Finite Group Databasebeta

← C2×C3×C42×C7×C29 #72197166

Subgroups — C2×C3×C42×C7×C29 #72197166

Order 19488.

432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C7×C29C213yesmaximal
2C3×C42×C7×C29C214yesmaximal, direct product factor
3C2×C42×C7×C29C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C7×C29C2211yescharacteristic
5C2×C3×C4×C7×C29C4112yesdirect product factor
6C2×C3×C4×C7×C29C2216yes—
7C22×C4×C7×C29C2×C313yes—
8C42×C7×C29C2×C314yesdirect product factor
9C2×C3×C42×C29C711yesmaximal, characteristic, direct product factor, Hall
10C22×C3×C7×C29C2×C416yes—
11C22×C3×C7×C29C2311yescharacteristic
12C3×C4×C7×C29C2×C4112yesdirect product factor
13C23×C7×C29C22×C311yescharacteristic
14C2×C4×C7×C29C3×C4112yesdirect product factor
15C2×C4×C7×C29C22×C316yes—
16C22×C3×C4×C29C2×C713yes—
17C3×C42×C29C2×C714yesdirect product factor
18C2×C3×C7×C29C4214yesdirect product factor
19C2×C3×C7×C29C22×C413yes—
20C2×C42×C29C3×C711yescharacteristic, direct product factor, Hall
21C22×C7×C29C2×C3×C416yes—
22C22×C7×C29C23×C311yescharacteristic
23C4×C7×C29C2×C3×C4112yesdirect product factor
24C23×C3×C29C22×C711yescharacteristic
25C2×C3×C4×C29C4×C7112yesdirect product factor
26C2×C3×C4×C29C22×C716yes—
27C2×C3×C42×C7C2911yesmaximal, characteristic, direct product factor, Hall
28C3×C7×C29C2×C4211yescharacteristic, direct product factor, Hall
29C22×C4×C29C2×C3×C713yes—
30C42×C29C2×C3×C714yesdirect product factor
31C2×C7×C29C3×C4214yesdirect product factor
32C2×C7×C29C22×C3×C413yes—
33C22×C3×C29C2×C4×C716yes—
34C22×C3×C29C23×C711yescharacteristic
35C3×C4×C29C2×C4×C7112yesdirect product factor
36C22×C3×C4×C7C2×C2913yes—
37C3×C42×C7C2×C2914yesdirect product factor
38C23×C29C22×C3×C711yescharacteristic
39C2×C4×C29C3×C4×C7112yesdirect product factor
40C2×C4×C29C22×C3×C716yes—
41C2×C42×C7C3×C2911yescharacteristic, direct product factor, Hall
42C7×C29C2×C3×C4211yescharacteristic, direct product factor, Hall
43C2×C3×C29C42×C714yesdirect product factor
44C2×C3×C29C22×C4×C713yes—
45C23×C3×C7C22×C2911yescharacteristic
46C2×C3×C4×C7C4×C29112yesdirect product factor
47C2×C3×C4×C7C22×C2916yes—
48C22×C29C2×C3×C4×C716yes—
49C22×C29C23×C3×C711yescharacteristic
50C4×C29C2×C3×C4×C7112yesdirect product factor
51C22×C4×C7C2×C3×C2913yes—
52C42×C7C2×C3×C2914yesdirect product factor
53C2×C3×C42C7×C2911yescharacteristic, direct product factor, Hall
54C3×C29C2×C42×C711yescharacteristic, direct product factor, Hall
55C22×C3×C7C2×C4×C2916yes—
56C22×C3×C7C23×C2911yescharacteristic
57C3×C4×C7C2×C4×C29112yesdirect product factor
58C2×C29C3×C42×C714yesdirect product factor
59C2×C29C22×C3×C4×C713yes—
60C23×C7C22×C3×C2911yescharacteristic
61C2×C4×C7C3×C4×C29112yesdirect product factor
62C2×C4×C7C22×C3×C2916yes—
63C22×C3×C4C2×C7×C2913yes—
64C3×C42C2×C7×C2914yesdirect product factor
65C2×C3×C7C42×C2914yesdirect product factor
66C2×C3×C7C22×C4×C2913yes—
67C2×C42C3×C7×C2911yescharacteristic, direct product factor, Sylow
68C29C2×C3×C42×C711yescharacteristic, direct product factor, Sylow
69C22×C7C2×C3×C4×C2916yes—
70C22×C7C23×C3×C2911yescharacteristic
71C4×C7C2×C3×C4×C29112yesdirect product factor
72C23×C3C22×C7×C2911yescharacteristic
73C2×C3×C4C4×C7×C29112yesdirect product factor
74C2×C3×C4C22×C7×C2916yes—
75C3×C7C2×C42×C2911yescharacteristic, direct product factor, Hall
76C22×C4C2×C3×C7×C2913yes—
77C42C2×C3×C7×C2914yesdirect product factor
78C2×C7C3×C42×C2914yesdirect product factor
79C2×C7C22×C3×C4×C2913yes—
80C22×C3C2×C4×C7×C2916yes—
81C22×C3C23×C7×C2911yescharacteristic
82C3×C4C2×C4×C7×C29112yesdirect product factor
83C23C22×C3×C7×C2911yescharacteristic
84C2×C4C3×C4×C7×C29112yesdirect product factor
85C2×C4C22×C3×C7×C2916yes—
86C7C2×C3×C42×C2911yescharacteristic, direct product factor, Sylow
87C2×C3C42×C7×C2914yesdirect product factor
88C2×C3C22×C4×C7×C2913yes—
89C22C2×C3×C4×C7×C2916yes—
90C22C23×C3×C7×C2911yescharacteristic
91C4C2×C3×C4×C7×C29112yesdirect product factor
92C3C2×C42×C7×C2911yescharacteristic, direct product factor, Sylow
93C2C3×C42×C7×C2914yesdirect product factor
94C2C22×C3×C4×C7×C2913yes—
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C7×C29
socle, prime radicalC23×C3×C7×C29C22
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C42×C7×C29C2direct (N × H)
3. C2×C42×C7×C29C3direct (N × H)
5. C2×C3×C4×C7×C29C4direct (N × H)
8. C42×C7×C29C2×C3direct (N × H)
9. C2×C3×C42×C29C7direct (N × H)
12. C3×C4×C7×C29C2×C4direct (N × H)
14. C2×C4×C7×C29C3×C4direct (N × H)
17. C3×C42×C29C2×C7direct (N × H)
18. C2×C3×C7×C29C42direct (N × H)
20. C2×C42×C29C3×C7direct (N × H)
23. C4×C7×C29C2×C3×C4direct (N × H)
25. C2×C3×C4×C29C4×C7direct (N × H)
27. C2×C3×C42×C7C29direct (N × H)
28. C3×C7×C29C2×C42direct (N × H)
30. C42×C29C2×C3×C7direct (N × H)
31. C2×C7×C29C3×C42direct (N × H)
35. C3×C4×C29C2×C4×C7direct (N × H)
37. C3×C42×C7C2×C29direct (N × H)
39. C2×C4×C29C3×C4×C7direct (N × H)
41. C2×C42×C7C3×C29direct (N × H)
42. C7×C29C2×C3×C42direct (N × H)
43. C2×C3×C29C42×C7direct (N × H)
46. C2×C3×C4×C7C4×C29direct (N × H)
50. C4×C29C2×C3×C4×C7direct (N × H)
52. C42×C7C2×C3×C29direct (N × H)
53. C2×C3×C42C7×C29direct (N × H)
54. C3×C29C2×C42×C7direct (N × H)
57. C3×C4×C7C2×C4×C29direct (N × H)
58. C2×C29C3×C42×C7direct (N × H)
61. C2×C4×C7C3×C4×C29direct (N × H)
64. C3×C42C2×C7×C29direct (N × H)
65. C2×C3×C7C42×C29direct (N × H)
67. C2×C42C3×C7×C29direct (N × H)
68. C29C2×C3×C42×C7direct (N × H)
71. C4×C7C2×C3×C4×C29direct (N × H)
73. C2×C3×C4C4×C7×C29direct (N × H)
75. C3×C7C2×C42×C29direct (N × H)
77. C42C2×C3×C7×C29direct (N × H)
78. C2×C7C3×C42×C29direct (N × H)
82. C3×C4C2×C4×C7×C29direct (N × H)
84. C2×C4C3×C4×C7×C29direct (N × H)
86. C7C2×C3×C42×C29direct (N × H)
87. C2×C3C42×C7×C29direct (N × H)
91. C4C2×C3×C4×C7×C29direct (N × H)
92. C3C2×C42×C7×C29direct (N × H)
93. C2C3×C42×C7×C29direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×C7×C292
C3×C42×C7×C292
C2×C42×C7×C293
C2×C3×C42×C297
C2×C3×C42×C729