Finite Group Databasebeta

← #23781934

Subgroups — #23781934

Order 10432.

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

normal subgroups only

This group has 108 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#19104763C211yesmaximal, characteristic, complemented
2#19104761C211yesmaximal, characteristic, complemented
3C2×#14579684C211yesmaximal, characteristic, complemented
4#19104743C211yesmaximal, characteristic, complemented
5#19104670C211yesmaximal, characteristic, complemented
6#19104651C211yesmaximal, characteristic, complemented
7#100×C163C211yesmaximal, characteristic, complemented
8#14579699C2211yescharacteristic
9C2×D652C2211yescharacteristic
10#14579688—21no—
11#14579687—21no—
12D1304—21no—
13#14579684—21no—
14#14579684—21no—
15#14579684—21no—
16#14579683C2211yescharacteristic
17#14579682—21no—
18C2×C163⋊C8C2211yescharacteristic
19C8×D163—21no—
20C2×D4×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
33C23×C163—21no—
34D4×C163—21no—
35D4×C163—21no—
36C2×C4×C163C2311yescharacteristic
37C8×C163—21no—
38C8×C163—21no—
39C22×C163—41no—
40C22×C163—81no—
41C22×C163#4111yescharacteristic
42C2×D163—21no—
43C2×D163—41no—
44C2×D163—81no—
45C4×C163C2×D411yescharacteristic
46C4×C163C2×D411yescharacteristic
47Dic163—21no—
48C2×C163—21no—
49C2×C163—81no—
50C2×C163#12111yescharacteristic
51D163—41no—
52D163—81no—
53C163#47211yescharacteristic, complemented, Sylow
54#472—1631nomaximal, Sylow
55AGL(1,ℤ/8)—1631no—
56AGL(1,ℤ/8)—1631no—
57C2×D8—1631no—
58#131—1631no—
59#108—1631no—
60#100—1631no—
61#100D16311yescharacteristic, complemented
62#41—1631no—
63C2×D4—1631no—
64C2×D4C2×D16311yescharacteristic
65SD16—3261no—
66SD16—3261no—
67D8—3261no—
68D8—3261no—
69D8—3261no—
70D8—3261no—
71M16—3261no—
72M16—1631no—
73M16C2×D16311yescharacteristic
74M16C2×D16311yescharacteristic
75C2×C8—3261no—
76C2×C8—1631no—
77C23—21no—
78C23—3261no—
79Q8—1631no—
80D4—21no—
81D4—21no—
82D4—3261no—
83D4—3261no—
84D4—3261no—
85D4—1631no—
86C2×C4—3261no—
87C2×C4C22×D16311yescharacteristic
88C8—21no—
89C8—21no—
90C8—3261no—
91C8—1631no—
92C8—1631no—
93C22—41no—
94C22—81no—
95C22—13041no—
96C22—3261no—
97C22—6521no—
98C22#1457969911yescharacteristic
99C4—3261no—
100C4D4×D16311yescharacteristic
101C4D4×D16311yescharacteristic
102C2—21no—
103C2—81no—
104C2—13041no—
105C2—6521no—
106C2#1910470811yescharacteristic
subgroupG/H
centerC2#19104708
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#100×C163C2
socleC2×C163#121
hypercenter#100D163
hypocenterC163#472
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #19104763C2semidirect
2. #19104761C2semidirect
3. C2×#14579684C2semidirect
4. #19104743C2semidirect
5. #19104670C2semidirect
6. #19104651C2semidirect
7. #100×C163C2semidirect
53. C163#472semidirect
61. #100D163semidirect