Finite Group Databasebeta

← #23782036

Subgroups — #23782036

Order 10432.

142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 47 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×#14579688C211yesmaximal, characteristic, complemented
2C2×#14579687C211yesmaximal, characteristic, complemented
3C2×#14579686C211yesmaximal, characteristic, complemented
4#19104733C211yesmaximal, characteristic, complemented
5#19104731C211yesmaximal, characteristic
6C8×Dic163C211yesmaximal, characteristic, complemented
7C2×SD16×C163C211yesmaximal, characteristic, complemented
8C2×Dic326C2211yescharacteristic
9C2×D652C2211yescharacteristic
10C2×C22⋊D163—22no—
11#14579688—22no—
12#14579687—22no—
13#14579686—22no—
14C2×C163⋊C8C2211yescharacteristic
15Dic163⋊C4—22no—
16C4×Dic163C2211yescharacteristic
17C2×Q8×C163C2211yescharacteristic
18C2×D4×C163C2211yescharacteristic
19SD16×C163—22no—
20C2×C8×C163C2211yescharacteristic
21C22×D163—21no—
22Dic326—21no—
23Dic326—21no—
24D652—21no—
25D652—21no—
26C22⋊D163—44no—
27C2×Dic163—21no—
28C2×Dic163D412yes—
29C163⋊C8D412yescomplemented
30C23×C163—21no—
31Q8×C163—21no—
32Q8×C163—21no—
33D4×C163—21no—
34D4×C163—21no—
35C2×C4×C163—21no—
36C2×C4×C163C2311yescharacteristic
37C8×C163D412yescomplemented
38C22×C163—41no—
39C22×C163—42no—
40C22×C163C2×D411yescharacteristic
41C2×D163—41no—
42C2×D163—42no—
43C4×C163—41no—
44C4×C163C2×D411yescharacteristic
45C4×C163C2×D411yescharacteristic
46Dic163—41no—
47Dic163SD1614yescomplemented
48C2×C163—81no—
49C2×C163#12711yescharacteristic
50C2×C163C2×SD1612yes—
51D163—81no—
52C163#49211yescharacteristic, complemented, Sylow
53#492—1631nomaximal, Sylow
54C2×SD16—1631no—
55C2×SD16—1631no—
56C2×SD16—1631no—
57C2×SD16D16311yescharacteristic, complemented
58C4⋊Q8—1631no—
59#127—1631no—
60C4×C8—1631no—
61C2×Q8—1631no—
62C2×Q8C2×D16311yescharacteristic
63C2×D4—3262no—
64C2×D4—1631no—
65C2×D4C2×D16311yescharacteristic
66SD16—22no—
67SD16—3262no—
68SD16—3262no—
69SD16—3262no—
70C2×C8—1631no—
71C2×C8C2×D16311yescharacteristic
72C4⋊C4—3262no—
73C42—1631no—
74C23—21no—
75C23—3261no—
76Q8—21no—
77Q8—21no—
78Q8—3261no—
79Q8—3261no—
80D4—21no—
81D4—21no—
82D4—3261no—
83D4—3261no—
84D4—6524no—
85C2×C4—21no—
86C2×C4—3261no—
87C2×C4—1632no—
88C2×C4C22×D16311yescharacteristic
89C8—1632no—
90C8C22⋊D16312yescomplemented
91C22—41no—
92C22—42no—
93C22—6521no—
94C22—6522no—
95C22D4×D16311yescharacteristic
96C4—41no—
97C4—6521no—
98C4—1634no—
99C4D4×D16311yescharacteristic
100C4C2×C22⋊D16311yescharacteristic
101C2—81no—
102C2—13041no—
103C2#1910473111yescharacteristic
104C2SD16×D16312yes—
subgroupG/H
centerC22D4×D163
commutator, cosocleC2×C4×C163C23
FrattiniC2×C4C22×D163
FittingC2×SD16×C163C2
socleC22×C163C2×D4
prime radical#19104731C2
hypercenterC2×SD16D163
hypocenterC163#492
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14579688C2semidirect
2. C2×#14579687C2semidirect
3. C2×#14579686C2semidirect
4. #19104733C2semidirect
6. C8×Dic163C2semidirect
7. C2×SD16×C163C2semidirect
29. C163⋊C8D4semidirect
37. C8×C163D4semidirect
47. Dic163SD16semidirect
52. C163#492semidirect
57. C2×SD16D163semidirect
90. C8C22⋊D163semidirect