Finite Group Databasebeta

← #23781577

Subgroups — #23781577

Order 10432.

202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C22×Dic326C211yesmaximal, characteristic, complemented
2C2×C22⋊Dic163C212yesmaximal
3C163⋊#95C212yesmaximal, complemented
4C163⋊#95C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×C163C211yesmaximal, characteristic
6C2×Dic326—24no—
7C2×Dic326—22no—
8C22×Dic163C2212yes—
9C22×Dic163C2212yes—
10C22⋊Dic163—24no—
11C24×C163C2211yescharacteristic
12C22×C4×C163C2211yescharacteristic
13C22×C4×C163C2211yescharacteristic
14C22⋊C4×C163—22no—
15Dic326—28no—
16C2×Dic163—22no—
17C2×Dic163—22no—
18C2×Dic163—22no—
19C2×Dic163—22no—
20C2×Dic163—22no—
21C2×Dic163D414yes—
22C23×C163—21no—
23C23×C163—22no—
24C23×C163—22no—
25C23×C163—21no—
26C23×C163Q812yescomplemented
27C23×C163C2311yescharacteristic
28C2×C4×C163—22no—
29C2×C4×C163—21no—
30C2×C4×C163—22no—
31C2×C4×C163D412yes—
32C22×C163—24no—
33C22×C163—22no—
34C22×C163—41no—
35C22×C163—42no—
36C22×C163—41no—
37C22×C163C2×D412yes—
38C22×C163C2×D411yescharacteristic
39C22×C163C2×Q811yescharacteristic
40C22×C163#4112yes—
41C22×C163#4111yescharacteristic
42C4×C163—22no—
43C4×C163—41no—
44Dic163—24no—
45Dic163—42no—
46C2×C163—42no—
47C2×C163#12011yescharacteristic
48C2×C163C22⋊Q812yes—
49C2×C163C22⋊Q811yescharacteristic
50C2×C163#12412yes—
51C2×C163#12411yescharacteristic
52C163#39311yescharacteristic, complemented, Sylow
53#393—1631nomaximal, Sylow
54C22×Q8—1631no—
55C2×C22⋊C4—1632no—
56C2×C22⋊C4D16311yescharacteristic
57#95—1631no—
58#95—1632no—
59C24C2×D16311yescharacteristic
60C2×Q8—3264no—
61C2×Q8—3262no—
62C22×C4—1632no—
63C22×C4—1632no—
64C22×C4C2×D16311yescharacteristic
65C22×C4C2×D16311yescharacteristic
66C22⋊C4—22no—
67C22⋊C4—3264no—
68C23—22no—
69C23—21no—
70C23—22no—
71C23—21no—
72C23Dic32612yescomplemented
73C23C22×D16311yescharacteristic
74Q8—3268no—
75C2×C4—22no—
76C2×C4—21no—
77C2×C4—22no—
78C2×C4—3262no—
79C2×C4—3262no—
80C2×C4—3262no—
81C2×C4—3262no—
82C2×C4—3262no—
83C2×C4—1634no—
84C2×C4C22⋊D16312yes—
85C22—24no—
86C22—22no—
87C22—41no—
88C22—42no—
89C22—41no—
90C22D4×D16312yes—
91C22C2×C22⋊D16311yescharacteristic
92C22C2×Dic32611yescharacteristic
93C22#1457969812yes—
94C22#1457969911yescharacteristic
95C4—22no—
96C4—41no—
97C4—3264no—
98C4—6522no—
99C2—42no—
100C2#1910470311yescharacteristic
101C2#1910471212yes—
102C2#1910471411yescharacteristic
103C2#1910472112yes—
104C2#1910472211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D163
commutator, socle, cosocleC23×C163C23
FittingC2×C22⋊C4×C163C2
prime radicalC24×C163C22
hypercenterC2×C22⋊C4D163
hypocenterC163#393
LCSG ▷ C23×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×Dic326C2semidirect
3. C163⋊#95C2semidirect
4. C163⋊#95C2semidirect
26. C23×C163Q8semidirect
52. C163#393semidirect
72. C23Dic326semidirect