Finite Group Databasebeta

← C2×#120×D163 #35227750

Subgroups — C2×#120×D163 #35227750

Order 20864.

4544 conjugacy classes of subgroups; only the 661 normal subgroups are shown.

normal subgroups only

This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 661 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
1C25×D163C211yesmaximal, characteristic, complemented
2C22×D4×D163C213yesmaximal, complemented
3C2×#19104705C213yesmaximal, complemented
4C2×#19104704C211yesmaximal, characteristic, complemented
5C2×#19104703C213yesmaximal, complemented
6#120×D163C2116yesmaximal, direct product factor
7C2×C22⋊C4×D163C213yesmaximal, complemented
8C2×#120×C163C211yesmaximal, characteristic, complemented
9C24×D163—224no—
10C24×D163C2213yes—
11C24×D163C2213yescomplemented
12C24×D163C2218yescomplemented
13C24×D163C2211yescharacteristic, complemented
14C22×D652C2213yescomplemented
15C22×C22⋊D163C2213yescomplemented
16C22×C22⋊D163C2213yescomplemented
17C2×D4×D163—224no—
18C2×D4×D163C22124yescomplemented
19C22×C4×D163C2213yescomplemented
20#19104705C22124yescomplemented
21#19104704C2218yescomplemented
22#19104703C22124yescomplemented
23C2×C22⋊Dic163C2213yescomplemented
24C2×(C2×D163)⋊C4C2216yescomplemented
25C22⋊C4×D163C22124yescomplemented
26C25×C163C2211yescharacteristic, complemented
27C22×D4×C163C2213yescomplemented
28#120×C163C2218yescomplemented
29C2×C22⋊C4×C163C2213yescomplemented
30C23×D163—2128no—
31C23×D163—224no—
32C23×D163—224no—
33C23×D163—296no—
34C23×D163—212no—
35C23×D163—212no—
36C23×D163D4124yescomplemented
37C23×D163C23112yes—
38C23×D163C2313yes—
39C23×D163C2311yescharacteristic
40C23×D163C23112yescomplemented
41C23×D163C2311yescharacteristic, complemented
42C23×D163C2314yescomplemented
43C2×D652—212no—
44C2×D652C23112yescomplemented
45C2×C22⋊D163—212no—
46C2×C22⋊D163—212no—
47C2×C22⋊D163C23112yescomplemented
48C2×C22⋊D163C23112yescomplemented
49D4×D163—296no—
50C22×Dic163C2313yescomplemented
51C2×C4×D163—212no—
52C2×C4×D163C23112yescomplemented
53C22⋊Dic163C23112yescomplemented
54(C2×D163)⋊C4C23124yescomplemented
55C24×C163—212no—
56C24×C163C2313yes—
57C24×C163C2314yescomplemented
58C24×C163C2311yescharacteristic, complemented
59C2×D4×C163—212no—
60C2×D4×C163C23112yescomplemented
61C22×C4×C163C2313yescomplemented
62C22⋊C4×C163C23112yescomplemented
63C22×D163—296no—
64C22×D163—2256no—
65C22×D163—212no—
66C22×D163—224no—
67C22×D163—296no—
68C22×D163—248no—
69C22×D163—248no—
70C22×D163—26no—
71C22×D163—224no—
72C22×D163—416no—
73C22×D163C2×D4112yes—
74C22×D163C2×D4148yescomplemented
75C22×D163C2×D4112yescomplemented
76C22×D163C2416yes—
77C22×D163C2412yes—
78C22×D163C2412yescomplemented
79D652—224no—
80C22⋊D163—224no—
81C22⋊D163—224no—
82C2×Dic163—26no—
83C2×Dic163C2416yescomplemented
84C4×D163—224no—
85C23×C163—232no—
86C23×C163—212no—
87C23×C163—224no—
88C23×C163—26no—
89C23×C163C2×D4112yescomplemented
90C23×C163C2416yes—
91C23×C163C2411yescharacteristic
92C23×C163C2412yescomplemented
93D4×C163—224no—
94C2×C4×C163—26no—
95C2×C4×C163C2416yescomplemented
96C22×C163—232no—
97C22×C163—224no—
98C22×C163—212no—
99C22×C163—26no—
100C22×C163—44no—
101C22×C163C22×D416yes—
102C22×C163C22×D4112yescomplemented
103C22×C163C2511yescharacteristic
104C2×D163—296no—
105C2×D163—224no—
106C2×D163—212no—
107C2×D163—296no—
108C2×D163—26no—
109C2×D163—44no—
110C2×D163—416no—
111C2×D163#120116yesdirect product factor
112C2×D163C22×D4112yes—
113C2×D163C22×D4112yescomplemented
114C4×C163—26no—
115Dic163—26no—
116C2×C163—212no—
117C2×C163—42no—
118C2×C163C2×#12014yescomplemented
119C2×C163C23×D413yes—
120D163—212no—
121D163—42no—
122D163C2×#12018yesdirect product factor
123C163C22×#12011yescharacteristic, complemented, Sylow
124C22×#120—1631nomaximal, Sylow
125C26—1631no—
126C23×D4—1633no—
127C2×#120—1631no—
128C2×#120—1633no—
129C2×#120—16316no—
130C2×#120—1633no—
131C2×#120D16311yescharacteristic, direct product factor
132C22×C22⋊C4—1633no—
133C25—32624no—
134C25—1633no—
135C25—1638no—
136C25—1631no—
137C25—1633no—
138C25C2×D16311yescharacteristic, complemented
139C22×D4—32624no—
140C22×D4—1633no—
141C22×D4—1633no—
142C22×D4—16324no—
143C22×D4—1633no—
144C22×D4C2×D16313yescomplemented
145C23×C4—1633no—
146#120—1638no—
147#120—16324no—
148#120—16324no—
149#120C2×D16318yesdirect product factor
150C2×C22⋊C4—1633no—
151C2×C22⋊C4—1636no—
152C2×C22⋊C4—16324no—
153C2×C22⋊C4C2×D16313yescomplemented
154C24—212no—
155C24—326128no—
156C24—32624no—
157C24—32624no—
158C24—32696no—
159C24—32612no—
160C24—32612no—
161C24—16312no—
162C24—1631no—
163C24—1634no—
164C24—16324no—
165C24—16312no—
166C24—1633no—
167C24—1631no—
168C24C22×D16313yes—
169C24C22×D16314yescomplemented
170C24C22×D16311yescharacteristic, complemented
171C2×D4—212no—
172C2×D4—32612no—
173C2×D4—32696no—
174C2×D4—32612no—
175C2×D4—32612no—
176C2×D4—16312no—
177C2×D4—16312no—
178C2×D4—16312no—
179C2×D4C22×D163112yescomplemented
180C22×C4—32612no—
181C22×C4—1633no—
182C22×C4—16312no—
183C22×C4C22×D16313yescomplemented
184C22⋊C4—16312no—
185C22⋊C4—16324no—
186C22⋊C4C22×D163112yescomplemented
187C23—232no—
188C23—212no—
189C23—224no—
190C23—26no—
191C23—326256no—
192C23—32696no—
193C23—32696no—
194C23—32648no—
195C23—32648no—
196C23—32624no—
197C23—32612no—
198C23—32624no—
199C23—3266no—
200C23—65216no—
201C23—1632no—
202C23—16312no—
203C23—16348no—
204C23—1636no—
205C23—16312no—
206C23—1632no—
207C23D4×D163112yescomplemented
208C23C23×D16316yes—
209C23C23×D16311yescharacteristic
210C23C23×D16312yescomplemented
211D4—224no—
212D4—32624no—
213D4—32624no—
214D4—32624no—
215C2×C4—26no—
216C2×C4—32624no—
217C2×C4—3266no—
218C2×C4—1636no—
219C2×C4C23×D16316yescomplemented
220C22—232no—
221C22—224no—
222C22—212no—
223C22—26no—
224C22—44no—
225C22—32696no—
226C22—32696no—
227C22—32624no—
228C22—32612no—
229C22—3266no—
230C22—65216no—
231C22—6524no—
232C22—16312no—
233C22—16316no—
234C22—16312no—
235C22C2×D4×D16316yes—
236C22C2×D4×D163112yescomplemented
237C22C24×D16311yescharacteristic
238C4—26no—
239C4—3266no—
240C2—212no—
241C2—42no—
242C2—32612no—
243C2—6522no—
244C2—1638no—
245C2#120×D16314yesdirect product factor
246C2C22×D4×D16313yes—
subgroupG/H
centerC23C23×D163
commutator, cosocleC22×C163C25
FrattiniC22C24×D163
FittingC2×#120×C163C2
socleC23×C163C24
hypercenterC2×#120D163
hypocenterC163C22×#120
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C25×D163C2semidirect
2. C22×D4×D163C2semidirect
3. C2×#19104705C2semidirect
4. C2×#19104704C2semidirect
5. C2×#19104703C2semidirect
6. #120×D163C2direct (N × H)
7. C2×C22⋊C4×D163C2semidirect
8. C2×#120×C163C2semidirect
11. C24×D163C22semidirect
12. C24×D163C22semidirect
13. C24×D163C22semidirect
14. C22×D652C22semidirect
15. C22×C22⋊D163C22semidirect
16. C22×C22⋊D163C22semidirect
18. C2×D4×D163C22semidirect
19. C22×C4×D163C22semidirect
20. #19104705C22semidirect
21. #19104704C22semidirect
22. #19104703C22semidirect
23. C2×C22⋊Dic163C22semidirect
24. C2×(C2×D163)⋊C4C22semidirect
25. C22⋊C4×D163C22semidirect
26. C25×C163C22semidirect
27. C22×D4×C163C22semidirect
28. #120×C163C22semidirect
29. C2×C22⋊C4×C163C22semidirect
36. C23×D163D4semidirect
40. C23×D163C23semidirect
41. C23×D163C23semidirect
42. C23×D163C23semidirect
44. C2×D652C23semidirect
47. C2×C22⋊D163C23semidirect
48. C2×C22⋊D163C23semidirect
50. C22×Dic163C23semidirect
52. C2×C4×D163C23semidirect
53. C22⋊Dic163C23semidirect
54. (C2×D163)⋊C4C23semidirect
57. C24×C163C23semidirect
58. C24×C163C23semidirect
60. C2×D4×C163C23semidirect
61. C22×C4×C163C23semidirect
62. C22⋊C4×C163C23semidirect
74. C22×D163C2×D4semidirect
75. C22×D163C2×D4semidirect
78. C22×D163C24semidirect
83. C2×Dic163C24semidirect
89. C23×C163C2×D4semidirect
92. C23×C163C24semidirect
95. C2×C4×C163C24semidirect
102. C22×C163C22×D4semidirect
111. C2×D163#120direct (N × H)
113. C2×D163C22×D4semidirect
118. C2×C163C2×#120semidirect
122. D163C2×#120direct (N × H)
123. C163C22×#120semidirect
131. C2×#120D163direct (N × H)
138. C25C2×D163semidirect
144. C22×D4C2×D163semidirect
149. #120C2×D163direct (N × H)
153. C2×C22⋊C4C2×D163semidirect
169. C24C22×D163semidirect
170. C24C22×D163semidirect
179. C2×D4C22×D163semidirect
183. C22×C4C22×D163semidirect
186. C22⋊C4C22×D163semidirect
207. C23D4×D163semidirect
210. C23C23×D163semidirect
219. C2×C4C23×D163semidirect
236. C22C2×D4×D163semidirect
245. C2#120×D163direct (N × H)

Maximal subgroups

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

subgroupindex
C25×D1632
C22×D4×D1632
C2×#191047052
C2×#191047042
C2×#191047032
#120×D1632
C2×C22⋊C4×D1632
C2×#120×C1632
C22×#120163