Finite Group Databasebeta

← C2×C3⋊#16838446 #37525528

Subgroups — C2×C3⋊#16838446 #37525528

Order 22932.

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×#14274263C211yesmaximal, characteristic, complemented
2C3⋊#16838446C212yesmaximal, direct product factor
3C2×C3⋊(C7⋊D91)C311yesmaximal, characteristic, complemented
4C2×#16838446—31nomaximal
5C3×#14274263C2211yescharacteristic, complemented, Hall
6C3⋊(C7⋊D91)C2×C312yescomplemented
7C2×#14274263—21no—
8C2×#14274263D311yescharacteristic, complemented
9#16838446—32no—
10C2×C3×C72×C13C2×C311yescharacteristic, complemented
11C2×C3⋊#10587722—78nomaximal
12C2×C7⋊D91—31noHall
13C3×C72×C13C22×C311yescharacteristic, complemented
14#14274263—21no—
15#14274263C2×D311yescharacteristic, complemented
16C2×C3⋊#64424—131nomaximal, Hall
17C2×C3×#63270—78no—
18C3⋊#10587722—716no—
19C2×C72×C13C3×D311yescharacteristic, complemented
20C7⋊D91—32no—
21C2×D273—78no—
22C2×#10587722—218no—
23C2×C3×#3861—131no—
24C3⋊#64424—132no—
25C3×#63270—78no—
26C72×C13C2×C3×D311yescharacteristic, complemented, Hall
27C2×C3⋊(C7⋊D7)—131no—
28C2×#64424—391no—
29C2×C3×C7×C13AGL(1,𝔽7)18yescomplemented
30D273—716no—
31C2×#63270—78no—
32C2×#63270—148no—
33#10587722—2116no—
34C2×C3⋊(D13⋊C3)—491noHall
35C3×#3861—131noHall
36C2×D91—218no—
37C2×C3×C72D13⋊C311yescharacteristic, complemented
38C3⋊(C7⋊D7)—132no—
39C2×#3861—131no—
40C2×#3861—261no—
41#64424—392no—
42C3×C7×C13C2×AGL(1,𝔽7)18yescomplemented
43#63270—78no—
44#63270—148no—
45C2×C3⋊AGL(1,𝔽7)—918no—
46C2×C3×C13⋊C3—491no—
47C3⋊(D13⋊C3)—492no—
48C2×C7⋊D7—391noHall
49C2×C7×C13C3⋊AGL(1,𝔽7)18yescomplemented
50D91—2116no—
51C2×D39—491no—
52C2×D13⋊C3—1471no—
53C3×C72C2×D13⋊C311yescharacteristic, complemented
54#3861—131no—
55#3861—261no—
56C2×C3×ΓL(1,𝔽8)—918no—
57C3⋊AGL(1,𝔽7)—9116no—
58C3×C13⋊C3—491noHall
59C2×C72C3⋊(D13⋊C3)11yescharacteristic, complemented
60C7⋊D7—392no—
61C7×C13C2×C3⋊AGL(1,𝔽7)18yescomplemented
62C2×D21—918no—
63C2×AGL(1,𝔽7)—2738no—
64C2×C3×C13#6442411yescharacteristic, complemented
65D39—492no—
66C2×C13⋊C3—491no—
67C2×C13⋊C3—981no—
68D13⋊C3—1472no—
69C3×ΓL(1,𝔽8)—918no—
70C2×D13—1471noHall
71C72C2×C3⋊(D13⋊C3)11yescharacteristic, complemented, Sylow
72C2×C3×C7#1058772218yescomplemented
73D21—9116no—
74C2×ΓL(1,𝔽8)—918no—
75C2×ΓL(1,𝔽8)—1828no—
76AGL(1,𝔽7)—27316no—
77C3×C13C2×#6442411yescharacteristic, complemented
78C13⋊C3—491no—
79C13⋊C3—981no—
80C2×C3×D3—6371noHall
81C2×D7—2738no—
82C2×C13C3⋊#6442411yescharacteristic, complemented
83D13—1472no—
84C3×C7C2×#1058772218yescomplemented
85ΓL(1,𝔽8)—918no—
86ΓL(1,𝔽8)—1828no—
87C2×C32—6371no—
88C3×D3—6372no—
89C2×C7C3⋊#1058772218yescomplemented
90D7—27316no—
91C13C2×C3⋊#6442411yescharacteristic, complemented, Sylow
92C22×C3—19111no—
93C2×D3—6371no—
94C32—6371noSylow
95C7C2×C3⋊#1058772218yescomplemented
96C2×C3—19112no—
97C2×C3—6371no—
98C2×C3—12741no—
99C2×C3#1683844611yescharacteristic, complemented
100D3—6372no—
101C22—19111noSylow
102C3—6371no—
103C3—12741no—
104C3C2×#1683844611yescharacteristic, complemented
105C2—19112no—
106C2C3⋊#1683844611yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊#16838446
commutator, cosocle, hypocenterC3×C72×C13C22×C3
FrattiniC1G
Fitting, socleC2×C3×C72×C13C2×C3
LCSG ▷ C3×C72×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#14274263C2semidirect
2. C3⋊#16838446C2direct (N × H)
3. C2×C3⋊(C7⋊D91)C3semidirect
5. C3×#14274263C22semidirect
6. C3⋊(C7⋊D91)C2×C3semidirect
8. C2×#14274263D3semidirect
10. C2×C3×C72×C13C2×C3semidirect
13. C3×C72×C13C22×C3semidirect
15. #14274263C2×D3semidirect
19. C2×C72×C13C3×D3semidirect
26. C72×C13C2×C3×D3semidirect
29. C2×C3×C7×C13AGL(1,𝔽7)semidirect
37. C2×C3×C72D13⋊C3semidirect
42. C3×C7×C13C2×AGL(1,𝔽7)semidirect
49. C2×C7×C13C3⋊AGL(1,𝔽7)semidirect
53. C3×C72C2×D13⋊C3semidirect
59. C2×C72C3⋊(D13⋊C3)semidirect
61. C7×C13C2×C3⋊AGL(1,𝔽7)semidirect
64. C2×C3×C13#64424semidirect
71. C72C2×C3⋊(D13⋊C3)semidirect
72. C2×C3×C7#10587722semidirect
77. C3×C13C2×#64424semidirect
82. C2×C13C3⋊#64424semidirect
84. C3×C7C2×#10587722semidirect
89. C2×C7C3⋊#10587722semidirect
91. C13C2×C3⋊#64424semidirect
95. C7C2×C3⋊#10587722semidirect
99. C2×C3#16838446semidirect
104. C3C2×#16838446semidirect
106. C2C3⋊#16838446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#142742632
C3⋊#168384462
C2×C3⋊(C7⋊D91)3
C2×#168384463
C2×C3⋊#105877227
C2×C3⋊#6442413