Finite Group Databasebeta

← #23781830

Subgroups — #23781830

Order 10432.

152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14579700C211yesmaximal, characteristic
2C2×#14579689C211yesmaximal, characteristic, complemented
3C2×#14579688C211yesmaximal, characteristic, complemented
4#19104715C211yesmaximal, characteristic, complemented
5#19104655C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
7#103×C163C211yesmaximal, characteristic, complemented
8#14579700—22no—
9#14579700—22no—
10C2×Dic326C2211yescharacteristic
11C2×D652—21no—
12C2×D652C2211yescharacteristic
13C2×C4×D163—21no—
14C2×C4×D163C2211yescharacteristic
15#14579689—22no—
16#14579688—22no—
17C2×C163⋊C8C2211yescharacteristic
18C4⋊Dic163—21no—
19(C2×D163)⋊C4—21no—
20C2×Q8×C163C2211yescharacteristic
21C2×C8×C163C2211yescharacteristic
22C4⋊C4×C163C2211yescharacteristic
23C22×D163—21no—
24C22×D163D411yescharacteristic
25Dic326—21no—
26Dic326—21no—
27D652—24no—
28D652—21no—
29D652D412yes—
30C2×Dic163—21no—
31C2×Dic163D411yescharacteristic
32C4×D163—24no—
33C4×D163—21no—
34C4×D163—21no—
35C163⋊C8—21no—
36Q8×C163—21no—
37Q8×C163D412yes—
38C2×C4×C163—21no—
39C2×C4×C163—21no—
40C2×C4×C163C2311yescharacteristic
41C8×C163—21no—
42C22×C163C2×D411yescharacteristic
43C2×D163—21no—
44C2×D163—22no—
45C2×D163—21no—
46C2×D163—21no—
47C2×D163—41no—
48C2×D163—41no—
49C4×C163—22no—
50C4×C163—41no—
51C4×C163C2×D411yescharacteristic
52C4×C163C2×D411yescharacteristic
53Dic163—21no—
54Dic163—41no—
55C2×C163#12011yescharacteristic
56C2×C163#13511yescharacteristic
57C2×C163#13711yescharacteristic
58D163—41no—
59D163—42no—
60C163#45211yescharacteristic, complemented, Sylow
61#452—1631nomaximal, Sylow
62C2×#41—1631no—
63C2×Q16—1631no—
64C2×SD16—1631no—
65C22⋊Q8—1631no—
66#103D16311yescharacteristic, complemented
67#102—1631no—
68C22⋊C8—1631no—
69#41—3262no—
70#41—3262no—
71C2×Q8—1631no—
72C2×Q8C2×D16311yescharacteristic
73C2×D4—3261no—
74C2×D4—1631no—
75C22×C4—3261no—
76C22×C4—1631no—
77Q16—3262no—
78SD16—3262no—
79C2×C8—1631no—
80C2×C8C2×D16311yescharacteristic
81C4⋊C4—3261no—
82C4⋊C4C2×D16311yescharacteristic
83C22⋊C4—3261no—
84C23—3261no—
85C23—1631no—
86Q8—21no—
87Q8—3261no—
88Q8—3261no—
89Q8D65212yes—
90D4—3264no—
91D4—3261no—
92D4—1632no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—3264no—
96C2×C4—3261no—
97C2×C4—3261no—
98C2×C4—3261no—
99C2×C4—1631no—
100C2×C4C22×D16311yescharacteristic
101C8—21no—
102C8—3261no—
103C22—3261no—
104C22—3262no—
105C22—3261no—
106C22—3261no—
107C22—6521no—
108C22—6521no—
109C22D4×D16311yescharacteristic
110C4—22no—
111C4—41no—
112C4—3261no—
113C4—6521no—
114C4D4×D16311yescharacteristic
115C4C2×D65211yescharacteristic
116C2—6521no—
117C2—6522no—
118C2#1910470511yescharacteristic
119C2#1910475611yescharacteristic
120C2#1910476711yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#103×C163C2
socleC22×C163C2×D4
prime radicalC2×#14579700C2
hypercenter#103D163
hypocenterC163#452
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#14579689C2semidirect
3. C2×#14579688C2semidirect
4. #19104715C2semidirect
5. #19104655C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. #103×C163C2semidirect
60. C163#452semidirect
66. #103D163semidirect