Finite Group Databasebeta

← #23781805

Subgroups — #23781805

Order 10432.

158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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×Q8×D163C211yesmaximal, characteristic, complemented
2C2×#14579688C211yesmaximal, characteristic, complemented
3C2×#14579686C211yesmaximal, characteristic, complemented
4#19104710C211yesmaximal, characteristic
5#19104658C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
7#103×C163C211yesmaximal, characteristic, complemented
8C2×Dic326—21no—
9C2×Dic326C2211yescharacteristic
10Q8×D163—22no—
11Q8×D163—22no—
12C2×D652—21no—
13C2×D652C2211yescharacteristic
14C2×C4×D163—21no—
15C2×C4×D163C2211yescharacteristic
16#14579688—22no—
17#14579686—22no—
18C2×C163⋊C8C2211yescharacteristic
19(C2×D163)⋊C4—21no—
20C2×Q8×C163C2211yescharacteristic
21C2×C8×C163C2211yescharacteristic
22C4⋊C4×C163C2211yescharacteristic
23C22×D163—21no—
24C22×D163D411yescharacteristic
25Dic326—24no—
26Dic326—21no—
27Dic326D412yescomplemented
28D652—21no—
29D652—21no—
30D652—42no—
31C2×Dic163—21no—
32C2×Dic163D411yescharacteristic
33C4×D163—24no—
34C4×D163—21no—
35C4×D163—21no—
36C163⋊C8—21no—
37Q8×C163—21no—
38Q8×C163D412yescomplemented
39C2×C4×C163—21no—
40C2×C4×C163—21no—
41C2×C4×C163C2311yescharacteristic
42C8×C163—21no—
43C22×C163C2×D411yescharacteristic
44C2×D163—21no—
45C2×D163—21no—
46C2×D163—41no—
47C2×D163—41no—
48C2×D163—41no—
49C2×D163SD1612yescomplemented
50C4×C163—22no—
51C4×C163—41no—
52C4×C163C2×D411yescharacteristic
53C4×C163C2×D411yescharacteristic
54Dic163—22no—
55Dic163—21no—
56C2×C163#12011yescharacteristic
57C2×C163C2×SD1611yescharacteristic
58C2×C163#13711yescharacteristic
59D163—22no—
60D163—81no—
61C163#44811yescharacteristic, complemented, Sylow
62#448—1631nomaximal, Sylow
63C22×Q8—1631no—
64C2×SD16—1631no—
65C2×SD16—1631no—
66#121—1631no—
67#103—1631no—
68#103D16311yescharacteristic, complemented
69C22⋊C8—1631no—
70C2×Q8—3261no—
71C2×Q8—3262no—
72C2×Q8—3262no—
73C2×Q8—1631no—
74C2×Q8C2×D16311yescharacteristic
75C2×D4—3261no—
76C2×D4—1631no—
77C22×C4—3261no—
78C22×C4—1631no—
79SD16—3262no—
80SD16—3262no—
81C2×C8—1631no—
82C2×C8C2×D16311yescharacteristic
83C4⋊C4C2×D16311yescharacteristic
84C22⋊C4—3261no—
85C23—3261no—
86C23—1631no—
87Q8—21no—
88Q8—3264no—
89Q8—3261no—
90Q8—1632no—
91Q8D65212yescomplemented
92D4—3261no—
93D4—3261no—
94D4—6522no—
95C2×C4—21no—
96C2×C4—21no—
97C2×C4—3264no—
98C2×C4—3261no—
99C2×C4—3261no—
100C2×C4—3261no—
101C2×C4—1631no—
102C2×C4C22×D16311yescharacteristic
103C8—21no—
104C8—3261no—
105C22—3261no—
106C22—3261no—
107C22—6521no—
108C22—6521no—
109C22—6521no—
110C22—1632no—
111C22D4×D16311yescharacteristic
112C4—22no—
113C4—41no—
114C4—3262no—
115C4—3261no—
116C4D4×D16311yescharacteristic
117C4C2×D65211yescharacteristic
118C2—13041no—
119C2—3262no—
120C2#1910470511yescharacteristic
121C2SD16×D16311yescharacteristic
122C2#1910476711yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#103×C163C2
socleC22×C163C2×D4
prime radical#19104710C2
hypercenter#103D163
hypocenterC163#448
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
1. C2×Q8×D163C2semidirect
2. C2×#14579688C2semidirect
3. C2×#14579686C2semidirect
5. #19104658C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. #103×C163C2semidirect
27. Dic326D4semidirect
38. Q8×C163D4semidirect
49. C2×D163SD16semidirect
61. C163#448semidirect
68. #103D163semidirect
91. Q8D652semidirect