Finite Group Databasebeta

← #23781600

Subgroups — #23781600

Order 10432.

186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 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×Dic163⋊C4C212yesmaximal, complemented
2C2×(C2×D163)⋊C4C212yesmaximal
3C2×(C2×D163)⋊C4C211yesmaximal, characteristic
4C163⋊#95C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×C163C211yesmaximal, characteristic, complemented
6C23×D163C2211yescharacteristic
7C22×Dic163C2211yescharacteristic
8C22×Dic163C2212yes—
9Dic163⋊C4—24no—
10(C2×D163)⋊C4—24no—
11(C2×D163)⋊C4—22no—
12C22×C4×C163C2212yes—
13C22×C4×C163C2211yescharacteristic
14C4⋊C4×C163—22no—
15C22×D163—22no—
16C22×D163—21no—
17C22×D163—22no—
18C22×D163—21no—
19C22×D163Q812yes—
20C2×Dic163—22no—
21C2×Dic163—22no—
22C2×Dic163—21no—
23C2×Dic163—22no—
24C2×Dic163D414yes—
25C23×C163C2311yescharacteristic
26C2×C4×C163—22no—
27C2×C4×C163—22no—
28C2×C4×C163—22no—
29C2×C4×C163—22no—
30C2×C4×C163D412yes—
31C22×C163C2×D412yes—
32C22×C163C2×D411yescharacteristic
33C22×C163C2×Q811yescharacteristic
34C22×C163#4112yes—
35C22×C163#4111yescharacteristic
36C2×D163—22no—
37C2×D163—24no—
38C2×D163—41no—
39C2×D163—42no—
40C2×D163—41no—
41C4×C163—22no—
42C4×C163—42no—
43Dic163—24no—
44Dic163—41no—
45C2×C163C22⋊Q811yescharacteristic
46C2×C163C22⋊Q812yes—
47C2×C163#12311yescharacteristic
48C2×C163#12312yes—
49C2×C163#12711yescharacteristic
50D163—42no—
51C163#39911yescharacteristic, complemented, Sylow
52#399—1631nomaximal, Sylow
53C2×C4⋊C4—1632no—
54C2×C4⋊C4D16311yescharacteristic, complemented
55C2×C22⋊C4—1632no—
56C2×C22⋊C4—1631no—
57#95—1631no—
58C24—1631no—
59C22×C4—1631no—
60C22×C4—1632no—
61C22×C4C2×D16312yes—
62C22×C4C2×D16311yescharacteristic
63C4⋊C4—22no—
64C4⋊C4—3264no—
65C22⋊C4—3264no—
66C22⋊C4—3262no—
67C23—3262no—
68C23—3261no—
69C23—3262no—
70C23—3261no—
71C23—1632no—
72C23C22×D16311yescharacteristic
73C2×C4—22no—
74C2×C4—22no—
75C2×C4—22no—
76C2×C4—22no—
77C2×C4—3262no—
78C2×C4—3262no—
79C2×C4—3262no—
80C2×C4—3261no—
81C2×C4—1634no—
82C2×C4C22⋊D16312yes—
83C22—3262no—
84C22—3264no—
85C22—6521no—
86C22—6522no—
87C22—6521no—
88C22D4×D16312yes—
89C22C2×C22⋊D16311yescharacteristic
90C22Q8×D16311yescharacteristic
91C22#1457969912yes—
92C22#1457970011yescharacteristic
93C4—22no—
94C4—42no—
95C4—3264no—
96C4—6521no—
97C2—6522no—
98C2#1910471111yescharacteristic
99C2#1910471312yes—
100C2#1910471811yescharacteristic
101C2#1910472012yes—
102C2#1910473111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D163
commutator, socle, cosocleC23×C163C23
FittingC2×C4⋊C4×C163C2
prime radicalC23×D163C22
hypercenterC2×C4⋊C4D163
hypocenterC163#399
LCSG ▷ C23×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×Dic163⋊C4C2semidirect
4. C163⋊#95C2semidirect
5. C2×C4⋊C4×C163C2semidirect
51. C163#399semidirect
54. C2×C4⋊C4D163semidirect