Finite Group Databasebeta

← C3⋊#19150288 #30660823

Subgroups — C3⋊#19150288 #30660823

Order 16758.

180 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C3×C19×#3861C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C7⋊D133)C311yesmaximal, characteristic, complemented
3#19150288—31nomaximal
4C19×#3861—21no—
5C19×#3861D311yescharacteristic, complemented
6C3×C72×C19C2×C311yescharacteristic, complemented
7C3⋊(ΓL(1,𝔽8)⋊D19)—71nomaximal
8C3⋊(ΓL(1,𝔽8)⋊D19)—71nomaximal
9C3⋊(ΓL(1,𝔽8)⋊D19)—72nomaximal
10C3⋊(ΓL(1,𝔽8)⋊D19)—71nomaximal
11C3⋊(ΓL(1,𝔽8)⋊D19)—73nomaximal
12C7⋊D133—31noHall
13C3×C19×ΓL(1,𝔽8)—71no—
14C3×C19×ΓL(1,𝔽8)—141no—
15C3×C19×ΓL(1,𝔽8)—142no—
16C3×C19×ΓL(1,𝔽8)—141no—
17C3×C19×ΓL(1,𝔽8)—143no—
18C72×C19C3×D311yescharacteristic, complemented, Hall
19C3⋊#64424—191nomaximal, Hall
20D399—71no—
21D399—72no—
22D399—71no—
23D399—71no—
24D399—73no—
25ΓL(1,𝔽8)⋊D19—212no—
26ΓL(1,𝔽8)⋊D19—211no—
27ΓL(1,𝔽8)⋊D19—211no—
28ΓL(1,𝔽8)⋊D19—211no—
29ΓL(1,𝔽8)⋊D19—213no—
30C3×#3861D1911yescharacteristic, complemented, Hall
31C3×C7×C19AGL(1,𝔽7)11yescharacteristic, complemented
32C3×C7×C19AGL(1,𝔽7)12yescomplemented
33C3×C7×C19AGL(1,𝔽7)11yescharacteristic, complemented
34C3×C7×C19AGL(1,𝔽7)11yescharacteristic, complemented
35C3×C7×C19AGL(1,𝔽7)13yescomplemented
36C19×ΓL(1,𝔽8)—72no—
37C19×ΓL(1,𝔽8)—71no—
38C19×ΓL(1,𝔽8)—141no—
39C19×ΓL(1,𝔽8)—141no—
40C19×ΓL(1,𝔽8)—141no—
41C19×ΓL(1,𝔽8)—142no—
42C19×ΓL(1,𝔽8)—141no—
43C19×ΓL(1,𝔽8)—141no—
44C19×ΓL(1,𝔽8)—143no—
45C19×ΓL(1,𝔽8)—143no—
46C3×D57—491noHall
47C3⋊(C7⋊D7)—191no—
48#64424—571no—
49D133—212no—
50D133—211no—
51D133—211no—
52D133—211no—
53D133—213no—
54C32×C19—981noHall
55C3×C72C3×D1911yescharacteristic, complemented
56#3861—21no—
57#3861D5711yescharacteristic, complemented
58C7×C19C3⋊AGL(1,𝔽7)12yescomplemented
59C7×C19C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
60C7×C19C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
61C7×C19C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
62C7×C19C3⋊AGL(1,𝔽7)13yescomplemented
63C3⋊AGL(1,𝔽7)—1331no—
64C3⋊AGL(1,𝔽7)—1332no—
65C3⋊AGL(1,𝔽7)—1331no—
66C3⋊AGL(1,𝔽7)—1331no—
67C3⋊AGL(1,𝔽7)—1333no—
68D57—491no—
69C3×D19—1471no—
70C7⋊D7—571noHall
71C3×ΓL(1,𝔽8)—71no—
72C3×ΓL(1,𝔽8)—142no—
73C3×ΓL(1,𝔽8)—141no—
74C3×ΓL(1,𝔽8)—141no—
75C3×ΓL(1,𝔽8)—143no—
76C3×C19—981no—
77C3×C19—981no—
78C3×C19#6442411yescharacteristic, complemented
79C72C3×D5711yescharacteristic, complemented, Sylow
80D21—1331no—
81D21—1332no—
82D21—1331no—
83D21—1331no—
84D21—1333no—
85AGL(1,𝔽7)—3991no—
86AGL(1,𝔽7)—3992no—
87AGL(1,𝔽7)—3991no—
88AGL(1,𝔽7)—3991no—
89AGL(1,𝔽7)—3993no—
90D19—1471noHall
91C3×C7ΓL(1,𝔽8)⋊D1911yescharacteristic, complemented
92C3×C7ΓL(1,𝔽8)⋊D1912yescomplemented
93C3×C7ΓL(1,𝔽8)⋊D1911yescharacteristic, complemented
94C3×C7ΓL(1,𝔽8)⋊D1911yescharacteristic, complemented
95C3×C7ΓL(1,𝔽8)⋊D1913yescomplemented
96ΓL(1,𝔽8)—71no—
97ΓL(1,𝔽8)—72no—
98ΓL(1,𝔽8)—141no—
99ΓL(1,𝔽8)—142no—
100ΓL(1,𝔽8)—141no—
101ΓL(1,𝔽8)—141no—
102ΓL(1,𝔽8)—143no—
103ΓL(1,𝔽8)—141no—
104ΓL(1,𝔽8)—141no—
105ΓL(1,𝔽8)—143no—
106C19C3⋊#6442411yescharacteristic, complemented, Sylow
107C3×D3—9311noHall
108D7—3992no—
109D7—3991no—
110D7—3991no—
111D7—3991no—
112D7—3993no—
113C32—981noSylow
114C7C3⋊(ΓL(1,𝔽8)⋊D19)12yescomplemented
115C7C3⋊(ΓL(1,𝔽8)⋊D19)11yescharacteristic, complemented
116C7C3⋊(ΓL(1,𝔽8)⋊D19)11yescharacteristic, complemented
117C7C3⋊(ΓL(1,𝔽8)⋊D19)11yescharacteristic, complemented
118C7C3⋊(ΓL(1,𝔽8)⋊D19)13yescomplemented
119C2×C3—27931no—
120D3—9311no—
121C3—981no—
122C3—981no—
123C3#1915028811yescharacteristic, complemented
124C2—27931noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C19C2×C3
LCSG ▷ C3×C72×C19
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C19×#3861C2semidirect
2. C3⋊(C7⋊D133)C3semidirect
5. C19×#3861D3semidirect
6. C3×C72×C19C2×C3semidirect
18. C72×C19C3×D3semidirect
30. C3×#3861D19semidirect
31. C3×C7×C19AGL(1,𝔽7)semidirect
32. C3×C7×C19AGL(1,𝔽7)semidirect
33. C3×C7×C19AGL(1,𝔽7)semidirect
34. C3×C7×C19AGL(1,𝔽7)semidirect
35. C3×C7×C19AGL(1,𝔽7)semidirect
55. C3×C72C3×D19semidirect
57. #3861D57semidirect
58. C7×C19C3⋊AGL(1,𝔽7)semidirect
59. C7×C19C3⋊AGL(1,𝔽7)semidirect
60. C7×C19C3⋊AGL(1,𝔽7)semidirect
61. C7×C19C3⋊AGL(1,𝔽7)semidirect
62. C7×C19C3⋊AGL(1,𝔽7)semidirect
78. C3×C19#64424semidirect
79. C72C3×D57semidirect
91. C3×C7ΓL(1,𝔽8)⋊D19semidirect
92. C3×C7ΓL(1,𝔽8)⋊D19semidirect
93. C3×C7ΓL(1,𝔽8)⋊D19semidirect
94. C3×C7ΓL(1,𝔽8)⋊D19semidirect
95. C3×C7ΓL(1,𝔽8)⋊D19semidirect
106. C19C3⋊#64424semidirect
114. C7C3⋊(ΓL(1,𝔽8)⋊D19)semidirect
115. C7C3⋊(ΓL(1,𝔽8)⋊D19)semidirect
116. C7C3⋊(ΓL(1,𝔽8)⋊D19)semidirect
117. C7C3⋊(ΓL(1,𝔽8)⋊D19)semidirect
118. C7C3⋊(ΓL(1,𝔽8)⋊D19)semidirect
123. C3#19150288semidirect

Maximal subgroups

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

subgroupindex
C3×C19×#38612
C3⋊(C7⋊D133)3
#191502883
C3⋊(ΓL(1,𝔽8)⋊D19)7
C3⋊#6442419