Finite Group Databasebeta

← #23781802

Subgroups — #23781802

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×#14579687C211yesmaximal, characteristic, complemented
3#19104706C211yesmaximal, characteristic
4#19104660C211yesmaximal, characteristic, complemented
5#19104659C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
7C2×SD16×C163C211yesmaximal, characteristic, complemented
8C2×Dic326—21no—
9C2×Dic326C2211yescharacteristic
10Q8×D163—22no—
11Q8×D163—22no—
12C2×C22⋊D163—21no—
13C2×C4×D163—21no—
14C2×C4×D163C2211yescharacteristic
15#14579687—22no—
16C2×C163⋊C8C2211yescharacteristic
17C4⋊Dic163C2211yescharacteristic
18C22⋊Dic163—21no—
19C2×Q8×C163C2211yescharacteristic
20C2×D4×C163C2211yescharacteristic
21SD16×C163—22no—
22C2×C8×C163C2211yescharacteristic
23C22×D163D411yescharacteristic
24Dic326—24no—
25Dic326—21no—
26Dic326D412yescomplemented
27C22⋊D163—42no—
28C2×Dic163—21no—
29C2×Dic163—21no—
30C2×Dic163D411yescharacteristic
31C4×D163—24no—
32C4×D163—21no—
33C4×D163—21no—
34C163⋊C8—21no—
35C23×C163—21no—
36Q8×C163—21no—
37Q8×C163D412yescomplemented
38D4×C163—21no—
39D4×C163—21no—
40C2×C4×C163—21no—
41C2×C4×C163C2311yescharacteristic
42C8×C163—21no—
43C22×C163—41no—
44C22×C163—41no—
45C22×C163—41no—
46C22×C163C2×D411yescharacteristic
47C2×D163—21no—
48C2×D163—21no—
49C2×D163SD1612yescomplemented
50C4×C163—22no—
51C4×C163C2×D411yescharacteristic
52C4×C163C2×D411yescharacteristic
53Dic163—22no—
54Dic163—21no—
55Dic163—41no—
56C2×C163—81no—
57C2×C163#12011yescharacteristic
58C2×C163C2×SD1611yescharacteristic
59C2×C163#13711yescharacteristic
60D163—22no—
61C163#44811yescharacteristic, complemented, Sylow
62#448—1631nomaximal, Sylow
63C22×Q8—1631no—
64C2×SD16—1631no—
65C2×SD16D16311yescharacteristic, complemented
66#121—1631no—
67#103—1631no—
68#103—1631no—
69C22⋊C8—1631no—
70C2×Q8—3261no—
71C2×Q8—3262no—
72C2×Q8—3262no—
73C2×Q8—1631no—
74C2×Q8C2×D16311yescharacteristic
75C2×D4—3261no—
76C2×D4C2×D16311yescharacteristic
77C22×C4—3261no—
78C22×C4—1631no—
79SD16—22no—
80SD16—3262no—
81C2×C8—1631no—
82C2×C8C2×D16311yescharacteristic
83C4⋊C4—1631no—
84C22⋊C4—3261no—
85C23—21no—
86C23—1631no—
87Q8—21no—
88Q8—3264no—
89Q8—3261no—
90Q8—1632no—
91Q8C22⋊D16312yescomplemented
92D4—21no—
93D4—21no—
94D4—6522no—
95C2×C4—21no—
96C2×C4—3264no—
97C2×C4—3261no—
98C2×C4—3261no—
99C2×C4—3261no—
100C2×C4—3261no—
101C2×C4—1631no—
102C2×C4C22×D16311yescharacteristic
103C8—21no—
104C8—3261no—
105C22—41no—
106C22—41no—
107C22—41no—
108C22—3261no—
109C22—3261no—
110C22—1632no—
111C22D4×D16311yescharacteristic
112C4—22no—
113C4—3262no—
114C4—3261no—
115C4—6521no—
116C4D4×D16311yescharacteristic
117C4C2×C22⋊D16311yescharacteristic
118C2—81no—
119C2—3262no—
120C2#1910470311yescharacteristic
121C2SD16×D16311yescharacteristic
122C2#1910476411yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×SD16×C163C2
socleC22×C163C2×D4
prime radical#19104706C2
hypercenterC2×SD16D163
hypocenterC163#448
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
1. C2×Q8×D163C2semidirect
2. C2×#14579687C2semidirect
4. #19104660C2semidirect
5. #19104659C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. C2×SD16×C163C2semidirect
26. Dic326D4semidirect
37. Q8×C163D4semidirect
49. C2×D163SD16semidirect
61. C163#448semidirect
65. C2×SD16D163semidirect
91. Q8C22⋊D163semidirect