Finite Group Databasebeta

← #23782219

Subgroups — #23782219

Order 10432.

222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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#19104734C211yesmaximal, characteristic, complemented
2#19104733C211yesmaximal, characteristic, complemented
3#19104725C212yesmaximal, complemented
4#19104715C211yesmaximal, characteristic
5#19104713C212yesmaximal
6#19104711C211yesmaximal, characteristic
7C4×Dic326C211yesmaximal, characteristic, complemented
8C4×Dic326C212yesmaximal, complemented
9#19104692C212yesmaximal
10C42×D163C211yesmaximal, characteristic
11C4×Q8×C163C211yesmaximal, characteristic, complemented
12C2×Dic326C2212yes—
13C2×Dic326C2211yescharacteristic
14C2×C4×D163C2211yescharacteristic
15C2×C4×D163C2211yescharacteristic
16C2×C4×D163C2211yescharacteristic
17C4⋊Dic163C2211yescharacteristic
18C4⋊Dic163C2212yes—
19Dic163⋊C4C2212yes—
20Dic163⋊C4C2212yes—
21Dic163⋊C4C2212yes—
22Dic163⋊C4C2212yes—
23Dic163⋊C4C2212yes—
24(C2×D163)⋊C4C2212yes—
25(C2×D163)⋊C4C2212yes—
26C4×Dic163C2211yescharacteristic
27C4×Dic163C2211yescharacteristic
28C4×Dic163C2211yescharacteristic
29C4×Dic163C2212yes—
30C2×Q8×C163C2211yescharacteristic
31C4⋊C4×C163C2212yes—
32C4⋊C4×C163C2211yescharacteristic
33C42×C163C2211yescharacteristic
34C42×C163C2212yes—
35C22×D163C2311yescharacteristic
36Dic326—22no—
37Dic326—24no—
38C2×Dic163C2311yescharacteristic
39C2×Dic163C2312yes—
40C2×Dic163C2312yes—
41C2×Dic163C2311yescharacteristic
42C2×Dic163C2311yescharacteristic
43C4×D163—22no—
44C4×D163—22no—
45C4×D163Q814yescomplemented
46Q8×C163—22no—
47C2×C4×C163C2311yescharacteristic
48C2×C4×C163C2312yes—
49C2×C4×C163C2312yes—
50C2×C4×C163C2311yescharacteristic
51C2×C4×C163C2311yescharacteristic
52C22×C163C2411yescharacteristic
53C2×D163—21no—
54C2×D163—21no—
55C2×D163C2×Q812yes—
56C4×C163—22no—
57C4×C163—21no—
58C4×C163—22no—
59C4×C163C2×Q812yes—
60C4×C163#4112yes—
61Dic163—21no—
62Dic163—22no—
63Dic163—22no—
64Dic163C2×Q812yes—
65Dic163#4112yes—
66C2×C163C22×Q811yescharacteristic
67C2×C163C2×#4111yescharacteristic
68C2×C163C2×#4111yescharacteristic
69D163—22no—
70C163#53311yescharacteristic, complemented, Sylow
71#533—1631nomaximal, Sylow
72C4⋊Q8—1631no—
73C4⋊Q8—1631no—
74#125—1632no—
75C22⋊Q8—1631no—
76C22⋊Q8—1632no—
77C22⋊Q8—1631no—
78C4×Q8—1632no—
79C4×Q8—1631no—
80C4×Q8D16311yescharacteristic, complemented
81#117—1632no—
82C2×C42—1631no—
83C2×Q8—1631no—
84C2×Q8—1632no—
85C2×Q8C2×D16311yescharacteristic
86C22×C4—1631no—
87C22×C4—1631no—
88C22×C4—1631no—
89C4⋊C4—1632no—
90C4⋊C4—1632no—
91C4⋊C4—1632no—
92C4⋊C4—1632no—
93C4⋊C4—1632no—
94C4⋊C4—1632no—
95C4⋊C4—1631no—
96C4⋊C4C2×D16312yes—
97C4⋊C4C2×D16311yescharacteristic
98C22⋊C4—1632no—
99C22⋊C4—1632no—
100C42—1631no—
101C42—1631no—
102C42—1631no—
103C42—1632no—
104C42C2×D16311yescharacteristic
105C42C2×D16312yes—
106C23—1631no—
107Q8—22no—
108Q8—3264no—
109Q8—3262no—
110C2×C4—3262no—
111C2×C4—3262no—
112C2×C4—1631no—
113C2×C4—1632no—
114C2×C4—1632no—
115C2×C4—1631no—
116C2×C4—1631no—
117C2×C4—1634no—
118C2×C4C22×D16311yescharacteristic
119C2×C4C22×D16312yes—
120C2×C4C22×D16312yes—
121C2×C4C22×D16311yescharacteristic
122C2×C4C22×D16311yescharacteristic
123C22—3261no—
124C22—3261no—
125C22—1632no—
126C22C23×D16311yescharacteristic
127C4—21no—
128C4—22no—
129C4—22no—
130C4—3262no—
131C4—3261no—
132C4—3262no—
133C4—1632no—
134C4—1632no—
135C4Q8×D16312yes—
136C4#1457969912yes—
137C2—3262no—
138C2C2×Q8×D16311yescharacteristic
139C2#41×D16311yescharacteristic
140C2C2×#1457969911yescharacteristic
subgroupG/H
centerC2×C4C22×D163
commutator, socle, cosocleC22×C163C24
FrattiniC22C23×D163
FittingC4×Q8×C163C2
prime radicalC22×D163C23
hypercenterC4×Q8D163
hypocenterC163#533
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #19104734C2semidirect
2. #19104733C2semidirect
3. #19104725C2semidirect
7. C4×Dic326C2semidirect
8. C4×Dic326C2semidirect
11. C4×Q8×C163C2semidirect
45. C4×D163Q8semidirect
70. C163#533semidirect
80. C4×Q8D163semidirect