Finite Group Databasebeta

← #23781539

Subgroups — #23781539

Order 10432.

234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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×Dic163⋊C4C211yesmaximal, characteristic, complemented
4C2×(C2×D163)⋊C4C211yesmaximal, characteristic
5C2×(C2×D163)⋊C4C211yesmaximal, characteristic
6C163⋊#95C211yesmaximal, characteristic, complemented
7#95×C163C211yesmaximal, characteristic, complemented
8C23×D163C2211yescharacteristic
9C22×Dic163C2211yescharacteristic
10C22×Dic163C2211yescharacteristic
11C22×Dic163C2211yescharacteristic
12C2×C4×D163—22no—
13C2×C4×D163—22no—
14C2×C4×D163—22no—
15C4⋊Dic163—22no—
16Dic163⋊C4—22no—
17(C2×D163)⋊C4—22no—
18(C2×D163)⋊C4C414yescomplemented
19C22×C4×C163C2211yescharacteristic
20C22×C4×C163C2211yescharacteristic
21C22×C4×C163C2211yescharacteristic
22C22×D163—21no—
23C22×D163—21no—
24C22×D163—21no—
25C22×D163—21no—
26C22×D163C2×C412yes—
27C22×D163D412yes—
28C22×D163Q812yes—
29C2×Dic163—21no—
30C2×Dic163—21no—
31C2×Dic163—21no—
32C2×Dic163—21no—
33C2×Dic163—21no—
34C2×Dic163—21no—
35C2×Dic163—21no—
36C2×Dic163C2×C412yescomplemented
37C2×Dic163D412yes—
38C4×D163—28no—
39C23×C163C2311yescharacteristic
40C2×C4×C163—21no—
41C2×C4×C163—21no—
42C2×C4×C163—21no—
43C2×C4×C163—21no—
44C2×C4×C163—21no—
45C2×C4×C163—21no—
46C2×C4×C163—21no—
47C2×C4×C163C2×C412yescomplemented
48C2×C4×C163D412yes—
49C22×C163C22×C411yescharacteristic
50C22×C163C2×D411yescharacteristic
51C22×C163C2×D411yescharacteristic
52C22×C163C2×D411yescharacteristic
53C22×C163C2×Q811yescharacteristic
54C22×C163#4111yescharacteristic
55C22×C163#4111yescharacteristic
56C2×D163—22no—
57C2×D163—22no—
58C2×D163—22no—
59C2×D163—22no—
60C2×D163—22no—
61C2×D163—22no—
62C2×D163C4⋊C414yescomplemented
63C4×C163—22no—
64C4×C163—22no—
65C4×C163—41no—
66Dic163—22no—
67Dic163—22no—
68Dic163—41no—
69C2×C163C2×C4⋊C411yescharacteristic
70C2×C163C4×D411yescharacteristic
71C2×C163C4×D411yescharacteristic
72C2×C163#12011yescharacteristic
73C2×C163C22⋊Q811yescharacteristic
74C2×C163C22⋊Q811yescharacteristic
75C2×C163#12311yescharacteristic
76D163—24no—
77C163#38511yescharacteristic, complemented, Sylow
78#385—1631nomaximal, Sylow
79C23×C4—1631no—
80C2×C4⋊C4—1631no—
81C2×C4⋊C4—1631no—
82C2×C22⋊C4—1631no—
83C2×C22⋊C4—1631no—
84#95—1631no—
85#95D16311yescharacteristic, complemented
86C24—1631no—
87C22×C4—3262no—
88C22×C4—3262no—
89C22×C4—3262no—
90C22×C4—1631no—
91C22×C4—1631no—
92C22×C4—1631no—
93C22×C4C2×D16311yescharacteristic
94C22×C4C2×D16311yescharacteristic
95C22×C4C2×D16311yescharacteristic
96C4⋊C4—3262no—
97C4⋊C4—3262no—
98C22⋊C4—3262no—
99C22⋊C4—1634no—
100C23—3261no—
101C23—3261no—
102C23—3261no—
103C23—3261no—
104C23—1632no—
105C23—1632no—
106C23—1632no—
107C23C22×D16311yescharacteristic
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—3268no—
116C2×C4—3261no—
117C2×C4—3261no—
118C2×C4—3261no—
119C2×C4—3261no—
120C2×C4—3261no—
121C2×C4—3261no—
122C2×C4—3261no—
123C2×C4—1632no—
124C2×C4—1632no—
125C2×C4C4×D16312yescomplemented
126C2×C4D65212yes—
127C22—3262no—
128C22—3262no—
129C22—3262no—
130C22—3262no—
131C22—3262no—
132C22—3262no—
133C22—1634no—
134C22C2×C4×D16311yescharacteristic
135C22D4×D16311yescharacteristic
136C22D4×D16311yescharacteristic
137C22C2×D65211yescharacteristic
138C22Q8×D16311yescharacteristic
139C22#1457969811yescharacteristic
140C22#1457969911yescharacteristic
141C4—22no—
142C4—22no—
143C4—41no—
144C4—3262no—
145C4—3262no—
146C4—6521no—
147C2—3264no—
148C2C4⋊C4×D16311yescharacteristic
149C2(C22⋊D163)⋊C411yescharacteristic
150C2C4×D65211yescharacteristic
151C2#1910470511yescharacteristic
152C2#1910471311yescharacteristic
153C2#1910471511yescharacteristic
154C2#1910471711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D163
commutatorC22×C163C22×C4
Fitting#95×C163C2
socle, cosocleC23×C163C23
prime radicalC23×D163C22
hypercenter#95D163
hypocenterC163#385
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Dic163C2semidirect
3. C2×Dic163⋊C4C2semidirect
6. C163⋊#95C2semidirect
7. #95×C163C2semidirect
18. (C2×D163)⋊C4C4semidirect
36. C2×Dic163C2×C4semidirect
47. C2×C4×C163C2×C4semidirect
62. C2×D163C4⋊C4semidirect
77. C163#385semidirect
85. #95D163semidirect
125. C2×C4C4×D163semidirect