Finite Group Databasebeta

← #23782058

Subgroups — #23782058

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×#14579689C211yesmaximal, characteristic, complemented
2C2×#14579688C211yesmaximal, characteristic
3C2×#14579686C211yesmaximal, characteristic
4#19104733C211yesmaximal, characteristic, complemented
5#19104724C211yesmaximal, characteristic
6#19104645C211yesmaximal, characteristic, complemented
7C2×Q16×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×D652C2211yescharacteristic
10#14579689—22no—
11#14579688—22no—
12#14579686—22no—
13C2×C163⋊C8C2211yescharacteristic
14Dic163⋊C4—22no—
15(C2×D163)⋊C4—22no—
16C4×Dic163C2211yescharacteristic
17C2×Q8×C163C2211yescharacteristic
18C2×Q8×C163C2211yescharacteristic
19Q16×C163—22no—
20C2×C8×C163C2211yescharacteristic
21C22×D163—21no—
22Dic326—21no—
23Dic326—21no—
24D652—21no—
25D652—21no—
26C2×Dic163—21no—
27C2×Dic163D412yes—
28C163⋊C8D412yes—
29Q8×C163—21no—
30Q8×C163—21no—
31Q8×C163—21no—
32Q8×C163—21no—
33C2×C4×C163—21no—
34C2×C4×C163—21no—
35C2×C4×C163C2311yescharacteristic
36C8×C163D412yes—
37C22×C163C2×D411yescharacteristic
38C2×D163—41no—
39C2×D163—42no—
40C4×C163—41no—
41C4×C163—41no—
42C4×C163C2×D411yescharacteristic
43C4×C163C2×D411yescharacteristic
44Dic163—22no—
45Dic163—41no—
46C2×C163#12711yescharacteristic
47C2×C163#13712yes—
48D163—81no—
49C163#49711yescharacteristic, complemented, Sylow
50#497—1631nomaximal, Sylow
51C2×Q16—1631no—
52C2×Q16D16311yescharacteristic, complemented
53C2×SD16—1631no—
54C2×SD16—1631no—
55C4⋊Q8—1631no—
56#124—1631no—
57#97—1631no—
58C2×Q8—1631no—
59C2×Q8C2×D16311yescharacteristic
60C2×Q8C2×D16311yescharacteristic
61C2×D4—1631no—
62Q16—22no—
63Q16—3262no—
64SD16—3262no—
65SD16—3262no—
66C2×C8—1631no—
67C2×C8C2×D16311yescharacteristic
68C4⋊C4—3262no—
69C22⋊C4—3262no—
70C42—1631no—
71C23—3261no—
72Q8—21no—
73Q8—21no—
74Q8—21no—
75Q8—21no—
76Q8—3261no—
77Q8—3261no—
78D4—3261no—
79D4—3261no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3261no—
83C2×C4—1632no—
84C2×C4C22×D16311yescharacteristic
85C8—1632no—
86C8C22⋊D16312yes—
87C22—6521no—
88C22—6522no—
89C22D4×D16311yescharacteristic
90C4—41no—
91C4—41no—
92C4—3262no—
93C4—6521no—
94C4D4×D16311yescharacteristic
95C4C2×C22⋊D16311yescharacteristic
96C2—13041no—
97C2#1910473111yescharacteristic
98C2#1910476712yes—
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×Q16×C163C2
socleC22×C163C2×D4
prime radicalC2×D652C22
hypercenterC2×Q16D163
hypocenterC163#497
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#14579689C2semidirect
4. #19104733C2semidirect
6. #19104645C2semidirect
7. C2×Q16×C163C2semidirect
49. C163#497semidirect
52. C2×Q16D163semidirect