Finite Group Databasebeta

← #23781910

Subgroups — #23781910

Order 10432.

120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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, complemented
2C2×#14579682C211yesmaximal, characteristic, complemented
3#19104715C211yesmaximal, characteristic, complemented
4#19104706C211yesmaximal, characteristic
5#19104668C211yesmaximal, characteristic, complemented
6#19104660C211yesmaximal, characteristic, complemented
7#102×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×C22⋊D163—21no—
10C2×C4×D163C2211yescharacteristic
11#14579687—22no—
12#14579682—22no—
13C2×C163⋊C8C2211yescharacteristic
14C4⋊Dic163—21no—
15C4⋊Dic163C2211yescharacteristic
16C22⋊Dic163—21no—
17(C2×D163)⋊C4—21no—
18C2×D4×C163C2211yescharacteristic
19C2×C8×C163C2211yescharacteristic
20C4⋊C4×C163C2211yescharacteristic
21C22×D163D411yescharacteristic
22Dic326—21no—
23Dic326—21no—
24C22⋊D163—42no—
25C2×Dic163—21no—
26C2×Dic163—21no—
27C2×Dic163D411yescharacteristic
28C4×D163—21no—
29C4×D163—21no—
30C163⋊C8D412yescomplemented
31C23×C163—21no—
32D4×C163—21no—
33D4×C163—21no—
34C2×C4×C163—21no—
35C2×C4×C163C2311yescharacteristic
36C8×C163—21no—
37C22×C163—41no—
38C22×C163—41no—
39C22×C163—41no—
40C22×C163C2×D411yescharacteristic
41C2×D163—21no—
42C2×D163—21no—
43C2×D163—21no—
44C4×C163—41no—
45C4×C163C2×D411yescharacteristic
46C4×C163#4111yescharacteristic
47Dic163—21no—
48Dic163—41no—
49Dic163—41no—
50C2×C163—81no—
51C2×C163#12111yescharacteristic
52C2×C163AGL(1,ℤ/8)11yescharacteristic
53C2×C163#13711yescharacteristic
54D163—41no—
55C163#46811yescharacteristic, complemented, Sylow
56#468—1631nomaximal, Sylow
57C2×SD16—1631no—
58C2×M16—1631no—
59C22⋊Q8—1631no—
60#121—1631no—
61#107—1631no—
62#103—1631no—
63#102D16311yescharacteristic, complemented
64C2×Q8—1631no—
65C2×D4—3261no—
66C2×D4C2×D16311yescharacteristic
67C22×C4—1631no—
68SD16—3262no—
69M16—3262no—
70C2×C8—1631no—
71C2×C8C2×D16311yescharacteristic
72C4⋊C4—3261no—
73C4⋊C4—1631no—
74C4⋊C4C2×D16311yescharacteristic
75C22⋊C4—3261no—
76C22⋊C4—3261no—
77C23—21no—
78C23—1631no—
79Q8—3261no—
80Q8—3261no—
81D4—21no—
82D4—21no—
83D4—6522no—
84C2×C4—21no—
85C2×C4—3261no—
86C2×C4—3261no—
87C2×C4—3261no—
88C2×C4—3261no—
89C2×C4—1631no—
90C2×C4C22×D16311yescharacteristic
91C8—21no—
92C8—1632no—
93C22—41no—
94C22—41no—
95C22—41no—
96C22—3261no—
97C22—3261no—
98C22—3261no—
99C22D4×D16311yescharacteristic
100C4—41no—
101C4—3261no—
102C4—6521no—
103C4—6521no—
104C4D4×D16311yescharacteristic
105C4#1457969911yescharacteristic
106C2—81no—
107C2—6521no—
108C2#1910470811yescharacteristic
109C2#1910475911yescharacteristic
110C2#1910476411yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
prime radical#19104706C2
hypercenter#102D163
hypocenterC163#468
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. C2×#14579687C2semidirect
2. C2×#14579682C2semidirect
3. #19104715C2semidirect
5. #19104668C2semidirect
6. #19104660C2semidirect
7. #102×C163C2semidirect
30. C163⋊C8D4semidirect
55. C163#468semidirect
63. #102D163semidirect