Finite Group Databasebeta

← C2×#127×D163 #35227806

Subgroups — C2×#127×D163 #35227806

Order 20864.

3000 conjugacy classes of subgroups; only the 661 normal subgroups are shown.

normal subgroups only

This group has 3000 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
1C22×D4×D163C216yesmaximal, complemented
2C2×#19104732C211yesmaximal, characteristic, complemented
3C2×#19104731C216yesmaximal, complemented
4#127×D163C2116yesmaximal, direct product factor
5C2×C42×D163C211yesmaximal, characteristic, complemented
6C2×#127×C163C211yesmaximal, characteristic, complemented
7C24×D163C2214yes—
8C22×D652C2216yescomplemented
9C22×C22⋊D163C22112yescomplemented
10C2×D4×D163—248no—
11C2×D4×D163C22148yescomplemented
12C22×C4×D163C2213yes—
13#19104732C2218yescomplemented
14#19104731C22148yescomplemented
15C2×C4×Dic163C2213yescomplemented
16C42×D163C2218yescomplemented
17C22×D4×C163C2216yescomplemented
18#127×C163C2218yescomplemented
19C2×C42×C163C2211yescharacteristic, complemented
20C23×D163—248no—
21C23×D163C23116yes—
22C23×D163C2314yes—
23C23×D163C2311yescharacteristic
24C2×D652—224no—
25C2×D652C23124yescomplemented
26C2×C22⋊D163—248no—
27C2×C22⋊D163C23148yescomplemented
28D4×D163—2192no—
29C22×Dic163C2313yes—
30C2×C4×D163D4124yescomplemented
31C2×C4×D163C23112yes—
32C4×Dic163C23112yescomplemented
33C24×C163C2314yes—
34C2×D4×C163—224no—
35C2×D4×C163C23124yescomplemented
36C22×C4×C163C2313yes—
37C42×C163C2314yescomplemented
38C22×D163—224no—
39C22×D163—296no—
40C22×D163—464no—
41C22×D163C2×D4112yes—
42C22×D163C2418yes—
43C22×D163C2412yes—
44D652—248no—
45C22⋊D163—296no—
46C2×Dic163C2×D4112yescomplemented
47C2×Dic163C2416yes—
48C4×D163C2×D4148yescomplemented
49C23×C163—224no—
50C23×C163C2418yes—
51C23×C163C2411yescharacteristic
52D4×C163—248no—
53C2×C4×C163C2×D4112yescomplemented
54C2×C4×C163C2416yes—
55C22×C163—224no—
56C22×C163—416no—
57C22×C163C22×D416yes—
58C22×C163C2511yescharacteristic
59C2×D163—224no—
60C2×D163—416no—
61C2×D163—464no—
62C2×D163#127116yesdirect product factor
63C2×D163C22×D4112yes—
64C4×C163C22×D4112yescomplemented
65Dic163C22×D4112yescomplemented
66C2×C163—48no—
67C2×C163C2×#12714yescomplemented
68C2×C163C23×D413yes—
69D163—48no—
70D163C2×#12718yesdirect product factor
71C163C22×#12711yescharacteristic, complemented, Sylow
72C22×#127—1631nomaximal, Sylow
73C23×D4—1636no—
74C2×#127—1636no—
75C2×#127—16316no—
76C2×#127—1631no—
77C2×#127D16311yescharacteristic, direct product factor
78C22×C42—1631no—
79C25—1634no—
80C22×D4—32648no—
81C22×D4—16312no—
82C22×D4—16348no—
83C22×D4—1636no—
84C22×D4C2×D16316yescomplemented
85C23×C4—1633no—
86#127—16348no—
87#127—1638no—
88#127C2×D16318yesdirect product factor
89C2×C42—1633no—
90C2×C42—1638no—
91C2×C42C2×D16311yescharacteristic, complemented
92C24—32648no—
93C24—16316no—
94C24—1634no—
95C24—1631no—
96C24C22×D16314yes—
97C2×D4—224no—
98C2×D4—326192no—
99C2×D4—32648no—
100C2×D4—32624no—
101C2×D4—16348no—
102C2×D4—16324no—
103C2×D4C22×D163124yescomplemented
104C22×C4—1633no—
105C22×C4—16324no—
106C22×C4—16312no—
107C22×C4C22×D16313yes—
108C42—16312no—
109C42C22×D16314yescomplemented
110C23—224no—
111C23—32696no—
112C23—32624no—
113C23—65264no—
114C23—1638no—
115C23—16312no—
116C23—1632no—
117C23C23×D16318yes—
118C23C23×D16311yescharacteristic
119D4—248no—
120D4—32696no—
121D4—32648no—
122C2×C4—16312no—
123C2×C4—1636no—
124C2×C4—16348no—
125C2×C4D4×D163112yescomplemented
126C2×C4C23×D16316yes—
127C22—224no—
128C22—416no—
129C22—32624no—
130C22—65264no—
131C22—65216no—
132C22—16316no—
133C22—16312no—
134C22C2×D4×D16316yes—
135C22C24×D16311yescharacteristic
136C4—16312no—
137C4C2×D4×D163112yescomplemented
138C2—48no—
139C2—6528no—
140C2—1638no—
141C2#127×D16314yesdirect product factor
142C2C22×D4×D16313yes—
subgroupG/H
centerC23C23×D163
commutator, cosocleC22×C163C25
FrattiniC22C24×D163
FittingC2×#127×C163C2
socleC23×C163C24
hypercenterC2×#127D163
hypocenterC163C22×#127
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D163C2semidirect
2. C2×#19104732C2semidirect
3. C2×#19104731C2semidirect
4. #127×D163C2direct (N × H)
5. C2×C42×D163C2semidirect
6. C2×#127×C163C2semidirect
8. C22×D652C22semidirect
9. C22×C22⋊D163C22semidirect
11. C2×D4×D163C22semidirect
13. #19104732C22semidirect
14. #19104731C22semidirect
15. C2×C4×Dic163C22semidirect
16. C42×D163C22semidirect
17. C22×D4×C163C22semidirect
18. #127×C163C22semidirect
19. C2×C42×C163C22semidirect
25. C2×D652C23semidirect
27. C2×C22⋊D163C23semidirect
30. C2×C4×D163D4semidirect
32. C4×Dic163C23semidirect
35. C2×D4×C163C23semidirect
37. C42×C163C23semidirect
46. C2×Dic163C2×D4semidirect
48. C4×D163C2×D4semidirect
53. C2×C4×C163C2×D4semidirect
62. C2×D163#127direct (N × H)
64. C4×C163C22×D4semidirect
65. Dic163C22×D4semidirect
67. C2×C163C2×#127semidirect
70. D163C2×#127direct (N × H)
71. C163C22×#127semidirect
77. C2×#127D163direct (N × H)
84. C22×D4C2×D163semidirect
88. #127C2×D163direct (N × H)
91. C2×C42C2×D163semidirect
103. C2×D4C22×D163semidirect
109. C42C22×D163semidirect
125. C2×C4D4×D163semidirect
137. C4C2×D4×D163semidirect
141. C2#127×D163direct (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
C2×#191047322
C2×#191047312
#127×D1632
C2×C42×D1632
C2×#127×C1632
C22×#127163