Finite Group Databasebeta

← C2×C3⋊#19150285 #45692641

Subgroups — C2×C3⋊#19150285 #45692641

Order 33516.

440 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#14584116C211yesmaximal, characteristic, complemented
2C3⋊#19150285C212yesmaximal, direct product factor
3C2×C3⋊(C7⋊D133)C311yesmaximal, characteristic, complemented
4C2×#19150285—31nomaximal
5C3×#14584116C2211yescharacteristic, complemented, Hall
6C3⋊(C7⋊D133)C2×C312yescomplemented
7C2×#14584116—21no—
8C2×#14584116D311yescharacteristic, complemented
9#19150285—32no—
10C2×C3×C72×C19C2×C311yescharacteristic, complemented
11C2×C3⋊#11716328—78nomaximal
12C2×C7⋊D133—31noHall
13#14584116—21no—
14#14584116C2×D311yescharacteristic, complemented
15C3×C72×C19C22×C311yescharacteristic, complemented
16C2×C3×#87705—78no—
17C3⋊#11716328—716no—
18C2×C72×C19C3×D311yescharacteristic, complemented
19C7⋊D133—32no—
20C2×C3⋊#64424—191nomaximal, Hall
21C2×D399—78no—
22C2×#11716328—218no—
23C3×#87705—78no—
24C72×C19C2×C3×D311yescharacteristic, complemented, Hall
25C2×C3×#3861—191no—
26C3⋊#64424—192no—
27C2×C3×C7×C19AGL(1,𝔽7)18yescomplemented
28D399—716no—
29C2×#87705—78no—
30C2×#87705—148no—
31#11716328—2116no—
32C2×C3⋊(D19⋊C3)—491noHall
33C2×C3⋊(C7⋊D7)—191no—
34C2×#64424—571no—
35C2×D133—218no—
36C3×#3861—191noHall
37C3×C7×C19C2×AGL(1,𝔽7)18yescomplemented
38#87705—78no—
39#87705—148no—
40C2×C3×C19⋊C3—491no—
41C3⋊(D19⋊C3)—492no—
42C2×C3×C72D19⋊C311yescharacteristic, complemented
43C3⋊(C7⋊D7)—192no—
44C2×#3861—191no—
45C2×#3861—381no—
46#64424—572no—
47C2×C7×C19C3⋊AGL(1,𝔽7)18yescomplemented
48D133—2116no—
49C2×C3⋊AGL(1,𝔽7)—1338no—
50C2×D57—491no—
51C2×D19⋊C3—1471no—
52C2×C7⋊D7—571noHall
53C3×C19⋊C3—491noHall
54C3×C72C2×D19⋊C311yescharacteristic, complemented
55#3861—191no—
56#3861—381no—
57C7×C19C2×C3⋊AGL(1,𝔽7)18yescomplemented
58C2×C3×ΓL(1,𝔽8)—1338no—
59C3⋊AGL(1,𝔽7)—13316no—
60C2×C3×C19#6442411yescharacteristic, complemented
61D57—492no—
62C2×C19⋊C3—491no—
63C2×C19⋊C3—981no—
64D19⋊C3—1472no—
65C2×C72C3⋊(D19⋊C3)11yescharacteristic, complemented
66C7⋊D7—572no—
67C2×D21—1338no—
68C2×AGL(1,𝔽7)—3998no—
69C2×D19—1471noHall
70C3×ΓL(1,𝔽8)—1338no—
71C3×C19C2×#6442411yescharacteristic, complemented
72C19⋊C3—491no—
73C19⋊C3—981no—
74C72C2×C3⋊(D19⋊C3)11yescharacteristic, complemented, Sylow
75C2×C3×C7#1171632818yescomplemented
76D21—13316no—
77C2×ΓL(1,𝔽8)—2668no—
78C2×ΓL(1,𝔽8)—1338no—
79AGL(1,𝔽7)—39916no—
80C2×C19C3⋊#6442411yescharacteristic, complemented
81D19—1472no—
82C2×C3×D3—9311noHall
83C2×D7—3998no—
84C3×C7C2×#1171632818yescomplemented
85ΓL(1,𝔽8)—2668no—
86ΓL(1,𝔽8)—1338no—
87C19C2×C3⋊#6442411yescharacteristic, complemented, Sylow
88C2×C32—9311no—
89C3×D3—9312no—
90C2×C7C3⋊#1171632818yescomplemented
91D7—39916no—
92C22×C3—27931no—
93C2×D3—9311no—
94C32—9311noSylow
95C7C2×C3⋊#1171632818yescomplemented
96C2×C3—18621no—
97C2×C3—9311no—
98C2×C3—27932no—
99C2×C3#1915028511yescharacteristic, complemented
100D3—9312no—
101C22—27931noSylow
102C3—18621no—
103C3—9311no—
104C3C2×#1915028511yescharacteristic, complemented
105C2—27932no—
106C2C3⋊#1915028511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊#19150285
commutator, cosocle, hypocenterC3×C72×C19C22×C3
FrattiniC1G
Fitting, socleC2×C3×C72×C19C2×C3
LCSG ▷ C3×C72×C19
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#14584116C2semidirect
2. C3⋊#19150285C2direct (N × H)
3. C2×C3⋊(C7⋊D133)C3semidirect
5. C3×#14584116C22semidirect
6. C3⋊(C7⋊D133)C2×C3semidirect
8. C2×#14584116D3semidirect
10. C2×C3×C72×C19C2×C3semidirect
14. #14584116C2×D3semidirect
15. C3×C72×C19C22×C3semidirect
18. C2×C72×C19C3×D3semidirect
24. C72×C19C2×C3×D3semidirect
27. C2×C3×C7×C19AGL(1,𝔽7)semidirect
37. C3×C7×C19C2×AGL(1,𝔽7)semidirect
42. C2×C3×C72D19⋊C3semidirect
47. C2×C7×C19C3⋊AGL(1,𝔽7)semidirect
54. C3×C72C2×D19⋊C3semidirect
57. C7×C19C2×C3⋊AGL(1,𝔽7)semidirect
60. C2×C3×C19#64424semidirect
65. C2×C72C3⋊(D19⋊C3)semidirect
71. C3×C19C2×#64424semidirect
74. C72C2×C3⋊(D19⋊C3)semidirect
75. C2×C3×C7#11716328semidirect
80. C2×C19C3⋊#64424semidirect
84. C3×C7C2×#11716328semidirect
87. C19C2×C3⋊#64424semidirect
90. C2×C7C3⋊#11716328semidirect
95. C7C2×C3⋊#11716328semidirect
99. C2×C3#19150285semidirect
104. C3C2×#19150285semidirect
106. C2C3⋊#19150285direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#145841162
C3⋊#191502852
C2×C3⋊(C7⋊D133)3
C2×#191502853
C2×C3⋊#117163287
C2×C3⋊#6442419