Finite Group Databasebeta

← C2×#19104725 #23782185

Subgroups — C2×#19104725 #23782185

Order 10432.

226 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 119 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#19104725C218yesmaximal, direct product factor
2C2×C4⋊Dic163C211yesmaximal, characteristic
3C2×Dic163⋊C4C211yesmaximal, characteristic
4C2×Dic163⋊C4C211yesmaximal, characteristic
5C2×Dic163⋊C4C211yesmaximal, characteristic
6C2×Dic163⋊C4C211yesmaximal, characteristic
7C2×C4×Dic163C211yesmaximal, characteristic
8C2×C4⋊C4×C163C211yesmaximal, characteristic
9C22×Dic163C2211yescharacteristic
10C22×Dic163C2211yescharacteristic
11C22×Dic163C2211yescharacteristic
12C22×Dic163C2211yescharacteristic
13C4⋊Dic163C2214yes—
14Dic163⋊C4C2214yes—
15Dic163⋊C4C2214yes—
16Dic163⋊C4C2214yes—
17Dic163⋊C4C2214yes—
18C4×Dic163C2214yes—
19C22×C4×C163C2211yescharacteristic
20C22×C4×C163C2211yescharacteristic
21C22×C4×C163C2211yescharacteristic
22C4⋊C4×C163C2214yes—
23C2×Dic163—22no—
24C2×Dic163—22no—
25C2×Dic163—22no—
26C2×Dic163Q814yes—
27C2×Dic163C2312yes—
28C2×Dic163C2312yes—
29C2×Dic163C2312yes—
30C2×Dic163C2312yes—
31C23×C163C2311yescharacteristic
32C2×C4×C163—22no—
33C2×C4×C163—22no—
34C2×C4×C163—22no—
35C2×C4×C163C2312yes—
36C2×C4×C163C2312yes—
37C2×C4×C163C2312yes—
38C22×C163C2×Q812yes—
39C22×C163#4112yes—
40C22×C163#4112yes—
41C22×C163C2411yescharacteristic
42C4×C163—22no—
43C4×C163—22no—
44C4×C163—22no—
45Dic163—22no—
46Dic163—22no—
47Dic163—22no—
48Dic163C2×Q814yes—
49C2×C163#12514yescomplemented
50C2×C163C22×Q811yescharacteristic
51C2×C163C2×#4111yescharacteristic
52C2×C163C2×#4111yescharacteristic
53C163C2×#12511yescharacteristic, complemented, Sylow
54C2×#125—1631nomaximal, Sylow
55#125—1638no—
56C2×C4⋊C4—1631no—
57C2×C4⋊C4—1631no—
58C2×C4⋊C4—1631no—
59C2×C4⋊C4—1631no—
60C2×C4⋊C4—1631no—
61C2×C4⋊C4D16311yescharacteristic
62C2×C42—1631no—
63C22×C4—1631no—
64C22×C4—1631no—
65C22×C4—1631no—
66C22×C4—1631no—
67C22×C4C2×D16311yescharacteristic
68C22×C4C2×D16311yescharacteristic
69C22×C4C2×D16311yescharacteristic
70C4⋊C4—1634no—
71C4⋊C4—1634no—
72C4⋊C4—1634no—
73C4⋊C4—1634no—
74C4⋊C4—1634no—
75C4⋊C4C2×D16314yes—
76C42—1634no—
77C23C22×D16311yescharacteristic
78C2×C4—22no—
79C2×C4—22no—
80C2×C4—22no—
81C2×C4—3262no—
82C2×C4—3262no—
83C2×C4—3262no—
84C2×C4—1632no—
85C2×C4—1632no—
86C2×C4—1632no—
87C2×C4—1634no—
88C2×C4—1632no—
89C2×C4C22×D16312yes—
90C2×C4C22×D16312yes—
91C2×C4C22×D16312yes—
92C22Q8×D16312yes—
93C22#1457969812yes—
94C22#1457969912yes—
95C22C23×D16311yescharacteristic
96C4—22no—
97C4—22no—
98C4—22no—
99C4—3262no—
100C4—3262no—
101C4—3262no—
102C4—1634no—
103C2#1910472514yesdirect product factor
104C2C2×Q8×D16311yescharacteristic
105C2C2×#1457969811yescharacteristic
106C2C2×#1457969911yescharacteristic
subgroupG/H
centerC23C22×D163
commutator, cosocleC22×C163C24
FrattiniC22C23×D163
FittingC2×C4⋊C4×C163C2
socle, prime radicalC23×C163C23
hypercenterC2×C4⋊C4D163
hypocenterC163C2×#125
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #19104725C2direct (N × H)
49. C2×C163#125semidirect
53. C163C2×#125semidirect
103. C2#19104725direct (N × H)