Finite Group Databasebeta

← C3×Dic19×#3862 #45691875

Subgroups — C3×Dic19×#3862 #45691875

Order 33516.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C19×#3862C211yesmaximal, characteristic
2C3×C72×Dic19C311yesmaximal, characteristic, complemented
3Dic19×#3862C313yesmaximal, direct product factor
4C3×C19×#3862C411yescharacteristic, complemented, Hall
5C2×C19×#3862C2×C313yes—
6C2×C3×C72×C19C2×C311yescharacteristic
7C3×ΓL(1,𝔽8)×Dic19—72nomaximal
8C72×Dic19C3211yescharacteristic, complemented, Hall
9C19×#3862C3×C413yescomplemented
10C3×C72×C19C3×C411yescharacteristic, complemented
11C2×C3×C19×ΓL(1,𝔽8)—72no—
12C2×C72×C19C2×C3211yescharacteristic
13C3×C4×#3862—191nomaximal, Hall
14C3×C7×Dic19—32no—
15C3×C7×Dic19ΓL(1,𝔽8)12yescomplemented
16ΓL(1,𝔽8)×Dic19—76no—
17C3×C19×ΓL(1,𝔽8)—72no—
18C72×C19C32×C411yescharacteristic, complemented, Hall
19C2×C3×#3862D1911yescharacteristic
20C2×C3×C7×C19—32no—
21C2×C3×C7×C19C2×ΓL(1,𝔽8)12yes—
22C2×C19×ΓL(1,𝔽8)—76no—
23C32×Dic19—491noHall
24C3×C4×C72—191no—
25C4×#3862—193no—
26C7×Dic19—32no—
27C7×Dic19C3×ΓL(1,𝔽8)12yescomplemented
28C3×#3862Dic1911yescharacteristic, direct product factor, Hall
29C3×C7×C19—32no—
30C3×C7×C19C4×ΓL(1,𝔽8)12yescomplemented
31C19×ΓL(1,𝔽8)—76no—
32C2×C32×C19—491no—
33C2×C3×C72C3×D1911yescharacteristic
34C2×#3862C3×D1913yes—
35C2×C7×C19—32no—
36C2×C7×C19C2×C3×ΓL(1,𝔽8)12yes—
37C3×C4×ΓL(1,𝔽8)—1332no—
38C3×Dic19—493no—
39C3×Dic19#386211yescharacteristic, direct product factor
40C4×C72—191noHall
41C32×C19—491noHall
42C3×C72C3×Dic1911yescharacteristic, complemented
43#3862C3×Dic1913yesdirect product factor
44C7×C19—32no—
45C7×C19C3×C4×ΓL(1,𝔽8)12yescomplemented
46C2×C3×ΓL(1,𝔽8)—72no—
47C2×C3×C19—493no—
48C2×C3×C19C2×#386211yescharacteristic
49C2×C72C32×D1911yescharacteristic
50C3×C4×C7—192no—
51C3×C4×C7—572no—
52C4×ΓL(1,𝔽8)—1336no—
53Dic19C3×#386211yescharacteristic, direct product factor, Hall
54C3×ΓL(1,𝔽8)—72no—
55C3×C19—493no—
56C3×C19C4×#386211yescharacteristic, complemented
57C72C32×Dic1911yescharacteristic, complemented, Sylow
58C2×C3×C7—32no—
59C2×C3×C7ΓL(1,𝔽8)×D1912yes—
60C2×ΓL(1,𝔽8)—76no—
61C2×C19C2×C3×#386211yescharacteristic
62C32×C4—9311noHall
63C4×C7—192no—
64C4×C7—572no—
65C3×C7—32no—
66C3×C7ΓL(1,𝔽8)×Dic1912yescomplemented
67ΓL(1,𝔽8)—76no—
68C19C3×C4×#386211yescharacteristic, complemented, Sylow
69C2×C32—491no—
70C2×C7—32no—
71C2×C7C3×ΓL(1,𝔽8)×D1912yes—
72C3×C4—191no—
73C3×C4—9313no—
74C32—491noSylow
75C7—32no—
76C7C3×ΓL(1,𝔽8)×Dic1912yescomplemented
77C2×C3—493no—
78C2×C3D19×#386211yescharacteristic
79C4—191noSylow
80C3—493no—
81C3Dic19×#386211yescharacteristic, direct product factor
82C2C3×D19×#386211yescharacteristic
subgroupG/H
center, hypercenterC2×C3D19×#3862
commutator, hypocenterC72×C19C32×C4
FrattiniC2C3×D19×#3862
Fitting, socleC2×C3×C72×C19C2×C3
prime radicalC2×C3×C19×#3862C2
cosocleC2×C72×C19C2×C32
LCSG ▷ C72×C19
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C72×Dic19C3semidirect
3. Dic19×#3862C3direct (N × H)
4. C3×C19×#3862C4semidirect
8. C72×Dic19C32semidirect
9. C19×#3862C3×C4semidirect
10. C3×C72×C19C3×C4semidirect
15. C3×C7×Dic19ΓL(1,𝔽8)semidirect
18. C72×C19C32×C4semidirect
27. C7×Dic19C3×ΓL(1,𝔽8)semidirect
28. C3×#3862Dic19direct (N × H)
30. C3×C7×C19C4×ΓL(1,𝔽8)semidirect
39. C3×Dic19#3862direct (N × H)
42. C3×C72C3×Dic19semidirect
43. #3862C3×Dic19direct (N × H)
45. C7×C19C3×C4×ΓL(1,𝔽8)semidirect
53. Dic19C3×#3862direct (N × H)
56. C3×C19C4×#3862semidirect
57. C72C32×Dic19semidirect
66. C3×C7ΓL(1,𝔽8)×Dic19semidirect
68. C19C3×C4×#3862semidirect
76. C7C3×ΓL(1,𝔽8)×Dic19semidirect
81. C3Dic19×#3862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C19×#38622
C3×C72×Dic193
Dic19×#38623
C3×ΓL(1,𝔽8)×Dic197
C3×C4×#386219