Finite Group Databasebeta

← C2×#23781814 #35223716

Subgroups — C2×#23781814 #35223716

Order 20864.

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

normal subgroups only

This group has 996 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×D4×D163C211yesmaximal, characteristic
2C22×#14579686C211yesmaximal, characteristic, complemented
3C2×#19104711C211yesmaximal, characteristic, complemented
4#23781814C218yesmaximal, direct product factor
5C2×#19104657C211yesmaximal, characteristic, complemented
6C2×#19104656C211yesmaximal, characteristic, complemented
7C2×(C2×D163)⋊C8C211yesmaximal, characteristic, complemented
8C22×SD16×C163C211yesmaximal, characteristic, complemented
9C24×D163—21no—
10C22×D652C2211yescharacteristic
11C22×C22⋊D163—21no—
12C2×D4×D163—24no—
13C2×D4×D163—22no—
14C2×D4×D163—24no—
15C2×D4×D163C2214yes—
16C22×C4×D163C2211yescharacteristic
17C2×#14579686—24no—
18C2×#14579686C2214yescomplemented
19C22×C163⋊C8C2211yescharacteristic, complemented
20#19104711—22no—
21#19104711C2214yescomplemented
22C2×C4⋊Dic163C2211yescharacteristic, complemented
23C2×Dic163⋊C4—21no—
24C2×(C2×D163)⋊C4—21no—
25#19104657C2214yescomplemented
26#19104656C2214yescomplemented
27(C2×D163)⋊C8C2214yescomplemented
28C22×Q8×C163C2211yescharacteristic, complemented
29C22×D4×C163C2211yescharacteristic
30C2×SD16×C163—24no—
31C2×SD16×C163C2214yescomplemented
32C22×C8×C163C2211yescharacteristic, complemented
33C23×D163—28no—
34C23×D163—24no—
35C23×D163—21no—
36C23×D163—44no—
37C23×D163—44no—
38C23×D163D411yescharacteristic
39C2×D652—21no—
40C2×D652—22no—
41C2×D652D414yes—
42C2×D652C2312yes—
43C2×C22⋊D163—28no—
44C2×C22⋊D163—24no—
45D4×D163—216no—
46D4×D163—28no—
47D4×D163—28no—
48C22×Dic163—21no—
49C22×Dic163D411yescharacteristic
50C2×C4×D163—22no—
51C2×C4×D163—22no—
52C2×C4×D163D412yes—
53C2×C4×D163C2312yes—
54#14579686—28no—
55C2×C163⋊C8—22no—
56C2×C163⋊C8C2312yescomplemented
57C4⋊Dic163—21no—
58C4⋊Dic163C2312yescomplemented
59Dic163⋊C4—24no—
60(C2×D163)⋊C4—24no—
61C24×C163—21no—
62C2×Q8×C163—21no—
63C2×Q8×C163—22no—
64C2×Q8×C163—22no—
65C2×Q8×C163C2312yescomplemented
66C2×D4×C163—21no—
67C2×D4×C163—22no—
68C2×D4×C163D414yes—
69C2×D4×C163C2312yes—
70C22×C4×C163—21no—
71C22×C4×C163C2311yescharacteristic
72SD16×C163—28no—
73C2×C8×C163—22no—
74C2×C8×C163C2312yescomplemented
75C22×D163—22no—
76C22×D163—22no—
77C22×D163—216no—
78C22×D163—24no—
79C22×D163—22no—
80C22×D163—48no—
81C22×D163—432no—
82C22×D163—42no—
83C22×D163—42no—
84C22×D163—48no—
85C22×D163SD1614yescomplemented
86C22×D163C2×D412yes—
87D652—24no—
88D652—22no—
89D652C2×D414yes—
90C22⋊D163—216no—
91C2×Dic163—22no—
92C2×Dic163—22no—
93C2×Dic163—42no—
94C2×Dic163C2×D412yes—
95C4×D163—24no—
96C4×D163—22no—
97C4×D163—22no—
98C163⋊C8—22no—
99C23×C163—24no—
100C23×C163—22no—
101C23×C163—42no—
102C23×C163—42no—
103C23×C163C2×D411yescharacteristic
104Q8×C163—22no—
105Q8×C163—22no—
106Q8×C163—42no—
107D4×C163—24no—
108D4×C163—22no—
109D4×C163C2×D414yes—
110C2×C4×C163—22no—
111C2×C4×C163—42no—
112C2×C4×C163C2×D411yescharacteristic
113C2×C4×C163C2×D412yes—
114C2×C4×C163C2×D412yes—
115C2×C4×C163C2411yescharacteristic
116C8×C163—22no—
117C22×C163—24no—
118C22×C163—42no—
119C22×C163—42no—
120C22×C163—48no—
121C22×C163#12012yes—
122C22×C163C2×SD1612yes—
123C22×C163AGL(1,ℤ/8)12yes—
124C22×C163C22×D411yescharacteristic
125C2×D163—22no—
126C2×D163—22no—
127C2×D163—28no—
128C2×D163—24no—
129C2×D163—432no—
130C2×D163—42no—
131C2×D163—42no—
132C2×D163—48no—
133C2×D163C2×SD1614yescomplemented
134C4×C163—42no—
135C4×C163#12012yes—
136C4×C163C22×D411yescharacteristic
137C4×C163C22×D411yescharacteristic
138Dic163—22no—
139Dic163—42no—
140C2×C163—44no—
141C2×C163#45014yescomplemented
142C2×C163C2×#12011yescharacteristic
143C2×C163C22×SD1611yescharacteristic
144C2×C163C2×AGL(1,ℤ/8)11yescharacteristic
145D163—24no—
146D163—44no—
147C163C2×#45011yescharacteristic, complemented, Sylow
148C2×#450—1631nomaximal, Sylow
149C23×D4—1631no—
150C22×SD16—1631no—
151C22×SD16D16311yescharacteristic, complemented
152C2×C22⋊Q8—1631no—
153#450—1638no—
154C2×#102—1631no—
155C2×#102—1631no—
156C2×C22⋊C8—1631no—
157C25—3261no—
158C22×Q8C2×D16311yescharacteristic, complemented
159C22×D4—3264no—
160C22×D4—3264no—
161C22×D4—3262no—
162C22×D4—3261no—
163C22×D4—1634no—
164C22×D4—1631no—
165C22×D4C2×D16311yescharacteristic
166C23×C4—1631no—
167C2×SD16—24no—
168C2×SD16—3264no—
169C2×SD16—1634no—
170C2×SD16C2×D16314yescomplemented
171C22×C8—1631no—
172C22×C8C2×D16311yescharacteristic, complemented
173C22⋊Q8—3262no—
174C22⋊Q8—1634no—
175C2×C4⋊C4—3261no—
176C2×C4⋊C4—1631no—
177C2×C22⋊C4—3261no—
178#102—1634no—
179#102—1634no—
180C22⋊C8—1634no—
181C24—21no—
182C24—3268no—
183C24—3264no—
184C24—3261no—
185C24—6524no—
186C24—6524no—
187C24—1631no—
188C2×Q8—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8C22×D16312yescomplemented
192C2×D4—22no—
193C2×D4—21no—
194C2×D4—32616no—
195C2×D4—3268no—
196C2×D4—3268no—
197C2×D4—3268no—
198C2×D4—3264no—
199C2×D4—3261no—
200C2×D4—3262no—
201C2×D4—1634no—
202C2×D4—1632no—
203C2×D4C22⋊D16314yes—
204C2×D4C22×D16312yes—
205C22×C4—21no—
206C22×C4—3262no—
207C22×C4—3262no—
208C22×C4—3261no—
209C22×C4—1631no—
210C22×C4—1632no—
211C22×C4—1632no—
212C22×C4C22×D16311yescharacteristic
213SD16—28no—
214SD16—3268no—
215C2×C8—22no—
216C2×C8—3262no—
217C2×C8—1632no—
218C2×C8C22×D16312yescomplemented
219C4⋊C4—3264no—
220C4⋊C4—3261no—
221C4⋊C4—1632no—
222C22⋊C4—3264no—
223C23—22no—
224C23—24no—
225C23—42no—
226C23—42no—
227C23—32616no—
228C23—3262no—
229C23—3262no—
230C23—3262no—
231C23—3264no—
232C23—6528no—
233C23—65232no—
234C23—6528no—
235C23—6522no—
236C23—6522no—
237C23—1632no—
238C23—1634no—
239C23D4×D16311yescharacteristic
240Q8—22no—
241Q8—22no—
242Q8—42no—
243D4—22no—
244D4—24no—
245D4—32616no—
246D4—3262no—
247D4—3264no—
248D4—1634no—
249D4C2×C22⋊D16314yes—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—3262no—
253C2×C4—3262no—
254C2×C4—3262no—
255C2×C4—3264no—
256C2×C4—3262no—
257C2×C4—6522no—
258C2×C4—1632no—
259C2×C4D4×D16312yes—
260C2×C4D4×D16311yescharacteristic
261C2×C4C2×C22⋊D16312yes—
262C2×C4C23×D16311yescharacteristic
263C8—22no—
264C8—3262no—
265C22—24no—
266C22—42no—
267C22—42no—
268C22—48no—
269C22—3262no—
270C22—3262no—
271C22—3268no—
272C22—3264no—
273C22—65232no—
274C22—6522no—
275C22—6522no—
276C22—6528no—
277C22—1634no—
278C22#1910470312yes—
279C22SD16×D16312yes—
280C22#1910476212yes—
281C22C2×D4×D16311yescharacteristic
282C4—42no—
283C4—3262no—
284C4—6522no—
285C4#1910470312yes—
286C4C2×D4×D16311yescharacteristic
287C4C22×C22⋊D16311yescharacteristic
288C2—44no—
289C2—3264no—
290C2—6524no—
291C2#2378181414yesdirect product factor
292C2C2×#1910470311yescharacteristic
293C2C2×SD16×D16311yescharacteristic
294C2C2×#1910476211yescharacteristic
subgroupG/H
centerC23D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC22×SD16×C163C2
socleC23×C163C2×D4
prime radicalC22×D4×D163C2
hypercenterC22×SD16D163
hypocenterC163C2×#450
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C22×#14579686C2semidirect
3. C2×#19104711C2semidirect
4. #23781814C2direct (N × H)
5. C2×#19104657C2semidirect
6. C2×#19104656C2semidirect
7. C2×(C2×D163)⋊C8C2semidirect
8. C22×SD16×C163C2semidirect
18. C2×#14579686C22semidirect
19. C22×C163⋊C8C22semidirect
21. #19104711C22semidirect
22. C2×C4⋊Dic163C22semidirect
25. #19104657C22semidirect
26. #19104656C22semidirect
27. (C2×D163)⋊C8C22semidirect
28. C22×Q8×C163C22semidirect
31. C2×SD16×C163C22semidirect
32. C22×C8×C163C22semidirect
56. C2×C163⋊C8C23semidirect
58. C4⋊Dic163C23semidirect
65. C2×Q8×C163C23semidirect
74. C2×C8×C163C23semidirect
85. C22×D163SD16semidirect
133. C2×D163C2×SD16semidirect
141. C2×C163#450semidirect
147. C163C2×#450semidirect
151. C22×SD16D163semidirect
158. C22×Q8C2×D163semidirect
170. C2×SD16C2×D163semidirect
172. C22×C8C2×D163semidirect
191. C2×Q8C22×D163semidirect
218. C2×C8C22×D163semidirect
291. C2#23781814direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1632
C22×#145796862
C2×#191047112
#237818142
C2×#191046572
C2×#191046562
C2×(C2×D163)⋊C82
C22×SD16×C1632
C2×#450163