Finite Group Databasebeta

← C2×C3×D19×#3862 #45692596

Subgroups — C2×C3×D19×#3862 #45692596

Order 33516.

280 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 84 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×C19×#3862C211yesmaximal, characteristic, complemented
2C3×D19×#3862C212yesmaximal, direct product factor
3C2×C3×C72×D19C311yesmaximal, characteristic, complemented
4C2×D19×#3862C313yesmaximal, direct product factor
5C3×C19×#3862C2211yescharacteristic, complemented, Hall
6C3×C72×D19C2×C312yescomplemented
7C2×C19×#3862C2×C313yescomplemented
8D19×#3862C2×C316yesdirect product factor
9C2×C3×C72×C19C2×C311yescharacteristic, complemented
10C2×C3×ΓL(1,𝔽8)×D19—72nomaximal
11C2×C72×D19C3211yescharacteristic, complemented, Hall
12C19×#3862C22×C313yescomplemented
13C3×C72×C19C22×C311yescharacteristic, complemented
14C2×C3×C19×ΓL(1,𝔽8)—72no—
15C3×ΓL(1,𝔽8)×D19—74no—
16C2×C72×C19C2×C3211yescharacteristic, complemented
17C72×D19C2×C3212yescomplemented
18C22×C3×#3862—191nomaximal, Hall
19C2×C3×C7×D19—32no—
20C2×C3×C7×D19ΓL(1,𝔽8)12yescomplemented
21C2×ΓL(1,𝔽8)×D19—76no—
22C3×C19×ΓL(1,𝔽8)—72no—
23C72×C19C22×C3211yescharacteristic, complemented, Hall
24C2×C3×#3862—192no—
25C2×C3×#3862D1911yescharacteristic, direct product factor
26C2×C3×C7×C19—32no—
27C2×C3×C7×C19C2×ΓL(1,𝔽8)12yescomplemented
28C3×C7×D19—34no—
29C3×C7×D19C2×ΓL(1,𝔽8)14yescomplemented
30C2×C19×ΓL(1,𝔽8)—76no—
31ΓL(1,𝔽8)×D19—712no—
32C2×C32×D19—491noHall
33C22×C3×C72—191no—
34C22×#3862—193no—
35C2×C7×D19—32no—
36C2×C7×D19C3×ΓL(1,𝔽8)12yescomplemented
37C3×#3862C2×D1911yescharacteristic, direct product factor, Hall
38C3×C7×C19—32no—
39C3×C7×C19C22×ΓL(1,𝔽8)12yescomplemented
40C19×ΓL(1,𝔽8)—76no—
41C2×C32×C19—491no—
42C32×D19—492no—
43C2×C3×C72—192no—
44C2×C3×C72C3×D1911yescharacteristic, complemented
45C2×#3862—196no—
46C2×#3862C3×D1913yesdirect product factor
47C2×C7×C19—32no—
48C2×C7×C19C2×C3×ΓL(1,𝔽8)12yescomplemented
49C7×D19—34no—
50C7×D19C2×C3×ΓL(1,𝔽8)14yescomplemented
51C22×C3×ΓL(1,𝔽8)—1332no—
52C2×C3×D19—493no—
53C2×C3×D19#386211yescharacteristic, direct product factor
54C22×C72—191noHall
55C32×C19—491noHall
56C3×C72C2×C3×D1911yescharacteristic, complemented
57#3862C2×C3×D1913yesdirect product factor
58C7×C19—32no—
59C7×C19C22×C3×ΓL(1,𝔽8)12yescomplemented
60C2×C3×ΓL(1,𝔽8)—72no—
61C2×C3×ΓL(1,𝔽8)—1334no—
62C2×C3×C19—493no—
63C2×C3×C19C2×#386211yescharacteristic, complemented
64C3×D19—496no—
65C3×D19C2×#386212yesdirect product factor
66C2×C72—192no—
67C2×C72C32×D1911yescharacteristic, complemented
68C22×C3×C7—192no—
69C22×C3×C7—572no—
70C22×ΓL(1,𝔽8)—1336no—
71C2×D19C3×#386211yescharacteristic, direct product factor, Hall
72C3×ΓL(1,𝔽8)—72no—
73C3×C19—493no—
74C3×C19C22×#386211yescharacteristic, complemented
75C72C2×C32×D1911yescharacteristic, complemented, Sylow
76C2×C3×C7—32no—
77C2×C3×C7—194no—
78C2×C3×C7—574no—
79C2×C3×C7ΓL(1,𝔽8)×D1912yescomplemented
80C2×ΓL(1,𝔽8)—76no—
81C2×ΓL(1,𝔽8)—13312no—
82C2×C19C2×C3×#386211yescharacteristic, complemented
83D19C2×C3×#386212yesdirect product factor
84C22×C32—9311noHall
85C22×C7—192no—
86C22×C7—572no—
87C3×C7—32no—
88C3×C7C2×ΓL(1,𝔽8)×D1912yescomplemented
89ΓL(1,𝔽8)—76no—
90C19C22×C3×#386211yescharacteristic, complemented, Sylow
91C2×C32—491no—
92C2×C32—9312no—
93C2×C7—32no—
94C2×C7—194no—
95C2×C7—574no—
96C2×C7C3×ΓL(1,𝔽8)×D1912yescomplemented
97C22×C3—191no—
98C22×C3—9313no—
99C32—491noSylow
100C7—32no—
101C7C2×C3×ΓL(1,𝔽8)×D1912yescomplemented
102C2×C3—192no—
103C2×C3—493no—
104C2×C3—9316no—
105C2×C3D19×#386211yescharacteristic, direct product factor
106C22—191noSylow
107C3—493no—
108C3C2×D19×#386211yescharacteristic, direct product factor
109C2—192no—
110C2C3×D19×#386211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3D19×#3862
commutator, cosocle, hypocenterC72×C19C22×C32
FrattiniC1G
Fitting, socleC2×C3×C72×C19C2×C3
LCSG ▷ C72×C19
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×C19×#3862C2semidirect
2. C3×D19×#3862C2direct (N × H)
3. C2×C3×C72×D19C3semidirect
4. C2×D19×#3862C3direct (N × H)
5. C3×C19×#3862C22semidirect
6. C3×C72×D19C2×C3semidirect
7. C2×C19×#3862C2×C3semidirect
8. D19×#3862C2×C3direct (N × H)
9. C2×C3×C72×C19C2×C3semidirect
11. C2×C72×D19C32semidirect
12. C19×#3862C22×C3semidirect
13. C3×C72×C19C22×C3semidirect
16. C2×C72×C19C2×C32semidirect
17. C72×D19C2×C32semidirect
20. C2×C3×C7×D19ΓL(1,𝔽8)semidirect
23. C72×C19C22×C32semidirect
25. C2×C3×#3862D19direct (N × H)
27. C2×C3×C7×C19C2×ΓL(1,𝔽8)semidirect
29. C3×C7×D19C2×ΓL(1,𝔽8)semidirect
36. C2×C7×D19C3×ΓL(1,𝔽8)semidirect
37. C3×#3862C2×D19direct (N × H)
39. C3×C7×C19C22×ΓL(1,𝔽8)semidirect
44. C2×C3×C72C3×D19semidirect
46. C2×#3862C3×D19direct (N × H)
48. C2×C7×C19C2×C3×ΓL(1,𝔽8)semidirect
50. C7×D19C2×C3×ΓL(1,𝔽8)semidirect
53. C2×C3×D19#3862direct (N × H)
56. C3×C72C2×C3×D19semidirect
57. #3862C2×C3×D19direct (N × H)
59. C7×C19C22×C3×ΓL(1,𝔽8)semidirect
63. C2×C3×C19C2×#3862semidirect
65. C3×D19C2×#3862direct (N × H)
67. C2×C72C32×D19semidirect
71. C2×D19C3×#3862direct (N × H)
74. C3×C19C22×#3862semidirect
75. C72C2×C32×D19semidirect
79. C2×C3×C7ΓL(1,𝔽8)×D19semidirect
82. C2×C19C2×C3×#3862semidirect
83. D19C2×C3×#3862direct (N × H)
88. C3×C7C2×ΓL(1,𝔽8)×D19semidirect
90. C19C22×C3×#3862semidirect
96. C2×C7C3×ΓL(1,𝔽8)×D19semidirect
101. C7C2×C3×ΓL(1,𝔽8)×D19semidirect
105. C2×C3D19×#3862direct (N × H)
108. C3C2×D19×#3862direct (N × H)
110. C2C3×D19×#3862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C19×#38622
C3×D19×#38622
C2×C3×C72×D193
C2×D19×#38623
C2×C3×ΓL(1,𝔽8)×D197
C22×C3×#386219