Finite Group Databasebeta

← C23×D4×D113 #28405365

Subgroups — C23×D4×D113 #28405365

Order 14464.

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×D113C212yesmaximal, complemented
2C23×D452C211yesmaximal, characteristic, complemented
3C23×C22⋊D113C212yesmaximal, complemented
4C22×D4×D113C2156yesmaximal, direct product factor
5C23×C4×D113C211yesmaximal, characteristic, complemented
6C23×D4×C113C211yesmaximal, characteristic, complemented
7C24×D113—232no—
8C24×D113C2211yescharacteristic
9C24×D113C2212yescomplemented
10C24×D113C22156yescomplemented
11C22×D452C22128yescomplemented
12C22×C22⋊D113C22156yescomplemented
13C2×D4×D113C221448yesdirect product factor
14C23×Dic113C2211yescharacteristic, complemented
15C22×C4×D113C22128yescomplemented
16C25×C113C2212yescomplemented
17C22×D4×C113C22128yescomplemented
18C23×C4×C113C2211yescharacteristic, complemented
19C23×D113—216no—
20C23×D113—2448no—
21C23×D113D4116yesdirect product factor
22C23×D113C23114yes—
23C23×D113C231224yescomplemented
24C23×D113C23128yescomplemented
25C2×D452C231112yescomplemented
26C2×C22⋊D113C231224yescomplemented
27D4×D113C231512yesdirect product factor
28C22×Dic113C23114yescomplemented
29C2×C4×D113C231112yescomplemented
30C24×C113—216no—
31C24×C113C2311yescharacteristic
32C24×C113C23128yescomplemented
33C2×D4×C113C231112yescomplemented
34C22×C4×C113C23114yescomplemented
35C23×C113—2112no—
36C23×C113C2×D418yescomplemented
37C23×C113C2417yes—
38C23×C113C24156yescomplemented
39C22×D113—2112no—
40C22×D113—2896no—
41C22×D113C2×D41112yesdirect product factor
42C22×D113C24128yes—
43C22×D113C241128yescomplemented
44C22×D113C24156yescomplemented
45D4×C113C24164yescomplemented
46C2×C4×C113C24128yescomplemented
47C22⋊D113C241128yescomplemented
48C2×Dic113C24128yescomplemented
49D452C24164yescomplemented
50C4×D113C24164yescomplemented
51C22×C113—2112no—
52C22×C113C22×D4128yescomplemented
53C22×C113C2517yes—
54C22×C113C25116yescomplemented
55C2×D113—2112no—
56C2×D113—2256no—
57C2×D113C22×D41112yesdirect product factor
58C2×D113C2518yes—
59C2×D113C25116yescomplemented
60C4×C113C2518yescomplemented
61Dic113C2518yescomplemented
62C2×C113—216no—
63C2×C113C23×D4114yescomplemented
64C2×C113C2611yescharacteristic
65D113—216no—
66D113C23×D4116yesdirect product factor
67C24×D4—1131nomaximal, Sylow
68C113C24×D411yescharacteristic, complemented, Sylow
69C26—1132no—
70C23×D4—1132no—
71C23×D4—11356no—
72C23×D4—1131no—
73C23×D4D11311yescharacteristic, direct product factor
74C24×C4—1131no—
75C25—1131no—
76C25—1132no—
77C25—11356no—
78C25—22632no—
79C25C2×D11312yescomplemented
80C22×D4—11356no—
81C22×D4—113448no—
82C22×D4—11328no—
83C22×D4C2×D113128yesdirect product factor
84C23×C4—1131no—
85C23×C4—11328no—
86C23×C4C2×D11311yescharacteristic, complemented
87C24—216no—
88C24—11316no—
89C24—11314no—
90C24—11328no—
91C24—113224no—
92C24—226448no—
93C24—22616no—
94C24C22×D11311yescharacteristic
95C24C22×D113128yescomplemented
96C2×D4—113224no—
97C2×D4—113512no—
98C2×D4—113112no—
99C2×D4C22×D1131112yesdirect product factor
100C22×C4—11314no—
101C22×C4—113112no—
102C22×C4C22×D113114yescomplemented
103C23—2112no—
104C23—113112no—
105C23—11328no—
106C23—11356no—
107C23—113128no—
108C23—226896no—
109C23—226112no—
110C23D4×D11318yesdirect product factor
111C23C23×D11317yes—
112C23C23×D113156yescomplemented
113D4—113128no—
114D4—11364no—
115D4C23×D113164yesdirect product factor
116C2×C4—11328no—
117C2×C4—11364no—
118C2×C4C23×D113128yescomplemented
119C22—2112no—
120C22—113112no—
121C22—1138no—
122C22—11316no—
123C22—226256no—
124C22—226112no—
125C22C2×D4×D113128yesdirect product factor
126C22C24×D11317yes—
127C22C24×D113116yescomplemented
128C4—1138no—
129C4C24×D11318yescomplemented
130C2—216no—
131C2—11316no—
132C2—22616no—
133C2C22×D4×D113114yesdirect product factor
134C2C25×D11311yescharacteristic
subgroupG/H
centerC24C22×D113
commutator, cosocleC2×C113C26
FrattiniC2C25×D113
FittingC23×D4×C113C2
socleC24×C113C23
hypercenterC23×D4D113
hypocenterC113C24×D4
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C25×D113C2semidirect
2. C23×D452C2semidirect
3. C23×C22⋊D113C2semidirect
4. C22×D4×D113C2direct (N × H)
5. C23×C4×D113C2semidirect
6. C23×D4×C113C2semidirect
9. C24×D113C22semidirect
10. C24×D113C22semidirect
11. C22×D452C22semidirect
12. C22×C22⋊D113C22semidirect
13. C2×D4×D113C22direct (N × H)
14. C23×Dic113C22semidirect
15. C22×C4×D113C22semidirect
16. C25×C113C22semidirect
17. C22×D4×C113C22semidirect
18. C23×C4×C113C22semidirect
21. C23×D113D4direct (N × H)
23. C23×D113C23semidirect
24. C23×D113C23semidirect
25. C2×D452C23semidirect
26. C2×C22⋊D113C23semidirect
27. D4×D113C23direct (N × H)
28. C22×Dic113C23semidirect
29. C2×C4×D113C23semidirect
32. C24×C113C23semidirect
33. C2×D4×C113C23semidirect
34. C22×C4×C113C23semidirect
36. C23×C113C2×D4semidirect
38. C23×C113C24semidirect
41. C22×D113C2×D4direct (N × H)
43. C22×D113C24semidirect
44. C22×D113C24semidirect
45. D4×C113C24semidirect
46. C2×C4×C113C24semidirect
47. C22⋊D113C24semidirect
48. C2×Dic113C24semidirect
49. D452C24semidirect
50. C4×D113C24semidirect
52. C22×C113C22×D4semidirect
54. C22×C113C25semidirect
57. C2×D113C22×D4direct (N × H)
59. C2×D113C25semidirect
60. C4×C113C25semidirect
61. Dic113C25semidirect
63. C2×C113C23×D4semidirect
66. D113C23×D4direct (N × H)
68. C113C24×D4semidirect
73. C23×D4D113direct (N × H)
79. C25C2×D113semidirect
83. C22×D4C2×D113direct (N × H)
86. C23×C4C2×D113semidirect
95. C24C22×D113semidirect
99. C2×D4C22×D113direct (N × H)
102. C22×C4C22×D113semidirect
110. C23D4×D113direct (N × H)
112. C23C23×D113semidirect
115. D4C23×D113direct (N × H)
118. C2×C4C23×D113semidirect
125. C22C2×D4×D113direct (N × H)
127. C22C24×D113semidirect
129. C4C24×D113semidirect
133. C2C22×D4×D113direct (N × H)

Maximal subgroups

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

subgroupindex
C25×D1132
C23×D4522
C23×C22⋊D1132
C22×D4×D1132
C23×C4×D1132
C23×D4×C1132
C24×D4113