Finite Group Databasebeta

← C23×D4×D139 #31821195

Subgroups — C23×D4×D139 #31821195

Order 17792.

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×D139C212yesmaximal, complemented
2C23×D556C211yesmaximal, characteristic, complemented
3C23×C22⋊D139C212yesmaximal, complemented
4C22×D4×D139C2156yesmaximal, direct product factor
5C23×C4×D139C211yesmaximal, characteristic, complemented
6C23×D4×C139C211yesmaximal, characteristic, complemented
7C24×D139—232no—
8C24×D139C2211yescharacteristic
9C24×D139C2212yescomplemented
10C24×D139C22156yescomplemented
11C22×D556C22128yescomplemented
12C22×C22⋊D139C22156yescomplemented
13C2×D4×D139C221448yesdirect product factor
14C23×Dic139C2211yescharacteristic, complemented
15C22×C4×D139C22128yescomplemented
16C25×C139C2212yescomplemented
17C22×D4×C139C22128yescomplemented
18C23×C4×C139C2211yescharacteristic, complemented
19C23×D139—2448no—
20C23×D139—216no—
21C23×D139D4116yesdirect product factor
22C23×D139C23114yes—
23C23×D139C23128yescomplemented
24C23×D139C231224yescomplemented
25C2×D556C231112yescomplemented
26C2×C22⋊D139C231224yescomplemented
27D4×D139C231512yesdirect product factor
28C22×Dic139C23114yescomplemented
29C2×C4×D139C231112yescomplemented
30C24×C139—216no—
31C24×C139C2311yescharacteristic
32C24×C139C23128yescomplemented
33C2×D4×C139C231112yescomplemented
34C22×C4×C139C23114yescomplemented
35C22×D139—2112no—
36C22×D139—2896no—
37C22×D139C2×D41112yesdirect product factor
38C22×D139C24128yes—
39C22×D139C241128yescomplemented
40C22×D139C24156yescomplemented
41D556C24164yescomplemented
42C22⋊D139C241128yescomplemented
43C2×Dic139C24128yescomplemented
44C4×D139C24164yescomplemented
45C23×C139—2112no—
46C23×C139C2×D418yescomplemented
47C23×C139C2417yes—
48C23×C139C24156yescomplemented
49D4×C139C24164yescomplemented
50C2×C4×C139C24128yescomplemented
51C22×C139—2112no—
52C22×C139C22×D4128yescomplemented
53C22×C139C2517yes—
54C22×C139C25116yescomplemented
55C2×D139—2112no—
56C2×D139—2256no—
57C2×D139C22×D41112yesdirect product factor
58C2×D139C2518yes—
59C2×D139C25116yescomplemented
60C4×C139C2518yescomplemented
61Dic139C2518yescomplemented
62C2×C139—216no—
63C2×C139C23×D4114yescomplemented
64C2×C139C2611yescharacteristic
65D139—216no—
66D139C23×D4116yesdirect product factor
67C139C24×D411yescharacteristic, complemented, Sylow
68C24×D4—1391nomaximal, Sylow
69C26—1392no—
70C23×D4—1392no—
71C23×D4—13956no—
72C23×D4—1391no—
73C23×D4D13911yescharacteristic, direct product factor
74C24×C4—1391no—
75C25—27832no—
76C25—1392no—
77C25—13956no—
78C25—1391no—
79C25C2×D13912yescomplemented
80C22×D4—13956no—
81C22×D4—139448no—
82C22×D4—13928no—
83C22×D4C2×D139128yesdirect product factor
84C23×C4—1391no—
85C23×C4—13928no—
86C23×C4C2×D13911yescharacteristic, complemented
87C24—216no—
88C24—278448no—
89C24—27816no—
90C24—13928no—
91C24—139224no—
92C24—13916no—
93C24—13914no—
94C24C22×D13911yescharacteristic
95C24C22×D139128yescomplemented
96C2×D4—139224no—
97C2×D4—139512no—
98C2×D4—139112no—
99C2×D4C22×D1391112yesdirect product factor
100C22×C4—13914no—
101C22×C4—139112no—
102C22×C4C22×D139114yescomplemented
103C23—2112no—
104C23—278896no—
105C23—278112no—
106C23—13956no—
107C23—139128no—
108C23—139112no—
109C23—13928no—
110C23D4×D13918yesdirect product factor
111C23C23×D13917yes—
112C23C23×D139156yescomplemented
113D4—139128no—
114D4—13964no—
115D4C23×D139164yesdirect product factor
116C2×C4—13928no—
117C2×C4—13964no—
118C2×C4C23×D139128yescomplemented
119C22—2112no—
120C22—278256no—
121C22—278112no—
122C22—13916no—
123C22—139112no—
124C22—1398no—
125C22C2×D4×D139128yesdirect product factor
126C22C24×D13917yes—
127C22C24×D139116yescomplemented
128C4—1398no—
129C4C24×D13918yescomplemented
130C2—216no—
131C2—27816no—
132C2—13916no—
133C2C22×D4×D139114yesdirect product factor
134C2C25×D13911yescharacteristic
subgroupG/H
centerC24C22×D139
commutator, cosocleC2×C139C26
FrattiniC2C25×D139
FittingC23×D4×C139C2
socleC24×C139C23
hypercenterC23×D4D139
hypocenterC139C24×D4
LCSG ▷ C2×C139 ▷ C139
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C25×D139C2semidirect
2. C23×D556C2semidirect
3. C23×C22⋊D139C2semidirect
4. C22×D4×D139C2direct (N × H)
5. C23×C4×D139C2semidirect
6. C23×D4×C139C2semidirect
9. C24×D139C22semidirect
10. C24×D139C22semidirect
11. C22×D556C22semidirect
12. C22×C22⋊D139C22semidirect
13. C2×D4×D139C22direct (N × H)
14. C23×Dic139C22semidirect
15. C22×C4×D139C22semidirect
16. C25×C139C22semidirect
17. C22×D4×C139C22semidirect
18. C23×C4×C139C22semidirect
21. C23×D139D4direct (N × H)
23. C23×D139C23semidirect
24. C23×D139C23semidirect
25. C2×D556C23semidirect
26. C2×C22⋊D139C23semidirect
27. D4×D139C23direct (N × H)
28. C22×Dic139C23semidirect
29. C2×C4×D139C23semidirect
32. C24×C139C23semidirect
33. C2×D4×C139C23semidirect
34. C22×C4×C139C23semidirect
37. C22×D139C2×D4direct (N × H)
39. C22×D139C24semidirect
40. C22×D139C24semidirect
41. D556C24semidirect
42. C22⋊D139C24semidirect
43. C2×Dic139C24semidirect
44. C4×D139C24semidirect
46. C23×C139C2×D4semidirect
48. C23×C139C24semidirect
49. D4×C139C24semidirect
50. C2×C4×C139C24semidirect
52. C22×C139C22×D4semidirect
54. C22×C139C25semidirect
57. C2×D139C22×D4direct (N × H)
59. C2×D139C25semidirect
60. C4×C139C25semidirect
61. Dic139C25semidirect
63. C2×C139C23×D4semidirect
66. D139C23×D4direct (N × H)
67. C139C24×D4semidirect
73. C23×D4D139direct (N × H)
79. C25C2×D139semidirect
83. C22×D4C2×D139direct (N × H)
86. C23×C4C2×D139semidirect
95. C24C22×D139semidirect
99. C2×D4C22×D139direct (N × H)
102. C22×C4C22×D139semidirect
110. C23D4×D139direct (N × H)
112. C23C23×D139semidirect
115. D4C23×D139direct (N × H)
118. C2×C4C23×D139semidirect
125. C22C2×D4×D139direct (N × H)
127. C22C24×D139semidirect
129. C4C24×D139semidirect
133. C2C22×D4×D139direct (N × H)

Maximal subgroups

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

subgroupindex
C25×D1392
C23×D5562
C23×C22⋊D1392
C22×D4×D1392
C23×C4×D1392
C23×D4×C1392
C24×D4139