Finite Group Databasebeta

← #442×D163 #35223325

Subgroups — #442×D163 #35223325

Order 20864.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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×D8×D163C211yesmaximal, characteristic
2C4×D4×D163C212yesmaximal, complemented
3#23781778C211yesmaximal, characteristic, complemented
4#23781777C211yesmaximal, characteristic, complemented
5#23781776C211yesmaximal, characteristic, complemented
6#23781775C212yesmaximal, complemented
7#23781774C212yesmaximal, complemented
8#106×D163C211yesmaximal, characteristic, complemented
9#102×D163C212yesmaximal, complemented
10#97×D163C211yesmaximal, characteristic, complemented
11#442×C163C211yesmaximal, characteristic, complemented
12C2×D4×D163C2212yes—
13C22×C4×D163—22no—
14C2×D1304C2211yescharacteristic
15C2×#14579684C2212yes—
16D8×D163C418yescomplemented
17C2×C8×D163C2211yescharacteristic
18C2×C8×D163C2211yescharacteristic
19C4×D652C2212yescomplemented
20D4×Dic163C2212yescomplemented
21#19104697C2212yescomplemented
22C4×C22⋊D163—22no—
23(C22⋊D163)⋊C4—22no—
24C4⋊C4×D163C2212yes—
25C22⋊C4×D163—22no—
26C42×D163C2211yescharacteristic
27#19104667C2211yescharacteristic, complemented
28#19104666C2212yescomplemented
29#19104657C2212yescomplemented
30#19104656C2212yescomplemented
31#19104655C2212yescomplemented
32#19104646C2211yescharacteristic, complemented
33#19104645C2211yescharacteristic, complemented
34#19104645C2211yescharacteristic, complemented
35C2×D8×C163C2211yescharacteristic
36C4×D4×C163C2212yescomplemented
37#106×C163C2211yescharacteristic, complemented
38#102×C163C2212yescomplemented
39#97×C163C2211yescharacteristic, complemented
40C23×D163—22no—
41C2×D652C2312yes—
42C2×C22⋊D163—22no—
43D4×D163—24no—
44D4×D163C2×C418yescomplemented
45C22×Dic163—22no—
46C2×C4×D163—22no—
47C2×C4×D163—22no—
48C2×C4×D163—22no—
49C2×C4×D163—48no—
50C2×C4×D163D412yes—
51C2×C4×D163C2311yescharacteristic
52D1304C2×C414yescomplemented
53#14579684C2×C418yescomplemented
54C2×C163⋊C8C2311yescharacteristic
55C2×C163⋊C8C2311yescharacteristic
56C8×D163—22no—
57C8×D163C2×C414yescomplemented
58C4⋊Dic163C2312yes—
59Dic163⋊C4—22no—
60C22⋊Dic163—22no—
61(C2×D163)⋊C4—22no—
62(C2×D163)⋊C4—22no—
63C4×Dic163D412yes—
64C4×Dic163C2311yescharacteristic
65C2×D4×C163C2312yes—
66C22×C4×C163—22no—
67D8×C163C2×C414yescomplemented
68C2×C8×C163C2311yescharacteristic
69C2×C8×C163C2311yescharacteristic
70C4⋊C4×C163C2312yes—
71C22⋊C4×C163—22no—
72C42×C163C2311yescharacteristic
73C22×D163—22no—
74C22×D163—28no—
75C22×D163—44no—
76C22×D163—44no—
77C22×D163C2×D411yescharacteristic
78D652—22no—
79D652C22×C414yescomplemented
80C22⋊D163—28no—
81C2×Dic163—22no—
82C2×Dic163—44no—
83C2×Dic163C2×D412yes—
84C2×Dic163C2×D411yescharacteristic
85C4×D163—24no—
86C4×D163—44no—
87C4×D163—44no—
88C4×D163—44no—
89C4×D163C22×C412yes—
90C4×D163#4112yes—
91C163⋊C8—21no—
92C163⋊C8C22×C412yescomplemented
93C23×C163—22no—
94D4×C163—22no—
95D4×C163C22×C414yescomplemented
96C2×C4×C163—22no—
97C2×C4×C163—44no—
98C2×C4×C163C2×D412yes—
99C2×C4×C163C2411yescharacteristic
100C8×C163—21no—
101C8×C163C22×C412yescomplemented
102C22×C163—24no—
103C22×C163—42no—
104C22×C163—42no—
105C22×C163C22×D411yescharacteristic
106C2×D163—24no—
107C2×D163—42no—
108C2×D163—42no—
109C2×D163—416no—
110C2×D163C4×D412yes—
111C2×D163AGL(1,ℤ/8)14yes—
112C4×C163—22no—
113C4×C163—42no—
114C4×C163C23×C411yescharacteristic
115C4×C163C2×#4111yescharacteristic
116Dic163—22no—
117Dic163—42no—
118Dic163C4×D412yes—
119C2×C163—44no—
120C2×C163C2×C4×D411yescharacteristic
121C2×C163C2×AGL(1,ℤ/8)12yes—
122D163—44no—
123D163#44214yesdirect product factor
124C163C2×#44211yescharacteristic, complemented, Sylow
125C2×#442—1631nomaximal, Sylow
126C22×D8—1631no—
127C2×C4×D4—1632no—
128#442—1631no—
129#442—1632no—
130#442—1631no—
131#442—1632no—
132#442—1631no—
133#442D16311yescharacteristic, direct product factor
134C2×#106—1631no—
135C2×#102—1632no—
136C2×#97—1631no—
137C22×D4—1632no—
138C23×C4—3262no—
139C2×D8—1632no—
140C2×D8—1638no—
141C2×D8—1631no—
142C2×D8C2×D16311yescharacteristic
143C22×C8—1631no—
144C22×C8—1631no—
145C4×D4—3262no—
146C4×D4—3262no—
147C4×D4—1632no—
148C4×D4—1632no—
149C4×D4—1632no—
150C4×D4C2×D16312yescomplemented
151C2×C4⋊C4—1632no—
152C2×C22⋊C4—3262no—
153C2×C42—1631no—
154#106—1631no—
155#106—1632no—
156#106C2×D16311yescharacteristic, complemented
157#102—1632no—
158#102—1632no—
159#102—1632no—
160#102C2×D16312yescomplemented
161#97—1631no—
162#97—1631no—
163#97—1631no—
164#97C2×D16311yescharacteristic, complemented
165C24—3262no—
166C2×D4—3264no—
167C2×D4—3262no—
168C2×D4—1638no—
169C2×D4—1632no—
170C2×D4C22×D16312yes—
171C22×C4—22no—
172C22×C4—3262no—
173C22×C4—3262no—
174C22×C4—3262no—
175C22×C4—3262no—
176C22×C4—6528no—
177C22×C4—1632no—
178C22×C4—1631no—
179D8—1638no—
180D8—1634no—
181D8C4×D16314yescomplemented
182C2×C8—3262no—
183C2×C8—1631no—
184C2×C8—1631no—
185C2×C8—1634no—
186C2×C8C22×D16311yescharacteristic
187C2×C8C22×D16311yescharacteristic
188C4⋊C4—3262no—
189C4⋊C4—1632no—
190C4⋊C4C22×D16312yes—
191C22⋊C4—22no—
192C22⋊C4—3262no—
193C22⋊C4—3262no—
194C22⋊C4—3262no—
195C42—1632no—
196C42—1631no—
197C42C22×D16311yescharacteristic
198C23—22no—
199C23—3268no—
200C23—3262no—
201C23—6524no—
202C23—6524no—
203C23—1631no—
204D4—22no—
205D4—3268no—
206D4—3262no—
207D4—1634no—
208D4C2×C4×D16314yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—3264no—
212C2×C4—3262no—
213C2×C4—6524no—
214C2×C4—6524no—
215C2×C4—6524no—
216C2×C4—6524no—
217C2×C4—1632no—
218C2×C4—1631no—
219C2×C4—1632no—
220C2×C4—1632no—
221C2×C4D4×D16312yes—
222C2×C4C23×D16311yescharacteristic
223C8—21no—
224C8—3261no—
225C8—1632no—
226C8C2×C4×D16312yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—3264no—
231C22—65216no—
232C22—6522no—
233C22—6522no—
234C22—1634no—
235C22—1632no—
236C22C2×D4×D16311yescharacteristic
237C4—22no—
238C4—42no—
239C4—3262no—
240C4—6522no—
241C4—1632no—
242C4C22×C4×D16311yescharacteristic
243C4#41×D16311yescharacteristic
244C2—44no—
245C2—6524no—
246C2—1634no—
247C2C4×D4×D16311yescharacteristic
248C2AGL(1,ℤ/8)×D16312yes—
subgroupG/H
centerC22C2×D4×D163
commutatorC4×C163C23×C4
FrattiniC2×C4C23×D163
Fitting#442×C163C2
socleC22×C163C22×D4
prime radicalC2×D8×D163C2
cosocleC2×C4×C163C24
hypercenter#442D163
hypocenterC163C2×#442
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D163C2semidirect
3. #23781778C2semidirect
4. #23781777C2semidirect
5. #23781776C2semidirect
6. #23781775C2semidirect
7. #23781774C2semidirect
8. #106×D163C2semidirect
9. #102×D163C2semidirect
10. #97×D163C2semidirect
11. #442×C163C2semidirect
16. D8×D163C4semidirect
19. C4×D652C22semidirect
20. D4×Dic163C22semidirect
21. #19104697C22semidirect
27. #19104667C22semidirect
28. #19104666C22semidirect
29. #19104657C22semidirect
30. #19104656C22semidirect
31. #19104655C22semidirect
32. #19104646C22semidirect
33. #19104645C22semidirect
34. #19104645C22semidirect
36. C4×D4×C163C22semidirect
37. #106×C163C22semidirect
38. #102×C163C22semidirect
39. #97×C163C22semidirect
44. D4×D163C2×C4semidirect
52. D1304C2×C4semidirect
53. #14579684C2×C4semidirect
57. C8×D163C2×C4semidirect
67. D8×C163C2×C4semidirect
79. D652C22×C4semidirect
92. C163⋊C8C22×C4semidirect
95. D4×C163C22×C4semidirect
101. C8×C163C22×C4semidirect
123. D163#442direct (N × H)
124. C163C2×#442semidirect
133. #442D163direct (N × H)
150. C4×D4C2×D163semidirect
156. #106C2×D163semidirect
160. #102C2×D163semidirect
164. #97C2×D163semidirect
181. D8C4×D163semidirect
208. D4C2×C4×D163semidirect
226. C8C2×C4×D163semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1632
C4×D4×D1632
#237817782
#237817772
#237817762
#237817752
#237817742
#106×D1632
#102×D1632
#97×D1632
#442×C1632
C2×#442163