Finite Group Databasebeta

← C4×#19104781 #35227743

Subgroups — C4×#19104781 #35227743

Order 20864.

1660 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19104781C211yesmaximal, characteristic
2#23782148C211yesmaximal, characteristic, complemented
3#23782147C212yesmaximal, complemented
4#23782145C213yesmaximal, complemented
5#23782139C213yesmaximal, complemented
6#23782137C216yesmaximal, complemented
7C4×#14579700C212yesmaximal, complemented
8C4×#14579699C213yesmaximal, complemented
9C2×C4×D652C213yesmaximal, complemented
10C4×D4×D163C216yesmaximal, complemented
11C4×#41×C163C211yesmaximal, characteristic, complemented
12#19104781C4116yesdirect product factor
13C2×#14579700C2212yes—
14C2×#14579699C2213yes—
15C22×D652C2213yes—
16C2×D4×D163C2216yes—
17C22×C4×D163C2216yescomplemented
18Q8×Dic163C2212yescomplemented
19C4×Dic326C2213yescomplemented
20C4×Dic326C2211yescharacteristic, complemented
21C4×D652C2216yescomplemented
22C4×D652C2216yescomplemented
23C4×D652C2216yescomplemented
24C4×D652C2213yescomplemented
25C4×D652C2213yescomplemented
26D4×Dic163C2216yescomplemented
27#19104697C2216yescomplemented
28#19104697C2216yescomplemented
29C4×C22⋊D163C2216yescomplemented
30C4×C22⋊D163C2216yescomplemented
31(C22⋊D163)⋊C4C22112yescomplemented
32#19104694C2213yescomplemented
33#19104693C2216yescomplemented
34#19104692C2216yescomplemented
35C2×C4⋊Dic163C2213yescomplemented
36C4⋊C4×D163C2216yescomplemented
37C2×(C2×D163)⋊C4C2216yescomplemented
38C22⋊C4×D163C22112yescomplemented
39C42×D163C2216yescomplemented
40C2×#41×C163C2211yescharacteristic
41C4×Q8×C163C2211yescharacteristic, complemented
42C4×Q8×C163C2211yescharacteristic, complemented
43C4×D4×C163C2213yescomplemented
44C4×D4×C163C2213yescomplemented
45#117×C163C2213yescomplemented
46C2×C42×C163C2213yescomplemented
47C23×D163C2316yes—
48#14579700C2×C4116yescomplemented
49#14579699C2×C4124yescomplemented
50C2×Dic326C2311yescharacteristic
51C2×D652C2×C4124yescomplemented
52C2×D652C2316yes—
53C2×D652C2313yes—
54C2×C22⋊D163C2316yes—
55D4×D163C2×C4148yescomplemented
56C22×Dic163C2316yes—
57C2×C4×D163—412no—
58C2×C4×D163C2316yes—
59C2×C4×D163C23112yes—
60C2×C4×D163C2316yes—
61C2×C4×D163C2316yes—
62C4⋊Dic163C2316yes—
63C4⋊Dic163C2313yes—
64C4⋊Dic163C2311yescharacteristic
65Dic163⋊C4C2316yes—
66Dic163⋊C4C2312yes—
67C22⋊Dic163C2316yes—
68(C2×D163)⋊C4C2316yes—
69(C2×D163)⋊C4C23112yes—
70(C2×D163)⋊C4C2316yes—
71C4×Dic163C2312yes—
72C4×Dic163C2316yes—
73C4×Dic163C2316yes—
74#41×C163C2×C418yescomplemented
75C2×Q8×C163C2311yescharacteristic
76C2×D4×C163C2313yes—
77C22×C4×C163C2313yes—
78C22×C4×C163C2313yes—
79C22×C4×C163C2313yes—
80C4⋊C4×C163C2313yes—
81C4⋊C4×C163C2313yes—
82C22⋊C4×C163C2316yes—
83C42×C163C2311yescharacteristic
84C42×C163C2313yes—
85C42×C163C2313yes—
86C42×C163C2313yes—
87C22×D163—46no—
88C22×D163—46no—
89C22×D163C22×C4124yescomplemented
90C22×D163C2416yes—
91Dic326C22×C414yescomplemented
92D652C22×C4124yescomplemented
93D652C22×C4112yescomplemented
94C22⋊D163C22×C4124yescomplemented
95C2×Dic163—46no—
96C2×Dic163C2412yes—
97C2×Dic163C2416yes—
98C2×Dic163C2412yes—
99C4×D163—212no—
100C4×D163—412no—
101C4×D163—46no—
102C4×D163C22×C4124yescomplemented
103C23×C163C2413yes—
104Q8×C163C22×C414yescomplemented
105D4×C163C22×C4112yescomplemented
106C2×C4×C163—26no—
107C2×C4×C163—43no—
108C2×C4×C163C22×C4112yescomplemented
109C2×C4×C163C2411yescharacteristic
110C2×C4×C163C2413yes—
111C2×C4×C163C2413yes—
112C2×C4×C163C2411yescharacteristic
113C2×C4×C163C2413yes—
114C2×C4×C163C2411yescharacteristic
115C22×C163—23no—
116C22×C163—23no—
117C22×C163C23×C416yes—
118C22×C163C2511yescharacteristic
119C2×D163—26no—
120C2×D163—26no—
121C2×D163—424no—
122C2×D163C23×C4112yes—
123C4×C163—23no—
124C4×C163—21no—
125C4×C163—23no—
126C4×C163C23×C412yes—
127C4×C163C23×C416yes—
128C4×C163H(5,𝔽2)12yescomplemented
129Dic163—26no—
130Dic163—22no—
131Dic163C23×C414yes—
132C2×C163—26no—
133C2×C163C24×C411yescharacteristic
134C2×C163C2×H(5,𝔽2)11yescharacteristic
135C2×C163#58511yescharacteristic
136D163—212no—
137C163C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
138C4×H(5,𝔽2)—1631nomaximal, Sylow
139C2×H(5,𝔽2)—1631no—
140#520—1631no—
141#520—1632no—
142#520—1633no—
143#518—1636no—
144#518—1633no—
145C4×#41—1632no—
146C4×#41—1633no—
147C4×#41D16311yescharacteristic, complemented
148C2×C4×D4—1636no—
149C2×C4×D4—1633no—
150H(5,𝔽2)—16316no—
151C2×#41—1632no—
152C2×#41—1633no—
153C2×#41C2×D16311yescharacteristic
154C22×D4—1636no—
155C22×D4—1633no—
156C23×C4—1636no—
157C4×Q8—1632no—
158C4×Q8—1631no—
159C4×Q8—1633no—
160C4×Q8C2×D16311yescharacteristic, complemented
161C4×Q8C2×D16311yescharacteristic, complemented
162C4×D4—1636no—
163C4×D4—1636no—
164C4×D4—1636no—
165C4×D4—1636no—
166C4×D4—1636no—
167C4×D4—16312no—
168C4×D4—1636no—
169C4×D4—1633no—
170C4×D4—1636no—
171C4×D4—1636no—
172C4×D4—1633no—
173C4×D4C2×D16313yescomplemented
174C4×D4C2×D16313yescomplemented
175#117—1633no—
176#117—1636no—
177#117—1636no—
178#117C2×D16313yescomplemented
179C2×C4⋊C4—1633no—
180C2×C4⋊C4—1636no—
181C2×C22⋊C4—1636no—
182C2×C22⋊C4—16312no—
183C2×C42—1636no—
184C2×C42C2×D16313yescomplemented
185C24—1636no—
186#41—16316no—
187#41—16324no—
188#41C4×D16318yescomplemented
189C2×Q8—1631no—
190C2×Q8C22×D16311yescharacteristic
191C2×D4—1636no—
192C2×D4—16348no—
193C2×D4—16324no—
194C2×D4—1636no—
195C2×D4—1633no—
196C2×D4C22×D16313yes—
197C22×C4—65212no—
198C22×C4—1636no—
199C22×C4—1636no—
200C22×C4—1636no—
201C22×C4—16312no—
202C22×C4—1636no—
203C22×C4C22×D16313yes—
204C22×C4C22×D16313yes—
205C22×C4C22×D16313yes—
206C4⋊C4—1636no—
207C4⋊C4—1636no—
208C4⋊C4—1633no—
209C4⋊C4—1632no—
210C4⋊C4—1631no—
211C4⋊C4C22×D16313yes—
212C4⋊C4C22×D16313yes—
213C22⋊C4—1636no—
214C22⋊C4—1636no—
215C22⋊C4—16312no—
216C22⋊C4—1636no—
217C22⋊C4C22×D16316yes—
218C42—1636no—
219C42—1636no—
220C42—1632no—
221C42C22×D16313yes—
222C42C22×D16313yes—
223C42C22×D16313yes—
224C42C22×D16311yescharacteristic
225C23—6526no—
226C23—6526no—
227C23—1636no—
228C23—16324no—
229C23C23×D16313yes—
230Q8—1634no—
231Q8C2×C4×D16314yescomplemented
232D4—16324no—
233D4—16324no—
234D4—16312no—
235D4C2×C4×D163112yescomplemented
236C2×C4—26no—
237C2×C4—43no—
238C2×C4—32612no—
239C2×C4—65212no—
240C2×C4—6526no—
241C2×C4—6526no—
242C2×C4—1632no—
243C2×C4—1636no—
244C2×C4—1632no—
245C2×C4—16324no—
246C2×C4C2×C4×D163112yescomplemented
247C2×C4C23×D16313yes—
248C2×C4C23×D16311yescharacteristic
249C2×C4C23×D16313yes—
250C2×C4C23×D16313yes—
251C2×C4C23×D16311yescharacteristic
252C2×C4C23×D16311yescharacteristic
253C22—23no—
254C22—23no—
255C22—3266no—
256C22—3266no—
257C22—65224no—
258C22—16312no—
259C22C22×C4×D16316yes—
260C22C24×D16311yescharacteristic
261C4—23no—
262C4—21no—
263C4—23no—
264C4—3266no—
265C4—3262no—
266C4—1634no—
267C4C22×C4×D16316yes—
268C4C22×C4×D16312yes—
269C4#1910478112yesdirect product factor
270C2—26no—
271C2—32612no—
272C2C23×C4×D16311yescharacteristic
273C2C2×#1910478111yescharacteristic
274C2#2378250111yescharacteristic
subgroupG/H
centerC2×C4C23×D163
commutatorC2×C163C24×C4
FrattiniC22C24×D163
FittingC4×#41×C163C2
socle, cosocleC22×C163C25
prime radicalC2×#19104781C2
hypercenterC4×#41D163
hypocenterC163C4×H(5,𝔽2)
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #23782148C2semidirect
3. #23782147C2semidirect
4. #23782145C2semidirect
5. #23782139C2semidirect
6. #23782137C2semidirect
7. C4×#14579700C2semidirect
8. C4×#14579699C2semidirect
9. C2×C4×D652C2semidirect
10. C4×D4×D163C2semidirect
11. C4×#41×C163C2semidirect
12. #19104781C4direct (N × H)
17. C22×C4×D163C22semidirect
18. Q8×Dic163C22semidirect
19. C4×Dic326C22semidirect
20. C4×Dic326C22semidirect
21. C4×D652C22semidirect
22. C4×D652C22semidirect
23. C4×D652C22semidirect
24. C4×D652C22semidirect
25. C4×D652C22semidirect
26. D4×Dic163C22semidirect
27. #19104697C22semidirect
28. #19104697C22semidirect
29. C4×C22⋊D163C22semidirect
30. C4×C22⋊D163C22semidirect
31. (C22⋊D163)⋊C4C22semidirect
32. #19104694C22semidirect
33. #19104693C22semidirect
34. #19104692C22semidirect
35. C2×C4⋊Dic163C22semidirect
36. C4⋊C4×D163C22semidirect
37. C2×(C2×D163)⋊C4C22semidirect
38. C22⋊C4×D163C22semidirect
39. C42×D163C22semidirect
41. C4×Q8×C163C22semidirect
42. C4×Q8×C163C22semidirect
43. C4×D4×C163C22semidirect
44. C4×D4×C163C22semidirect
45. #117×C163C22semidirect
46. C2×C42×C163C22semidirect
48. #14579700C2×C4semidirect
49. #14579699C2×C4semidirect
51. C2×D652C2×C4semidirect
55. D4×D163C2×C4semidirect
74. #41×C163C2×C4semidirect
89. C22×D163C22×C4semidirect
91. Dic326C22×C4semidirect
92. D652C22×C4semidirect
93. D652C22×C4semidirect
94. C22⋊D163C22×C4semidirect
102. C4×D163C22×C4semidirect
104. Q8×C163C22×C4semidirect
105. D4×C163C22×C4semidirect
108. C2×C4×C163C22×C4semidirect
128. C4×C163H(5,𝔽2)semidirect
137. C163C4×H(5,𝔽2)semidirect
147. C4×#41D163semidirect
160. C4×Q8C2×D163semidirect
161. C4×Q8C2×D163semidirect
173. C4×D4C2×D163semidirect
174. C4×D4C2×D163semidirect
178. #117C2×D163semidirect
184. C2×C42C2×D163semidirect
188. #41C4×D163semidirect
231. Q8C2×C4×D163semidirect
235. D4C2×C4×D163semidirect
246. C2×C4C2×C4×D163semidirect
269. C4#19104781direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191047812
#237821482
#237821472
#237821452
#237821392
#237821372
C4×#145797002
C4×#145796992
C2×C4×D6522
C4×D4×D1632
C4×#41×C1632
C4×H(5,𝔽2)163