Finite Group Databasebeta

← #35214985

Subgroups — #35214985

Order 20864.

358 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#19104694C211yesmaximal, characteristic, complemented
2C2×#19104662C212yesmaximal, complemented
3#23781629C211yesmaximal, characteristic, complemented
4#23781424C212yesmaximal, complemented
5#525×C163C211yesmaximal, characteristic
6C2×#14579683C2212yes—
7#19104694—24no—
8C2×C4⋊Dic163—21no—
9C2×C22⋊Dic163—21no—
10C2×C4×Dic163C2212yes—
11#19104662—24no—
12C22⋊(C163⋊C8)—22no—
13C2×#41×C163C2211yescharacteristic
14C23×C4×C163C2211yescharacteristic
15#123×C163—21no—
16C22⋊Q8×C163C412yescomplemented
17#121×C163C412yescomplemented
18#120×C163—21no—
19C4×D4×C163—22no—
20#117×C163C2211yescharacteristic
21C22×Dic163—22no—
22#14579683—22no—
23#14579683—22no—
24C2×C163⋊C8—22no—
25C4⋊Dic163—24no—
26C22⋊Dic163—24no—
27C4×Dic163—22no—
28C4×Dic163D414yescomplemented
29C24×C163D411yescharacteristic
30#41×C163—22no—
31#41×C163—22no—
32C2×Q8×C163C2×C411yescharacteristic
33C2×D4×C163—22no—
34C2×D4×C163—21no—
35C2×D4×C163C2×C411yescharacteristic
36C22×C4×C163—22no—
37C22×C4×C163—22no—
38C22×C4×C163—21no—
39C22×C4×C163C2×C412yes—
40C22×C4×C163D411yescharacteristic
41C22×C4×C163D412yes—
42C22×C4×C163C2311yescharacteristic
43C4⋊C4×C163—22no—
44C4⋊C4×C163C2×C412yes—
45C22⋊C4×C163—22no—
46C22⋊C4×C163—21no—
47C22⋊C4×C163—22no—
48C42×C163—21no—
49C2×Dic163—24no—
50C2×Dic163—44no—
51C163⋊C8—42no—
52C23×C163—21no—
53C23×C163—21no—
54C23×C163—21no—
55C23×C163—42no—
56C23×C163C22⋊C412yes—
57C23×C163C2×D411yescharacteristic
58Q8×C163—22no—
59D4×C163—22no—
60D4×C163—44no—
61D4×C163—41no—
62D4×C163—41no—
63C2×C4×C163—21no—
64C2×C4×C163—21no—
65C2×C4×C163—24no—
66C2×C4×C163—24no—
67C2×C4×C163—22no—
68C2×C4×C163—21no—
69C2×C4×C163—42no—
70C2×C4×C163C22⋊C412yes—
71C2×C4×C163C22×C411yescharacteristic
72C2×C4×C163C2×D412yes—
73C2×C4×C163C2×D411yescharacteristic
74C2×C4×C163#4112yes—
75C22×C163—22no—
76C22×C163—22no—
77C22×C163—22no—
78C22×C163—22no—
79C22×C163—42no—
80C22×C163—42no—
81C22×C163—41no—
82C22×C163—42no—
83C22×C163C2×C22⋊C411yescharacteristic
84C22×C163#12011yescharacteristic
85C22×C163#12311yescharacteristic
86C4×C163—22no—
87C4×C163—41no—
88C4×C163—42no—
89C4×C163C4×D412yes—
90C4×C163#12112yes—
91Dic163—44no—
92C2×C163—21no—
93C2×C163—21no—
94C2×C163—42no—
95C2×C163—81no—
96C2×C163#38611yescharacteristic
97C2×C163#42112yes—
98C163#189711yescharacteristic, complemented, Sylow
99#1897—1631nomaximal, Sylow
100#525D16311yescharacteristic
101C2×#117—1631no—
102C2×#104—1632no—
103#407—1631no—
104#339—1632no—
105C2×#41C2×D16311yescharacteristic
106C23×C4C2×D16311yescharacteristic
107C2×M16—1632no—
108#123—21no—
109C22⋊Q8Dic16312yescomplemented
110#121Dic16312yescomplemented
111#120—21no—
112C4×D4—22no—
113#117—3264no—
114#117C2×D16311yescharacteristic
115C2×C4⋊C4—3261no—
116C2×C22⋊C4—3261no—
117C2×C42—1632no—
118#104—3264no—
119C22⋊C8—3262no—
120C24C22⋊D16311yescharacteristic
121#41—22no—
122#41—22no—
123C2×Q8C2×Dic16311yescharacteristic
124C2×D4—22no—
125C2×D4—21no—
126C2×D4C2×Dic16311yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—3262no—
131C22×C4C2×Dic16312yes—
132C22×C4C22⋊D16311yescharacteristic
133C22×C4C22⋊D16312yes—
134C22×C4C22×D16311yescharacteristic
135M16—3262no—
136M16—3262no—
137C2×C8—3262no—
138C4⋊C4—22no—
139C4⋊C4—3264no—
140C4⋊C4C2×Dic16312yes—
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—3264no—
145C42—21no—
146C42—3262no—
147C42—1634no—
148C23—21no—
149C23—21no—
150C23—21no—
151C23—42no—
152C23C22⋊Dic16312yes—
153C23C2×C22⋊D16311yescharacteristic
154Q8—22no—
155D4—22no—
156D4—44no—
157D4—41no—
158D4—41no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—3264no—
167C2×C4—6524no—
168C2×C4C22⋊Dic16312yes—
169C2×C4C22×Dic16311yescharacteristic
170C2×C4D4×D16312yes—
171C2×C4C2×C22⋊D16311yescharacteristic
172C2×C4#1457969812yes—
173C8—6522no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—41no—
182C22C2×C22⋊Dic16311yescharacteristic
183C22#1910470311yescharacteristic
184C22#1910471611yescharacteristic
185C4—22no—
186C4—42no—
187C4—41no—
188C4—6524no—
189C4D4×Dic16312yes—
190C4#1910470712yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—81no—
195C2#2378154511yescharacteristic
196C2#2378168212yes—
subgroupG/H
centerC2×C4C2×C22⋊D163
commutatorC2×C4×C163C22×C4
FrattiniC22×C4C22×D163
Fitting, prime radical#525×C163C2
socleC22×C163C2×C22⋊C4
cosocleC22×C4×C163C23
hypercenter#525D163
hypocenterC163#1897
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#19104694C2semidirect
2. C2×#19104662C2semidirect
3. #23781629C2semidirect
4. #23781424C2semidirect
16. C22⋊Q8×C163C4semidirect
17. #121×C163C4semidirect
28. C4×Dic163D4semidirect
98. C163#1897semidirect
109. C22⋊Q8Dic163semidirect
110. #121Dic163semidirect

Maximal subgroups

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

subgroupindex
C2×#191046942
C2×#191046622
#237816292
#237814242
#525×C1632
#1897163