Finite Group Databasebeta

← #23782294

Subgroups — #23782294

Order 10432.

206 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 103 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
1#19104734C212yesmaximal, complemented
2#19104733C212yesmaximal, complemented
3#19104725C212yesmaximal, complemented
4#19104725C212yesmaximal, complemented
5#19104714C211yesmaximal, characteristic
6#19104712C212yesmaximal
7#19104691C212yesmaximal
8C2×Dic163⋊C4C211yesmaximal, characteristic
9C22⋊Q8×C163C211yesmaximal, characteristic
10C2×Dic326C2212yes—
11C2×Dic326C2211yescharacteristic
12C22×Dic163C2211yescharacteristic
13C22×Dic163C2211yescharacteristic
14C4⋊Dic163C2212yes—
15C4⋊Dic163C2211yescharacteristic
16Dic163⋊C4C2212yes—
17Dic163⋊C4C2212yes—
18Dic163⋊C4C2212yes—
19Dic163⋊C4C2212yes—
20Dic163⋊C4C2212yes—
21Dic163⋊C4C2212yes—
22Dic163⋊C4C2212yes—
23C22⋊Dic163C2212yes—
24C4×Dic163C2212yes—
25C4×Dic163C2212yes—
26C2×Q8×C163C2211yescharacteristic
27C22×C4×C163C2211yescharacteristic
28C4⋊C4×C163C2211yescharacteristic
29C4⋊C4×C163C2212yes—
30C22⋊C4×C163C2212yes—
31Dic326—42no—
32Dic326—41no—
33C2×Dic163—41no—
34C2×Dic163Q814yescomplemented
35C2×Dic163C2312yes—
36C2×Dic163C2312yes—
37C2×Dic163C2312yes—
38C2×Dic163C2312yes—
39C23×C163C2311yescharacteristic
40Q8×C163—41no—
41C2×C4×C163—41no—
42C2×C4×C163C2312yes—
43C2×C4×C163C2312yes—
44C2×C4×C163C2311yescharacteristic
45C2×C4×C163C2311yescharacteristic
46C22×C163—21no—
47C22×C163—21no—
48C22×C163C2×Q812yes—
49C22×C163C2411yescharacteristic
50C4×C163—21no—
51C4×C163—21no—
52C4×C163—22no—
53C4×C163—22no—
54Dic163—22no—
55Dic163—22no—
56Dic163—22no—
57Dic163C2×Q814yes—
58C2×C163—22no—
59C2×C163C22×Q811yescharacteristic
60C2×C163H(5,𝔽2)11yescharacteristic
61C2×C1632−1+411yescharacteristic
62C163#54411yescharacteristic, complemented, Sylow
63#544—1631nomaximal, Sylow
64C4⋊Q8—1632no—
65C4⋊Q8—1632no—
66#125—1632no—
67#125—1632no—
68C22⋊Q8—1631no—
69C22⋊Q8—1632no—
70C22⋊Q8D16311yescharacteristic
71#117—1632no—
72C2×C4⋊C4—1631no—
73C2×Q8—1631no—
74C2×Q8—1632no—
75C2×Q8C2×D16311yescharacteristic
76C22×C4—1631no—
77C22×C4—1631no—
78C22×C4C2×D16311yescharacteristic
79C4⋊C4—1632no—
80C4⋊C4—1632no—
81C4⋊C4—1632no—
82C4⋊C4—1632no—
83C4⋊C4—1632no—
84C4⋊C4—1631no—
85C4⋊C4—1632no—
86C4⋊C4—1632no—
87C4⋊C4—1632no—
88C4⋊C4C2×D16311yescharacteristic
89C4⋊C4C2×D16312yes—
90C22⋊C4—1632no—
91C22⋊C4C2×D16312yes—
92C42—1632no—
93C42—1632no—
94C23C22×D16311yescharacteristic
95Q8—41no—
96Q8—6521no—
97Q8—6522no—
98C2×C4—41no—
99C2×C4—6521no—
100C2×C4—1632no—
101C2×C4—1632no—
102C2×C4—1632no—
103C2×C4—1634no—
104C2×C4—1632no—
105C2×C4C22×D16312yes—
106C2×C4C22×D16312yes—
107C2×C4C22×D16311yescharacteristic
108C2×C4C22×D16311yescharacteristic
109C22—21no—
110C22—21no—
111C22Q8×D16312yes—
112C22C23×D16311yescharacteristic
113C4—21no—
114C4—21no—
115C4—22no—
116C4—22no—
117C4—3262no—
118C4—3262no—
119C4—3262no—
120C4—1634no—
121C2—22no—
122C2C2×Q8×D16311yescharacteristic
123C2#1910478011yescharacteristic
124C2#1910478211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D163
commutator, socle, cosocleC22×C163C24
FittingC22⋊Q8×C163C2
prime radicalC23×C163C23
hypercenterC22⋊Q8D163
hypocenterC163#544
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #19104734C2semidirect
2. #19104733C2semidirect
3. #19104725C2semidirect
4. #19104725C2semidirect
34. C2×Dic163Q8semidirect
62. C163#544semidirect