Finite Group Databasebeta

← C4×#19104780 #35227741

Subgroups — C4×#19104780 #35227741

Order 20864.

1660 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19104780C211yesmaximal, characteristic
2#23782146C212yesmaximal, complemented
3#23782144C214yesmaximal, complemented
4#23782140C211yesmaximal, characteristic, complemented
5#23782138C214yesmaximal, complemented
6#23782137C214yesmaximal, complemented
7C4×#14579699C212yesmaximal, complemented
8C4×#14579698C214yesmaximal, complemented
9C2×C4×C22⋊D163C214yesmaximal, complemented
10C4×D4×D163C214yesmaximal, complemented
11C2×C4×D4×C163C211yesmaximal, characteristic, complemented
12#19104780C4116yesdirect product factor
13C2×#14579699C2212yes—
14C2×#14579698C2214yes—
15C22×C22⋊D163C2214yes—
16C2×D4×D163C2214yes—
17C22×C4×D163C2214yescomplemented
18C4×Dic326C2212yescomplemented
19C4×Dic326C2212yescomplemented
20#19104700C2214yescomplemented
21C4×D652C2212yescomplemented
22C4×D652C2212yescomplemented
23D4×Dic163C2214yescomplemented
24D4×Dic163C2214yescomplemented
25#19104697C2214yescomplemented
26C4×C22⋊D163C2218yescomplemented
27C4×C22⋊D163C2218yescomplemented
28C4×C22⋊D163C2218yescomplemented
29C4×C22⋊D163C2214yescomplemented
30C4×C22⋊D163C2214yescomplemented
31(C22⋊D163)⋊C4C2218yescomplemented
32(C22⋊D163)⋊C4C2218yescomplemented
33#19104694C2212yescomplemented
34#19104693C2214yescomplemented
35#19104692C2214yescomplemented
36#19104691C2218yescomplemented
37C2×Dic163⋊C4C2214yescomplemented
38C4⋊C4×D163C2214yescomplemented
39C2×C22⋊Dic163C2214yescomplemented
40C2×(C2×D163)⋊C4C2214yescomplemented
41C22⋊C4×D163C2218yescomplemented
42C2×C4×Dic163C2214yescomplemented
43C42×D163C2214yescomplemented
44C22×D4×C163C2211yescharacteristic
45C23×C4×C163C2212yescomplemented
46C4×D4×C163C2214yescomplemented
47C4×D4×C163C2214yescomplemented
48C2×C4⋊C4×C163C2211yescharacteristic, complemented
49C2×C22⋊C4×C163C2212yescomplemented
50C2×C42×C163C2211yescharacteristic, complemented
51C23×D163C2314yes—
52#14579699C2×C4116yescomplemented
53#14579698C2×C4132yescomplemented
54C2×Dic326C2312yes—
55C2×D652C2312yes—
56C2×C22⋊D163C2×C4132yescomplemented
57C2×C22⋊D163C2318yes—
58C2×C22⋊D163C2314yes—
59D4×D163C2×C4132yescomplemented
60C22×Dic163C2314yes—
61C22×Dic163C2314yes—
62C22×Dic163C2314yes—
63C2×C4×D163—48no—
64C2×C4×D163C2314yes—
65C2×C4×D163C2318yes—
66C2×C4×D163C2314yes—
67C2×C4×D163C2314yes—
68C4⋊Dic163C2312yes—
69C4⋊Dic163C2312yes—
70Dic163⋊C4C2318yes—
71Dic163⋊C4C2314yes—
72Dic163⋊C4C2314yes—
73C22⋊Dic163C2318yes—
74C22⋊Dic163C2314yes—
75(C2×D163)⋊C4C2314yes—
76(C2×D163)⋊C4C2318yes—
77(C2×D163)⋊C4C2314yes—
78C4×Dic163C2314yes—
79C4×Dic163C2314yes—
80C4×Dic163C2314yes—
81C4×Dic163C2318yes—
82C24×C163C2312yes—
83C2×D4×C163C2×C418yescomplemented
84C2×D4×C163C2314yes—
85C22×C4×C163—44no—
86C22×C4×C163C2314yes—
87C22×C4×C163C2311yescharacteristic
88C22×C4×C163C2311yescharacteristic
89C22×C4×C163C2312yes—
90C22×C4×C163C2314yes—
91C22×C4×C163C2311yescharacteristic
92C4⋊C4×C163C2314yes—
93C22⋊C4×C163C2318yes—
94C42×C163C2312yes—
95C42×C163C2312yes—
96C22×D163—44no—
97C22×D163—44no—
98C22×D163C22×C4116yescomplemented
99C22×D163C2414yes—
100Dic326C22×C418yescomplemented
101D652C22×C418yescomplemented
102C22⋊D163C22×C4132yescomplemented
103C22⋊D163C22×C4116yescomplemented
104C2×Dic163—44no—
105C2×Dic163—44no—
106C2×Dic163C22×C4116yescomplemented
107C2×Dic163C2414yes—
108C2×Dic163C2414yes—
109C2×Dic163C2414yes—
110C4×D163—28no—
111C4×D163—48no—
112C4×D163—44no—
113C4×D163C22×C4116yescomplemented
114C23×C163—42no—
115C23×C163—42no—
116C23×C163C22×C418yescomplemented
117C23×C163C2414yes—
118C23×C163C2411yescharacteristic
119D4×C163C22×C4116yescomplemented
120C2×C4×C163—22no—
121C2×C4×C163—28no—
122C2×C4×C163—44no—
123C2×C4×C163—42no—
124C2×C4×C163—41no—
125C2×C4×C163C22×C414yescomplemented
126C2×C4×C163C2412yes—
127C2×C4×C163C2411yescharacteristic
128C2×C4×C163C2414yes—
129C2×C4×C163C2412yes—
130C2×C4×C163C2411yescharacteristic
131C22×C163—21no—
132C22×C163—24no—
133C22×C163—21no—
134C22×C163—24no—
135C22×C163—48no—
136C22×C163C23×C412yes—
137C22×C163C23×C418yes—
138C22×C163C2511yescharacteristic
139C2×D163—24no—
140C2×D163—24no—
141C2×D163—416no—
142C2×D163C23×C418yes—
143C4×C163—21no—
144C4×C163—24no—
145C4×C163—22no—
146C4×C163C23×C414yes—
147C4×C163H(5,𝔽2)12yescomplemented
148Dic163—24no—
149Dic163—24no—
150Dic163C23×C418yes—
151C2×C163—28no—
152C2×C163—22no—
153C2×C163C24×C411yescharacteristic
154C2×C163C2×H(5,𝔽2)11yescharacteristic
155C2×C163#58511yescharacteristic
156D163—28no—
157C163C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
158C4×H(5,𝔽2)—1631nomaximal, Sylow
159C2×H(5,𝔽2)—1631no—
160#520—1634no—
161#520—1632no—
162#518—1631no—
163#518—1634no—
164#518—1634no—
165C4×#41—1634no—
166C4×#41—1632no—
167C2×C4×D4—1634no—
168C2×C4×D4—1634no—
169C2×C4×D4D16311yescharacteristic, complemented
170H(5,𝔽2)—16316no—
171C2×#41—1634no—
172C2×#41—1632no—
173C22×D4—1634no—
174C22×D4—1634no—
175C22×D4C2×D16311yescharacteristic
176C23×C4—1634no—
177C23×C4C2×D16312yescomplemented
178C4×Q8—1634no—
179C4×Q8—1632no—
180C4×Q8—1632no—
181C4×D4—1634no—
182C4×D4—1634no—
183C4×D4—1638no—
184C4×D4—1634no—
185C4×D4—1638no—
186C4×D4—1638no—
187C4×D4—1634no—
188C4×D4—1634no—
189C4×D4—1638no—
190C4×D4—1638no—
191C4×D4—1632no—
192C4×D4—1632no—
193C4×D4C2×D16314yescomplemented
194C4×D4C2×D16314yescomplemented
195#117—1632no—
196#117—1634no—
197#117—1638no—
198#117—1634no—
199C2×C4⋊C4—1634no—
200C2×C4⋊C4—1634no—
201C2×C4⋊C4C2×D16311yescharacteristic, complemented
202C2×C22⋊C4—1634no—
203C2×C22⋊C4—1634no—
204C2×C22⋊C4—1638no—
205C2×C22⋊C4C2×D16312yescomplemented
206C2×C42—1634no—
207C2×C42—1634no—
208C2×C42C2×D16311yescharacteristic, complemented
209C24—1634no—
210C24C22×D16312yes—
211#41—16332no—
212#41—16316no—
213C2×Q8—1632no—
214C2×D4—16332no—
215C2×D4—1634no—
216C2×D4—1638no—
217C2×D4—16332no—
218C2×D4—1632no—
219C2×D4C4×D16318yescomplemented
220C2×D4C22×D16314yes—
221C22×C4—44no—
222C22×C4—6528no—
223C22×C4—1634no—
224C22×C4—1634no—
225C22×C4—1634no—
226C22×C4—1634no—
227C22×C4—1638no—
228C22×C4—1634no—
229C22×C4—1634no—
230C22×C4C22×D16314yes—
231C22×C4C22×D16311yescharacteristic
232C22×C4C22×D16311yescharacteristic
233C22×C4C22×D16314yes—
234C22×C4C22×D16312yes—
235C22×C4C22×D16311yescharacteristic
236C4⋊C4—1638no—
237C4⋊C4—1634no—
238C4⋊C4—1632no—
239C4⋊C4—1634no—
240C4⋊C4—1632no—
241C4⋊C4C22×D16314yes—
242C22⋊C4—1634no—
243C22⋊C4—1638no—
244C22⋊C4—1638no—
245C22⋊C4—1634no—
246C22⋊C4—1634no—
247C22⋊C4C22×D16318yes—
248C42—1634no—
249C42—1638no—
250C42—1634no—
251C42—1634no—
252C42C22×D16312yes—
253C42C22×D16312yes—
254C23—42no—
255C23—42no—
256C23—6524no—
257C23—6524no—
258C23—1634no—
259C23—16316no—
260C23C2×C4×D16318yescomplemented
261C23C23×D16311yescharacteristic
262C23C23×D16314yes—
263Q8—1638no—
264D4—16332no—
265D4—16316no—
266D4—1638no—
267D4C2×C4×D163116yescomplemented
268C2×C4—22no—
269C2×C4—28no—
270C2×C4—44no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—3268no—
274C2×C4—6528no—
275C2×C4—6524no—
276C2×C4—6524no—
277C2×C4—6524no—
278C2×C4—1634no—
279C2×C4—1634no—
280C2×C4—16316no—
281C2×C4—1634no—
282C2×C4—16316no—
283C2×C4C2×C4×D16314yescomplemented
284C2×C4C23×D16312yes—
285C2×C4C23×D16314yes—
286C2×C4C23×D16311yescharacteristic
287C2×C4C23×D16312yes—
288C2×C4C23×D16311yescharacteristic
289C22—21no—
290C22—24no—
291C22—21no—
292C22—24no—
293C22—48no—
294C22—3264no—
295C22—3264no—
296C22—65216no—
297C22—1638no—
298C22C22×C4×D16318yes—
299C22C22×C4×D16312yes—
300C22C24×D16311yescharacteristic
301C4—21no—
302C4—24no—
303C4—22no—
304C4—3264no—
305C4—3264no—
306C4—1638no—
307C4C22×C4×D16314yes—
308C4#1910478012yesdirect product factor
309C2—22no—
310C2—28no—
311C2—3268no—
312C2C23×C4×D16311yescharacteristic
313C2C2×#1910478011yescharacteristic
314C2#2378250111yescharacteristic
subgroupG/H
centerC2×C4C23×D163
commutatorC2×C163C24×C4
FrattiniC22C24×D163
FittingC2×C4×D4×C163C2
socle, cosocleC22×C163C25
prime radicalC2×#19104780C2
hypercenterC2×C4×D4D163
hypocenterC163C4×H(5,𝔽2)
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #23782146C2semidirect
3. #23782144C2semidirect
4. #23782140C2semidirect
5. #23782138C2semidirect
6. #23782137C2semidirect
7. C4×#14579699C2semidirect
8. C4×#14579698C2semidirect
9. C2×C4×C22⋊D163C2semidirect
10. C4×D4×D163C2semidirect
11. C2×C4×D4×C163C2semidirect
12. #19104780C4direct (N × H)
17. C22×C4×D163C22semidirect
18. C4×Dic326C22semidirect
19. C4×Dic326C22semidirect
20. #19104700C22semidirect
21. C4×D652C22semidirect
22. C4×D652C22semidirect
23. D4×Dic163C22semidirect
24. D4×Dic163C22semidirect
25. #19104697C22semidirect
26. C4×C22⋊D163C22semidirect
27. C4×C22⋊D163C22semidirect
28. C4×C22⋊D163C22semidirect
29. C4×C22⋊D163C22semidirect
30. C4×C22⋊D163C22semidirect
31. (C22⋊D163)⋊C4C22semidirect
32. (C22⋊D163)⋊C4C22semidirect
33. #19104694C22semidirect
34. #19104693C22semidirect
35. #19104692C22semidirect
36. #19104691C22semidirect
37. C2×Dic163⋊C4C22semidirect
38. C4⋊C4×D163C22semidirect
39. C2×C22⋊Dic163C22semidirect
40. C2×(C2×D163)⋊C4C22semidirect
41. C22⋊C4×D163C22semidirect
42. C2×C4×Dic163C22semidirect
43. C42×D163C22semidirect
45. C23×C4×C163C22semidirect
46. C4×D4×C163C22semidirect
47. C4×D4×C163C22semidirect
48. C2×C4⋊C4×C163C22semidirect
49. C2×C22⋊C4×C163C22semidirect
50. C2×C42×C163C22semidirect
52. #14579699C2×C4semidirect
53. #14579698C2×C4semidirect
56. C2×C22⋊D163C2×C4semidirect
59. D4×D163C2×C4semidirect
83. C2×D4×C163C2×C4semidirect
98. C22×D163C22×C4semidirect
100. Dic326C22×C4semidirect
101. D652C22×C4semidirect
102. C22⋊D163C22×C4semidirect
103. C22⋊D163C22×C4semidirect
106. C2×Dic163C22×C4semidirect
113. C4×D163C22×C4semidirect
116. C23×C163C22×C4semidirect
119. D4×C163C22×C4semidirect
125. C2×C4×C163C22×C4semidirect
147. C4×C163H(5,𝔽2)semidirect
157. C163C4×H(5,𝔽2)semidirect
169. C2×C4×D4D163semidirect
177. C23×C4C2×D163semidirect
193. C4×D4C2×D163semidirect
194. C4×D4C2×D163semidirect
201. C2×C4⋊C4C2×D163semidirect
205. C2×C22⋊C4C2×D163semidirect
208. C2×C42C2×D163semidirect
219. C2×D4C4×D163semidirect
260. C23C2×C4×D163semidirect
267. D4C2×C4×D163semidirect
283. C2×C4C2×C4×D163semidirect
308. C4#19104780direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191047802
#237821462
#237821442
#237821402
#237821382
#237821372
C4×#145796992
C4×#145796982
C2×C4×C22⋊D1632
C4×D4×D1632
C2×C4×D4×C1632
C4×H(5,𝔽2)163