Finite Group Databasebeta

← #23781864

Subgroups — #23781864

Order 10432.

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

normal subgroups only

This group has 128 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, complemented
2C2×#14579687C211yesmaximal, characteristic, complemented
3#19104731C211yesmaximal, characteristic
4#19104700C211yesmaximal, characteristic, complemented
5Dic163⋊C8C211yesmaximal, characteristic, complemented
6#19104655C211yesmaximal, characteristic, complemented
7#102×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×D652C2211yescharacteristic
10C2×C22⋊D163—21no—
11C2×C22⋊D163—21no—
12#14579688—22no—
13#14579687—22no—
14C2×C163⋊C8C2211yescharacteristic
15Dic163⋊C4—21no—
16C4×Dic163—21no—
17C4×Dic163C2211yescharacteristic
18C2×D4×C163C2211yescharacteristic
19C2×C8×C163C2211yescharacteristic
20C4⋊C4×C163C2211yescharacteristic
21C22×D163—21no—
22Dic326—21no—
23Dic326D412yescomplemented
24D652—21no—
25D652—21no—
26C22⋊D163—42no—
27C22⋊D163—42no—
28C2×Dic163—21no—
29C2×Dic163D411yescharacteristic
30C2×Dic163D411yescharacteristic
31C163⋊C8—21no—
32C23×C163—21no—
33D4×C163—21no—
34D4×C163—21no—
35C2×C4×C163—21no—
36C2×C4×C163C2311yescharacteristic
37C8×C163—21no—
38C22×C163—41no—
39C22×C163—41no—
40C22×C163—41no—
41C22×C163C2×D411yescharacteristic
42C2×D163—41no—
43C2×D163—41no—
44C2×D163—41no—
45C4×C163—41no—
46C4×C163C2×D411yescharacteristic
47C4×C163#4111yescharacteristic
48Dic163—22no—
49Dic163—21no—
50Dic163SD1612yescomplemented
51C2×C163—81no—
52C2×C163#12111yescharacteristic
53C2×C163C2×SD1611yescharacteristic
54C2×C163AGL(1,ℤ/8)11yescharacteristic
55D163—81no—
56C163#46011yescharacteristic, complemented, Sylow
57#460—1631nomaximal, Sylow
58C2×SD16—1631no—
59C2×SD16—1631no—
60#127—1631no—
61C4×Q8—1631no—
62C4⋊C8—1631no—
63#102—1631no—
64#102D16311yescharacteristic, complemented
65C2×Q8—1631no—
66C2×D4—3261no—
67C2×D4—3261no—
68C2×D4—1631no—
69C2×D4C2×D16311yescharacteristic
70SD16—3262no—
71SD16—3262no—
72C2×C8—1631no—
73C2×C8C2×D16311yescharacteristic
74C4⋊C4—3261no—
75C4⋊C4C2×D16311yescharacteristic
76C42—3261no—
77C42—1631no—
78C23—21no—
79C23—3261no—
80Q8—3261no—
81Q8—1632no—
82D4—21no—
83D4—21no—
84D4—3261no—
85D4—3261no—
86D4—6522no—
87D4—6522no—
88C2×C4—21no—
89C2×C4—3261no—
90C2×C4—1631no—
91C2×C4—1631no—
92C2×C4C22×D16311yescharacteristic
93C8—21no—
94C8—3261no—
95C22—41no—
96C22—41no—
97C22—41no—
98C22—6521no—
99C22—6521no—
100C22—6521no—
101C22D4×D16311yescharacteristic
102C4—41no—
103C4—3262no—
104C4—3261no—
105C4—1632no—
106C4D4×D16311yescharacteristic
107C4#1457969911yescharacteristic
108C2—81no—
109C2—13041no—
110C2#1910470811yescharacteristic
111C2SD16×D16311yescharacteristic
112C2#1910475911yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
prime radical#19104731C2
hypercenter#102D163
hypocenterC163#460
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×#14579688C2semidirect
2. C2×#14579687C2semidirect
4. #19104700C2semidirect
5. Dic163⋊C8C2semidirect
6. #19104655C2semidirect
7. #102×C163C2semidirect
23. Dic326D4semidirect
50. Dic163SD16semidirect
56. C163#460semidirect
64. #102D163semidirect