Finite Group Databasebeta

← C23×D4×D163 #35229327

Subgroups — C23×D4×D163 #35229327

Order 20864.

10552 conjugacy classes of subgroups; only the 3557 normal subgroups are shown.

normal subgroups only

This group has 10552 conjugacy classes of subgroups — too many to draw. Only its 3557 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×D163C212yesmaximal, complemented
2C23×D652C211yesmaximal, characteristic, complemented
3C23×C22⋊D163C212yesmaximal, complemented
4C22×D4×D163C2156yesmaximal, direct product factor
5C23×C4×D163C211yesmaximal, characteristic, complemented
6C23×D4×C163C211yesmaximal, characteristic, complemented
7C24×D163—232no—
8C24×D163C2211yescharacteristic
9C24×D163C2212yescomplemented
10C24×D163C22156yescomplemented
11C22×D652C22128yescomplemented
12C22×C22⋊D163C22156yescomplemented
13C2×D4×D163C221448yesdirect product factor
14C23×Dic163C2211yescharacteristic, complemented
15C22×C4×D163C22128yescomplemented
16C25×C163C2212yescomplemented
17C22×D4×C163C22128yescomplemented
18C23×C4×C163C2211yescharacteristic, complemented
19C23×D163—2448no—
20C23×D163—216no—
21C23×D163D4116yesdirect product factor
22C23×D163C23114yes—
23C23×D163C23128yescomplemented
24C23×D163C231224yescomplemented
25C2×D652C231112yescomplemented
26C2×C22⋊D163C231224yescomplemented
27D4×D163C231512yesdirect product factor
28C22×Dic163C23114yescomplemented
29C2×C4×D163C231112yescomplemented
30C24×C163—216no—
31C24×C163C2311yescharacteristic
32C24×C163C23128yescomplemented
33C2×D4×C163C231112yescomplemented
34C22×C4×C163C23114yescomplemented
35C22×D163—2112no—
36C22×D163—2896no—
37C22×D163C2×D41112yesdirect product factor
38C22×D163C24128yes—
39C22×D163C241128yescomplemented
40C22×D163C24156yescomplemented
41D652C24164yescomplemented
42C22⋊D163C241128yescomplemented
43C2×Dic163C24128yescomplemented
44C4×D163C24164yescomplemented
45C23×C163—2112no—
46C23×C163C2×D418yescomplemented
47C23×C163C2417yes—
48C23×C163C24156yescomplemented
49D4×C163C24164yescomplemented
50C2×C4×C163C24128yescomplemented
51C22×C163—2112no—
52C22×C163C22×D4128yescomplemented
53C22×C163C2517yes—
54C22×C163C25116yescomplemented
55C2×D163—2112no—
56C2×D163—2256no—
57C2×D163C22×D41112yesdirect product factor
58C2×D163C2518yes—
59C2×D163C25116yescomplemented
60C4×C163C2518yescomplemented
61Dic163C2518yescomplemented
62C2×C163—216no—
63C2×C163C23×D4114yescomplemented
64C2×C163C2611yescharacteristic
65D163—216no—
66D163C23×D4116yesdirect product factor
67C163C24×D411yescharacteristic, complemented, Sylow
68C24×D4—1631nomaximal, Sylow
69C26—1632no—
70C23×D4—1632no—
71C23×D4—16356no—
72C23×D4—1631no—
73C23×D4D16311yescharacteristic, direct product factor
74C24×C4—1631no—
75C25—32632no—
76C25—1632no—
77C25—16356no—
78C25—1631no—
79C25C2×D16312yescomplemented
80C22×D4—16356no—
81C22×D4—163448no—
82C22×D4—16328no—
83C22×D4C2×D163128yesdirect product factor
84C23×C4—1631no—
85C23×C4—16328no—
86C23×C4C2×D16311yescharacteristic, complemented
87C24—216no—
88C24—326448no—
89C24—32616no—
90C24—16328no—
91C24—163224no—
92C24—16316no—
93C24—16314no—
94C24C22×D16311yescharacteristic
95C24C22×D163128yescomplemented
96C2×D4—163224no—
97C2×D4—163512no—
98C2×D4—163112no—
99C2×D4C22×D1631112yesdirect product factor
100C22×C4—16314no—
101C22×C4—163112no—
102C22×C4C22×D163114yescomplemented
103C23—2112no—
104C23—326896no—
105C23—326112no—
106C23—16356no—
107C23—163128no—
108C23—163112no—
109C23—16328no—
110C23D4×D16318yesdirect product factor
111C23C23×D16317yes—
112C23C23×D163156yescomplemented
113D4—163128no—
114D4—16364no—
115D4C23×D163164yesdirect product factor
116C2×C4—16328no—
117C2×C4—16364no—
118C2×C4C23×D163128yescomplemented
119C22—2112no—
120C22—326256no—
121C22—326112no—
122C22—16316no—
123C22—163112no—
124C22—1638no—
125C22C2×D4×D163128yesdirect product factor
126C22C24×D16317yes—
127C22C24×D163116yescomplemented
128C4—1638no—
129C4C24×D16318yescomplemented
130C2—216no—
131C2—32616no—
132C2—16316no—
133C2C22×D4×D163114yesdirect product factor
134C2C25×D16311yescharacteristic
subgroupG/H
centerC24C22×D163
commutator, cosocleC2×C163C26
FrattiniC2C25×D163
FittingC23×D4×C163C2
socleC24×C163C23
hypercenterC23×D4D163
hypocenterC163C24×D4
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C25×D163C2semidirect
2. C23×D652C2semidirect
3. C23×C22⋊D163C2semidirect
4. C22×D4×D163C2direct (N × H)
5. C23×C4×D163C2semidirect
6. C23×D4×C163C2semidirect
9. C24×D163C22semidirect
10. C24×D163C22semidirect
11. C22×D652C22semidirect
12. C22×C22⋊D163C22semidirect
13. C2×D4×D163C22direct (N × H)
14. C23×Dic163C22semidirect
15. C22×C4×D163C22semidirect
16. C25×C163C22semidirect
17. C22×D4×C163C22semidirect
18. C23×C4×C163C22semidirect
21. C23×D163D4direct (N × H)
23. C23×D163C23semidirect
24. C23×D163C23semidirect
25. C2×D652C23semidirect
26. C2×C22⋊D163C23semidirect
27. D4×D163C23direct (N × H)
28. C22×Dic163C23semidirect
29. C2×C4×D163C23semidirect
32. C24×C163C23semidirect
33. C2×D4×C163C23semidirect
34. C22×C4×C163C23semidirect
37. C22×D163C2×D4direct (N × H)
39. C22×D163C24semidirect
40. C22×D163C24semidirect
41. D652C24semidirect
42. C22⋊D163C24semidirect
43. C2×Dic163C24semidirect
44. C4×D163C24semidirect
46. C23×C163C2×D4semidirect
48. C23×C163C24semidirect
49. D4×C163C24semidirect
50. C2×C4×C163C24semidirect
52. C22×C163C22×D4semidirect
54. C22×C163C25semidirect
57. C2×D163C22×D4direct (N × H)
59. C2×D163C25semidirect
60. C4×C163C25semidirect
61. Dic163C25semidirect
63. C2×C163C23×D4semidirect
66. D163C23×D4direct (N × H)
67. C163C24×D4semidirect
73. C23×D4D163direct (N × H)
79. C25C2×D163semidirect
83. C22×D4C2×D163direct (N × H)
86. C23×C4C2×D163semidirect
95. C24C22×D163semidirect
99. C2×D4C22×D163direct (N × H)
102. C22×C4C22×D163semidirect
110. C23D4×D163direct (N × H)
112. C23C23×D163semidirect
115. D4C23×D163direct (N × H)
118. C2×C4C23×D163semidirect
125. C22C2×D4×D163direct (N × H)
127. C22C24×D163semidirect
129. C4C24×D163semidirect
133. C2C22×D4×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
C23×D6522
C23×C22⋊D1632
C22×D4×D1632
C23×C4×D1632
C23×D4×C1632
C24×D4163