Finite Group Databasebeta

← C3×#21439530 #37524716

Subgroups — C3×#21439530 #37524716

Order 22932.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C13×#3862C211yesmaximal, characteristic
2C3×C7⋊Dic91C311yesmaximal, characteristic, complemented
3#21439530C313yesmaximal, direct product factor
4C3×C13×#3862C411yescharacteristic, complemented, Hall
5C2×C13×#3862C2×C313yes—
6C2×C3×C72×C13C2×C311yescharacteristic
7C3×ΓL(1,𝔽8)⋊Dic13—72nomaximal
8C7⋊Dic91C3211yescharacteristic, complemented, Hall
9C3×C72×C13C3×C411yescharacteristic, complemented
10C13×#3862C3×C413yescomplemented
11C3×#10596875—131nomaximal, Hall
12C2×C3×C13×ΓL(1,𝔽8)—72no—
13C2×C72×C13C2×C3211yescharacteristic
14C3×Dic91—212no—
15C3×Dic91—212no—
16ΓL(1,𝔽8)⋊Dic13—76no—
17C2×C3×#3862D1311yescharacteristic
18C3×C13×ΓL(1,𝔽8)—72no—
19C72×C13C32×C411yescharacteristic, complemented, Hall
20C3×C7⋊Dic7—131no—
21#10596875—133no—
22C2×C3×C7×C13—32no—
23C2×C3×C7×C13AGL(1,𝔽7)12yes—
24C2×C13×ΓL(1,𝔽8)—76no—
25C32×Dic13—491noHall
26C3×#3862Dic1311yescharacteristic, complemented, Hall
27Dic91—212no—
28Dic91—212no—
29C2×C3×C72C3×D1311yescharacteristic
30C2×#3862C3×D1313yes—
31C3×C7×C13—32no—
32C3×C7×C13ΓL(1,𝔽8)⋊C412yescomplemented
33C13×ΓL(1,𝔽8)—76no—
34C3×ΓL(1,𝔽8)⋊C4—912no—
35C2×C32×C13—491no—
36C7⋊Dic7—131noHall
37C2×C7×C13—32no—
38C2×C7×C13C3×AGL(1,𝔽7)12yes—
39C3×Dic13—493no—
40C3×Dic13—1471no—
41C3×C72C3×Dic1311yescharacteristic, complemented
42#3862C3×Dic1313yescomplemented
43C2×C3×ΓL(1,𝔽8)—72no—
44C32×C13—491noHall
45C2×C72C32×D1311yescharacteristic
46C7×C13—32no—
47C7×C13C3×ΓL(1,𝔽8)⋊C412yescomplemented
48C3×Dic7—2732no—
49C3×Dic7—2732no—
50ΓL(1,𝔽8)⋊C4—916no—
51C2×C3×C13—493no—
52C2×C3×C13#6442511yescharacteristic
53C3×ΓL(1,𝔽8)—72no—
54Dic13—1471noHall
55C72C32×Dic1311yescharacteristic, complemented, Sylow
56C2×C3×C7—32no—
57C2×C3×C7ΓL(1,𝔽8)⋊D1312yes—
58C2×ΓL(1,𝔽8)—76no—
59C3×C13—493no—
60C3×C13#1059687511yescharacteristic, complemented
61C32×C4—6371noHall
62Dic7—2732no—
63Dic7—2732no—
64C2×C13C3×#6442511yescharacteristic
65C3×C7—32no—
66C3×C7ΓL(1,𝔽8)⋊Dic1312yescomplemented
67ΓL(1,𝔽8)—76no—
68C2×C32—491no—
69C2×C7—32no—
70C2×C7C3×ΓL(1,𝔽8)⋊D1312yes—
71C13C3×#1059687511yescharacteristic, complemented, Sylow
72C3×C4—19111no—
73C3×C4—6373no—
74C32—491noSylow
75C7—32no—
76C7C3×ΓL(1,𝔽8)⋊Dic1312yescomplemented
77C2×C3—493no—
78C2×C3#1683845411yescharacteristic
79C4—19111noSylow
80C3—493no—
81C3#2143953011yescharacteristic, direct product factor
82C2C3×#1683845411yescharacteristic
subgroupG/H
center, hypercenterC2×C3#16838454
commutator, hypocenterC72×C13C32×C4
FrattiniC2C3×#16838454
Fitting, socleC2×C3×C72×C13C2×C3
prime radicalC2×C3×C13×#3862C2
cosocleC2×C72×C13C2×C32
LCSG ▷ C72×C13
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C7⋊Dic91C3semidirect
3. #21439530C3direct (N × H)
4. C3×C13×#3862C4semidirect
8. C7⋊Dic91C32semidirect
9. C3×C72×C13C3×C4semidirect
10. C13×#3862C3×C4semidirect
19. C72×C13C32×C4semidirect
26. C3×#3862Dic13semidirect
32. C3×C7×C13ΓL(1,𝔽8)⋊C4semidirect
41. C3×C72C3×Dic13semidirect
42. #3862C3×Dic13semidirect
47. C7×C13C3×ΓL(1,𝔽8)⋊C4semidirect
55. C72C32×Dic13semidirect
60. C3×C13#10596875semidirect
66. C3×C7ΓL(1,𝔽8)⋊Dic13semidirect
71. C13C3×#10596875semidirect
76. C7C3×ΓL(1,𝔽8)⋊Dic13semidirect
81. C3#21439530direct (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×#38622
C3×C7⋊Dic913
#214395303
C3×ΓL(1,𝔽8)⋊Dic137
C3×#1059687513