Finite Group Databasebeta

← C23×D4×D157 #34114927

Subgroups — C23×D4×D157 #34114927

Order 20096.

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×D157C212yesmaximal, complemented
2C23×D628C211yesmaximal, characteristic, complemented
3C23×C22⋊D157C212yesmaximal, complemented
4C22×D4×D157C2156yesmaximal, direct product factor
5C23×C4×D157C211yesmaximal, characteristic, complemented
6C23×D4×C157C211yesmaximal, characteristic, complemented
7C24×D157—232no—
8C24×D157C2211yescharacteristic
9C24×D157C22156yescomplemented
10C24×D157C2212yescomplemented
11C22×D628C22128yescomplemented
12C22×C22⋊D157C22156yescomplemented
13C2×D4×D157C221448yesdirect product factor
14C23×Dic157C2211yescharacteristic, complemented
15C22×C4×D157C22128yescomplemented
16C25×C157C2212yescomplemented
17C22×D4×C157C22128yescomplemented
18C23×C4×C157C2211yescharacteristic, complemented
19C23×D157—2448no—
20C23×D157—216no—
21C23×D157D4116yesdirect product factor
22C23×D157C23114yes—
23C23×D157C23128yescomplemented
24C23×D157C231224yescomplemented
25C2×D628C231112yescomplemented
26C2×C22⋊D157C231224yescomplemented
27D4×D157C231512yesdirect product factor
28C22×Dic157C23114yescomplemented
29C2×C4×D157C231112yescomplemented
30C24×C157—216no—
31C24×C157C2311yescharacteristic
32C24×C157C23128yescomplemented
33C2×D4×C157C231112yescomplemented
34C22×C4×C157C23114yescomplemented
35C22×D157—2112no—
36C22×D157—2896no—
37C22×D157C2×D41112yesdirect product factor
38C22×D157C24128yes—
39C22×D157C241128yescomplemented
40C22×D157C24156yescomplemented
41D628C24164yescomplemented
42C22⋊D157C241128yescomplemented
43C2×Dic157C24128yescomplemented
44C4×D157C24164yescomplemented
45C23×C157—2112no—
46C23×C157C2×D418yescomplemented
47C23×C157C2417yes—
48C23×C157C24156yescomplemented
49D4×C157C24164yescomplemented
50C2×C4×C157C24128yescomplemented
51C22×C157—2112no—
52C22×C157C22×D4128yescomplemented
53C22×C157C2517yes—
54C22×C157C25116yescomplemented
55C2×D157—2112no—
56C2×D157—2256no—
57C2×D157C22×D41112yesdirect product factor
58C2×D157C2518yes—
59C2×D157C25116yescomplemented
60C4×C157C2518yescomplemented
61Dic157C2518yescomplemented
62C2×C157—216no—
63C2×C157C23×D4114yescomplemented
64C2×C157C2611yescharacteristic
65D157—216no—
66D157C23×D4116yesdirect product factor
67C157C24×D411yescharacteristic, complemented, Sylow
68C24×D4—1571nomaximal, Sylow
69C26—1572no—
70C23×D4—1572no—
71C23×D4—15756no—
72C23×D4—1571no—
73C23×D4D15711yescharacteristic, direct product factor
74C24×C4—1571no—
75C25—31432no—
76C25—1572no—
77C25—15756no—
78C25—1571no—
79C25C2×D15712yescomplemented
80C22×D4—15756no—
81C22×D4—157448no—
82C22×D4—15728no—
83C22×D4C2×D157128yesdirect product factor
84C23×C4—1571no—
85C23×C4—15728no—
86C23×C4C2×D15711yescharacteristic, complemented
87C24—216no—
88C24—314448no—
89C24—31416no—
90C24—15728no—
91C24—157224no—
92C24—15716no—
93C24—15714no—
94C24C22×D15711yescharacteristic
95C24C22×D157128yescomplemented
96C2×D4—157224no—
97C2×D4—157512no—
98C2×D4—157112no—
99C2×D4C22×D1571112yesdirect product factor
100C22×C4—15714no—
101C22×C4—157112no—
102C22×C4C22×D157114yescomplemented
103C23—2112no—
104C23—314896no—
105C23—314112no—
106C23—15756no—
107C23—157128no—
108C23—157112no—
109C23—15728no—
110C23D4×D15718yesdirect product factor
111C23C23×D15717yes—
112C23C23×D157156yescomplemented
113D4—157128no—
114D4—15764no—
115D4C23×D157164yesdirect product factor
116C2×C4—15728no—
117C2×C4—15764no—
118C2×C4C23×D157128yescomplemented
119C22—2112no—
120C22—314256no—
121C22—314112no—
122C22—15716no—
123C22—157112no—
124C22—1578no—
125C22C2×D4×D157128yesdirect product factor
126C22C24×D15717yes—
127C22C24×D157116yescomplemented
128C4—1578no—
129C4C24×D15718yescomplemented
130C2—216no—
131C2—31416no—
132C2—15716no—
133C2C22×D4×D157114yesdirect product factor
134C2C25×D15711yescharacteristic
subgroupG/H
centerC24C22×D157
commutator, cosocleC2×C157C26
FrattiniC2C25×D157
FittingC23×D4×C157C2
socleC24×C157C23
hypercenterC23×D4D157
hypocenterC157C24×D4
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C25×D157C2semidirect
2. C23×D628C2semidirect
3. C23×C22⋊D157C2semidirect
4. C22×D4×D157C2direct (N × H)
5. C23×C4×D157C2semidirect
6. C23×D4×C157C2semidirect
9. C24×D157C22semidirect
10. C24×D157C22semidirect
11. C22×D628C22semidirect
12. C22×C22⋊D157C22semidirect
13. C2×D4×D157C22direct (N × H)
14. C23×Dic157C22semidirect
15. C22×C4×D157C22semidirect
16. C25×C157C22semidirect
17. C22×D4×C157C22semidirect
18. C23×C4×C157C22semidirect
21. C23×D157D4direct (N × H)
23. C23×D157C23semidirect
24. C23×D157C23semidirect
25. C2×D628C23semidirect
26. C2×C22⋊D157C23semidirect
27. D4×D157C23direct (N × H)
28. C22×Dic157C23semidirect
29. C2×C4×D157C23semidirect
32. C24×C157C23semidirect
33. C2×D4×C157C23semidirect
34. C22×C4×C157C23semidirect
37. C22×D157C2×D4direct (N × H)
39. C22×D157C24semidirect
40. C22×D157C24semidirect
41. D628C24semidirect
42. C22⋊D157C24semidirect
43. C2×Dic157C24semidirect
44. C4×D157C24semidirect
46. C23×C157C2×D4semidirect
48. C23×C157C24semidirect
49. D4×C157C24semidirect
50. C2×C4×C157C24semidirect
52. C22×C157C22×D4semidirect
54. C22×C157C25semidirect
57. C2×D157C22×D4direct (N × H)
59. C2×D157C25semidirect
60. C4×C157C25semidirect
61. Dic157C25semidirect
63. C2×C157C23×D4semidirect
66. D157C23×D4direct (N × H)
67. C157C24×D4semidirect
73. C23×D4D157direct (N × H)
79. C25C2×D157semidirect
83. C22×D4C2×D157direct (N × H)
86. C23×C4C2×D157semidirect
95. C24C22×D157semidirect
99. C2×D4C22×D157direct (N × H)
102. C22×C4C22×D157semidirect
110. C23D4×D157direct (N × H)
112. C23C23×D157semidirect
115. D4C23×D157direct (N × H)
118. C2×C4C23×D157semidirect
125. C22C2×D4×D157direct (N × H)
127. C22C24×D157semidirect
129. C4C24×D157semidirect
133. C2C22×D4×D157direct (N × H)

Maximal subgroups

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

subgroupindex
C25×D1572
C23×D6282
C23×C22⋊D1572
C22×D4×D1572
C23×C4×D1572
C23×D4×C1572
C24×D4157