Finite Group Databasebeta

← C19×#13183634 #45692426

Subgroups — C19×#13183634 #45692426

Order 33516.

248 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C19×C3⋊#64423C212yesmaximal, complemented
2C3×C19×#64424C211yesmaximal, characteristic, complemented
3C19×D21⋊D7C311yesmaximal, characteristic, complemented
4C19×#64423⋊C2—31nomaximal
5C3×C19×#3861C2211yescharacteristic, complemented, Hall
6C7×C19×D21C2×C312yescomplemented
7C3×C19×C7⋊D7C2×C311yescharacteristic, complemented
8C19×#64423—32no—
9C19×#64424—21no—
10C19×#64424D311yescharacteristic, complemented
11D3×C19×AGL(1,𝔽7)—72nomaximal
12D72×C19—31noHall
13C19×#3861—21no—
14C19×#3861C2×D311yescharacteristic, complemented
15C3×C72×C19C22×C311yescharacteristic, complemented
16D3×C19×ΓL(1,𝔽8)—72no—
17C19×C3⋊AGL(1,𝔽7)—72no—
18C3×C19×AGL(1,𝔽7)—72no—
19C3×C19×AGL(1,𝔽7)—143no—
20C19×C7⋊D7C3×D311yescharacteristic, complemented
21C7×D7×C19—32no—
22#13183634C1911yesmaximal, characteristic, direct product factor, Hall
23D3×D7×C19—72no—
24C2×C19×AGL(1,𝔽7)—212no—
25C3×C19×ΓL(1,𝔽8)—72no—
26C3×C19×ΓL(1,𝔽8)—143no—
27C72×C19C2×C3×D311yescharacteristic, complemented, Hall
28C3⋊#64423C2×C1912yescomplemented
29C3×#64424C2×C1911yescharacteristic, complemented
30C19×D21AGL(1,𝔽7)12yescomplemented
31D3×C7×C19—72no—
32C3×D7×C19—72no—
33C3×D7×C19—143no—
34C2×C19×ΓL(1,𝔽8)—212no—
35C19×AGL(1,𝔽7)—72no—
36C19×AGL(1,𝔽7)—143no—
37C19×AGL(1,𝔽7)—142no—
38C19×AGL(1,𝔽7)—146no—
39C19×AGL(1,𝔽7)—212no—
40C2×C3×D3×C19—491noHall
41D21⋊D7C3×C1911yescharacteristic, complemented
42#64423⋊C2—31no—
43C2×D7×C19—212no—
44C3×#3861C22×C1911yescharacteristic, complemented, Hall
45C3×C7×C19—23no—
46C3×C7×C19C2×AGL(1,𝔽7)12yescomplemented
47C19×ΓL(1,𝔽8)—72no—
48C19×ΓL(1,𝔽8)—143no—
49C19×ΓL(1,𝔽8)—146no—
50C19×ΓL(1,𝔽8)—142no—
51C2×C32×C19—491no—
52C3×D3×C19—492no—
53C7×D21C2×C3×C1912yescomplemented
54C3×C7⋊D7C2×C3×C1911yescharacteristic, complemented
55#64424—21no—
56#64424D3×C1911yescharacteristic, complemented
57#64423—32no—
58C2×C7×C19—212no—
59D7×C19—32no—
60D7×C19—72no—
61D7×C19—143no—
62D3×AGL(1,𝔽7)—72no—
63C22×C3×C19—1471no—
64C2×D3×C19—491no—
65D72—31noHall
66C32×C19—491noHall
67C3×C72C22×C3×C1911yescharacteristic, complemented
68#3861—21no—
69#3861C2×D3×C1911yescharacteristic, complemented
70C7×C19—23no—
71C7×C19D3×AGL(1,𝔽7)12yescomplemented
72C3⋊AGL(1,𝔽7)—72no—
73D3×ΓL(1,𝔽8)—72no—
74C3×AGL(1,𝔽7)—72no—
75C3×AGL(1,𝔽7)—143no—
76C2×C3×C19—491no—
77C2×C3×C19—491no—
78C2×C3×C19—981no—
79C2×C3×C19—1472no—
80D3×C19—72no—
81C7⋊D7C3×D3×C1911yescharacteristic, complemented
82C7×D7—32no—
83D3×D7—72no—
84C2×AGL(1,𝔽7)—212no—
85C22×C19—1471noHall
86C3×ΓL(1,𝔽8)—72no—
87C3×ΓL(1,𝔽8)—143no—
88C3×C19—491no—
89C3×C19—981no—
90C3×C19#64423⋊C211yescharacteristic, complemented
91C72C2×C3×D3×C1911yescharacteristic, complemented, Sylow
92D21C19×AGL(1,𝔽7)12yescomplemented
93C3×D7—72no—
94C3×D7—143no—
95D3×C7—72no—
96C2×ΓL(1,𝔽8)—212no—
97AGL(1,𝔽7)—72no—
98AGL(1,𝔽7)—143no—
99AGL(1,𝔽7)—142no—
100AGL(1,𝔽7)—146no—
101AGL(1,𝔽7)—212no—
102C2×C19—212no—
103C2×C19—491no—
104C2×C3×D3—491noHall
105C2×D7—212no—
106C3×C7—23no—
107C3×C7C2×C19×AGL(1,𝔽7)12yescomplemented
108ΓL(1,𝔽8)—72no—
109ΓL(1,𝔽8)—143no—
110ΓL(1,𝔽8)—146no—
111ΓL(1,𝔽8)—142no—
112C19#1318363411yescharacteristic, direct product factor, Sylow
113C2×C32—491no—
114C3×D3—492no—
115C2×C7—212no—
116D7—32no—
117D7—72no—
118D7—143no—
119C22×C3—1471no—
120C2×D3—491no—
121C32—491noSylow
122C7—23no—
123C7D3×C19×AGL(1,𝔽7)12yescomplemented
124C2×C3—491no—
125C2×C3—491no—
126C2×C3—981no—
127C2×C3—1472no—
128D3—72no—
129C22—1471noSylow
130C3—491no—
131C3—981no—
132C3C19×#64423⋊C211yescharacteristic, complemented
133C2—212no—
134C2—491no—
subgroupG/H
center, hypercenterC19#13183634
commutator, cosocle, hypocenterC3×C72C22×C3×C19
FrattiniC1G
Fitting, socleC3×C72×C19C22×C3
LCSG ▷ C3×C72
UCSC1 ◁ C19

Complements

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

NH ≅ G/Ntype
1. C19×C3⋊#64423C2semidirect
2. C3×C19×#64424C2semidirect
3. C19×D21⋊D7C3semidirect
5. C3×C19×#3861C22semidirect
6. C7×C19×D21C2×C3semidirect
7. C3×C19×C7⋊D7C2×C3semidirect
10. C19×#64424D3semidirect
14. C19×#3861C2×D3semidirect
15. C3×C72×C19C22×C3semidirect
20. C19×C7⋊D7C3×D3semidirect
22. #13183634C19direct (N × H)
27. C72×C19C2×C3×D3semidirect
28. C3⋊#64423C2×C19semidirect
29. C3×#64424C2×C19semidirect
30. C19×D21AGL(1,𝔽7)semidirect
41. D21⋊D7C3×C19semidirect
44. C3×#3861C22×C19semidirect
46. C3×C7×C19C2×AGL(1,𝔽7)semidirect
53. C7×D21C2×C3×C19semidirect
54. C3×C7⋊D7C2×C3×C19semidirect
56. #64424D3×C19semidirect
67. C3×C72C22×C3×C19semidirect
69. #3861C2×D3×C19semidirect
71. C7×C19D3×AGL(1,𝔽7)semidirect
81. C7⋊D7C3×D3×C19semidirect
90. C3×C19#64423⋊C2semidirect
91. C72C2×C3×D3×C19semidirect
92. D21C19×AGL(1,𝔽7)semidirect
107. C3×C7C2×C19×AGL(1,𝔽7)semidirect
112. C19#13183634direct (N × H)
123. C7D3×C19×AGL(1,𝔽7)semidirect
132. C3C19×#64423⋊C2semidirect

Maximal subgroups

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

subgroupindex
C19×C3⋊#644232
C3×C19×#644242
C19×D21⋊D73
C19×#64423⋊C23
D3×C19×AGL(1,𝔽7)7
#1318363419