Finite Group Databasebeta

← #23781887

Subgroups — #23781887

Order 10432.

112 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14579689C211yesmaximal, characteristic, complemented
2C2×#14579686C211yesmaximal, characteristic
3#19104723C211yesmaximal, characteristic
4C4⋊(C163⋊C8)C211yesmaximal, characteristic, complemented
5#19104658C211yesmaximal, characteristic, complemented
6#19104655C211yesmaximal, characteristic
7C4×Q8×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×D652C2211yescharacteristic
10#14579689—22no—
11#14579686—22no—
12C2×C163⋊C8C2211yescharacteristic
13C2×C163⋊C8C2211yescharacteristic
14(C2×D163)⋊C4—21no—
15(C2×D163)⋊C4—21no—
16C2×Q8×C163C2211yescharacteristic
17C4⋊C4×C163—21no—
18C4⋊C4×C163C2211yescharacteristic
19C42×C163—21no—
20C42×C163C2211yescharacteristic
21C22×D163—21no—
22Dic326—21no—
23Dic326—21no—
24D652—21no—
25D652—21no—
26C2×Dic163—21no—
27C163⋊C8—21no—
28C163⋊C8—21no—
29Q8×C163—21no—
30Q8×C163D412yes—
31C2×C4×C163—21no—
32C2×C4×C163—21no—
33C2×C4×C163D411yescharacteristic
34C2×C4×C163D411yescharacteristic
35C2×C4×C163C2311yescharacteristic
36C22×C163C2×D411yescharacteristic
37C2×D163—41no—
38C2×D163—41no—
39C2×D163—41no—
40C4×C163—22no—
41C4×C163—21no—
42C4×C163—21no—
43C4×C163—41no—
44C4×C163C2×D411yescharacteristic
45C4×C163#4111yescharacteristic
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×Q8D16311yescharacteristic, complemented
57C4⋊C8—1631no—
58#103—1631no—
59#102—1631no—
60C2×Q8—1631no—
61C2×Q8C2×D16311yescharacteristic
62C2×D4—1631no—
63Q16—3262no—
64SD16—3262no—
65C2×C8—1631no—
66C2×C8—1631no—
67C4⋊C4—21no—
68C4⋊C4C2×D16311yescharacteristic
69C22⋊C4—3261no—
70C22⋊C4—3261no—
71C42—21no—
72C42C2×D16311yescharacteristic
73C23—3261no—
74Q8—21no—
75Q8—3261no—
76Q8—3261no—
77Q8D65212yes—
78D4—3261no—
79D4—3261no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3261no—
83C2×C4C22⋊D16311yescharacteristic
84C2×C4C22⋊D16311yescharacteristic
85C2×C4C22×D16311yescharacteristic
86C8—3261no—
87C8—3261no—
88C22—6521no—
89C22—6521no—
90C22—6521no—
91C22C2×C22⋊D16311yescharacteristic
92C4—22no—
93C4—21no—
94C4—21no—
95C4—41no—
96C4—6521no—
97C4C2×D65211yescharacteristic
98C4#1457969911yescharacteristic
99C2—13041no—
100C2#1910470911yescharacteristic
101C2#1910475511yescharacteristic
102C2#1910476611yescharacteristic
subgroupG/H
centerC22C2×C22⋊D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC4×Q8×C163C2
socleC22×C163C2×D4
prime radicalC2×D652C22
hypercenterC4×Q8D163
hypocenterC163#464
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14579689C2semidirect
4. C4⋊(C163⋊C8)C2semidirect
5. #19104658C2semidirect
7. C4×Q8×C163C2semidirect
51. C163#464semidirect
56. C4×Q8D163semidirect