Finite Group Databasebeta

← C2×C3⋊#16861350 #37567944

Subgroups — C2×C3⋊#16861350 #37567944

Order 24444.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#14523272C211yesmaximal, characteristic, complemented
2C3⋊#16861350C212yesmaximal, direct product factor
3C2×C7×D291C311yesmaximal, characteristic, complemented
4C2×#16861350—31nomaximal
5C3×#14523272C2211yescharacteristic, complemented, Hall
6#16861350—32no—
7C7×D291C2×C312yescomplemented
8C2×#14523272—21no—
9C2×#14523272D311yescharacteristic, complemented
10C2×C3×C7×C97C2×C311yescharacteristic, complemented
11C2×C3⋊(D97⋊C3)—71nomaximal, Hall
12C2×C7×D97—31noHall
13C3×C7×C97C22×C311yescharacteristic, complemented
14#14523272—21no—
15#14523272C2×D311yescharacteristic, complemented
16C2×C3×C97⋊C3—71no—
17C3⋊(D97⋊C3)—72no—
18C2×C7×C97C3×D311yescharacteristic, complemented
19C7×D97—32no—
20C2×D291ΓL(1,𝔽8)11yescharacteristic, complemented
21C2×D97⋊C3—211no—
22C3×C97⋊C3—71noHall
23C7×C97C2×C3×D311yescharacteristic, complemented, Hall
24C2×C3×C97C2×ΓL(1,𝔽8)11yescharacteristic, complemented
25D291C2×ΓL(1,𝔽8)12yescomplemented
26C2×C97⋊C3—71no—
27C2×C97⋊C3—141no—
28D97⋊C3—212no—
29C2×D97—31noHall
30C3×C97C22×ΓL(1,𝔽8)11yescharacteristic, complemented
31C97⋊C3—71no—
32C97⋊C3—141no—
33C2×D3×ΓL(1,𝔽8)—971nomaximal, Hall
34C2×C97D3×ΓL(1,𝔽8)11yescharacteristic, complemented
35D97—32no—
36C2×C3×ΓL(1,𝔽8)—1941no—
37D3×ΓL(1,𝔽8)—972no—
38C97C2×D3×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
39C2×D3×C7—971no—
40C22×ΓL(1,𝔽8)—2911no—
41C3×ΓL(1,𝔽8)—1941noHall
42C2×C3×C7D97⋊C311yescharacteristic, complemented
43D3×C7—972no—
44C2×ΓL(1,𝔽8)—2912no—
45C2×ΓL(1,𝔽8)—1941no—
46C2×ΓL(1,𝔽8)—1941no—
47C2×C3×D3—6791noHall
48C22×C7—2911noHall
49C3×C7C2×D97⋊C311yescharacteristic, complemented
50ΓL(1,𝔽8)—1941no—
51ΓL(1,𝔽8)—1941no—
52C2×C32—13581no—
53C3×D3—6792no—
54C2×C7—2912no—
55C2×C7C3⋊(D97⋊C3)11yescharacteristic, complemented
56C22×C3—20371no—
57C2×D3—971no—
58C32—13581noSylow
59C7C2×C3⋊(D97⋊C3)11yescharacteristic, complemented, Sylow
60C2×C3—13581no—
61C2×C3—13581no—
62C2×C3—20372no—
63C2×C3#1686135011yescharacteristic, complemented
64D3—972no—
65C22—2911noSylow
66C3—13581no—
67C3—13581no—
68C3C2×#1686135011yescharacteristic, complemented
69C2—2912no—
70C2C3⋊#1686135011yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊#16861350
commutator, cosocle, hypocenterC3×C7×C97C22×C3
FrattiniC1G
Fitting, socleC2×C3×C7×C97C2×C3
LCSG ▷ C3×C7×C97
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#14523272C2semidirect
2. C3⋊#16861350C2direct (N × H)
3. C2×C7×D291C3semidirect
5. C3×#14523272C22semidirect
7. C7×D291C2×C3semidirect
9. C2×#14523272D3semidirect
10. C2×C3×C7×C97C2×C3semidirect
13. C3×C7×C97C22×C3semidirect
15. #14523272C2×D3semidirect
18. C2×C7×C97C3×D3semidirect
20. C2×D291ΓL(1,𝔽8)semidirect
23. C7×C97C2×C3×D3semidirect
24. C2×C3×C97C2×ΓL(1,𝔽8)semidirect
25. D291C2×ΓL(1,𝔽8)semidirect
30. C3×C97C22×ΓL(1,𝔽8)semidirect
34. C2×C97D3×ΓL(1,𝔽8)semidirect
38. C97C2×D3×ΓL(1,𝔽8)semidirect
42. C2×C3×C7D97⋊C3semidirect
49. C3×C7C2×D97⋊C3semidirect
55. C2×C7C3⋊(D97⋊C3)semidirect
59. C7C2×C3⋊(D97⋊C3)semidirect
63. C2×C3#16861350semidirect
68. C3C2×#16861350semidirect
70. C2C3⋊#16861350direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#145232722
C3⋊#168613502
C2×C7×D2913
C2×#168613503
C2×C3⋊(D97⋊C3)7
C2×D3×ΓL(1,𝔽8)97