Finite Group Databasebeta

← C3×C7×C22⋊#87705 #45692750

Subgroups — C3×C7×C22⋊#87705 #45692750

Order 33516.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C22⋊#87705C313yesmaximal, direct product factor
2C22×C3×C72×C19C311yesmaximal, characteristic, complemented
3C3×C7×#87705—41nomaximal, Hall
4C2×C3×C72×C19—31no—
5C3×C7×C22⋊(C19⋊C3)—71nomaximal
6C3×C22⋊#87705C711yesmaximal, characteristic, direct product factor
7C22×C72×C19C3211yescharacteristic, complemented, Hall
8C7×#87705—43no—
9C3×C72×C19A411yescharacteristic, complemented
10C2×C72×C19—31no—
11C3×C7×C22⋊ΓL(1,𝔽8)—191nomaximal, Hall
12C22×C3×C7×C19—32no—
13C22×C3×C7×C19ΓL(1,𝔽8)11yescharacteristic, complemented
14C22×C3×C7×C19C3×C711yescharacteristic, complemented
15C22⋊#87705C3×C713yesdirect product factor
16C7×C22⋊(C19⋊C3)—73no—
17C3×#87705—41no—
18C3×C7×C19⋊C3—281no—
19C72×C19C3×A411yescharacteristic, complemented, Hall
20C2×C3×C7×C19—36no—
21C2×C3×C7×C19—31no—
22C2×C3×C7×C19—31no—
23C3×C22⋊(C19⋊C3)—71noHall
24C22×C3×C72C19⋊C311yescharacteristic, complemented
25C7×C22⋊ΓL(1,𝔽8)—193no—
26C22×C7×C19—32no—
27C22×C7×C19C3×ΓL(1,𝔽8)11yescharacteristic, complemented
28C22×C7×C19C32×C711yescharacteristic, complemented
29C3×C7×ΓL(1,𝔽8)—761noHall
30C3×C7×C19—32no—
31C3×C7×C19C7×A411yescharacteristic, complemented
32C3×C7×C19C22⋊ΓL(1,𝔽8)11yescharacteristic, complemented
33#87705—43no—
34C7×C19⋊C3—283no—
35C2×C3×C72—31no—
36C2×C7×C19—36no—
37C2×C7×C19—31no—
38C2×C7×C19—31no—
39C3×C22⋊ΓL(1,𝔽8)—191no—
40C3×C7×A4—1331no—
41C22×C3×C19C7×ΓL(1,𝔽8)11yescharacteristic, complemented
42C22⋊(C19⋊C3)—73no—
43C22×C72C3×C19⋊C311yescharacteristic, complemented, Hall
44C3×C19⋊C3—281noHall
45C3×C72C22⋊(C19⋊C3)11yescharacteristic, complemented
46C7×ΓL(1,𝔽8)—763no—
47C7×C19—32no—
48C7×C19C3×C7×A411yescharacteristic, complemented
49C7×C19C3×C22⋊ΓL(1,𝔽8)11yescharacteristic, complemented
50C2×C3×C19—31no—
51C2×C72—31no—
52C22×C3×C7—32no—
53C22×C3×C7C7×C19⋊C311yescharacteristic, complemented
54C22×C3×C7#8770511yescharacteristic, complemented
55C22⋊ΓL(1,𝔽8)—193no—
56C7×A4—1333no—
57C22×C19C3×C7×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
58C32×C7—5321no—
59C3×ΓL(1,𝔽8)—761no—
60C3×C19C7×C22⋊ΓL(1,𝔽8)11yescharacteristic, complemented
61C19⋊C3—283no—
62C72C3×C22⋊(C19⋊C3)11yescharacteristic, complemented, Sylow
63C2×C3×C7—36no—
64C2×C3×C7—31no—
65C2×C3×C7—31no—
66C2×C19—31no—
67C3×A4—1331noHall
68C22×C7—32no—
69C22×C7C3×C7×C19⋊C311yescharacteristic, complemented
70C22×C7C3×#8770511yescharacteristic, complemented
71C3×C7—32no—
72C3×C7—5323no—
73C3×C7C7×C22⋊(C19⋊C3)11yescharacteristic, complemented
74C3×C7C22⋊#8770511yescharacteristic, direct product factor
75ΓL(1,𝔽8)—763no—
76C19C3×C7×C22⋊ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
77C2×C7—36no—
78C2×C7—31no—
79C2×C7—31no—
80C22×C3C7×#8770511yescharacteristic, complemented
81A4—1333no—
82C32—5321noSylow
83C7—32no—
84C7C3×C22⋊#8770511yescharacteristic, direct product factor
85C7C3×C7×C22⋊(C19⋊C3)11yescharacteristic, complemented
86C2×C3—31no—
87C22C3×C7×#8770511yescharacteristic, complemented, Sylow
88C3—5323no—
89C3C7×C22⋊#8770511yescharacteristic, direct product factor
90C2—31no—
subgroupG/H
center, hypercenterC3×C7C22⋊#87705
commutator, cosocle, hypocenterC22×C7×C19C32×C7
FrattiniC1G
Fitting, socleC22×C3×C72×C19C3
LCSG ▷ C22×C7×C19
UCSC1 ◁ C3×C7

Complements

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

NH ≅ G/Ntype
1. C7×C22⋊#87705C3direct (N × H)
2. C22×C3×C72×C19C3semidirect
6. C3×C22⋊#87705C7direct (N × H)
7. C22×C72×C19C32semidirect
9. C3×C72×C19A4semidirect
13. C22×C3×C7×C19ΓL(1,𝔽8)semidirect
14. C22×C3×C7×C19C3×C7semidirect
15. C22⋊#87705C3×C7direct (N × H)
19. C72×C19C3×A4semidirect
24. C22×C3×C72C19⋊C3semidirect
27. C22×C7×C19C3×ΓL(1,𝔽8)semidirect
28. C22×C7×C19C32×C7semidirect
31. C3×C7×C19C7×A4semidirect
32. C3×C7×C19C22⋊ΓL(1,𝔽8)semidirect
41. C22×C3×C19C7×ΓL(1,𝔽8)semidirect
43. C22×C72C3×C19⋊C3semidirect
45. C3×C72C22⋊(C19⋊C3)semidirect
48. C7×C19C3×C7×A4semidirect
49. C7×C19C3×C22⋊ΓL(1,𝔽8)semidirect
53. C22×C3×C7C7×C19⋊C3semidirect
54. C22×C3×C7#87705semidirect
57. C22×C19C3×C7×ΓL(1,𝔽8)semidirect
60. C3×C19C7×C22⋊ΓL(1,𝔽8)semidirect
62. C72C3×C22⋊(C19⋊C3)semidirect
69. C22×C7C3×C7×C19⋊C3semidirect
70. C22×C7C3×#87705semidirect
73. C3×C7C7×C22⋊(C19⋊C3)semidirect
74. C3×C7C22⋊#87705direct (N × H)
76. C19C3×C7×C22⋊ΓL(1,𝔽8)semidirect
80. C22×C3C7×#87705semidirect
84. C7C3×C22⋊#87705direct (N × H)
85. C7C3×C7×C22⋊(C19⋊C3)semidirect
87. C22C3×C7×#87705semidirect
89. C3C7×C22⋊#87705direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C22⋊#877053
C22×C3×C72×C193
C3×C7×#877054
C3×C7×C22⋊(C19⋊C3)7
C3×C22⋊#877057
C3×C7×C22⋊ΓL(1,𝔽8)19