Finite Group Databasebeta

← #23781931

Subgroups — #23781931

Order 10432.

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

normal subgroups only

This group has 104 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#19104766C211yesmaximal, characteristic, complemented
2#19104763C211yesmaximal, characteristic
3C2×#14579686C211yesmaximal, characteristic, complemented
4#19104743C211yesmaximal, characteristic, complemented
5#19104670C211yesmaximal, characteristic, complemented
6#19104651C211yesmaximal, characteristic, complemented
7#101×C163C211yesmaximal, characteristic, complemented
8#14579699C2211yescharacteristic
9C2×D652C2211yescharacteristic
10#14579689—21no—
11#14579688—21no—
12#14579686—21no—
13#14579686—21no—
14#14579686—21no—
15D1304—21no—
16#14579683C2211yescharacteristic
17#14579682—21no—
18C2×C163⋊C8C2211yescharacteristic
19C8×D163—21no—
20C2×Q8×C163C2211yescharacteristic
21M16×C163C2211yescharacteristic
22M16×C163C2211yescharacteristic
23C22×D163—21no—
24Dic326D411yescharacteristic
25D652—21no—
26D652—21no—
27D652D411yescharacteristic
28C22⋊D163—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—
41C2×D163—41no—
42C2×D163—81no—
43C4×C163—41no—
44C4×C163C2×D411yescharacteristic
45C4×C163C2×D411yescharacteristic
46Dic163—21no—
47C2×C163—21no—
48C2×C163#12111yescharacteristic
49D163—41no—
50D163—81no—
51C163#47111yescharacteristic, complemented, Sylow
52#471—1631nomaximal, Sylow
53#137—1631no—
54AGL(1,ℤ/8)—1631no—
55C2×SD16—1631no—
56#131—1631no—
57#108—1631no—
58#101D16311yescharacteristic, complemented
59#100—1631no—
60#41—1631no—
61C2×Q8C2×D16311yescharacteristic
62C2×D4—1631no—
63Q16—3261no—
64SD16—3261no—
65SD16—3261no—
66SD16—3261no—
67SD16—3261no—
68D8—3261no—
69M16—3261no—
70M16—1631no—
71M16C2×D16311yescharacteristic
72M16C2×D16311yescharacteristic
73C2×C8—3261no—
74C2×C8—1631no—
75C23—3261no—
76Q8—21no—
77Q8—21no—
78Q8—1631no—
79D4—3261no—
80D4—3261no—
81D4—3261no—
82D4—1631no—
83C2×C4—21no—
84C2×C4—3261no—
85C2×C4C22×D16311yescharacteristic
86C8—21no—
87C8—21no—
88C8—3261no—
89C8—1631no—
90C8—1631no—
91C22—13041no—
92C22—3261no—
93C22—6521no—
94C22#1457969911yescharacteristic
95C4—41no—
96C4—3261no—
97C4D4×D16311yescharacteristic
98C4D4×D16311yescharacteristic
99C2—21no—
100C2—13041no—
101C2—6521no—
102C2#1910470811yescharacteristic
subgroupG/H
centerC2#19104708
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#101×C163C2
socleC2×C163#121
prime radical#19104763C2
hypercenter#101D163
hypocenterC163#471
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
1. #19104766C2semidirect
3. C2×#14579686C2semidirect
4. #19104743C2semidirect
5. #19104670C2semidirect
6. #19104651C2semidirect
7. #101×C163C2semidirect
51. C163#471semidirect
58. #101D163semidirect