Finite Group Databasebeta

← #23781829

Subgroups — #23781829

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×#14579699C211yesmaximal, characteristic
2C2×Dic652C211yesmaximal, characteristic, complemented
3C2×#14579688C211yesmaximal, characteristic, complemented
4#19104714C211yesmaximal, characteristic, complemented
5#19104660C211yesmaximal, characteristic, complemented
6#19104657C211yesmaximal, characteristic, complemented
7C22⋊C8×C163C211yesmaximal, characteristic, complemented
8#14579699—22no—
9#14579699—22no—
10C2×Dic326C2211yescharacteristic
11C2×Dic326C2211yescharacteristic
12C2×D652C2211yescharacteristic
13C2×C22⋊D163—21no—
14C2×C4×D163—21no—
15Dic652—22no—
16#14579688—22no—
17C4⋊Dic163C2211yescharacteristic
18Dic163⋊C4—21no—
19C22⋊Dic163—21no—
20C22×C4×C163C2211yescharacteristic
21C2×C8×C163C2211yescharacteristic
22C2×C8×C163C2211yescharacteristic
23C22×D163—21no—
24Dic326—21no—
25Dic326—21no—
26Dic326—21no—
27Dic326D412yes—
28D652—21no—
29D652D412yes—
30C22⋊D163—24no—
31C2×Dic163—21no—
32C2×Dic163—21no—
33C2×Dic163—21no—
34C4×D163—24no—
35C23×C163D411yescharacteristic
36C2×C4×C163—21no—
37C2×C4×C163—21no—
38C2×C4×C163D411yescharacteristic
39C2×C4×C163C2311yescharacteristic
40C8×C163—21no—
41C8×C163—21no—
42C22×C163—21no—
43C22×C163—21no—
44C22×C163—21no—
45C22×C163C2×D411yescharacteristic
46C2×D163—22no—
47C2×D163—41no—
48C2×D163—41no—
49C4×C163—21no—
50C4×C163C2×D411yescharacteristic
51C4×C163C2×D411yescharacteristic
52Dic163—22no—
53Dic163—41no—
54Dic163—41no—
55C2×C163—41no—
56C2×C163#12011yescharacteristic
57C2×C163#13511yescharacteristic
58C2×C163#13711yescharacteristic
59D163—42no—
60C163#45211yescharacteristic, complemented, Sylow
61#452—1631nomaximal, Sylow
62C2×#41—1631no—
63C2×Q16—1631no—
64C2×SD16—1631no—
65C22⋊Q8—1631no—
66#103—1631no—
67#102—1631no—
68C22⋊C8D16311yescharacteristic, complemented
69#41—3262no—
70#41—3262no—
71C2×Q8—1631no—
72C2×Q8—1631no—
73C2×D4—3261no—
74C2×D4—1631no—
75C22×C4—3261no—
76C22×C4C2×D16311yescharacteristic
77Q16—3262no—
78SD16—3262no—
79C2×C8C2×D16311yescharacteristic
80C2×C8C2×D16311yescharacteristic
81C4⋊C4—3261no—
82C4⋊C4—1631no—
83C22⋊C4—3261no—
84C23—3261no—
85C23D65211yescharacteristic
86Q8—3261no—
87Q8—3261no—
88Q8—3261no—
89Q8—1632no—
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×C4D65211yescharacteristic
100C2×C4C22×D16311yescharacteristic
101C8—21no—
102C8—21no—
103C22—21no—
104C22—21no—
105C22—21no—
106C22—3262no—
107C22—6521no—
108C22—6521no—
109C22C2×D65211yescharacteristic
110C4—21no—
111C4—3262no—
112C4—6521no—
113C4—6521no—
114C4D4×D16311yescharacteristic
115C4D4×D16311yescharacteristic
116C2—41no—
117C2—6522no—
118C2#1910470511yescharacteristic
119C2#1910475711yescharacteristic
120C2#1910476811yescharacteristic
subgroupG/H
centerC22C2×D652
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC22⋊C8×C163C2
socleC22×C163C2×D4
prime radicalC2×#14579699C2
hypercenterC22⋊C8D163
hypocenterC163#452
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×Dic652C2semidirect
3. C2×#14579688C2semidirect
4. #19104714C2semidirect
5. #19104660C2semidirect
6. #19104657C2semidirect
7. C22⋊C8×C163C2semidirect
60. C163#452semidirect
68. C22⋊C8D163semidirect