Finite Group Databasebeta

← #23781869

Subgroups — #23781869

Order 10432.

120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#14579688C211yesmaximal, characteristic
2C2×#14579686C211yesmaximal, characteristic
3#19104733C211yesmaximal, characteristic, complemented
4#19104697C211yesmaximal, characteristic
5Dic163⋊C8C211yesmaximal, characteristic, complemented
6#19104658C211yesmaximal, characteristic, complemented
7#103×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×D652C2211yescharacteristic
10C2×C4×D163—21no—
11#14579688—22no—
12#14579686—22no—
13C2×C163⋊C8C2211yescharacteristic
14Dic163⋊C4—21no—
15Dic163⋊C4—21no—
16(C2×D163)⋊C4—21no—
17C4×Dic163C2211yescharacteristic
18C2×Q8×C163C2211yescharacteristic
19C2×C8×C163C2211yescharacteristic
20C4⋊C4×C163C2211yescharacteristic
21C22×D163—21no—
22Dic326—21no—
23Dic326—21no—
24D652—21no—
25D652D412yes—
26C2×Dic163—21no—
27C2×Dic163D411yescharacteristic
28C2×Dic163D411yescharacteristic
29C4×D163—42no—
30C163⋊C8—21no—
31Q8×C163—21no—
32Q8×C163—21no—
33C2×C4×C163—21no—
34C2×C4×C163—21no—
35C2×C4×C163C2311yescharacteristic
36C8×C163—21no—
37C22×C163C2×D411yescharacteristic
38C2×D163—22no—
39C2×D163—41no—
40C2×D163—41no—
41C4×C163—41no—
42C4×C163—41no—
43C4×C163C2×D411yescharacteristic
44C4×C163#4111yescharacteristic
45Dic163—21no—
46Dic163—41no—
47Dic163SD1612yescomplemented
48C2×C163#12111yescharacteristic
49C2×C163C2×SD1611yescharacteristic
50C2×C163#13711yescharacteristic
51D163—42no—
52C163#46111yescharacteristic, complemented, Sylow
53#461—1631nomaximal, Sylow
54C2×SD16—1631no—
55C2×SD16—1631no—
56C4⋊Q8—1631no—
57C4×D4—1631no—
58C4⋊C8—1631no—
59#103—1631no—
60#103D16311yescharacteristic, complemented
61C2×Q8—1631no—
62C2×Q8C2×D16311yescharacteristic
63C2×D4—1631no—
64C22×C4—3261no—
65SD16—3262no—
66SD16—3262no—
67C2×C8—1631no—
68C2×C8C2×D16311yescharacteristic
69C4⋊C4—3261no—
70C4⋊C4—3261no—
71C4⋊C4C2×D16311yescharacteristic
72C22⋊C4—3261no—
73C42—1631no—
74C23—3261no—
75Q8—21no—
76Q8—21no—
77Q8—3261no—
78Q8—3261no—
79D4—3261no—
80D4—1632no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—3261no—
84C2×C4—6522no—
85C2×C4—1631no—
86C2×C4—1631no—
87C2×C4C22×D16311yescharacteristic
88C8—21no—
89C8—3261no—
90C22—3262no—
91C22—6521no—
92C22—6521no—
93C22D4×D16311yescharacteristic
94C4—41no—
95C4—41no—
96C4—3261no—
97C4—6521no—
98C4—1632no—
99C4D4×D16311yescharacteristic
100C4#1457969911yescharacteristic
101C2—6522no—
102C2#1910470811yescharacteristic
103C2SD16×D16311yescharacteristic
104C2#1910476711yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#103×C163C2
socleC22×C163C2×D4
prime radicalC2×D652C22
hypercenter#103D163
hypocenterC163#461
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #19104733C2semidirect
5. Dic163⋊C8C2semidirect
6. #19104658C2semidirect
7. #103×C163C2semidirect
47. Dic163SD16semidirect
52. C163#461semidirect
60. #103D163semidirect