Finite Group Databasebeta

← #23781797

Subgroups — #23781797

Order 10432.

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

normal subgroups only

This group has 198 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×D4×D163C211yesmaximal, characteristic, complemented
2C2×#14579684C211yesmaximal, characteristic, complemented
3#19104706C211yesmaximal, characteristic, complemented
4#19104657C211yesmaximal, characteristic, complemented
5#19104656C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
7C2×D8×C163C211yesmaximal, characteristic, complemented
8C23×D163—21no—
9C2×D652C2211yescharacteristic
10C2×C22⋊D163—21no—
11C2×C22⋊D163—21no—
12D4×D163—22no—
13D4×D163—22no—
14C2×C4×D163C2211yescharacteristic
15#14579684—22no—
16C2×C163⋊C8C2211yescharacteristic, complemented
17C4⋊Dic163C2211yescharacteristic, complemented
18C22⋊Dic163—21no—
19C2×D4×C163C2211yescharacteristic
20C2×D4×C163C2211yescharacteristic, complemented
21D8×C163—22no—
22C2×C8×C163C2211yescharacteristic, complemented
23C22×D163—24no—
24C22×D163—21no—
25C22×D163—42no—
26C22×D163—42no—
27C22×D163D411yescharacteristic
28D652—21no—
29D652D412yescomplemented
30C22⋊D163—24no—
31C22⋊D163—42no—
32C2×Dic163—21no—
33C2×Dic163D411yescharacteristic
34C4×D163—21no—
35C4×D163—21no—
36C163⋊C8—21no—
37C23×C163—21no—
38C23×C163—21no—
39D4×C163—21no—
40D4×C163—21no—
41D4×C163—21no—
42D4×C163D412yescomplemented
43C2×C4×C163C2311yescharacteristic
44C8×C163—21no—
45C22×C163—22no—
46C22×C163—41no—
47C22×C163—41no—
48C22×C163—41no—
49C22×C163—41no—
50C22×C163—41no—
51C22×C163C2×D411yescharacteristic
52C2×D163—21no—
53C2×D163—21no—
54C2×D163—22no—
55C2×D163—48no—
56C2×D163—41no—
57C2×D163—41no—
58C2×D163D812yescomplemented
59C4×C163C2×D411yescharacteristic
60C4×C163C2×D411yescharacteristic
61Dic163—21no—
62Dic163—41no—
63C2×C163—42no—
64C2×C163—81no—
65C2×C163#12011yescharacteristic
66C2×C163C2×D811yescharacteristic
67C2×C163AGL(1,ℤ/8)11yescharacteristic
68D163—22no—
69D163—42no—
70C163#44711yescharacteristic, complemented, Sylow
71#447—1631nomaximal, Sylow
72C22×D4—1631no—
73C2×D8—1631no—
74C2×D8D16311yescharacteristic, complemented
75#121—1631no—
76#102—1631no—
77#102—1631no—
78C22⋊C8—1631no—
79C24—3261no—
80C2×D4—3262no—
81C2×D4—3262no—
82C2×D4—3261no—
83C2×D4—3261no—
84C2×D4—1631no—
85C2×D4C2×D16311yescharacteristic
86C2×D4C2×D16311yescharacteristic, complemented
87C22×C4—1631no—
88D8—22no—
89D8—3262no—
90C2×C8—1631no—
91C2×C8C2×D16311yescharacteristic, complemented
92C4⋊C4—1631no—
93C22⋊C4—3261no—
94C23—21no—
95C23—21no—
96C23—3264no—
97C23—3261no—
98C23—6522no—
99C23—6522no—
100C23—1631no—
101D4—21no—
102D4—21no—
103D4—21no—
104D4—3264no—
105D4—3261no—
106D4—6522no—
107D4—1632no—
108D4C22⋊D16312yescomplemented
109C2×C4—3261no—
110C2×C4—3261no—
111C2×C4—3261no—
112C2×C4—1631no—
113C2×C4C22×D16311yescharacteristic
114C8—21no—
115C8—3261no—
116C22—22no—
117C22—41no—
118C22—41no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—3261no—
123C22—3261no—
124C22—3262no—
125C22—6528no—
126C22—6521no—
127C22—6521no—
128C22—1632no—
129C22D4×D16311yescharacteristic
130C4—3261no—
131C4—6521no—
132C4D4×D16311yescharacteristic
133C4C2×C22⋊D16311yescharacteristic
134C2—42no—
135C2—81no—
136C2—3262no—
137C2—6522no—
138C2#1910470311yescharacteristic
139C2D8×D16311yescharacteristic
140C2#1910475911yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×D8×C163C2
socleC22×C163C2×D4
hypercenterC2×D8D163
hypocenterC163#447
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×D163C2semidirect
2. C2×#14579684C2semidirect
3. #19104706C2semidirect
4. #19104657C2semidirect
5. #19104656C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. C2×D8×C163C2semidirect
16. C2×C163⋊C8C22semidirect
17. C4⋊Dic163C22semidirect
20. C2×D4×C163C22semidirect
22. C2×C8×C163C22semidirect
29. D652D4semidirect
42. D4×C163D4semidirect
58. C2×D163D8semidirect
70. C163#447semidirect
74. C2×D8D163semidirect
86. C2×D4C2×D163semidirect
91. C2×C8C2×D163semidirect
108. D4C22⋊D163semidirect