Finite Group Databasebeta

← C3⋊#26013942 #45692274

Subgroups — C3⋊#26013942 #45692274

Order 33516.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#19150286C211yesmaximal, characteristic
2C19×C3⋊#5997C311yesmaximal, characteristic, complemented
3#26013942—31nomaximal
4C3×#14584115C411yescharacteristic, complemented, Hall
5C3×C19×C7⋊D7C2×C311yescharacteristic
6#19150286—21no—
7#19150286D311yescharacteristic
8C19×#5997—31noHall
9#14584115—21no—
10#14584115Dic311yescharacteristic, complemented
11C3×C72×C19C3×C411yescharacteristic, complemented
12C3×#11716325—144no—
13C19×C7⋊D7C3×D311yescharacteristic
14C3⋊(#5997⋊C3)—191nomaximal, Hall
15C3×#87704—144no—
16C72×C19C3×Dic311yescharacteristic, complemented, Hall
17C3×#64424—191no—
18C3×D7×C19—144no—
19#11716325—144no—
20#11716325—148no—
21Dic3×C19⋊C3—491nomaximal, Hall
22C3⋊#5997C19⋊C311yescharacteristic, complemented
23#5997⋊C3—571no—
24C3×#3861—191noHall
25C3×C7×C19—24no—
26#87704—144no—
27#87704—148no—
28C2×C3×C19⋊C3—491no—
29C3×C7⋊D7C2×C19⋊C311yescharacteristic
30#64424—191no—
31#64424—381no—
32D7×C19—144no—
33Dic3×C19—491no—
34C4×C19⋊C3—1471no—
35#5997—31noHall
36C3×C19⋊C3—491noHall
37C3×C72C4×C19⋊C311yescharacteristic, complemented
38#3861—191no—
39#3861—381no—
40C7×C19—24no—
41C3×AGL(1,𝔽7)—2664no—
42C2×C3×C19—491no—
43C2×C19⋊C3—491no—
44C2×C19⋊C3—981no—
45C7⋊D7D3×C19⋊C311yescharacteristic
46C4×C19—1471noHall
47C3×ΓL(1,𝔽8)—2664no—
48C3×C19#5997⋊C311yescharacteristic, complemented
49C19⋊C3—491no—
50C19⋊C3—981no—
51C72Dic3×C19⋊C311yescharacteristic, complemented, Sylow
52C3×D7—144no—
53AGL(1,𝔽7)—2668no—
54AGL(1,𝔽7)—2664no—
55C2×C19—491no—
56C3×Dic3—9311noHall
57C3×C7—24no—
58ΓL(1,𝔽8)—2668no—
59ΓL(1,𝔽8)—2664no—
60C19C3⋊(#5997⋊C3)11yescharacteristic, complemented, Sylow
61C2×C32—9311no—
62D7—144no—
63C3×C4—27931no—
64Dic3—491no—
65C32—9311noSylow
66C7—24no—
67C2×C3—491no—
68C2×C3—18621no—
69C2×C3—9311no—
70C4—1471noSylow
71C3—18621no—
72C3—9311no—
73C3#2601394211yescharacteristic, complemented
74C2—491no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C72×C19C3×C4
prime radicalC3×#19150286C2
cosocleC3×C19×C7⋊D7C2×C3
LCSG ▷ C3×C72×C19
UCSC1

Complements

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

NH ≅ G/Ntype
2. C19×C3⋊#5997C3semidirect
4. C3×#14584115C4semidirect
10. #14584115Dic3semidirect
11. C3×C72×C19C3×C4semidirect
16. C72×C19C3×Dic3semidirect
22. C3⋊#5997C19⋊C3semidirect
37. C3×C72C4×C19⋊C3semidirect
48. C3×C19#5997⋊C3semidirect
51. C72Dic3×C19⋊C3semidirect
60. C19C3⋊(#5997⋊C3)semidirect
73. C3#26013942semidirect

Maximal subgroups

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

subgroupindex
C3×#191502862
C19×C3⋊#59973
#260139423
C3⋊(#5997⋊C3)19
Dic3×C19⋊C349