C2semidirect
3. #15693000C2semidirect
4. #15692954C2semidirect
5. #15692944C2semidirect
6. #15692942C2semidirect
36. C103⋊C8D4semidirect
55. C103#468semidirect