Finite Group Databasebeta

← #23781828

Subgroups — #23781828

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×#14579698C211yesmaximal, characteristic
2C2×Dic652C211yesmaximal, characteristic, complemented
3C2×#14579687C211yesmaximal, characteristic, complemented
4#19104715C211yesmaximal, characteristic, complemented
5#19104658C211yesmaximal, characteristic, complemented
6(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
7#102×C163C211yesmaximal, characteristic, complemented
8#14579698—22no—
9#14579698—22no—
10C2×Dic326C2211yescharacteristic
11C2×Dic326C2211yescharacteristic
12C2×C22⋊D163—21no—
13C22×Dic163—21no—
14C2×C4×D163C2211yescharacteristic
15Dic652—22no—
16#14579687—22no—
17C2×C163⋊C8C2211yescharacteristic
18C4⋊Dic163—21no—
19(C2×D163)⋊C4—21no—
20C2×D4×C163C2211yescharacteristic
21C2×C8×C163C2211yescharacteristic
22C4⋊C4×C163C2211yescharacteristic
23C22×D163D411yescharacteristic
24Dic326—21no—
25Dic326—21no—
26Dic326—21no—
27Dic326D412yes—
28C22⋊D163—24no—
29C2×Dic163—24no—
30C2×Dic163—21no—
31C2×Dic163—21no—
32C2×Dic163D411yescharacteristic
33C4×D163—21no—
34C4×D163—21no—
35C163⋊C8—21no—
36C23×C163—21no—
37D4×C163—21no—
38D4×C163D412yes—
39C2×C4×C163—21no—
40C2×C4×C163C2311yescharacteristic
41C8×C163—21no—
42C22×C163—22no—
43C22×C163—41no—
44C22×C163—41no—
45C22×C163C2×D411yescharacteristic
46C2×D163—21no—
47C2×D163—21no—
48C2×D163—21no—
49C4×C163—41no—
50C4×C163C2×D411yescharacteristic
51C4×C163C2×D411yescharacteristic
52Dic163—21no—
53Dic163—22no—
54Dic163—41no—
55C2×C163—42no—
56C2×C163#12011yescharacteristic
57C2×C163#13511yescharacteristic
58C2×C163#13711yescharacteristic
59D163—41no—
60C163#45211yescharacteristic, complemented, Sylow
61#452—1631nomaximal, Sylow
62C2×#41—1631no—
63C2×Q16—1631no—
64C2×SD16—1631no—
65C22⋊Q8—1631no—
66#103—1631no—
67#102D16311yescharacteristic, complemented
68C22⋊C8—1631no—
69#41—3262no—
70#41—3262no—
71C2×Q8—1631no—
72C2×Q8—1631no—
73C2×D4—3261no—
74C2×D4C2×D16311yescharacteristic
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—21no—
85C23—1631no—
86Q8—3261no—
87Q8—3261no—
88Q8—3261no—
89Q8—1632no—
90D4—21no—
91D4—3264no—
92D4D65212yes—
93C2×C4—21no—
94C2×C4—3264no—
95C2×C4—3261no—
96C2×C4—3261no—
97C2×C4—3261no—
98C2×C4—3261no—
99C2×C4—1631no—
100C2×C4C22×D16311yescharacteristic
101C8—21no—
102C8—3261no—
103C22—22no—
104C22—41no—
105C22—41no—
106C22—3261no—
107C22—3261no—
108C22—3261no—
109C22D4×D16311yescharacteristic
110C4—41no—
111C4—3261no—
112C4—3262no—
113C4—6521no—
114C4D4×D16311yescharacteristic
115C4C2×D65211yescharacteristic
116C2—42no—
117C2—6521no—
118C2#1910470511yescharacteristic
119C2#1910475411yescharacteristic
120C2#1910476411yescharacteristic
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#102×C163C2
socleC22×C163C2×D4
prime radicalC2×#14579698C2
hypercenter#102D163
hypocenterC163#452
LCSG ▷ C2×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×Dic652C2semidirect
3. C2×#14579687C2semidirect
4. #19104715C2semidirect
5. #19104658C2semidirect
6. (C2×D163)⋊C8C2semidirect
7. #102×C163C2semidirect
60. C163#452semidirect
67. #102D163semidirect