Finite Group Databasebeta

← #23781663

Subgroups — #23781663

Order 10432.

162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×#14579698C211yesmaximal, characteristic
2C2×#14579682C211yesmaximal, characteristic, complemented
3C4⋊C4×D163C211yesmaximal, characteristic, complemented
4#19104660C211yesmaximal, characteristic, complemented
5#19104658C211yesmaximal, characteristic, complemented
6#19104656C211yesmaximal, characteristic, complemented
7#102×C163C211yesmaximal, characteristic, complemented
8#14579698—22no—
9#14579698C414yescomplemented
10C2×Dic326C2211yescharacteristic
11C2×C22⋊D163—21no—
12C22×Dic163—21no—
13C2×C4×D163—21no—
14C2×C4×D163C2211yescharacteristic
15#14579682—22no—
16C2×C163⋊C8C2211yescharacteristic
17C4⋊Dic163C2211yescharacteristic
18Dic163⋊C4—21no—
19C2×D4×C163C2211yescharacteristic
20C2×C8×C163C2211yescharacteristic
21C4⋊C4×C163C2211yescharacteristic
22C22×D163D411yescharacteristic
23Dic326—21no—
24Dic326C2×C412yescomplemented
25C22⋊D163—24no—
26C2×Dic163—21no—
27C2×Dic163—24no—
28C2×Dic163—21no—
29C2×Dic163D411yescharacteristic
30C4×D163—42no—
31C4×D163C2×C412yes—
32C4×D163D412yes—
33C163⋊C8—21no—
34C23×C163—21no—
35D4×C163—21no—
36D4×C163C2×C412yescomplemented
37C2×C4×C163—21no—
38C2×C4×C163C2311yescharacteristic
39C8×C163—21no—
40C22×C163—22no—
41C22×C163—41no—
42C22×C163—41no—
43C22×C163C2×D411yescharacteristic
44C2×D163—21no—
45C2×D163—21no—
46C2×D163C22⋊C412yes—
47C4×C163—41no—
48C4×C163C22×C411yescharacteristic
49C4×C163C2×D411yescharacteristic
50Dic163—22no—
51Dic163—41no—
52Dic163C22⋊C412yes—
53C2×C163—42no—
54C2×C163C2×C22⋊C411yescharacteristic
55C2×C163AGL(1,ℤ/8)11yescharacteristic
56C2×C163#13711yescharacteristic
57D163—22no—
58C163#41711yescharacteristic, complemented, Sylow
59#417—1631nomaximal, Sylow
60C2×#41—1631no—
61C2×M16—1631no—
62C2×C4⋊C4—1631no—
63#103—1631no—
64#103—1631no—
65#102—1631no—
66#102D16311yescharacteristic, complemented
67#41—3262no—
68#41—1634no—
69C2×Q8—1631no—
70C2×D4—3261no—
71C2×D4C2×D16311yescharacteristic
72C22×C4—3261no—
73C22×C4—3261no—
74C22×C4—1631no—
75M16—3262no—
76C2×C8—1631no—
77C2×C8C2×D16311yescharacteristic
78C4⋊C4—3261no—
79C4⋊C4—1631no—
80C4⋊C4C2×D16311yescharacteristic
81C23—21no—
82C23—1631no—
83Q8—3261no—
84Q8—1632no—
85D4—21no—
86D4—3264no—
87D4C4×D16312yescomplemented
88C2×C4—21no—
89C2×C4—3261no—
90C2×C4—3264no—
91C2×C4—3261no—
92C2×C4—6522no—
93C2×C4—1631no—
94C2×C4—1632no—
95C2×C4—1632no—
96C2×C4C22×D16311yescharacteristic
97C8—21no—
98C8—3261no—
99C22—22no—
100C22—41no—
101C22—41no—
102C22—3261no—
103C22—3261no—
104C22—1632no—
105C22D4×D16311yescharacteristic
106C4—41no—
107C4—3262no—
108C4—6521no—
109C4—1632no—
110C4C2×C4×D16311yescharacteristic
111C4D4×D16311yescharacteristic
112C2—42no—
113C2—3262no—
114C2C22⋊C4×D16311yescharacteristic
115C2#1910475911yescharacteristic
116C2#1910476411yescharacteristic
subgroupG/H
centerC22D4×D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
prime radicalC2×#14579698C2
cosocleC2×C4×C163C23
hypercenter#102D163
hypocenterC163#417
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#14579682C2semidirect
3. C4⋊C4×D163C2semidirect
4. #19104660C2semidirect
5. #19104658C2semidirect
6. #19104656C2semidirect
7. #102×C163C2semidirect
9. #14579698C4semidirect
24. Dic326C2×C4semidirect
36. D4×C163C2×C4semidirect
58. C163#417semidirect
66. #102D163semidirect
87. D4C4×D163semidirect