Finite Group Databasebeta

← #23781938

Subgroups — #23781938

Order 10432.

100 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 37 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
1#19104765C211yesmaximal, characteristic
2C2×#14579689C211yesmaximal, characteristic, complemented
3#19104742C211yesmaximal, characteristic
4#19104670C211yesmaximal, characteristic, complemented
5#19104654C211yesmaximal, characteristic, complemented
6#19104653C211yesmaximal, characteristic, complemented
7#137×C163C211yesmaximal, characteristic
8C2×Dic326C2211yescharacteristic
9#14579689—21no—
10#14579689—21no—
11#14579689—21no—
12#14579687—21no—
13#14579683—21no—
14#14579683C2211yescharacteristic
15#14579683C2211yescharacteristic
16C2×C163⋊C8—21no—
17C2×C163⋊C8C2211yescharacteristic
18#41×C163C2211yescharacteristic
19C2×Q8×C163C2211yescharacteristic
20Q16×C163—21no—
21SD16×C163—21no—
22M16×C163C2211yescharacteristic
23Dic326—21no—
24Dic326—21no—
25C2×Dic163—21no—
26C163⋊C8—21no—
27C163⋊C8—21no—
28C163⋊C8D411yescharacteristic
29C163⋊C8D411yescharacteristic
30Q8×C163—21no—
31Q8×C163—21no—
32Q8×C163D411yescharacteristic
33D4×C163—21no—
34D4×C163D411yescharacteristic
35C2×C4×C163—21no—
36C2×C4×C163—21no—
37C2×C4×C163C2311yescharacteristic
38C8×C163—21no—
39C22×C163—21no—
40C22×C163#4111yescharacteristic
41C4×C163—21no—
42C4×C163—41no—
43C4×C163C2×D411yescharacteristic
44C4×C163C2×D411yescharacteristic
45Dic163—41no—
46C2×C163—21no—
47C2×C163—41no—
48C2×C163#12111yescharacteristic
49C163#47311yescharacteristic, complemented, Sylow
50#473—1631nomaximal, Sylow
51#137—1631no—
52#137D16311yescharacteristic
53C2×Q16—1631no—
54#131—1631no—
55#108—1631no—
56#101—1631no—
57#101—1631no—
58#41C2×D16311yescharacteristic
59C2×Q8—1631no—
60C2×Q8C2×D16311yescharacteristic
61Q16—21no—
62Q16—3261no—
63Q16—3261no—
64Q16—3261no—
65SD16—21no—
66SD16—3261no—
67M16—3261no—
68M16—1631no—
69M16—1631no—
70M16C2×D16311yescharacteristic
71C2×C8—3261no—
72C2×C8—1631no—
73Q8—21no—
74Q8—21no—
75Q8—3261no—
76Q8—3261no—
77Q8C22⋊D16311yescharacteristic
78D4—21no—
79D4C22⋊D16311yescharacteristic
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3261no—
83C2×C4C22×D16311yescharacteristic
84C8—21no—
85C8—3261no—
86C8—3261no—
87C8—1631no—
88C8—1631no—
89C22—21no—
90C22#1457969811yescharacteristic
91C4—21no—
92C4—41no—
93C4—6521no—
94C4D4×D16311yescharacteristic
95C4C2×C22⋊D16311yescharacteristic
96C2—21no—
97C2—41no—
98C2#1910470711yescharacteristic
subgroupG/H
centerC2#19104707
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#137×C163C2
socleC2×C163#121
prime radical#41×C163C22
hypercenter#137D163
hypocenterC163#473
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. C2×#14579689C2semidirect
4. #19104670C2semidirect
5. #19104654C2semidirect
6. #19104653C2semidirect
49. C163#473semidirect