Finite Group Databasebeta

← #23781784

Subgroups — #23781784

Order 10432.

104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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#19104755C211yesmaximal, characteristic
2#19104743C211yesmaximal, characteristic, complemented
3#19104742C211yesmaximal, characteristic, complemented
4#19104670C211yesmaximal, characteristic, complemented
5#19104663C211yesmaximal, characteristic, complemented
6#19104646C211yesmaximal, characteristic, complemented
7#104×C163C211yesmaximal, characteristic, complemented
8#14579699C2211yescharacteristic
9#14579689C411yescharacteristic, complemented
10#14579687C411yescharacteristic, complemented
11#14579686C411yescharacteristic, complemented
12#14579684C411yescharacteristic, complemented
13#14579683—21no—
14#14579683C2211yescharacteristic
15#14579682—21no—
16C2×C163⋊C8—21no—
17C2×C163⋊C8C2211yescharacteristic
18C2×C163⋊C8C2211yescharacteristic
19C8×D163—21no—
20#41×C163C2211yescharacteristic
21M16×C163C2211yescharacteristic
22C42×C163C2211yescharacteristic
23Dic326C2×C411yescharacteristic
24D652C2×C411yescharacteristic
25C22⋊D163—21no—
26C4×D163—21no—
27C163⋊C8—21no—
28C163⋊C8C2×C411yescharacteristic
29C163⋊C8C2×C411yescharacteristic
30C163⋊C8D411yescharacteristic
31C163⋊C8D411yescharacteristic
32Q8×C163C2×C411yescharacteristic
33D4×C163—21no—
34D4×C163C2×C411yescharacteristic
35C2×C4×C163—21no—
36C2×C4×C163—21no—
37C2×C4×C163C2311yescharacteristic
38C8×C163—21no—
39C22×C163—21no—
40C22×C163#4111yescharacteristic
41C2×D163—21no—
42C4×C163—21no—
43C4×C163—41no—
44C4×C163C22×C411yescharacteristic
45C4×C163C2×D411yescharacteristic
46Dic163—21no—
47C2×C163—21no—
48C2×C163—41no—
49C2×C163C4×D411yescharacteristic
50D163—41no—
51C163#44411yescharacteristic, complemented, Sylow
52#444—1631nomaximal, Sylow
53#135—1631no—
54#131—1631no—
55#131—1631no—
56#108—1631no—
57#104—1631no—
58#104D16311yescharacteristic, complemented
59#97—1631no—
60#41—1631no—
61#41C2×D16311yescharacteristic
62Q16—1631no—
63SD16—1631no—
64SD16—1631no—
65D8—1631no—
66M16—3261no—
67M16—3261no—
68M16—1631no—
69M16C2×D16311yescharacteristic
70C2×C8—3261no—
71C2×C8—3261no—
72C2×C8—1631no—
73C2×C8—1631no—
74C42C2×D16311yescharacteristic
75Q8—1631no—
76Q8C4×D16311yescharacteristic
77D4—21no—
78D4—3261no—
79D4—1631no—
80D4C4×D16311yescharacteristic
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—3261no—
84C2×C4C22×D16311yescharacteristic
85C8—21no—
86C8—3261no—
87C8—1631no—
88C8—1631no—
89C8—1631no—
90C8—1631no—
91C22—21no—
92C22—3261no—
93C22#1457969811yescharacteristic
94C4—21no—
95C4—41no—
96C4—3261no—
97C4C2×C4×D16311yescharacteristic
98C4D4×D16311yescharacteristic
99C2—21no—
100C2—41no—
101C2—6521no—
102C2(C22⋊D163)⋊C411yescharacteristic
subgroupG/H
centerC4D4×D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
Fitting#104×C163C2
socleC2×C163C4×D4
prime radical#19104755C2
cosocleC2×C4×C163C23
hypercenter#104D163
hypocenterC163#444
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #19104743C2semidirect
3. #19104742C2semidirect
4. #19104670C2semidirect
5. #19104663C2semidirect
6. #19104646C2semidirect
7. #104×C163C2semidirect
9. #14579689C4semidirect
10. #14579687C4semidirect
11. #14579686C4semidirect
12. #14579684C4semidirect
51. C163#444semidirect
58. #104D163semidirect