Finite Group Databasebeta

← #23781884

Subgroups — #23781884

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
2C2×#14579687C211yesmaximal, characteristic
3C4×Dic326C211yesmaximal, characteristic, complemented
4C4⋊(C163⋊C8)C211yesmaximal, characteristic, complemented
5#19104659C211yesmaximal, characteristic, complemented
6#19104656C211yesmaximal, characteristic
7#124×C163C211yesmaximal, characteristic
8C2×Dic326C2211yescharacteristic
9#14579689—22no—
10#14579687—22no—
11C2×C163⋊C8C2211yescharacteristic
12C2×C163⋊C8C2211yescharacteristic
13C4⋊Dic163C2211yescharacteristic
14Dic163⋊C4—21no—
15C4×Dic163—21no—
16C2×Q8×C163C2211yescharacteristic
17C2×D4×C163C2211yescharacteristic
18C22⋊C4×C163—21no—
19C22⋊C4×C163—21no—
20C42×C163C2211yescharacteristic
21Dic326—21no—
22Dic326D412yes—
23C2×Dic163—21no—
24C2×Dic163—21no—
25C163⋊C8—21no—
26C163⋊C8—21no—
27C23×C163—21no—
28Q8×C163—21no—
29Q8×C163—21no—
30D4×C163—21no—
31D4×C163—21no—
32C2×C4×C163—21no—
33C2×C4×C163D411yescharacteristic
34C2×C4×C163D411yescharacteristic
35C2×C4×C163C2311yescharacteristic
36C22×C163—41no—
37C22×C163—41no—
38C22×C163—41no—
39C22×C163C2×D411yescharacteristic
40C4×C163—21no—
41C4×C163—21no—
42C4×C163—41no—
43C4×C163C2×D411yescharacteristic
44C4×C163#4111yescharacteristic
45Dic163—22no—
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×SD16—1631no—
55#124D16311yescharacteristic
56C4×Q8—1631no—
57C4⋊C8—1631no—
58#103—1631no—
59#102—1631no—
60C2×Q8—1631no—
61C2×Q8C2×D16311yescharacteristic
62C2×D4C2×D16311yescharacteristic
63Q16—3262no—
64SD16—3262no—
65C2×C8—1631no—
66C2×C8—1631no—
67C4⋊C4—3261no—
68C4⋊C4—1631no—
69C22⋊C4—21no—
70C22⋊C4—21no—
71C42—3261no—
72C42C2×D16311yescharacteristic
73C23—21no—
74Q8—21no—
75Q8—21no—
76Q8—3261no—
77Q8—1632no—
78D4—21no—
79D4—21no—
80C2×C4—21no—
81C2×C4—3261no—
82C2×C4—3261no—
83C2×C4C22⋊D16311yescharacteristic
84C2×C4C22⋊D16311yescharacteristic
85C2×C4C22×D16311yescharacteristic
86C8—3261no—
87C8—3261no—
88C22—41no—
89C22—41no—
90C22—41no—
91C22C2×C22⋊D16311yescharacteristic
92C4—21no—
93C4—21no—
94C4—41no—
95C4—3262no—
96C4—6521no—
97C4D4×D16311yescharacteristic
98C4#1457969811yescharacteristic
99C2—81no—
100C2#1910470611yescharacteristic
101C2#1910475511yescharacteristic
102C2#1910476511yescharacteristic
subgroupG/H
centerC22C2×C22⋊D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#124×C163C2
socleC22×C163C2×D4
prime radicalC2×D4×C163C22
hypercenter#124D163
hypocenterC163#464
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C2×#14579689C2semidirect
3. C4×Dic326C2semidirect
4. C4⋊(C163⋊C8)C2semidirect
5. #19104659C2semidirect
51. C163#464semidirect