Finite Group Databasebeta

← C2×#23781805 #35223725

Subgroups — C2×#23781805 #35223725

Order 20864.

792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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×Q8×D163C211yesmaximal, characteristic, complemented
2C22×#14579688C211yesmaximal, characteristic, complemented
3C22×#14579686C211yesmaximal, characteristic, complemented
4C2×#19104710C211yesmaximal, characteristic
5#23781805C218yesmaximal, direct product factor
6C2×#19104658C211yesmaximal, characteristic, complemented
7C2×(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
8C2×#103×C163C211yesmaximal, characteristic, complemented
9C22×Dic326—21no—
10C22×Dic326C2211yescharacteristic
11C2×Q8×D163—24no—
12C2×Q8×D163—22no—
13C2×Q8×D163—24no—
14C2×Q8×D163C2214yescomplemented
15C22×D652—21no—
16C22×D652C2211yescharacteristic
17C22×C4×D163—21no—
18C22×C4×D163C2211yescharacteristic
19C2×#14579688—24no—
20C2×#14579688C2214yescomplemented
21C2×#14579686—24no—
22C2×#14579686C2214yescomplemented
23C22×C163⋊C8C2211yescharacteristic
24#19104710—22no—
25#19104710C2214yes—
26C2×(C2×D163)⋊C4—21no—
27#19104658C2214yescomplemented
28(C2×D163)⋊C8C2214yescomplemented
29C22×Q8×C163C2211yescharacteristic
30C22×C8×C163C2211yescharacteristic
31C2×C4⋊C4×C163C2211yescharacteristic
32#103×C163C2214yescomplemented
33C23×D163—21no—
34C23×D163D411yescharacteristic
35C2×Dic326—28no—
36C2×Dic326—24no—
37C2×Dic326—21no—
38C2×Dic326—22no—
39C2×Dic326D414yescomplemented
40C2×Dic326C2312yes—
41Q8×D163—216no—
42Q8×D163—28no—
43Q8×D163—28no—
44C2×D652—24no—
45C2×D652—22no—
46C2×D652—22no—
47C2×D652—21no—
48C2×D652—44no—
49C2×D652C2312yes—
50C22×Dic163—21no—
51C22×Dic163D411yescharacteristic
52C2×C4×D163—28no—
53C2×C4×D163—24no—
54C2×C4×D163—22no—
55C2×C4×D163—22no—
56C2×C4×D163D412yes—
57C2×C4×D163C2312yes—
58#14579688—28no—
59#14579686—28no—
60C2×C163⋊C8—22no—
61C2×C163⋊C8C2312yes—
62(C2×D163)⋊C4—24no—
63C2×Q8×C163—22no—
64C2×Q8×C163—21no—
65C2×Q8×C163D414yescomplemented
66C2×Q8×C163C2312yes—
67C22×C4×C163—21no—
68C22×C4×C163—21no—
69C22×C4×C163C2311yescharacteristic
70C2×C8×C163—22no—
71C2×C8×C163C2312yes—
72C4⋊C4×C163—21no—
73C4⋊C4×C163C2312yes—
74C22×D163—22no—
75C22×D163—22no—
76C22×D163—22no—
77C22×D163—42no—
78C22×D163—42no—
79C22×D163—42no—
80C22×D163SD1614yescomplemented
81C22×D163C2×D412yes—
82Dic326—216no—
83Dic326—24no—
84Dic326—22no—
85Dic326C2×D414yescomplemented
86D652—22no—
87D652—22no—
88D652—48no—
89D652—42no—
90C2×Dic163—24no—
91C2×Dic163—22no—
92C2×Dic163—22no—
93C2×Dic163C2×D412yes—
94C4×D163—216no—
95C4×D163—24no—
96C4×D163—22no—
97C4×D163—22no—
98C163⋊C8—22no—
99C23×C163C2×D411yescharacteristic
100Q8×C163—24no—
101Q8×C163—22no—
102Q8×C163C2×D414yescomplemented
103C2×C4×C163—24no—
104C2×C4×C163—22no—
105C2×C4×C163—22no—
106C2×C4×C163—42no—
107C2×C4×C163C2×D411yescharacteristic
108C2×C4×C163C2×D412yes—
109C2×C4×C163C2×D412yes—
110C2×C4×C163C2411yescharacteristic
111C8×C163—22no—
112C22×C163#12012yes—
113C22×C163C2×SD1612yes—
114C22×C163#13712yes—
115C22×C163C22×D411yescharacteristic
116C2×D163—22no—
117C2×D163—22no—
118C2×D163—28no—
119C2×D163—42no—
120C2×D163—42no—
121C2×D163—42no—
122C2×D163—84no—
123C2×D163C2×SD1614yescomplemented
124C4×C163—24no—
125C4×C163—42no—
126C4×C163#12012yes—
127C4×C163C22×D411yescharacteristic
128C4×C163C22×D411yescharacteristic
129Dic163—24no—
130Dic163—22no—
131C2×C163#44814yescomplemented
132C2×C163C2×#12011yescharacteristic
133C2×C163C22×SD1611yescharacteristic
134C2×C163C2×#13711yescharacteristic
135D163—24no—
136D163—82no—
137C163C2×#44811yescharacteristic, complemented, Sylow
138C2×#448—1631nomaximal, Sylow
139C23×Q8—1631no—
140C22×SD16—1631no—
141C22×SD16—1631no—
142C2×#121—1631no—
143#448—1638no—
144C2×#103—1631no—
145C2×#103D16311yescharacteristic, complemented
146C2×C22⋊C8—1631no—
147C22×Q8—3261no—
148C22×Q8—3264no—
149C22×Q8—3264no—
150C22×Q8—3262no—
151C22×Q8—1634no—
152C22×Q8—1631no—
153C22×Q8C2×D16311yescharacteristic
154C22×D4—3261no—
155C22×D4—1631no—
156C23×C4—3261no—
157C23×C4—1631no—
158C2×SD16—3264no—
159C2×SD16—3264no—
160C2×SD16—1634no—
161C2×SD16—1634no—
162C22×C8—1631no—
163C22×C8C2×D16311yescharacteristic
164#121—3262no—
165#121—1634no—
166C2×C4⋊C4C2×D16311yescharacteristic
167C2×C22⋊C4—3261no—
168#103—1634no—
169#103C2×D16314yescomplemented
170C22⋊C8—1634no—
171C24—3261no—
172C24—1631no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—3268no—
176C2×Q8—3264no—
177C2×Q8—32616no—
178C2×Q8—3268no—
179C2×Q8—3268no—
180C2×Q8—3261no—
181C2×Q8—3262no—
182C2×Q8—1634no—
183C2×Q8—1632no—
184C2×Q8D65214yescomplemented
185C2×Q8C22×D16312yes—
186C2×D4—3264no—
187C2×D4—3262no—
188C2×D4—3261no—
189C2×D4—3262no—
190C2×D4—6524no—
191C2×D4—1632no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—3268no—
195C22×C4—3264no—
196C22×C4—3261no—
197C22×C4—3262no—
198C22×C4—3262no—
199C22×C4—1631no—
200C22×C4—1632no—
201C22×C4—1632no—
202C22×C4C22×D16311yescharacteristic
203SD16—3268no—
204SD16—3268no—
205C2×C8—22no—
206C2×C8—3262no—
207C2×C8—1632no—
208C2×C8C22×D16312yes—
209C4⋊C4—21no—
210C4⋊C4C22×D16312yes—
211C22⋊C4—3264no—
212C23—3262no—
213C23—3262no—
214C23—3262no—
215C23—6522no—
216C23—6522no—
217C23—6522no—
218C23—1632no—
219C23—1634no—
220C23D4×D16311yescharacteristic
221Q8—22no—
222Q8—24no—
223Q8—32616no—
224Q8—3262no—
225Q8—3264no—
226Q8—1634no—
227Q8C2×D65214yescomplemented
228D4—3262no—
229D4—3262no—
230D4—6528no—
231D4—6522no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—32616no—
237C2×C4—3262no—
238C2×C4—3264no—
239C2×C4—3262no—
240C2×C4—3262no—
241C2×C4—3262no—
242C2×C4—3264no—
243C2×C4—1632no—
244C2×C4D4×D16312yes—
245C2×C4D4×D16311yescharacteristic
246C2×C4C2×D65212yes—
247C2×C4C23×D16311yescharacteristic
248C8—22no—
249C8—3262no—
250C22—13044no—
251C22—3262no—
252C22—3262no—
253C22—3268no—
254C22—6522no—
255C22—6522no—
256C22—6522no—
257C22—1634no—
258C22#1910470512yes—
259C22SD16×D16312yes—
260C22#1910476712yes—
261C22C2×D4×D16311yescharacteristic
262C4—24no—
263C4—42no—
264C4—3264no—
265C4—3262no—
266C4#1910470512yes—
267C4C2×D4×D16311yescharacteristic
268C4C22×D65211yescharacteristic
269C2—13042no—
270C2—3264no—
271C2#2378180514yesdirect product factor
272C2C2×#1910470511yescharacteristic
273C2C2×SD16×D16311yescharacteristic
274C2C2×#1910476711yescharacteristic
subgroupG/H
centerC23D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC2×#103×C163C2
socleC23×C163C2×D4
prime radicalC2×#19104710C2
hypercenterC2×#103D163
hypocenterC163C2×#448
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D163C2semidirect
2. C22×#14579688C2semidirect
3. C22×#14579686C2semidirect
5. #23781805C2direct (N × H)
6. C2×#19104658C2semidirect
7. C2×(C2×D163)⋊C8C2semidirect
8. C2×#103×C163C2semidirect
14. C2×Q8×D163C22semidirect
20. C2×#14579688C22semidirect
22. C2×#14579686C22semidirect
27. #19104658C22semidirect
28. (C2×D163)⋊C8C22semidirect
32. #103×C163C22semidirect
39. C2×Dic326D4semidirect
65. C2×Q8×C163D4semidirect
80. C22×D163SD16semidirect
85. Dic326C2×D4semidirect
102. Q8×C163C2×D4semidirect
123. C2×D163C2×SD16semidirect
131. C2×C163#448semidirect
137. C163C2×#448semidirect
145. C2×#103D163semidirect
169. #103C2×D163semidirect
184. C2×Q8D652semidirect
227. Q8C2×D652semidirect
271. C2#23781805direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D1632
C22×#145796882
C22×#145796862
C2×#191047102
#237818052
C2×#191046582
C2×(C2×D163)⋊C82
C2×#103×C1632
C2×#448163