Finite Group Databasebeta

← #23781882

Subgroups — #23781882

Order 10432.

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

normal subgroups only

This group has 124 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×#14579684C211yesmaximal, characteristic
2#19104724C211yesmaximal, characteristic, complemented
3D4×Dic163C211yesmaximal, characteristic, complemented
4Dic163⋊C8C211yesmaximal, characteristic, complemented
5#19104659C211yesmaximal, characteristic, complemented
6#19104657C211yesmaximal, characteristic, complemented
7C2×SD16×C163C211yesmaximal, characteristic, complemented
8C2×D652C2211yescharacteristic
9C22×Dic163—21no—
10#14579684—22no—
11C2×C163⋊C8C2211yescharacteristic
12C4⋊Dic163C2211yescharacteristic
13C22⋊Dic163—21no—
14(C2×D163)⋊C4—21no—
15(C2×D163)⋊C4—21no—
16C4×Dic163C2211yescharacteristic
17C2×Q8×C163C2211yescharacteristic
18C2×D4×C163C2211yescharacteristic
19SD16×C163—22no—
20C2×C8×C163C2211yescharacteristic
21C22×D163—21no—
22D652—21no—
23D652—21no—
24C2×Dic163—21no—
25C2×Dic163—42no—
26C2×Dic163D411yescharacteristic
27C2×Dic163D411yescharacteristic
28C163⋊C8—21no—
29C23×C163—21no—
30Q8×C163—21no—
31Q8×C163—21no—
32D4×C163—21no—
33D4×C163D412yes—
34C2×C4×C163—21no—
35C2×C4×C163C2311yescharacteristic
36C8×C163—21no—
37C22×C163—22no—
38C22×C163—41no—
39C22×C163—41no—
40C22×C163C2×D411yescharacteristic
41C2×D163—41no—
42C2×D163—41no—
43C2×D163—41no—
44C4×C163—41no—
45C4×C163C2×D411yescharacteristic
46C4×C163#4111yescharacteristic
47Dic163—21no—
48Dic163—21no—
49Dic163—41no—
50C2×C163—42no—
51C2×C163#12111yescharacteristic
52C2×C163#13511yescharacteristic
53C2×C163AGL(1,ℤ/8)11yescharacteristic
54D163—81no—
55C163#46311yescharacteristic, complemented, Sylow
56#463—1631nomaximal, Sylow
57C2×SD16D16311yescharacteristic, complemented
58C2×D8—1631no—
59#124—1631no—
60C4×D4—1631no—
61C4⋊C8—1631no—
62#103—1631no—
63#102—1631no—
64C2×Q8C2×D16311yescharacteristic
65C2×D4—1631no—
66C2×D4C2×D16311yescharacteristic
67C22×C4—3261no—
68SD16—22no—
69D8—3262no—
70C2×C8—1631no—
71C2×C8C2×D16311yescharacteristic
72C4⋊C4—1631no—
73C22⋊C4—3261no—
74C22⋊C4—3261no—
75C22⋊C4—3261no—
76C42—1631no—
77C23—21no—
78C23—3261no—
79Q8—21no—
80Q8—21no—
81D4—21no—
82D4—3261no—
83D4—3261no—
84D4C22⋊D16312yes—
85C2×C4—21no—
86C2×C4—3261no—
87C2×C4—6522no—
88C2×C4—1631no—
89C2×C4—1631no—
90C2×C4C22×D16311yescharacteristic
91C8—21no—
92C8—3261no—
93C22—22no—
94C22—41no—
95C22—41no—
96C22—6521no—
97C22—6521no—
98C22—6521no—
99C22D4×D16311yescharacteristic
100C4—41no—
101C4—3261no—
102C4—3261no—
103C4—6521no—
104C4C2×C22⋊D16311yescharacteristic
105C4#1457969811yescharacteristic
106C2—42no—
107C2—13041no—
108C2#1910470711yescharacteristic
109C2#1910475611yescharacteristic
110C2#1910476211yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×SD16×C163C2
socleC22×C163C2×D4
prime radicalC2×#14579684C2
hypercenterC2×SD16D163
hypocenterC163#463
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
2. #19104724C2semidirect
3. D4×Dic163C2semidirect
4. Dic163⋊C8C2semidirect
5. #19104659C2semidirect
6. #19104657C2semidirect
7. C2×SD16×C163C2semidirect
55. C163#463semidirect
57. C2×SD16D163semidirect