Finite Group Databasebeta

← C3⋊#26013825 #45691911

Subgroups — C3⋊#26013825 #45691911

Order 33516.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C19×#3862C211yesmaximal, characteristic
2C3⋊(C7⋊Dic133)C311yesmaximal, characteristic, complemented
3#26013825—31nomaximal
4C3×C19×#3862C411yescharacteristic, complemented, Hall
5C2×C19×#3862—21no—
6C2×C19×#3862D311yescharacteristic
7C2×C3×C72×C19C2×C311yescharacteristic
8C3⋊(ΓL(1,𝔽8)⋊Dic19)—72nomaximal
9C7⋊Dic133—31noHall
10C19×#3862—21no—
11C19×#3862Dic311yescharacteristic, complemented
12C3×C72×C19C3×C411yescharacteristic, complemented
13C2×C3×C19×ΓL(1,𝔽8)—72no—
14C2×C72×C19C3×D311yescharacteristic
15C3⋊#10596875—191nomaximal, Hall
16Dic399—72no—
17Dic399—212no—
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×C19AGL(1,𝔽7)12yes—
24C2×C19×ΓL(1,𝔽8)—72no—
25C2×C19×ΓL(1,𝔽8)—142no—
26C3×Dic57—491noHall
27C3⋊(C7⋊Dic7)—191no—
28#10596875—571no—
29Dic133—212no—
30Dic133—632no—
31C3×#3862Dic1911yescharacteristic, complemented, Hall
32C3×C7×C19—32no—
33C3×C7×C19ΓL(1,𝔽8)⋊C412yescomplemented
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×C19C3⋊AGL(1,𝔽7)12yes—
42C3⋊(ΓL(1,𝔽8)⋊C4)—1332no—
43Dic57—491no—
44C3×Dic19—1471no—
45C7⋊Dic7—571noHall
46C32×C19—491noHall
47C3×C72C3×Dic1911yescharacteristic, complemented
48#3862—21no—
49#3862Dic5711yescharacteristic, complemented
50C7×C19—32no—
51C7×C19C3⋊(ΓL(1,𝔽8)⋊C4)12yescomplemented
52C2×C3×ΓL(1,𝔽8)—72no—
53C2×C3×C19—491no—
54C2×C3×C19—981no—
55C2×C3×C19#6442511yescharacteristic
56C2×C72C3×D5711yescharacteristic
57Dic21—1332no—
58Dic21—3992no—
59ΓL(1,𝔽8)⋊C4—3992no—
60Dic19—1471noHall
61C3×ΓL(1,𝔽8)—72no—
62C3×C19—491no—
63C3×C19—981no—
64C3×C19#1059687511yescharacteristic, 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×C19C3⋊#6442511yescharacteristic
71C3×Dic3—9311noHall
72Dic7—3992no—
73Dic7—11972no—
74C3×C7—32no—
75C3×C7ΓL(1,𝔽8)⋊Dic1912yescomplemented
76ΓL(1,𝔽8)—72no—
77ΓL(1,𝔽8)—142no—
78C19C3⋊#1059687511yescharacteristic, complemented, Sylow
79C2×C32—491no—
80C2×C7—32no—
81C2×C7C3⋊(ΓL(1,𝔽8)⋊D19)12yes—
82C3×C4—27931no—
83Dic3—9311no—
84C32—491noSylow
85C7—32no—
86C7C3⋊(ΓL(1,𝔽8)⋊Dic19)12yescomplemented
87C2×C3—491no—
88C2×C3—981no—
89C2×C3#1915029211yescharacteristic
90C4—27931noSylow
91C3—491no—
92C3—981no—
93C3#2601382511yescharacteristic, complemented
94C2C3⋊#1915029211yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊#19150292
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. C3⋊(C7⋊Dic133)C3semidirect
4. C3×C19×#3862C4semidirect
11. C19×#3862Dic3semidirect
12. C3×C72×C19C3×C4semidirect
20. C72×C19C3×Dic3semidirect
31. C3×#3862Dic19semidirect
33. C3×C7×C19ΓL(1,𝔽8)⋊C4semidirect
47. C3×C72C3×Dic19semidirect
49. #3862Dic57semidirect
51. C7×C19C3⋊(ΓL(1,𝔽8)⋊C4)semidirect
64. C3×C19#10596875semidirect
65. C72C3×Dic57semidirect
75. C3×C7ΓL(1,𝔽8)⋊Dic19semidirect
78. C19C3⋊#10596875semidirect
86. C7C3⋊(ΓL(1,𝔽8)⋊Dic19)semidirect
93. C3#26013825semidirect

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⋊(C7⋊Dic133)3
#260138253
C3⋊(ΓL(1,𝔽8)⋊Dic19)7
C3⋊#1059687519