Finite Group Databasebeta

← #23781939

Subgroups — #23781939

Order 10432.

100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 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#19104768C211yesmaximal, characteristic
2#19104766C211yesmaximal, characteristic
3C2×#14579689C211yesmaximal, characteristic, complemented
4#19104743C211yesmaximal, characteristic
5#19104670C211yesmaximal, characteristic, complemented
6#19104653C211yesmaximal, characteristic, complemented
7#101×C163C211yesmaximal, characteristic, complemented
8#14579699C2211yescharacteristic
9C2×Dic326C2211yescharacteristic
10Dic652—21no—
11#14579689—21no—
12#14579689—21no—
13#14579689—21no—
14#14579688—21no—
15#14579686—21no—
16#14579683C2211yescharacteristic
17#14579682—21no—
18C2×C163⋊C8C2211yescharacteristic
19C8×D163—21no—
20C2×Q8×C163C2211yescharacteristic
21M16×C163C2211yescharacteristic
22M16×C163C2211yescharacteristic
23Dic326—21no—
24Dic326—21no—
25Dic326D411yescharacteristic
26D652D411yescharacteristic
27C22⋊D163—21no—
28C2×Dic163—21no—
29C4×D163—21no—
30C163⋊C8—21no—
31C163⋊C8D411yescharacteristic
32C163⋊C8D411yescharacteristic
33Q8×C163—21no—
34Q8×C163—21no—
35C2×C4×C163—21no—
36C2×C4×C163C2311yescharacteristic
37C8×C163—21no—
38C8×C163—21no—
39C22×C163#4111yescharacteristic
40C2×D163—21no—
41C4×C163—41no—
42C4×C163C2×D411yescharacteristic
43C4×C163C2×D411yescharacteristic
44Dic163—21no—
45Dic163—41no—
46C2×C163—21no—
47C2×C163#12111yescharacteristic
48D163—41no—
49C163#47311yescharacteristic, complemented, Sylow
50#473—1631nomaximal, Sylow
51#137—1631no—
52#137—1631no—
53C2×Q16—1631no—
54#131—1631no—
55#108—1631no—
56#101—1631no—
57#101D16311yescharacteristic, complemented
58#41—1631no—
59C2×Q8—1631no—
60C2×Q8C2×D16311yescharacteristic
61Q16—3261no—
62Q16—3261no—
63Q16—3261no—
64Q16—3261no—
65SD16—3261no—
66SD16—3261no—
67M16—3261no—
68M16—1631no—
69M16C2×D16311yescharacteristic
70M16C2×D16311yescharacteristic
71C2×C8—3261no—
72C2×C8—1631no—
73Q8—21no—
74Q8—21no—
75Q8—3261no—
76Q8—3261no—
77Q8—1631no—
78D4—3261no—
79D4—1631no—
80C2×C4—21no—
81C2×C4—3261no—
82C2×C4—3261no—
83C2×C4C22×D16311yescharacteristic
84C8—21no—
85C8—21no—
86C8—3261no—
87C8—1631no—
88C8—1631no—
89C22—3261no—
90C22#1457969911yescharacteristic
91C4—41no—
92C4—3261no—
93C4—6521no—
94C4D4×D16311yescharacteristic
95C4D4×D16311yescharacteristic
96C2—21no—
97C2—6521no—
98C2#1910470811yescharacteristic
subgroupG/H
centerC2#19104708
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#101×C163C2
socleC2×C163#121
prime radical#14579699C22
hypercenter#101D163
hypocenterC163#473
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
3. C2×#14579689C2semidirect
5. #19104670C2semidirect
6. #19104653C2semidirect
7. #101×C163C2semidirect
49. C163#473semidirect
57. #101D163semidirect