Finite Group Databasebeta

← C3×C19⋊C3×#737 #28356655

Subgroups — C3×C19⋊C3×#737 #28356655

Order 13851.

5804 conjugacy classes of subgroups; only the 2902 normal subgroups are shown.

normal subgroups only

This group has 5804 conjugacy classes of subgroups — too many to draw. Only its 2902 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×#13095333C3116yesmaximal, complemented
2C3×#13095332C318yesmaximal, complemented
3C3×#13095331C312yesmaximal, complemented
4C19⋊C3×#737C3181yesmaximal, direct product factor
5C3×3−1+2×C19⋊C3C318yesmaximal, complemented
6C3×H(3,𝔽3)×C19⋊C3C311yesmaximal, characteristic
7C32×C9×C19⋊C3C314yesmaximal, complemented
8C3×C19×#737C311yesmaximal, characteristic, complemented
9C33×C19⋊C3C3214yes—
10#13095333C321432yescomplemented
11#13095332C321216yescomplemented
12#13095331C32154yescomplemented
13C3×#10587025C32116yescomplemented
14C3×#10587022C32124yescomplemented
15C3×#10587023C32124yescomplemented
163−1+2×C19⋊C3C321216yescomplemented
17C3×C32⋊(C19⋊C3)C3218yes—
18H(3,𝔽3)×C19⋊C3C32127yes—
19C32×#4294C3218yescomplemented
20C3×C9×C19⋊C3C3211yescharacteristic
21C3×C9×C19⋊C3C3218yes—
22C3×C9×C19⋊C3C321108yescomplemented
23C3×C9×C19⋊C3C3218yescomplemented
24C3×C9×C19⋊C3C32116yescomplemented
25C19×#737C32127yescomplemented
26C3×C19×3−1+2C3218yescomplemented
27C3×C19×H(3,𝔽3)C3211yescharacteristic
28C32×C9×C19C3214yescomplemented
29C32×#737—191nomaximal, Sylow
30C33×C19C3314yes—
31C32×C19⋊C3—336no—
32C32×C19⋊C3C33136yes—
33C32×C19⋊C3C3318yes—
34C32×C19⋊C3C3311yescharacteristic
35C19×3−1+2C33172yescomplemented
36C19×H(3,𝔽3)C3319yes—
37C3×C9×C19C3318yes—
38C3×C9×C19C3311yescharacteristic
39C3×C9×C19C33136yescomplemented
40C32⋊(C19⋊C3)C33172yes—
41#10587025C331144yescomplemented
42C3×#4294C3312yes—
43C3×#4294C33116yes—
44C3×#4294C33172yescomplemented
45#10587023C331216yescomplemented
46#10587022C331216yescomplemented
47C9×C19⋊C3C3319yes—
48C9×C19⋊C3C33172yes—
49C9×C19⋊C3C33172yescomplemented
50C9×C19⋊C3C331144yescomplemented
51C3×#737—1981no—
52C3×#737—1916no—
53C3×#737—192no—
54C3×#737—198no—
55C3×#737C19⋊C311yescharacteristic, direct product factor
56C32×3−1+2—198no—
57C32×H(3,𝔽3)—191no—
58C33×C9—194no—
59C32×C19—312no—
60C32×C19C34112yes—
61C32×C19C3411yescharacteristic
62C3×C19⋊C3—324no—
63C3×C19⋊C3—3108no—
64C3×C19⋊C3#73719yesdirect product factor
65C3×C19⋊C3C34124yes—
66C3×C19⋊C3C3413yes—
67C9×C19C3413yes—
68C9×C19C34124yes—
69#4294C3416yes—
70#4294C34148yes—
71C34—194no—
72#737—19432no—
73#737—1954no—
74#737—19216no—
75#737C3×C19⋊C3127yesdirect product factor
76C3×3−1+2—1916no—
77C3×3−1+2—19216no—
78C3×3−1+2—1924no—
79C3×3−1+2—1924no—
80C3×3−1+2C3×C19⋊C318yescomplemented
81C3×H(3,𝔽3)—198no—
82C3×H(3,𝔽3)—1927no—
83C3×H(3,𝔽3)C3×C19⋊C311yescharacteristic
84C32×C9—198no—
85C32×C9—198no—
86C32×C9—1916no—
87C32×C9—191no—
88C32×C9—198no—
89C32×C9—19108no—
90C32×C9C3×C19⋊C314yescomplemented
91C3×C19—312no—
92C3×C19C3×#73713yescomplemented
93C3×C19C3511yescharacteristic
94C19⋊C3—324no—
95C19⋊C3C3×#73719yesdirect product factor
96C33—191no—
97C33—1936no—
98C33—198no—
99C33—5736no—
100C33C32×C19⋊C314yes—
1013−1+2—19144no—
1023−1+2—19216no—
1033−1+2—19216no—
1043−1+2C32×C19⋊C3172yescomplemented
105H(3,𝔽3)—1972no—
106H(3,𝔽3)C32×C19⋊C319yes—
107C3×C9—192no—
108C3×C9—1916no—
109C3×C9—1972no—
110C3×C9—199no—
111C3×C9—1972no—
112C3×C9—19144no—
113C3×C9—1972no—
114C3×C9C32×C19⋊C318yes—
115C3×C9C32×C19⋊C311yescharacteristic
116C3×C9C32×C19⋊C3136yescomplemented
117C19C32×#73711yescharacteristic, complemented, Sylow
118C32—312no—
119C32—199no—
120C32—193no—
121C32—1924no—
122C32—57108no—
123C32—5724no—
124C32C33×C19⋊C3112yes—
125C32C33×C19⋊C311yescharacteristic
126C9—196no—
127C9—1948no—
128C9C33×C19⋊C313yes—
129C9C33×C19⋊C3124yes—
130C3—312no—
131C3—199no—
132C3—5724no—
133C3C19⋊C3×#73713yesdirect product factor
134C3C34×C19⋊C311yescharacteristic
subgroupG/H
centerC3×C9C32×C19⋊C3
commutator, cosocleC3×C19C35
FrattiniC3C34×C19⋊C3
FittingC3×C19×#737C3
socleC32×C19C34
prime radicalC3×H(3,𝔽3)×C19⋊C3C3
hypercenterC3×#737C19⋊C3
hypocenterC19C32×#737
LCSG ▷ C3×C19 ▷ C19
UCSC1 ◁ C3×C9 ◁ C3×#737

Complements

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

NH ≅ G/Ntype
1. C3×#13095333C3semidirect
2. C3×#13095332C3semidirect
3. C3×#13095331C3semidirect
4. C19⋊C3×#737C3direct (N × H)
5. C3×3−1+2×C19⋊C3C3semidirect
7. C32×C9×C19⋊C3C3semidirect
8. C3×C19×#737C3semidirect
10. #13095333C32semidirect
11. #13095332C32semidirect
12. #13095331C32semidirect
13. C3×#10587025C32semidirect
14. C3×#10587022C32semidirect
15. C3×#10587023C32semidirect
16. 3−1+2×C19⋊C3C32semidirect
19. C32×#4294C32semidirect
22. C3×C9×C19⋊C3C32semidirect
23. C3×C9×C19⋊C3C32semidirect
24. C3×C9×C19⋊C3C32semidirect
25. C19×#737C32semidirect
26. C3×C19×3−1+2C32semidirect
28. C32×C9×C19C32semidirect
35. C19×3−1+2C33semidirect
39. C3×C9×C19C33semidirect
41. #10587025C33semidirect
44. C3×#4294C33semidirect
45. #10587023C33semidirect
46. #10587022C33semidirect
49. C9×C19⋊C3C33semidirect
50. C9×C19⋊C3C33semidirect
55. C3×#737C19⋊C3direct (N × H)
64. C3×C19⋊C3#737direct (N × H)
75. #737C3×C19⋊C3direct (N × H)
80. C3×3−1+2C3×C19⋊C3semidirect
90. C32×C9C3×C19⋊C3semidirect
92. C3×C19C3×#737semidirect
95. C19⋊C3C3×#737direct (N × H)
104. 3−1+2C32×C19⋊C3semidirect
116. C3×C9C32×C19⋊C3semidirect
117. C19C32×#737semidirect
133. C3C19⋊C3×#737direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#130953333
C3×#130953323
C3×#130953313
C19⋊C3×#7373
C3×3−1+2×C19⋊C33
C3×H(3,𝔽3)×C19⋊C33
C32×C9×C19⋊C33
C3×C19×#7373
C32×#73719