Finite Group Databasebeta

← #23781522

Subgroups — #23781522

Order 10432.

234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4×D163C211yesmaximal, characteristic
2C2×C4⋊Dic163C211yesmaximal, characteristic, complemented
3C2×(C2×D163)⋊C4C212yesmaximal
4C163⋊#95C212yesmaximal, complemented
5C2×C4⋊C4×C163C211yesmaximal, characteristic, complemented
6C23×D163C2211yescharacteristic
7C22×Dic163C2212yes—
8C22×Dic163C2211yescharacteristic
9C2×C4×D163—22no—
10C2×C4×D163—22no—
11C2×C4×D163C414yescomplemented
12C4⋊Dic163—22no—
13(C2×D163)⋊C4—24no—
14C22×C4×C163C2212yes—
15C22×C4×C163C2211yescharacteristic
16C4⋊C4×C163—22no—
17C22×D163—21no—
18C22×D163—21no—
19C22×D163—21no—
20C22×D163—21no—
21C22×D163C2×C412yes—
22C22×D163D412yes—
23C22×D163Q812yes—
24C2×Dic163—21no—
25C2×Dic163—21no—
26C2×Dic163—22no—
27C2×Dic163—22no—
28C2×Dic163—22no—
29C2×Dic163C2×C412yes—
30C4×D163—28no—
31C23×C163C2311yescharacteristic
32C2×C4×C163—22no—
33C2×C4×C163—22no—
34C2×C4×C163—22no—
35C2×C4×C163C2×C412yes—
36C2×C4×C163D412yes—
37C2×C4×C163D412yes—
38C22×C163C22×C411yescharacteristic
39C22×C163C2×D411yescharacteristic
40C22×C163C2×D411yescharacteristic
41C22×C163C2×D411yescharacteristic
42C22×C163C2×Q811yescharacteristic
43C22×C163#4111yescharacteristic
44C22×C163#4111yescharacteristic
45C2×D163—22no—
46C2×D163—22no—
47C2×D163—22no—
48C2×D163—22no—
49C2×D163—22no—
50C2×D163—22no—
51C2×D163C4⋊C414yescomplemented
52C4×C163—42no—
53C4×C163C22⋊C414yescomplemented
54Dic163—22no—
55Dic163—42no—
56C2×C163C2×C22⋊C411yescharacteristic
57C2×C163C2×C4⋊C411yescharacteristic
58C2×C163#11711yescharacteristic
59C2×C163#12111yescharacteristic
60C2×C163#12111yescharacteristic
61C2×C163C22⋊Q811yescharacteristic
62C2×C163C22⋊Q811yescharacteristic
63D163—24no—
64C163#38011yescharacteristic, complemented, Sylow
65#380—1631nomaximal, Sylow
66C23×C4—1631no—
67C2×C4⋊C4—1631no—
68C2×C4⋊C4D16311yescharacteristic, complemented
69C2×C22⋊C4—1632no—
70#95—1632no—
71C24—1631no—
72C22×C4—3262no—
73C22×C4—3262no—
74C22×C4—1632no—
75C22×C4—1631no—
76C22×C4—1634no—
77C22×C4C2×D16312yes—
78C22×C4C2×D16311yescharacteristic
79C4⋊C4—22no—
80C4⋊C4—3262no—
81C22⋊C4—3264no—
82C23—3261no—
83C23—3261no—
84C23—3261no—
85C23—3261no—
86C23—1632no—
87C23—1632no—
88C23—1632no—
89C23C22×D16311yescharacteristic
90C2×C4—22no—
91C2×C4—22no—
92C2×C4—22no—
93C2×C4—3261no—
94C2×C4—3261no—
95C2×C4—3268no—
96C2×C4—3262no—
97C2×C4—3262no—
98C2×C4—3262no—
99C2×C4—1632no—
100C2×C4C4×D16312yes—
101C2×C4C22⋊D16312yes—
102C2×C4D65212yes—
103C22—3262no—
104C22—3262no—
105C22—3262no—
106C22—3262no—
107C22—3262no—
108C22—3262no—
109C22—1634no—
110C22C2×C4×D16311yescharacteristic
111C22D4×D16311yescharacteristic
112C22C2×C22⋊D16311yescharacteristic
113C22C2×D65211yescharacteristic
114C22Q8×D16311yescharacteristic
115C22#1457969811yescharacteristic
116C22#1457970011yescharacteristic
117C4—42no—
118C4—3262no—
119C4—6522no—
120C4(C2×D163)⋊C414yescomplemented
121C2—3264no—
122C2C2×(C2×D163)⋊C411yescharacteristic
123C2C4⋊C4×D16311yescharacteristic
124C2#1910469311yescharacteristic
125C2#1910470611yescharacteristic
126C2#1910471011yescharacteristic
127C2#1910471111yescharacteristic
128C2#1910471511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D163
commutatorC22×C163C22×C4
FittingC2×C4⋊C4×C163C2
socle, cosocleC23×C163C23
prime radicalC23×D163C22
hypercenterC2×C4⋊C4D163
hypocenterC163#380
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Dic163C2semidirect
4. C163⋊#95C2semidirect
5. C2×C4⋊C4×C163C2semidirect
11. C2×C4×D163C4semidirect
51. C2×D163C4⋊C4semidirect
53. C4×C163C22⋊C4semidirect
64. C163#380semidirect
68. C2×C4⋊C4D163semidirect
120. C4(C2×D163)⋊C4semidirect