Finite Group Databasebeta

← #35213545

Subgroups — #35213545

Order 20864.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#23782294C211yesmaximal, characteristic
2#23781996C211yesmaximal, characteristic
3#23781993C211yesmaximal, characteristic
4#23781597C211yesmaximal, characteristic
5#23781401C211yesmaximal, characteristic
6#23781390C211yesmaximal, characteristic
7#328×C163C211yesmaximal, characteristic
8#19104734—21no—
9#19104733—21no—
10#19104725—21no—
11#19104725—21no—
12#19104714C2211yescharacteristic
13#19104712—21no—
14#19104691—21no—
15C2×C4⋊Dic163—21no—
16C2×C4⋊Dic163C2211yescharacteristic
17C2×Dic163⋊C4C2211yescharacteristic
18#19104667—21no—
19#19104666—21no—
20#19104660—21no—
21#19104659—21no—
22C22⋊(C163⋊C8)C2211yescharacteristic
23C163⋊#95—21no—
24C22⋊Q8×C163C2211yescharacteristic
25C22⋊C8×C163C2211yescharacteristic
26#95×C163C2211yescharacteristic
27C2×Dic326—21no—
28C2×Dic326D411yescharacteristic
29C22×Dic163—21no—
30C22×Dic163D411yescharacteristic
31C22×Dic163D411yescharacteristic
32C2×C163⋊C8—21no—
33C4⋊Dic163—21no—
34C4⋊Dic163—21no—
35C4⋊Dic163—21no—
36C4⋊Dic163—42no—
37C4⋊Dic163D411yescharacteristic
38Dic163⋊C4—21no—
39Dic163⋊C4—21no—
40Dic163⋊C4—21no—
41Dic163⋊C4—21no—
42Dic163⋊C4—21no—
43Dic163⋊C4—21no—
44Dic163⋊C4—21no—
45C22⋊Dic163—21no—
46C4×Dic163—21no—
47C4×Dic163—21no—
48C2×Q8×C163D411yescharacteristic
49C22×C4×C163—21no—
50C22×C4×C163C2311yescharacteristic
51C2×C8×C163—21no—
52C4⋊C4×C163—21no—
53C4⋊C4×C163D411yescharacteristic
54C22⋊C4×C163—21no—
55Dic326—41no—
56Dic326—81no—
57C2×Dic163—21no—
58C2×Dic163—21no—
59C2×Dic163—21no—
60C2×Dic163—21no—
61C2×Dic163—21no—
62C2×Dic163—41no—
63C2×Dic163—41no—
64C2×Dic163—41no—
65C2×Dic163—41no—
66C2×Dic163SD1612yes—
67C163⋊C8—41no—
68C23×C163C2×D411yescharacteristic
69Q8×C163—41no—
70C2×C4×C163—22no—
71C2×C4×C163—21no—
72C2×C4×C163—21no—
73C2×C4×C163—41no—
74C2×C4×C163—41no—
75C2×C4×C163—41no—
76C2×C4×C163C2×D411yescharacteristic
77C2×C4×C163C2×D411yescharacteristic
78C8×C163—41no—
79C22×C163—21no—
80C22×C163—21no—
81C22×C163#12011yescharacteristic
82C22×C163C2×SD1611yescharacteristic
83C22×C163#13711yescharacteristic
84C4×C163—21no—
85C4×C163—21no—
86C4×C163—42no—
87C4×C163—41no—
88C4×C163—41no—
89Dic163—22no—
90Dic163—41no—
91Dic163—41no—
92Dic163—41no—
93Dic163—81no—
94C2×C163—21no—
95C2×C163—21no—
96C2×C163#44811yescharacteristic
97C2×C163#45611yescharacteristic
98C2×C163#45811yescharacteristic
99C163#161111yescharacteristic, complemented, Sylow
100#1611—1631nomaximal, Sylow
101#544—1631no—
102#483—1631no—
103#483—1631no—
104#398—1631no—
105#328—1631no—
106#328D16311yescharacteristic
107#324—1631no—
108C4⋊Q8—3261no—
109C4⋊Q8—3261no—
110#125—3261no—
111#125—3261no—
112C22⋊Q8—3261no—
113C22⋊Q8—1631no—
114C22⋊Q8C2×D16311yescharacteristic
115#117—3261no—
116C2×C4⋊C4—3261no—
117C2×C4⋊C4—1631no—
118C2×C4⋊C4—1631no—
119#106—3261no—
120#106—3261no—
121#103—3261no—
122#103—3261no—
123C22⋊C8—1631no—
124C22⋊C8C2×D16311yescharacteristic
125#95—3261no—
126#95C2×D16311yescharacteristic
127C2×Q8—3261no—
128C2×Q8—1631no—
129C2×Q8D65211yescharacteristic
130C22×C4—21no—
131C22×C4—3261no—
132C22×C4—1631no—
133C22×C4—1631no—
134C22×C4C22×D16311yescharacteristic
135C2×C8—21no—
136C2×C8—3261no—
137C4⋊C4—21no—
138C4⋊C4—3261no—
139C4⋊C4—3261no—
140C4⋊C4—3261no—
141C4⋊C4—3261no—
142C4⋊C4—3261no—
143C4⋊C4—3261no—
144C4⋊C4—3261no—
145C4⋊C4—3261no—
146C4⋊C4—3261no—
147C4⋊C4—3261no—
148C4⋊C4—6522no—
149C4⋊C4—1631no—
150C4⋊C4D65211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3261no—
153C42—3261no—
154C42—3261no—
155C23D4×D16311yescharacteristic
156Q8—41no—
157Q8—13041no—
158Q8—6521no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—3261no—
166C2×C4—3261no—
167C2×C4—3261no—
168C2×C4—3261no—
169C2×C4—3261no—
170C2×C4—6521no—
171C2×C4—6521no—
172C2×C4—6521no—
173C2×C4—6521no—
174C2×C4—1632no—
175C2×C4D4×D16311yescharacteristic
176C2×C4C2×D65211yescharacteristic
177C8—41no—
178C8—6521no—
179C22—21no—
180C22—21no—
181C22#1910470511yescharacteristic
182C22SD16×D16311yescharacteristic
183C22#1910476711yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—13041no—
190C4—3262no—
191C4—6521no—
192C4—6521no—
193C4—6521no—
194C2—21no—
195C2—21no—
196C2#2378180511yescharacteristic
197C2#2378184911yescharacteristic
198C2#2378185611yescharacteristic
subgroupG/H
centerC22#19104705
commutator, cosocleC22×C4×C163C23
FrattiniC22×C4C22×D163
Fitting#328×C163C2
socleC22×C163#120
prime radicalC23×C163C2×D4
hypercenter#328D163
hypocenterC163#1611
LCSG ▷ C22×C4×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C163#1611semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237822942
#237819962
#237819932
#237815972
#237814012
#237813902
#328×C1632
#1611163