Finite Group Databasebeta

← #23781591

Subgroups — #23781591

Order 10432.

170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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×(C2×D163)⋊C4C212yesmaximal
2C2×(C2×D163)⋊C4C211yesmaximal, characteristic
3C163⋊#95C212yesmaximal, complemented
4C163⋊#95C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×C163C211yesmaximal, characteristic, complemented
6C23×D163C2211yescharacteristic
7C22×Dic163C2212yes—
8C22×Dic163C2211yescharacteristic
9(C2×D163)⋊C4—24no—
10(C2×D163)⋊C4—22no—
11C22×C4×C163C2212yes—
12C22×C4×C163C2211yescharacteristic
13C4⋊C4×C163—22no—
14C22×D163—21no—
15C22×D163—21no—
16C22×D163—22no—
17C22×D163—22no—
18C22×D163D412yes—
19C2×Dic163—22no—
20C2×Dic163—21no—
21C2×Dic163—22no—
22C2×Dic163—22no—
23C2×Dic163—22no—
24C23×C163C2311yescharacteristic
25C2×C4×C163—22no—
26C2×C4×C163—22no—
27C2×C4×C163—22no—
28C2×C4×C163—22no—
29C2×C4×C163D412yes—
30C22×C163C2×D411yescharacteristic
31C22×C163C2×D411yescharacteristic
32C22×C163#4111yescharacteristic
33C22×C163#4112yes—
34C22×C163#4112yes—
35C2×D163—22no—
36C2×D163—24no—
37C2×D163—41no—
38C2×D163—41no—
39C2×D163—42no—
40C4×C163—22no—
41C4×C163—42no—
42Dic163—42no—
43Dic163—41no—
44C2×C163#12111yescharacteristic
45C2×C163#12311yescharacteristic
46C2×C163#12312yes—
47C2×C163#12411yescharacteristic
48C2×C163#12612yes—
49D163—42no—
50C163#39711yescharacteristic, complemented, Sylow
51#397—1631nomaximal, Sylow
52C2×C4⋊C4D16311yescharacteristic, complemented
53C2×C22⋊C4—1632no—
54C2×C22⋊C4—1631no—
55#95—1632no—
56#95—1631no—
57C24—1631no—
58C22×C4—1632no—
59C22×C4—1631no—
60C22×C4C2×D16312yes—
61C22×C4C2×D16311yescharacteristic
62C4⋊C4—22no—
63C22⋊C4—3264no—
64C22⋊C4—3262no—
65C23—3261no—
66C23—3261no—
67C23—3262no—
68C23—3262no—
69C23—1632no—
70C23C22×D16311yescharacteristic
71C2×C4—22no—
72C2×C4—22no—
73C2×C4—22no—
74C2×C4—22no—
75C2×C4—3262no—
76C2×C4—3261no—
77C2×C4—3262no—
78C2×C4—3262no—
79C2×C4—3262no—
80C2×C4C22⋊D16312yes—
81C22—3262no—
82C22—3264no—
83C22—6521no—
84C22—6521no—
85C22—6522no—
86C22D4×D16311yescharacteristic
87C22C2×C22⋊D16311yescharacteristic
88C22#1457969811yescharacteristic
89C22#1457969912yes—
90C22#1457970012yes—
91C4—22no—
92C4—42no—
93C4—6522no—
94C4—6521no—
95C2—6522no—
96C2#1910470611yescharacteristic
97C2#1910471811yescharacteristic
98C2#1910472012yes—
99C2#1910472411yescharacteristic
100C2#1910473012yes—
subgroupG/H
center, FrattiniC23C22×D163
commutator, socle, cosocleC23×C163C23
FittingC2×C4⋊C4×C163C2
prime radicalC23×D163C22
hypercenterC2×C4⋊C4D163
hypocenterC163#397
LCSG ▷ C23×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C163⋊#95C2semidirect
4. C163⋊#95C2semidirect
5. C2×C4⋊C4×C163C2semidirect
50. C163#397semidirect
52. C2×C4⋊C4D163semidirect