Finite Group Databasebeta

← #23782056

Subgroups — #23782056

Order 10432.

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

normal subgroups only

This group has 124 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×Dic652C211yesmaximal, characteristic, complemented
2C2×#14579689C211yesmaximal, characteristic, complemented
3C2×#14579687C211yesmaximal, characteristic
4#19104733C211yesmaximal, characteristic, complemented
5#19104722C211yesmaximal, characteristic
6#19104645C211yesmaximal, characteristic, complemented
7C2×SD16×C163C211yesmaximal, characteristic
8C2×Dic326C2211yescharacteristic
9C2×Dic326C2211yescharacteristic
10Dic652—22no—
11#14579689—22no—
12#14579687—22no—
13C2×C163⋊C8C2211yescharacteristic
14Dic163⋊C4—22no—
15C22⋊Dic163—22no—
16C4×Dic163C2211yescharacteristic
17C2×Q8×C163C2211yescharacteristic
18C2×D4×C163C2211yescharacteristic
19SD16×C163—22no—
20C2×C8×C163C2211yescharacteristic
21Dic326—21no—
22Dic326—21no—
23Dic326—21no—
24Dic326—21no—
25C2×Dic163—21no—
26C2×Dic163—21no—
27C2×Dic163D412yes—
28C163⋊C8D412yes—
29C23×C163—21no—
30Q8×C163—21no—
31Q8×C163—21no—
32D4×C163—21no—
33D4×C163—21no—
34C2×C4×C163—21no—
35C2×C4×C163C2311yescharacteristic
36C8×C163D412yes—
37C22×C163—41no—
38C22×C163—42no—
39C22×C163C2×D411yescharacteristic
40C4×C163—41no—
41C4×C163C2×D411yescharacteristic
42C4×C163C2×D411yescharacteristic
43Dic163—22no—
44Dic163—41no—
45Dic163—41no—
46C2×C163—81no—
47C2×C163#12711yescharacteristic
48C2×C163#13712yes—
49C163#49711yescharacteristic, complemented, Sylow
50#497—1631nomaximal, Sylow
51C2×Q16—1631no—
52C2×Q16—1631no—
53C2×SD16—1631no—
54C2×SD16D16311yescharacteristic
55C4⋊Q8—1631no—
56#124—1631no—
57#97—1631no—
58C2×Q8—1631no—
59C2×Q8—1631no—
60C2×Q8C2×D16311yescharacteristic
61C2×D4C2×D16311yescharacteristic
62Q16—3262no—
63Q16—3262no—
64SD16—22no—
65SD16—3262no—
66C2×C8—1631no—
67C2×C8C2×D16311yescharacteristic
68C4⋊C4—3262no—
69C22⋊C4—3262no—
70C42—1631no—
71C23—21no—
72Q8—21no—
73Q8—21no—
74Q8—3261no—
75Q8—3261no—
76Q8—3261no—
77Q8—3261no—
78D4—21no—
79D4—21no—
80C2×C4—21no—
81C2×C4—3261no—
82C2×C4—3261no—
83C2×C4—1632no—
84C2×C4C22×D16311yescharacteristic
85C8—1632no—
86C8C22⋊D16312yes—
87C22—41no—
88C22—42no—
89C22D4×D16311yescharacteristic
90C4—41no—
91C4—3262no—
92C4—6521no—
93C4—6521no—
94C4D4×D16311yescharacteristic
95C4C2×C22⋊D16311yescharacteristic
96C2—81no—
97C2#1910473111yescharacteristic
98C2#1910476412yes—
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×SD16×C163C2
socleC22×C163C2×D4
prime radicalC2×D4×C163C22
hypercenterC2×SD16D163
hypocenterC163#497
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×Dic652C2semidirect
2. C2×#14579689C2semidirect
4. #19104733C2semidirect
6. #19104645C2semidirect
49. C163#497semidirect