Finite Group Databasebeta

← C2×C3×D13×#3861 #37525464

Subgroups — C2×C3×D13×#3861 #37525464

Order 22932.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13×#3861C211yesmaximal, characteristic, complemented
2C3×D13×#3861C212yesmaximal, direct product factor
3C2×C3×C72×D13C311yesmaximal, characteristic, complemented
4C2×D13×#3861C313yesmaximal, direct product factor
5C3×C13×#3861C2211yescharacteristic, complemented, Hall
6C3×C72×D13C2×C312yescomplemented
7C2×C13×#3861C2×C313yescomplemented
8D13×#3861C2×C316yesdirect product factor
9C2×C3×C72×C13C2×C311yescharacteristic, complemented
10C2×C3×ΓL(1,𝔽8)×D13—78nomaximal
11C2×C72×D13C3211yescharacteristic, complemented, Hall
12C3×C72×C13C22×C311yescharacteristic, complemented
13C13×#3861C22×C313yescomplemented
14C22×C3×#3861—131nomaximal, Hall
15C2×C3×C13×ΓL(1,𝔽8)—78no—
16C3×ΓL(1,𝔽8)×D13—716no—
17C2×C72×C13C2×C3211yescharacteristic, complemented
18C72×D13C2×C3212yescomplemented
19C2×C3×C7×D13ΓL(1,𝔽8)18yescomplemented
20C2×ΓL(1,𝔽8)×D13—724no—
21C2×C3×#3861—132no—
22C2×C3×#3861D1311yescharacteristic, direct product factor
23C3×C13×ΓL(1,𝔽8)—78no—
24C72×C13C22×C3211yescharacteristic, complemented, Hall
25C22×C3×C72—131no—
26C22×#3861—133no—
27C2×C3×C7×C13C2×ΓL(1,𝔽8)18yescomplemented
28C3×C7×D13C2×ΓL(1,𝔽8)116yescomplemented
29C2×C13×ΓL(1,𝔽8)—724no—
30ΓL(1,𝔽8)×D13—748no—
31C2×C32×D13—491noHall
32C3×#3861C2×D1311yescharacteristic, direct product factor, Hall
33C2×C7×D13C3×ΓL(1,𝔽8)18yescomplemented
34C2×C3×C72—132no—
35C2×C3×C72C3×D1311yescharacteristic, complemented
36C2×#3861—136no—
37C2×#3861C3×D1313yesdirect product factor
38C3×C7×C13C22×ΓL(1,𝔽8)18yescomplemented
39C13×ΓL(1,𝔽8)—724no—
40C22×C3×ΓL(1,𝔽8)—918no—
41C2×C32×C13—491no—
42C32×D13—492no—
43C22×C72—131noHall
44C2×C7×C13C2×C3×ΓL(1,𝔽8)18yescomplemented
45C7×D13C2×C3×ΓL(1,𝔽8)116yescomplemented
46C2×C3×D13—493no—
47C2×C3×D13#386111yescharacteristic, direct product factor
48C3×C72C2×C3×D1311yescharacteristic, complemented
49#3861C2×C3×D1313yesdirect product factor
50C2×C3×ΓL(1,𝔽8)—78no—
51C2×C3×ΓL(1,𝔽8)—9116no—
52C32×C13—491noHall
53C2×C72—132no—
54C2×C72C32×D1311yescharacteristic, complemented
55C7×C13C22×C3×ΓL(1,𝔽8)18yescomplemented
56C22×C3×C7—138no—
57C22×ΓL(1,𝔽8)—9124no—
58C2×C3×C13—493no—
59C2×C3×C13C2×#386111yescharacteristic, complemented
60C3×D13—496no—
61C3×D13C2×#386112yesdirect product factor
62C3×ΓL(1,𝔽8)—78no—
63C2×D13C3×#386111yescharacteristic, direct product factor, Hall
64C72C2×C32×D1311yescharacteristic, complemented, Sylow
65C2×C3×C7—1316no—
66C2×C3×C7ΓL(1,𝔽8)×D1318yescomplemented
67C2×ΓL(1,𝔽8)—724no—
68C2×ΓL(1,𝔽8)—9148no—
69C3×C13—493no—
70C3×C13C22×#386111yescharacteristic, complemented
71C22×C32—6371noHall
72C22×C7—138no—
73C2×C13C2×C3×#386111yescharacteristic, complemented
74D13C2×C3×#386112yesdirect product factor
75C3×C7C2×ΓL(1,𝔽8)×D1318yescomplemented
76ΓL(1,𝔽8)—724no—
77C2×C32—491no—
78C2×C32—6372no—
79C2×C7—1316no—
80C2×C7C3×ΓL(1,𝔽8)×D1318yescomplemented
81C13C22×C3×#386111yescharacteristic, complemented, Sylow
82C22×C3—131no—
83C22×C3—6373no—
84C32—491noSylow
85C7C2×C3×ΓL(1,𝔽8)×D1318yescomplemented
86C2×C3—132no—
87C2×C3—493no—
88C2×C3—6376no—
89C2×C3D13×#386111yescharacteristic, direct product factor
90C22—131noSylow
91C3—493no—
92C3C2×D13×#386111yescharacteristic, direct product factor
93C2—132no—
94C2C3×D13×#386111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D13×#3861
commutator, cosocle, hypocenterC72×C13C22×C32
FrattiniC1G
Fitting, socleC2×C3×C72×C13C2×C3
LCSG ▷ C72×C13
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C13×#3861C2semidirect
2. C3×D13×#3861C2direct (N × H)
3. C2×C3×C72×D13C3semidirect
4. C2×D13×#3861C3direct (N × H)
5. C3×C13×#3861C22semidirect
6. C3×C72×D13C2×C3semidirect
7. C2×C13×#3861C2×C3semidirect
8. D13×#3861C2×C3direct (N × H)
9. C2×C3×C72×C13C2×C3semidirect
11. C2×C72×D13C32semidirect
12. C3×C72×C13C22×C3semidirect
13. C13×#3861C22×C3semidirect
17. C2×C72×C13C2×C32semidirect
18. C72×D13C2×C32semidirect
19. C2×C3×C7×D13ΓL(1,𝔽8)semidirect
22. C2×C3×#3861D13direct (N × H)
24. C72×C13C22×C32semidirect
27. C2×C3×C7×C13C2×ΓL(1,𝔽8)semidirect
28. C3×C7×D13C2×ΓL(1,𝔽8)semidirect
32. C3×#3861C2×D13direct (N × H)
33. C2×C7×D13C3×ΓL(1,𝔽8)semidirect
35. C2×C3×C72C3×D13semidirect
37. C2×#3861C3×D13direct (N × H)
38. C3×C7×C13C22×ΓL(1,𝔽8)semidirect
44. C2×C7×C13C2×C3×ΓL(1,𝔽8)semidirect
45. C7×D13C2×C3×ΓL(1,𝔽8)semidirect
47. C2×C3×D13#3861direct (N × H)
48. C3×C72C2×C3×D13semidirect
49. #3861C2×C3×D13direct (N × H)
54. C2×C72C32×D13semidirect
55. C7×C13C22×C3×ΓL(1,𝔽8)semidirect
59. C2×C3×C13C2×#3861semidirect
61. C3×D13C2×#3861direct (N × H)
63. C2×D13C3×#3861direct (N × H)
64. C72C2×C32×D13semidirect
66. C2×C3×C7ΓL(1,𝔽8)×D13semidirect
70. C3×C13C22×#3861semidirect
73. C2×C13C2×C3×#3861semidirect
74. D13C2×C3×#3861direct (N × H)
75. C3×C7C2×ΓL(1,𝔽8)×D13semidirect
80. C2×C7C3×ΓL(1,𝔽8)×D13semidirect
81. C13C22×C3×#3861semidirect
85. C7C2×C3×ΓL(1,𝔽8)×D13semidirect
89. C2×C3D13×#3861direct (N × H)
92. C3C2×D13×#3861direct (N × H)
94. C2C3×D13×#3861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C13×#38612
C3×D13×#38612
C2×C3×C72×D133
C2×D13×#38613
C2×C3×ΓL(1,𝔽8)×D137
C22×C3×#386113