Finite Group Databasebeta

← #3862×Dic57 #45691939

Subgroups — #3862×Dic57 #45691939

Order 33516.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C19×#3862C211yesmaximal, characteristic
2C72×Dic57C311yesmaximal, characteristic, complemented
3Dic19×#3862—31nomaximal
4C3×C19×#3862C411yescharacteristic, complemented, Hall
5C2×C19×#3862—21no—
6C2×C19×#3862D311yescharacteristic
7C2×C3×C72×C19C2×C311yescharacteristic
8ΓL(1,𝔽8)×Dic57—72nomaximal
9C72×Dic19—31noHall
10C19×#3862—21no—
11C19×#3862Dic311yescharacteristic, complemented
12C3×C72×C19C3×C411yescharacteristic, complemented
13C2×C3×C19×ΓL(1,𝔽8)—72no—
14C2×C72×C19C3×D311yescharacteristic
15Dic3×#3862—191nomaximal, Hall
16C7×Dic57—32no—
17C7×Dic57ΓL(1,𝔽8)12yescomplemented
18ΓL(1,𝔽8)×Dic19—212no—
19C3×C19×ΓL(1,𝔽8)—72no—
20C72×C19C3×Dic311yescharacteristic, complemented, Hall
21C2×C3×#3862D1911yescharacteristic
22C2×C3×C7×C19—32no—
23C2×C3×C7×C19C2×ΓL(1,𝔽8)12yes—
24C2×C19×ΓL(1,𝔽8)—72no—
25C2×C19×ΓL(1,𝔽8)—142no—
26C3×Dic57—491noHall
27C72×Dic3—191no—
28C4×#3862—571no—
29C7×Dic19—32no—
30C7×Dic19—92no—
31C3×#3862Dic1911yescharacteristic, complemented, Hall
32C3×C7×C19—32no—
33C3×C7×C19C4×ΓL(1,𝔽8)12yescomplemented
34C19×ΓL(1,𝔽8)—72no—
35C19×ΓL(1,𝔽8)—142no—
36C2×C32×C19—491no—
37C2×C3×C72C3×D1911yescharacteristic
38C2×#3862—21no—
39C2×#3862D5711yescharacteristic
40C2×C7×C19—32no—
41C2×C7×C19D3×ΓL(1,𝔽8)12yes—
42Dic3×ΓL(1,𝔽8)—1332no—
43Dic57#386211yescharacteristic, direct product factor
44C3×Dic19—1471no—
45C4×C72—571noHall
46C32×C19—491noHall
47C3×C72C3×Dic1911yescharacteristic, complemented
48#3862—21no—
49#3862Dic5711yescharacteristic, direct product factor
50C7×C19—32no—
51C7×C19Dic3×ΓL(1,𝔽8)12yescomplemented
52C2×C3×ΓL(1,𝔽8)—72no—
53C2×C3×C19—491no—
54C2×C3×C19—981no—
55C2×C3×C19C2×#386211yescharacteristic
56C2×C72C3×D5711yescharacteristic
57C7×Dic3—192no—
58C7×Dic3—572no—
59C4×ΓL(1,𝔽8)—3992no—
60Dic19—31noHall
61C3×ΓL(1,𝔽8)—72no—
62C3×C19—491no—
63C3×C19—981no—
64C3×C19C4×#386211yescharacteristic, complemented
65C72C3×Dic5711yescharacteristic, complemented, Sylow
66C2×C3×C7—32no—
67C2×C3×C7ΓL(1,𝔽8)×D1912yes—
68C2×ΓL(1,𝔽8)—72no—
69C2×ΓL(1,𝔽8)—142no—
70C2×C19D3×#386211yescharacteristic
71C3×Dic3—9311noHall
72C4×C7—572no—
73C4×C7—1712no—
74C3×C7—32no—
75C3×C7ΓL(1,𝔽8)×Dic1912yescomplemented
76ΓL(1,𝔽8)—72no—
77ΓL(1,𝔽8)—142no—
78C19Dic3×#386211yescharacteristic, complemented, Sylow
79C2×C32—491no—
80C2×C7—32no—
81C2×C7ΓL(1,𝔽8)×D5712yes—
82C3×C4—27931no—
83Dic3—191no—
84C32—491noSylow
85C7—32no—
86C7ΓL(1,𝔽8)×Dic5712yescomplemented
87C2×C3—491no—
88C2×C3—981no—
89C2×C3D19×#386211yescharacteristic
90C4—571noSylow
91C3—491no—
92C3—981no—
93C3Dic19×#386211yescharacteristic, complemented
94C2D57×#386211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D57×#3862
commutator, hypocenterC3×C72×C19C3×C4
Fitting, socle, cosocleC2×C3×C72×C19C2×C3
prime radicalC2×C3×C19×#3862C2
LCSG ▷ C3×C72×C19
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C72×Dic57C3semidirect
4. C3×C19×#3862C4semidirect
11. C19×#3862Dic3semidirect
12. C3×C72×C19C3×C4semidirect
17. C7×Dic57ΓL(1,𝔽8)semidirect
20. C72×C19C3×Dic3semidirect
31. C3×#3862Dic19semidirect
33. C3×C7×C19C4×ΓL(1,𝔽8)semidirect
43. Dic57#3862direct (N × H)
47. C3×C72C3×Dic19semidirect
49. #3862Dic57direct (N × H)
51. C7×C19Dic3×ΓL(1,𝔽8)semidirect
64. C3×C19C4×#3862semidirect
65. C72C3×Dic57semidirect
75. C3×C7ΓL(1,𝔽8)×Dic19semidirect
78. C19Dic3×#3862semidirect
86. C7ΓL(1,𝔽8)×Dic57semidirect
93. C3Dic19×#3862semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C19×#38622
C72×Dic573
Dic19×#38623
ΓL(1,𝔽8)×Dic577
Dic3×#386219