Finite Group Databasebeta

← #20268012

Subgroups — #20268012

Order 6592.

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

normal subgroups only

This group has 112 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
1C2×Dic412C211yesmaximal, characteristic, complemented
2C2×#13110093C211yesmaximal, characteristic
3#15693008C211yesmaximal, characteristic
4#15692986C211yesmaximal, characteristic, complemented
5Dic103⋊C8C211yesmaximal, characteristic, complemented
6#15692944C211yesmaximal, characteristic, complemented
7#102×C103C211yesmaximal, characteristic
8C2×Dic206C2211yescharacteristic
9C2×Dic206C2211yescharacteristic
10Dic412—22no—
11#13110093—22no—
12C2×C103⋊C8C2211yescharacteristic
13Dic103⋊C4—21no—
14C22⋊Dic103—21no—
15C22⋊Dic103—21no—
16C4×Dic103—21no—
17C4×Dic103C2211yescharacteristic
18C2×D4×C103C2211yescharacteristic
19C2×C8×C103C2211yescharacteristic
20C4⋊C4×C103C2211yescharacteristic
21C23×C103—21no—
22D4×C103—21no—
23D4×C103—21no—
24C2×C4×C103—21no—
25C2×C4×C103C2311yescharacteristic
26C2×Dic103—21no—
27C2×Dic103—21no—
28C2×Dic103D411yescharacteristic
29C2×Dic103D411yescharacteristic
30Dic206—21no—
31Dic206—21no—
32Dic206—21no—
33Dic206D412yes—
34C8×C103—21no—
35C103⋊C8—21no—
36C22×C103—41no—
37C22×C103—41no—
38C22×C103—41no—
39C22×C103C2×D411yescharacteristic
40C4×C103—41no—
41C4×C103C2×D411yescharacteristic
42C4×C103#4111yescharacteristic
43Dic103—22no—
44Dic103—21no—
45Dic103—21no—
46Dic103—41no—
47C2×C103—81no—
48C2×C103#12111yescharacteristic
49C2×C103#13511yescharacteristic
50C2×C103#13711yescharacteristic
51C103#46411yescharacteristic, complemented, Sylow
52#464—1031nomaximal, Sylow
53C2×Q16—1031no—
54C2×SD16—1031no—
55#124—1031no—
56C4×Q8—1031no—
57C4⋊C8—1031no—
58#103—1031no—
59#102D10311yescharacteristic
60C2×Q8—1031no—
61C2×Q8—1031no—
62C2×D4C2×D10311yescharacteristic
63Q16—2062no—
64SD16—2062no—
65C2×C8—1031no—
66C2×C8C2×D10311yescharacteristic
67C4⋊C4—2061no—
68C4⋊C4C2×D10311yescharacteristic
69C22⋊C4—2061no—
70C22⋊C4—2061no—
71C42—1031no—
72C42—2061no—
73C23—21no—
74Q8—1032no—
75Q8—2061no—
76Q8—2061no—
77Q8—2061no—
78D4—21no—
79D4—21no—
80C2×C4—21no—
81C2×C4—1031no—
82C2×C4—1031no—
83C2×C4—2061no—
84C2×C4—2061no—
85C2×C4C22×D10311yescharacteristic
86C8—21no—
87C8—2061no—
88C22—41no—
89C22—41no—
90C22—41no—
91C22D4×D10311yescharacteristic
92C4—41no—
93C4—4121no—
94C4—2062no—
95C4—2061no—
96C4—2061no—
97C4D4×D10311yescharacteristic
98C4#1311010511yescharacteristic
99C2—81no—
100C2#1569299411yescharacteristic
101C2#1569304011yescharacteristic
102C2#1569305011yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#102×C103C2
socleC22×C103C2×D4
hypercenter#102D103
hypocenterC103#464
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
1. C2×Dic412C2semidirect
4. #15692986C2semidirect
5. Dic103⋊C8C2semidirect
6. #15692944C2semidirect
51. C103#464semidirect