Finite Group Databasebeta

← #23781785

Subgroups — #23781785

Order 10432.

104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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#19104741C211yesmaximal, characteristic, complemented
3#19104670C211yesmaximal, characteristic, complemented
4#19104662C211yesmaximal, characteristic, complemented
5#19104661C211yesmaximal, characteristic, complemented
6#19104645C211yesmaximal, characteristic, complemented
7#131×C163C211yesmaximal, characteristic, complemented
8#14579699C2211yescharacteristic
9#14579689C411yescharacteristic, complemented
10#14579687C411yescharacteristic, complemented
11#14579686C411yescharacteristic, complemented
12#14579684C411yescharacteristic, complemented
13#14579683C2211yescharacteristic
14#14579682—21no—
15C2×C163⋊C8C2211yescharacteristic
16C8×D163—21no—
17C4×Dic163C2211yescharacteristic
18#41×C163C2211yescharacteristic
19M16×C163—21no—
20M16×C163C2211yescharacteristic
21C2×C8×C163—21no—
22C2×C8×C163C2211yescharacteristic
23Dic326C2×C411yescharacteristic
24D652C2×C411yescharacteristic
25C22⋊D163—21no—
26C2×Dic163—21no—
27C4×D163—21no—
28C163⋊C8—21no—
29C163⋊C8C2×C411yescharacteristic
30C163⋊C8C2×C411yescharacteristic
31Q8×C163C2×C411yescharacteristic
32D4×C163—21no—
33D4×C163C2×C411yescharacteristic
34C2×C4×C163—21no—
35C2×C4×C163C2311yescharacteristic
36C8×C163—21no—
37C8×C163D411yescharacteristic
38C8×C163D411yescharacteristic
39C22×C163—21no—
40C22×C163#4111yescharacteristic
41C2×D163—21no—
42C4×C163—21no—
43C4×C163C22×C411yescharacteristic
44C4×C163C2×D411yescharacteristic
45Dic163—21no—
46Dic163—41no—
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#131D16311yescharacteristic, complemented
56#108—1631no—
57#104—1631no—
58#104—1631no—
59#97—1631no—
60#41—1631no—
61#41C2×D16311yescharacteristic
62Q16—1631no—
63SD16—1631no—
64SD16—1631no—
65D8—1631no—
66M16—21no—
67M16—3261no—
68M16—1631no—
69M16C2×D16311yescharacteristic
70C2×C8—21no—
71C2×C8—3261no—
72C2×C8—1631no—
73C2×C8C2×D16311yescharacteristic
74C42—1631no—
75Q8—1631no—
76Q8C4×D16311yescharacteristic
77D4—21no—
78D4—3261no—
79D4—1631no—
80D4C4×D16311yescharacteristic
81C2×C4—21no—
82C2×C4—3261no—
83C2×C4—3261no—
84C2×C4C22×D16311yescharacteristic
85C8—21no—
86C8—3261no—
87C8—1631no—
88C8—1631no—
89C8C22⋊D16311yescharacteristic
90C8C22⋊D16311yescharacteristic
91C22—21no—
92C22—3261no—
93C22#1457969911yescharacteristic
94C4—21no—
95C4—3261no—
96C4—6521no—
97C4C2×C4×D16311yescharacteristic
98C4C2×C22⋊D16311yescharacteristic
99C2—21no—
100C2—41no—
101C2—6521no—
102C2C4×C22⋊D16311yescharacteristic
subgroupG/H
centerC4C2×C22⋊D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
Fitting#131×C163C2
socleC2×C163C4×D4
prime radical#19104755C2
cosocleC2×C4×C163C23
hypercenter#131D163
hypocenterC163#444
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C4 ◁ C2×C8 ◁ #131

Complements

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

NH ≅ G/Ntype
2. #19104741C2semidirect
3. #19104670C2semidirect
4. #19104662C2semidirect
5. #19104661C2semidirect
6. #19104645C2semidirect
7. #131×C163C2semidirect
9. #14579689C4semidirect
10. #14579687C4semidirect
11. #14579686C4semidirect
12. #14579684C4semidirect
51. C163#444semidirect
55. #131D163semidirect