Finite Group Databasebeta

← #23781849

Subgroups — #23781849

Order 10432.

142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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#19104782C211yesmaximal, characteristic
2#19104768C211yesmaximal, characteristic, complemented
3#19104765C211yesmaximal, characteristic, complemented
4#19104735C211yesmaximal, characteristic, complemented
5#19104663C211yesmaximal, characteristic, complemented
6#19104653C211yesmaximal, characteristic, complemented
7#104×C163C211yesmaximal, characteristic, complemented
8#14579699—21no—
9#14579699C2211yescharacteristic
10#14579698—22no—
11#14579698—21no—
12C2×Dic326—21no—
13C2×Dic326C2211yescharacteristic
14C2×Dic326C2211yescharacteristic
15Q8×D163—21no—
16Dic652—21no—
17#14579689—21no—
18#14579688—21no—
19#14579687—21no—
20#14579683C2211yescharacteristic
21C4⋊Dic163—22no—
22#41×C163C2211yescharacteristic
23M16×C163C2211yescharacteristic
24C42×C163C2211yescharacteristic
25Dic326—22no—
26Dic326—21no—
27Dic326—21no—
28Dic326—21no—
29Dic326—21no—
30Dic326D411yescharacteristic
31D652D411yescharacteristic
32C22⋊D163—22no—
33C22⋊D163—21no—
34C2×Dic163—22no—
35C2×Dic163—21no—
36C2×Dic163D412yes—
37C4×D163—22no—
38C4×D163—21no—
39C163⋊C8—21no—
40Q8×C163D411yescharacteristic
41D4×C163—21no—
42D4×C163D411yescharacteristic
43C2×C4×C163—21no—
44C2×C4×C163—21no—
45C2×C4×C163C2311yescharacteristic
46C8×C163—21no—
47C22×C163—21no—
48C22×C163C2×D411yescharacteristic
49C2×D163—21no—
50C4×C163—22no—
51C4×C163—21no—
52C4×C163C2×D411yescharacteristic
53C4×C163C2×D411yescharacteristic
54Dic163—21no—
55Dic163—22no—
56Dic163—41no—
57C2×C163—21no—
58C2×C163—41no—
59C2×C163#12011yescharacteristic
60D163—41no—
61C163#45611yescharacteristic, complemented, Sylow
62#456—1631nomaximal, Sylow
632−1+4—1631no—
64#137—1631no—
65#137—1631no—
66C4⋊Q8—1631no—
67#104—1631no—
68#104D16311yescharacteristic, complemented
69#101—1631no—
70#41—3261no—
71#41—3261no—
72#41—3262no—
73#41—1631no—
74#41C2×D16311yescharacteristic
75C2×Q8—3261no—
76C2×Q8—3261no—
77C2×Q8—1631no—
78C2×Q8—1631no—
79Q16—3261no—
80Q16—3261no—
81SD16—3261no—
82SD16—3261no—
83M16—1631no—
84M16C2×D16311yescharacteristic
85C4⋊C4—3262no—
86C42C2×D16311yescharacteristic
87Q8—3262no—
88Q8—3261no—
89Q8—3261no—
90Q8—3261no—
91Q8—3261no—
92Q8—1631no—
93Q8D65211yescharacteristic
94D4—21no—
95D4—3262no—
96D4—3261no—
97D4—1631no—
98D4D65211yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3262no—
102C2×C4—3262no—
103C2×C4—3261no—
104C2×C4—3261no—
105C2×C4—1632no—
106C2×C4C22×D16311yescharacteristic
107C8—21no—
108C8—3261no—
109C22—21no—
110C22—3261no—
111C22D4×D16311yescharacteristic
112C4—22no—
113C4—21no—
114C4—3261no—
115C4—3262no—
116C4—6521no—
117C4D4×D16311yescharacteristic
118C4C2×D65211yescharacteristic
119C2—21no—
120C2—41no—
121C2—6521no—
122C2#1910470511yescharacteristic
subgroupG/H
centerC2#19104705
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
Fitting#104×C163C2
socleC2×C163#120
prime radical#19104782C2
hypercenter#104D163
hypocenterC163#456
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #19104768C2semidirect
3. #19104765C2semidirect
4. #19104735C2semidirect
5. #19104663C2semidirect
6. #19104653C2semidirect
7. #104×C163C2semidirect
61. C163#456semidirect
68. #104D163semidirect