Finite Group Databasebeta

← #23781888

Subgroups — #23781888

Order 10432.

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

normal subgroups only

This group has 112 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×Dic652C211yesmaximal, characteristic, complemented
2C2×#14579688C211yesmaximal, characteristic
3#19104723C211yesmaximal, characteristic
4C4×Dic326C211yesmaximal, characteristic, complemented
5#19104660C211yesmaximal, characteristic, complemented
6#19104657C211yesmaximal, characteristic
7C4⋊C8×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×Dic326C2211yescharacteristic
10C2×D652C2211yescharacteristic
11Dic652—22no—
12#14579688—22no—
13C4⋊Dic163C2211yescharacteristic
14Dic163⋊C4—21no—
15(C2×D163)⋊C4—21no—
16(C2×D163)⋊C4—21no—
17C4×Dic163—21no—
18C2×C8×C163C2211yescharacteristic
19C2×C8×C163C2211yescharacteristic
20C42×C163C2211yescharacteristic
21C22×D163—21no—
22Dic326—21no—
23Dic326—21no—
24Dic326—21no—
25Dic326D412yes—
26D652—21no—
27D652—21no—
28C2×Dic163—21no—
29C2×Dic163—21no—
30C2×Dic163—21no—
31C2×C4×C163D411yescharacteristic
32C2×C4×C163D411yescharacteristic
33C2×C4×C163C2311yescharacteristic
34C8×C163—21no—
35C8×C163—21no—
36C22×C163C2×D411yescharacteristic
37C2×D163—41no—
38C2×D163—41no—
39C2×D163—41no—
40C4×C163—21no—
41C4×C163—21no—
42C4×C163C2×D411yescharacteristic
43C4×C163#4111yescharacteristic
44Dic163—22no—
45Dic163—41no—
46Dic163—41no—
47C2×C163#12111yescharacteristic
48C2×C163#13511yescharacteristic
49C2×C163#13711yescharacteristic
50D163—81no—
51C163#46411yescharacteristic, complemented, Sylow
52#464—1631nomaximal, Sylow
53C2×Q16—1631no—
54C2×SD16—1631no—
55#124—1631no—
56C4×Q8—1631no—
57C4⋊C8D16311yescharacteristic, complemented
58#103—1631no—
59#102—1631no—
60C2×Q8—1631no—
61C2×Q8—1631no—
62C2×D4—1631no—
63Q16—3262no—
64SD16—3262no—
65C2×C8C2×D16311yescharacteristic
66C2×C8C2×D16311yescharacteristic
67C4⋊C4—3261no—
68C4⋊C4—1631no—
69C22⋊C4—3261no—
70C22⋊C4—3261no—
71C42—3261no—
72C42C2×D16311yescharacteristic
73C23—3261no—
74Q8—3261no—
75Q8—3261no—
76Q8—3261no—
77Q8—1632no—
78D4—3261no—
79D4—3261no—
80C2×C4—3261no—
81C2×C4—3261no—
82C2×C4—3261no—
83C2×C4D65211yescharacteristic
84C2×C4D65211yescharacteristic
85C2×C4C22×D16311yescharacteristic
86C8—21no—
87C8—21no—
88C22—6521no—
89C22—6521no—
90C22—6521no—
91C22C2×D65211yescharacteristic
92C4—21no—
93C4—21no—
94C4—3262no—
95C4—6521no—
96C4—6521no—
97C4D4×D16311yescharacteristic
98C4#1457970011yescharacteristic
99C2—13041no—
100C2#1910471011yescharacteristic
101C2#1910475711yescharacteristic
102C2#1910476811yescharacteristic
subgroupG/H
centerC22C2×D652
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC4⋊C8×C163C2
socleC22×C163C2×D4
prime radicalC2×D652C22
hypercenterC4⋊C8D163
hypocenterC163#464
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×Dic652C2semidirect
4. C4×Dic326C2semidirect
5. #19104660C2semidirect
7. C4⋊C8×C163C2semidirect
51. C163#464semidirect
57. C4⋊C8D163semidirect