Finite Group Databasebeta

← #23781885

Subgroups — #23781885

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×#14579689C211yesmaximal, characteristic, complemented
2#19104722C211yesmaximal, characteristic
3Q8×Dic163C211yesmaximal, characteristic, complemented
4Dic163⋊C8C211yesmaximal, characteristic, complemented
5#19104660C211yesmaximal, characteristic, complemented
6#19104656C211yesmaximal, characteristic
7C2×SD16×C163C211yesmaximal, characteristic
8C2×Dic326C2211yescharacteristic
9#14579689—22no—
10C2×C163⋊C8C2211yescharacteristic
11C4⋊Dic163—21no—
12C4⋊Dic163C2211yescharacteristic
13C22⋊Dic163—21no—
14C22⋊Dic163—21no—
15C4×Dic163—21no—
16C4×Dic163C2211yescharacteristic
17C2×Q8×C163C2211yescharacteristic
18C2×D4×C163C2211yescharacteristic
19SD16×C163—22no—
20C2×C8×C163C2211yescharacteristic
21Dic326—21no—
22Dic326—21no—
23C2×Dic163—21no—
24C2×Dic163—21no—
25C2×Dic163D411yescharacteristic
26C2×Dic163D411yescharacteristic
27C163⋊C8—21no—
28C23×C163—21no—
29Q8×C163—21no—
30Q8×C163D412yes—
31D4×C163—21no—
32D4×C163—21no—
33C2×C4×C163—21no—
34C2×C4×C163C2311yescharacteristic
35C8×C163—21no—
36C22×C163—41no—
37C22×C163—41no—
38C22×C163—41no—
39C22×C163C2×D411yescharacteristic
40C4×C163—22no—
41C4×C163C2×D411yescharacteristic
42C4×C163#4111yescharacteristic
43Dic163—21no—
44Dic163—21no—
45Dic163—41no—
46Dic163—41no—
47C2×C163—81no—
48C2×C163#12111yescharacteristic
49C2×C163#13511yescharacteristic
50C2×C163#13711yescharacteristic
51C163#46411yescharacteristic, complemented, Sylow
52#464—1631nomaximal, Sylow
53C2×Q16—1631no—
54C2×SD16D16311yescharacteristic
55#124—1631no—
56C4×Q8—1631no—
57C4⋊C8—1631no—
58#103—1631no—
59#102—1631no—
60C2×Q8—1631no—
61C2×Q8C2×D16311yescharacteristic
62C2×D4C2×D16311yescharacteristic
63Q16—3262no—
64SD16—22no—
65C2×C8—1631no—
66C2×C8C2×D16311yescharacteristic
67C4⋊C4—3261no—
68C4⋊C4—1631no—
69C22⋊C4—3261no—
70C22⋊C4—3261no—
71C42—3261no—
72C42—1631no—
73C23—21no—
74Q8—21no—
75Q8—3261no—
76Q8—3261no—
77Q8C22⋊D16312yes—
78D4—21no—
79D4—21no—
80C2×C4—21no—
81C2×C4—3261no—
82C2×C4—3261no—
83C2×C4—1631no—
84C2×C4—1631no—
85C2×C4C22×D16311yescharacteristic
86C8—21no—
87C8—3261no—
88C22—41no—
89C22—41no—
90C22—41no—
91C22D4×D16311yescharacteristic
92C4—22no—
93C4—3261no—
94C4—3261no—
95C4—6521no—
96C4—6521no—
97C4C2×C22⋊D16311yescharacteristic
98C4#1457969811yescharacteristic
99C2—81no—
100C2#1910470711yescharacteristic
101C2#1910475611yescharacteristic
102C2#1910476411yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×SD16×C163C2
socleC22×C163C2×D4
prime radicalC2×D4×C163C22
hypercenterC2×SD16D163
hypocenterC163#464
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14579689C2semidirect
3. Q8×Dic163C2semidirect
4. Dic163⋊C8C2semidirect
5. #19104660C2semidirect
51. C163#464semidirect