Finite Group Databasebeta

← #23781868

Subgroups — #23781868

Order 10432.

120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14579687C211yesmaximal, characteristic
2#19104733C211yesmaximal, characteristic, complemented
3D4×Dic163C211yesmaximal, characteristic
4Dic163⋊C8C211yesmaximal, characteristic, complemented
5#19104660C211yesmaximal, characteristic, complemented
6#19104659C211yesmaximal, characteristic, complemented
7C2×SD16×C163C211yesmaximal, characteristic
8C2×Dic326C2211yescharacteristic
9C22×Dic163—21no—
10#14579687—22no—
11C2×C163⋊C8C2211yescharacteristic
12C4⋊Dic163C2211yescharacteristic
13Dic163⋊C4—21no—
14Dic163⋊C4—21no—
15C22⋊Dic163—21no—
16C4×Dic163C2211yescharacteristic
17C2×Q8×C163C2211yescharacteristic
18C2×D4×C163C2211yescharacteristic
19SD16×C163—22no—
20C2×C8×C163C2211yescharacteristic
21Dic326—21no—
22Dic326—21no—
23C2×Dic163—21no—
24C2×Dic163—21no—
25C2×Dic163—42no—
26C2×Dic163D411yescharacteristic
27C2×Dic163D411yescharacteristic
28C163⋊C8—21no—
29C23×C163—21no—
30Q8×C163—21no—
31Q8×C163—21no—
32D4×C163—21no—
33D4×C163D412yes—
34C2×C4×C163—21no—
35C2×C4×C163C2311yescharacteristic
36C8×C163—21no—
37C22×C163—22no—
38C22×C163—41no—
39C22×C163—41no—
40C22×C163C2×D411yescharacteristic
41C4×C163—41no—
42C4×C163C2×D411yescharacteristic
43C4×C163#4111yescharacteristic
44Dic163—21no—
45Dic163—41no—
46Dic163—41no—
47Dic163SD1612yescomplemented
48C2×C163—42no—
49C2×C163#12111yescharacteristic
50C2×C163C2×SD1611yescharacteristic
51C2×C163#13711yescharacteristic
52C163#46111yescharacteristic, complemented, Sylow
53#461—1631nomaximal, Sylow
54C2×SD16—1631no—
55C2×SD16D16311yescharacteristic
56C4⋊Q8—1631no—
57C4×D4—1631no—
58C4⋊C8—1631no—
59#103—1631no—
60#103—1631no—
61C2×Q8—1631no—
62C2×Q8C2×D16311yescharacteristic
63C2×D4C2×D16311yescharacteristic
64C22×C4—3261no—
65SD16—22no—
66SD16—3262no—
67C2×C8—1631no—
68C2×C8C2×D16311yescharacteristic
69C4⋊C4—3261no—
70C4⋊C4—3261no—
71C4⋊C4—1631no—
72C22⋊C4—3261no—
73C42—1631no—
74C23—21no—
75Q8—21no—
76Q8—21no—
77Q8—3261no—
78Q8—3261no—
79D4—21no—
80D4C22⋊D16312yes—
81C2×C4—21no—
82C2×C4—3261no—
83C2×C4—3261no—
84C2×C4—6522no—
85C2×C4—1631no—
86C2×C4—1631no—
87C2×C4C22×D16311yescharacteristic
88C8—21no—
89C8—3261no—
90C22—22no—
91C22—41no—
92C22—41no—
93C22D4×D16311yescharacteristic
94C4—41no—
95C4—3261no—
96C4—6521no—
97C4—6521no—
98C4—1632no—
99C4C2×C22⋊D16311yescharacteristic
100C4#1457969811yescharacteristic
101C2—42no—
102C2#1910470711yescharacteristic
103C2SD16×D16311yescharacteristic
104C2#1910476411yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×SD16×C163C2
socleC22×C163C2×D4
prime radicalC2×D4×C163C22
hypercenterC2×SD16D163
hypocenterC163#461
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. #19104733C2semidirect
4. Dic163⋊C8C2semidirect
5. #19104660C2semidirect
6. #19104659C2semidirect
47. Dic163SD16semidirect
52. C163#461semidirect