Finite Group Databasebeta

← #35213565

Subgroups — #35213565

Order 20864.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#23782262C211yesmaximal, characteristic
2#23782000C211yesmaximal, characteristic, complemented
3#23781983C211yesmaximal, characteristic
4#23781401C211yesmaximal, characteristic, complemented
5#23781398C211yesmaximal, characteristic
6#23781391C211yesmaximal, characteristic, complemented
7#400×C163C211yesmaximal, characteristic, complemented
8#19104730—21no—
9#19104725—21no—
10#19104720—21no—
11#19104718—21no—
12#19104714C2211yescharacteristic
13#19104713—21no—
14#19104709C2211yescharacteristic
15C4×C22⋊D163—21no—
16#19104668—21no—
17#19104666—21no—
18#19104658—21no—
19#19104655—21no—
20C22⋊(C163⋊C8)C2211yescharacteristic
21C22⋊(C163⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C163C2211yescharacteristic
23C2×C4⋊C4×C163C2211yescharacteristic
24#95×C163—21no—
25#95×C163—21no—
26#95×C163C2211yescharacteristic
27C2×Dic326D411yescharacteristic
28C2×D652D411yescharacteristic
29C2×C22⋊D163—21no—
30C2×C4×D163—21no—
31C2×C163⋊C8—21no—
32C2×C163⋊C8—21no—
33C4⋊Dic163D411yescharacteristic
34C4⋊Dic163D411yescharacteristic
35Dic163⋊C4—21no—
36Dic163⋊C4—21no—
37Dic163⋊C4—21no—
38Dic163⋊C4—21no—
39C22⋊Dic163—21no—
40(C2×D163)⋊C4—21no—
41(C2×D163)⋊C4—21no—
42(C2×D163)⋊C4—21no—
43(C2×D163)⋊C4—21no—
44C4×Dic163—21no—
45C22×C4×C163—21no—
46C22×C4×C163—21no—
47C22×C4×C163D411yescharacteristic
48C22×C4×C163D411yescharacteristic
49C22×C4×C163C2311yescharacteristic
50C4⋊C4×C163—21no—
51C4⋊C4×C163—21no—
52C4⋊C4×C163—21no—
53C4⋊C4×C163—21no—
54C22×D163—21no—
55Dic326—41no—
56D652—41no—
57C22⋊D163—41no—
58C22⋊D163—41no—
59C2×Dic163—21no—
60C2×Dic163—21no—
61C2×Dic163—21no—
62C4×D163—81no—
63C163⋊C8—41no—
64C163⋊C8—41no—
65C23×C163C2×D411yescharacteristic
66C2×C4×C163—21no—
67C2×C4×C163—21no—
68C2×C4×C163—21no—
69C2×C4×C163—21no—
70C2×C4×C163—41no—
71C2×C4×C163—41no—
72C2×C4×C163—41no—
73C2×C4×C163—41no—
74C2×C4×C163—42no—
75C2×C4×C163—41no—
76C2×C4×C163—41no—
77C2×C4×C163C2×D411yescharacteristic
78C2×C4×C163C2×D411yescharacteristic
79C22×C163—21no—
80C22×C163—21no—
81C22×C163#12011yescharacteristic
82C22×C163#13511yescharacteristic
83C22×C163#13711yescharacteristic
84C2×D163—41no—
85C2×D163—41no—
86C2×D163—41no—
87C4×C163—21no—
88C4×C163—21no—
89C4×C163—41no—
90C4×C163—41no—
91C4×C163—81no—
92C4×C163—81no—
93Dic163—41no—
94Dic163—41no—
95Dic163—41no—
96C2×C163—21no—
97C2×C163—21no—
98C2×C163#45211yescharacteristic
99C2×C163#45411yescharacteristic
100C2×C163#45811yescharacteristic
101D163—81no—
102C163#161511yescharacteristic, complemented, Sylow
103#1615—1631nomaximal, Sylow
104#539—1631no—
105#484—1631no—
106#481—1631no—
107#400D16311yescharacteristic, complemented
108#328—1631no—
109#327—1631no—
110#324—1631no—
111#126—3261no—
112#125—3261no—
113#123—3261no—
114#123—3261no—
115C22⋊Q8—3261no—
116C22⋊Q8—1631no—
117#121—1631no—
118C4×D4—3261no—
119C2×C4⋊C4C2×D16311yescharacteristic
120C2×C4⋊C4C2×D16311yescharacteristic
121#107—3261no—
122#106—3261no—
123#103—3261no—
124#102—3261no—
125C22⋊C8—1631no—
126C22⋊C8—1631no—
127#95—21no—
128#95—21no—
129#95C2×D16311yescharacteristic
130C2×Q8—1631no—
131C2×D4—3261no—
132C2×D4—1631no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—3261no—
136C22×C4C22⋊D16311yescharacteristic
137C22×C4C22⋊D16311yescharacteristic
138C22×C4C22×D16311yescharacteristic
139C2×C8—3261no—
140C2×C8—3261no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—3261no—
146C4⋊C4—3261no—
147C4⋊C4—3261no—
148C4⋊C4—3261no—
149C4⋊C4—1631no—
150C4⋊C4—1631no—
151C22⋊C4—3261no—
152C22⋊C4—3261no—
153C22⋊C4—3261no—
154C22⋊C4—3261no—
155C22⋊C4—3261no—
156C42—3261no—
157C23—3261no—
158C23C2×C22⋊D16311yescharacteristic
159Q8—6521no—
160D4—6521no—
161D4—6521no—
162D4—6521no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—13041no—
175C2×C4—3261no—
176C2×C4—3261no—
177C2×C4—3261no—
178C2×C4D4×D16311yescharacteristic
179C2×C4D4×D16311yescharacteristic
180C8—6521no—
181C8—6521no—
182C22—21no—
183C22—21no—
184C22—6521no—
185C22—6521no—
186C22—6521no—
187C22#1910470311yescharacteristic
188C22#1910475511yescharacteristic
189C22#1910476611yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4—6521no—
197C4—6521no—
198C4—6521no—
199C2—21no—
200C2—21no—
201C2—13041no—
202C2#2378182511yescharacteristic
203C2#2378183711yescharacteristic
204C2#2378185411yescharacteristic
subgroupG/H
centerC22#19104703
commutator, cosocleC22×C4×C163C23
FrattiniC22×C4C22×D163
Fitting#400×C163C2
socleC22×C163#120
prime radical#19104709C22
hypercenter#400D163
hypocenterC163#1615
LCSG ▷ C22×C4×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #23782000C2semidirect
4. #23781401C2semidirect
6. #23781391C2semidirect
7. #400×C163C2semidirect
102. C163#1615semidirect
107. #400D163semidirect

Maximal subgroups

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

subgroupindex
#237822622
#237820002
#237819832
#237814012
#237813982
#237813912
#400×C1632
#1615163