Finite Group Databasebeta

← #23782275

Subgroups — #23782275

Order 10432.

192 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 95 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#19104733C211yesmaximal, characteristic, complemented
2#19104728C212yesmaximal
3#19104728C212yesmaximal
4#19104726C211yesmaximal, characteristic, complemented
5#19104726C212yesmaximal, complemented
6#19104725C212yesmaximal, complemented
7#19104714C211yesmaximal, characteristic
8Q8×Dic163C211yesmaximal, characteristic, complemented
9#19104700C211yesmaximal, characteristic, complemented
10#19104694C211yesmaximal, characteristic
11C22⋊Q8×C163C211yesmaximal, characteristic
12C2×Dic326C2211yescharacteristic
13C4⋊Dic163C2211yescharacteristic
14C4⋊Dic163C2211yescharacteristic
15C4⋊Dic163C2211yescharacteristic
16C4⋊Dic163C2212yes—
17C4⋊Dic163C2212yes—
18Dic163⋊C4C2212yes—
19Dic163⋊C4C2212yes—
20Dic163⋊C4C2212yes—
21Dic163⋊C4C2212yes—
22Dic163⋊C4C2212yes—
23C22⋊Dic163C2211yescharacteristic
24C22⋊Dic163C2211yescharacteristic
25C22⋊Dic163C2212yes—
26C4×Dic163C2211yescharacteristic
27C4×Dic163C2211yescharacteristic
28C4×Dic163C2212yes—
29C4×Dic163C2212yes—
30C2×Q8×C163C2211yescharacteristic
31C22×C4×C163C2211yescharacteristic
32C4⋊C4×C163C2211yescharacteristic
33C4⋊C4×C163C2212yes—
34C22⋊C4×C163C2212yes—
35Dic326—22no—
36C2×Dic163C2311yescharacteristic
37C2×Dic163C2311yescharacteristic
38C2×Dic163C2311yescharacteristic
39C2×Dic163C2312yes—
40C2×Dic163C2311yescharacteristic
41C2×Dic163C2312yes—
42C23×C163C2311yescharacteristic
43Q8×C163—22no—
44C2×C4×C163—22no—
45C2×C4×C163C2312yes—
46C2×C4×C163C2312yes—
47C2×C4×C163C2311yescharacteristic
48C2×C4×C163C2311yescharacteristic
49C22×C163—21no—
50C22×C163—21no—
51C22×C163—21no—
52C22×C163C2411yescharacteristic
53C4×C163—21no—
54C4×C163—22no—
55C4×C163—22no—
56C4×C163#4112yes—
57Dic163—22no—
58Dic163—21no—
59Dic163—21no—
60Dic163—21no—
61Dic163—21no—
62Dic163—22no—
63C2×C163—41no—
64C2×C163C2×#4111yescharacteristic
65C2×C1632−1+411yescharacteristic
66C2×C1632−1+411yescharacteristic
67C163#54111yescharacteristic, complemented, Sylow
68#541—1631nomaximal, Sylow
69C4⋊Q8—1631no—
70#126—1632no—
71#126—1632no—
72#125—1632no—
73#125—1631no—
74#125—1632no—
75C22⋊Q8—1631no—
76C22⋊Q8D16311yescharacteristic
77C4×Q8—1631no—
78C4×Q8—1631no—
79#117—1631no—
80C2×Q8—1631no—
81C2×Q8C2×D16311yescharacteristic
82C22×C4C2×D16311yescharacteristic
83C4⋊C4—1631no—
84C4⋊C4—1631no—
85C4⋊C4—1631no—
86C4⋊C4—1632no—
87C4⋊C4—1632no—
88C4⋊C4—1632no—
89C4⋊C4—1632no—
90C4⋊C4—1632no—
91C4⋊C4—1632no—
92C4⋊C4—1632no—
93C4⋊C4C2×D16311yescharacteristic
94C4⋊C4C2×D16312yes—
95C22⋊C4—1631no—
96C22⋊C4—1631no—
97C22⋊C4—1632no—
98C22⋊C4C2×D16312yes—
99C42—1631no—
100C42—1631no—
101C42—1632no—
102C42—1632no—
103C23C22×D16311yescharacteristic
104Q8—22no—
105Q8—3262no—
106C2×C4—22no—
107C2×C4—1631no—
108C2×C4—1631no—
109C2×C4—1631no—
110C2×C4—1631no—
111C2×C4—1632no—
112C2×C4—1632no—
113C2×C4C22×D16312yes—
114C2×C4C22×D16312yes—
115C2×C4C22×D16311yescharacteristic
116C2×C4C22×D16311yescharacteristic
117C22—21no—
118C22—21no—
119C22—21no—
120C22C23×D16311yescharacteristic
121C4—21no—
122C4—22no—
123C4—22no—
124C4—3262no—
125C4—3261no—
126C4—3261no—
127C4—3261no—
128C4—3261no—
129C4—3262no—
130C4#1457969812yes—
131C2—41no—
132C2C2×#1457969811yescharacteristic
133C2#1910478211yescharacteristic
134C2#1910478311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D163
commutator, socle, cosocleC22×C163C24
FittingC22⋊Q8×C163C2
prime radicalC23×C163C23
hypercenterC22⋊Q8D163
hypocenterC163#541
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #19104733C2semidirect
4. #19104726C2semidirect
5. #19104726C2semidirect
6. #19104725C2semidirect
8. Q8×Dic163C2semidirect
9. #19104700C2semidirect
67. C163#541semidirect