Finite Group Databasebeta

← C3⋊#26013844 #45691931

Subgroups — C3⋊#26013844 #45691931

Order 33516.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#14584115C211yesmaximal, characteristic
2C72×Dic57C311yesmaximal, characteristic, complemented
3#26013844—31nomaximal
4C3×#14584115C411yescharacteristic, complemented, Hall
5C2×#14584115—21no—
6C2×#14584115D311yescharacteristic
7C2×C3×C72×C19C2×C311yescharacteristic
8C3⋊#13097582—78nomaximal
9C72×Dic19—31noHall
10#14584115—21no—
11#14584115Dic311yescharacteristic, complemented
12C3×C72×C19C3×C411yescharacteristic, complemented
13C2×C3×#87704—78no—
14C2×C72×C19C3×D311yescharacteristic
15Dic3×#3861—191nomaximal, Hall
16C7×Dic57ΓL(1,𝔽8)18yescomplemented
17#13097582—218no—
18C3×#87704—78no—
19C72×C19C3×Dic311yescharacteristic, complemented, Hall
20C2×C3×#3861—191no—
21C2×C3×C7×C19C2×ΓL(1,𝔽8)18yes—
22C2×#87704—78no—
23C2×#87704—148no—
24C3⋊((C19⋊C3)⋊C4)—491noHall
25C72×Dic3—191no—
26C4×#3861—571no—
27C7×Dic19—38no—
28C3×#3861—191noHall
29C3×C7×C19C4×ΓL(1,𝔽8)18yescomplemented
30#87704—78no—
31#87704—148no—
32C2×C3×C19⋊C3—491no—
33C2×C3×C72D19⋊C311yescharacteristic
34C2×#3861—191no—
35C2×#3861—381no—
36C2×C7×C19D3×ΓL(1,𝔽8)18yes—
37Dic3×ΓL(1,𝔽8)—1338no—
38Dic57#386111yescharacteristic, complemented
39(C19⋊C3)⋊C4—1471no—
40C4×C72—571noHall
41C3×C19⋊C3—491noHall
42C3×C72(C19⋊C3)⋊C411yescharacteristic, complemented
43#3861—191no—
44#3861—381no—
45C7×C19Dic3×ΓL(1,𝔽8)18yescomplemented
46C2×C3×ΓL(1,𝔽8)—1338no—
47C2×C3×C19C2×#386111yescharacteristic
48C2×C19⋊C3—491no—
49C2×C19⋊C3—981no—
50C2×C72C3⋊(D19⋊C3)11yescharacteristic
51C7×Dic3—198no—
52C4×ΓL(1,𝔽8)—3998no—
53Dic19—31noHall
54C3×ΓL(1,𝔽8)—1338no—
55C3×C19C4×#386111yescharacteristic, complemented
56C19⋊C3—491no—
57C19⋊C3—981no—
58C72C3⋊((C19⋊C3)⋊C4)11yescharacteristic, complemented, Sylow
59C2×C3×C7#1171632118yes—
60C2×ΓL(1,𝔽8)—2668no—
61C2×ΓL(1,𝔽8)—1338no—
62C2×C19D3×#386111yescharacteristic
63C3×Dic3—9311noHall
64C4×C7—578no—
65C3×C7#1309758218yescomplemented
66ΓL(1,𝔽8)—2668no—
67ΓL(1,𝔽8)—1338no—
68C19Dic3×#386111yescharacteristic, complemented, Sylow
69C2×C32—9311no—
70C2×C7C3⋊#1171632118yes—
71C3×C4—27931no—
72Dic3—191no—
73C32—9311noSylow
74C7C3⋊#1309758218yescomplemented
75C2×C3—18621no—
76C2×C3—9311no—
77C2×C3#1915031111yescharacteristic
78C4—571noSylow
79C3—18621no—
80C3—9311no—
81C3#2601384411yescharacteristic, complemented
82C2C3⋊#1915031111yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊#19150311
commutator, hypocenterC3×C72×C19C3×C4
Fitting, socle, cosocleC2×C3×C72×C19C2×C3
prime radicalC2×C3×#14584115C2
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×#14584115C4semidirect
11. #14584115Dic3semidirect
12. C3×C72×C19C3×C4semidirect
16. C7×Dic57ΓL(1,𝔽8)semidirect
19. C72×C19C3×Dic3semidirect
29. C3×C7×C19C4×ΓL(1,𝔽8)semidirect
38. Dic57#3861semidirect
42. C3×C72(C19⋊C3)⋊C4semidirect
45. C7×C19Dic3×ΓL(1,𝔽8)semidirect
55. C3×C19C4×#3861semidirect
58. C72C3⋊((C19⋊C3)⋊C4)semidirect
65. C3×C7#13097582semidirect
68. C19Dic3×#3861semidirect
74. C7C3⋊#13097582semidirect
81. C3#26013844semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#145841152
C72×Dic573
#260138443
C3⋊#130975827
Dic3×#386119