Finite Group Databasebeta

← #23781524

Subgroups — #23781524

Order 10432.

234 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 79 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×C4×D163C211yesmaximal, characteristic
2C2×Dic163⋊C4C212yesmaximal, complemented
3C2×(C2×D163)⋊C4C212yesmaximal
4C163⋊#95C211yesmaximal, characteristic, complemented
5#95×C163C211yesmaximal, characteristic, complemented
6C23×D163C2211yescharacteristic
7C22×Dic163C2212yes—
8C22×Dic163C2211yescharacteristic
9C2×C4×D163—24no—
10C2×C4×D163C414yescomplemented
11Dic163⋊C4—24no—
12(C2×D163)⋊C4—24no—
13C22×C4×C163C2212yes—
14C22×C4×C163C2211yescharacteristic
15C22×D163—22no—
16C22×D163—22no—
17C22×D163C2×C412yes—
18C22×D163D412yes—
19C22×D163Q812yes—
20C2×Dic163—22no—
21C2×Dic163—22no—
22C2×Dic163—22no—
23C2×Dic163C2×C412yes—
24C2×Dic163D414yes—
25C4×D163—28no—
26C23×C163C2311yescharacteristic
27C2×C4×C163—22no—
28C2×C4×C163—22no—
29C2×C4×C163—22no—
30C2×C4×C163—22no—
31C2×C4×C163C2×C412yes—
32C22×C163C22×C411yescharacteristic
33C22×C163C2×D412yes—
34C22×C163C2×D411yescharacteristic
35C22×C163C2×Q811yescharacteristic
36C22×C163#4112yes—
37C2×D163—22no—
38C2×D163—22no—
39C2×D163—24no—
40C2×D163—24no—
41C2×D163C4⋊C414yescomplemented
42C4×C163—22no—
43C4×C163—42no—
44Dic163—42no—
45Dic163C22⋊C414yescomplemented
46C2×C163C2×C22⋊C411yescharacteristic
47C2×C163C2×C4⋊C411yescharacteristic
48C2×C163#11711yescharacteristic
49C2×C163#12112yes—
50C2×C163C22⋊Q812yes—
51D163—24no—
52C163#38011yescharacteristic, complemented, Sylow
53#380—1631nomaximal, Sylow
54C23×C4—1631no—
55C2×C4⋊C4—1632no—
56C2×C22⋊C4—1632no—
57#95—1631no—
58#95D16311yescharacteristic, complemented
59C24—1631no—
60C22×C4—3264no—
61C22×C4—1632no—
62C22×C4—1634no—
63C22×C4—1631no—
64C22×C4C2×D16312yes—
65C22×C4C2×D16311yescharacteristic
66C4⋊C4—3264no—
67C22⋊C4—3264no—
68C23—3262no—
69C23—3262no—
70C23—1632no—
71C23—1632no—
72C23—1632no—
73C23C22×D16311yescharacteristic
74C2×C4—22no—
75C2×C4—22no—
76C2×C4—22no—
77C2×C4—22no—
78C2×C4—3268no—
79C2×C4—3262no—
80C2×C4—3262no—
81C2×C4—3262no—
82C2×C4—1632no—
83C2×C4—1634no—
84C2×C4C4×D16312yes—
85C22—3262no—
86C22—3262no—
87C22—3264no—
88C22—3264no—
89C22—1634no—
90C22C2×C4×D16311yescharacteristic
91C22D4×D16312yes—
92C22D4×D16311yescharacteristic
93C22Q8×D16311yescharacteristic
94C22#1457969912yes—
95C4—22no—
96C4—42no—
97C4—6522no—
98C4—1634no—
99C2—3264no—
100C2C22⋊C4×D16311yescharacteristic
101C2C4⋊C4×D16311yescharacteristic
102C2#1910469211yescharacteristic
103C2#1910470812yes—
104C2#1910471312yes—
subgroupG/H
center, FrattiniC23C22×D163
commutatorC22×C163C22×C4
Fitting#95×C163C2
socle, cosocleC23×C163C23
prime radicalC23×D163C22
hypercenter#95D163
hypocenterC163#380
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×Dic163⋊C4C2semidirect
4. C163⋊#95C2semidirect
5. #95×C163C2semidirect
10. C2×C4×D163C4semidirect
41. C2×D163C4⋊C4semidirect
45. Dic163C22⋊C4semidirect
52. C163#380semidirect
58. #95D163semidirect