Finite Group Databasebeta

← #23781582

Subgroups — #23781582

Order 10432.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C22×D652C211yesmaximal, characteristic
2C2×(C2×D163)⋊C4C212yesmaximal, complemented
3C2×(C2×D163)⋊C4C212yesmaximal, complemented
4C163⋊#95C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×C163C211yesmaximal, characteristic, complemented
6C23×D163C2212yes—
7C2×D652—24no—
8C2×D652—22no—
9C22×Dic163C2212yes—
10(C2×D163)⋊C4—24no—
11(C2×D163)⋊C4—24no—
12C22×C4×C163C2211yescharacteristic
13C22×C4×C163C2211yescharacteristic
14C22×C4×C163C2211yescharacteristic
15C4⋊C4×C163—22no—
16C22×D163—22no—
17C22×D163—22no—
18C22×D163—22no—
19C22×D163—22no—
20C22×D163—22no—
21C22×D163—22no—
22C22×D163D414yes—
23D652—28no—
24C2×Dic163—22no—
25C2×Dic163—22no—
26C2×Dic163—22no—
27C23×C163C2311yescharacteristic
28C2×C4×C163—21no—
29C2×C4×C163—22no—
30C2×C4×C163—21no—
31C2×C4×C163—21no—
32C2×C4×C163—22no—
33C2×C4×C163D412yes—
34C2×C4×C163D412yescomplemented
35C22×C163C2×D412yes—
36C22×C163C2×D411yescharacteristic
37C22×C163C2×D411yescharacteristic
38C22×C163#4111yescharacteristic
39C22×C163#4112yes—
40C2×D163—24no—
41C2×D163—24no—
42C2×D163—24no—
43C2×D163—42no—
44C2×D163—42no—
45C2×D163—42no—
46C2×D163—42no—
47C4×C163—22no—
48C4×C163—22no—
49C4×C163—41no—
50Dic163—42no—
51C2×C163#12011yescharacteristic
52C2×C163#12111yescharacteristic
53C2×C163#12112yes—
54C2×C163#12312yes—
55C2×C163#12411yescharacteristic
56D163—44no—
57C163#39411yescharacteristic, complemented, Sylow
58#394—1631nomaximal, Sylow
59C22×D4—1631no—
60C2×C4⋊C4D16311yescharacteristic, complemented
61C2×C22⋊C4—1632no—
62C2×C22⋊C4—1632no—
63#95—1631no—
64C24—1632no—
65C2×D4—3264no—
66C2×D4—3262no—
67C22×C4—1632no—
68C22×C4C2×D16311yescharacteristic
69C22×C4C2×D16311yescharacteristic
70C22×C4C2×D16311yescharacteristic
71C4⋊C4—22no—
72C22⋊C4—3264no—
73C22⋊C4—3264no—
74C23—3262no—
75C23—3262no—
76C23—3262no—
77C23—3262no—
78C23—3262no—
79C23—3262no—
80C23—1634no—
81C23C22×D16311yescharacteristic
82D4—3268no—
83C2×C4—22no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—22no—
87C2×C4—21no—
88C2×C4—3262no—
89C2×C4—3262no—
90C2×C4—3262no—
91C2×C4C22⋊D16312yes—
92C2×C4D65212yescomplemented
93C22—3264no—
94C22—3264no—
95C22—3264no—
96C22—6522no—
97C22—6522no—
98C22—6522no—
99C22—6522no—
100C22D4×D16312yes—
101C22C2×C22⋊D16311yescharacteristic
102C22C2×D65211yescharacteristic
103C22#1457969911yescharacteristic
104C22#1457970012yes—
105C4—22no—
106C4—22no—
107C4—41no—
108C4—6522no—
109C2—6524no—
110C2#1910470311yescharacteristic
111C2#1910470911yescharacteristic
112C2#1910471012yes—
113C2#1910472012yes—
114C2#1910472411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D163
commutator, socle, cosocleC23×C163C23
FittingC2×C4⋊C4×C163C2
prime radicalC22×D652C2
hypercenterC2×C4⋊C4D163
hypocenterC163#394
LCSG ▷ C23×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×(C2×D163)⋊C4C2semidirect
3. C2×(C2×D163)⋊C4C2semidirect
4. C163⋊#95C2semidirect
5. C2×C4⋊C4×C163C2semidirect
34. C2×C4×C163D4semidirect
57. C163#394semidirect
60. C2×C4⋊C4D163semidirect
92. C2×C4D652semidirect