Finite Group Databasebeta

← C3×#15691695 #23748617

Subgroups — C3×#15691695 #23748617

Order 9477.

5588 conjugacy classes of subgroups; only the 2884 normal subgroups are shown.

normal subgroups only

This group has 5588 conjugacy classes of subgroups — too many to draw. Only its 2884 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
1#15691695C3181yesmaximal, direct product factor
2C3×#11760454C3116yesmaximal, complemented
3C3×#11760453C318yesmaximal, complemented
4C3×#11760452C312yesmaximal, complemented
5C32×#66849C314yesmaximal, complemented
6C3×3−1+2×C13⋊C3C318yesmaximal, complemented
7C3×H(3,𝔽3)×C13⋊C3C311yesmaximal, characteristic
8C3×C13×#737C311yesmaximal, characteristic, complemented
9C33×C13⋊C3C3214yes—
10#11760454C321432yescomplemented
11#11760453C321216yescomplemented
12#11760452C32154yescomplemented
13C3×#66851C32116yescomplemented
14C3×#66848C32124yescomplemented
15C3×#66849C3218yes—
16C3×#66849C3211yescharacteristic
17C3×#66849C321108yescomplemented
18C3×#66849C3218yescomplemented
19C3×#66849C32116yescomplemented
203−1+2×C13⋊C3C321216yescomplemented
21C3×C32⋊(C13⋊C3)C3218yes—
22H(3,𝔽3)×C13⋊C3C32127yes—
23C32×C13⋊C9C3218yescomplemented
24C3×C9×C13⋊C3C32124yescomplemented
25C13×#737C32127yescomplemented
26C3×C13×3−1+2C3218yescomplemented
27C3×C13×H(3,𝔽3)C3211yescharacteristic
28C32×C9×C13C3214yescomplemented
29C3×3−1+4—131nomaximal, Sylow
30C33×C13C3314yes—
31C32×C13⋊C3—912no—
32C32×C13⋊C3C3318yes—
33C32×C13⋊C3C3311yescharacteristic
34C32×C13⋊C3C33136yes—
35C13×3−1+2C33172yescomplemented
36C13×H(3,𝔽3)C3319yes—
37C3×C9×C13C3311yescharacteristic
38C3×C9×C13C3318yes—
39C3×C9×C13C33136yescomplemented
40C32⋊(C13⋊C3)C33172yes—
41#66851C331144yescomplemented
42C3×C13⋊C9C33116yes—
43C3×C13⋊C9C3312yes—
44C3×C13⋊C9C33172yescomplemented
45#66849C33172yes—
46#66849C3319yes—
47#66849C33172yescomplemented
48#66849C331144yescomplemented
49#66848C331216yescomplemented
50C9×C13⋊C3C331216yescomplemented
513−1+4—1381no—
52C3×#737—1316no—
53C3×#737—132no—
54C3×#737—138no—
55C3×#737C13⋊C311yescharacteristic, complemented
56C32×3−1+2—138no—
57C32×3−1+2—134no—
58C32×H(3,𝔽3)—131no—
59C32×C13—312no—
60C32×C13C34112yes—
61C32×C13C3411yescharacteristic
62C3×C13⋊C3—33no—
63C3×C13⋊C3—324no—
64C3×C13⋊C3—936no—
65C3×C13⋊C3C34124yes—
66C3×C13⋊C3C3413yes—
67C9×C13C34124yes—
68C9×C13C3413yes—
69C13⋊C9C34148yes—
70C13⋊C9C3416yes—
71C34—134no—
72#737—13432no—
73#737—1354no—
74#737—13216no—
75#737C3×C13⋊C3127yescomplemented
76C3×3−1+2—1316no—
77C3×3−1+2—13216no—
78C3×3−1+2—138no—
79C3×3−1+2—131no—
80C3×3−1+2—1316no—
81C3×3−1+2—138no—
82C3×3−1+2—1324no—
83C3×3−1+2—13108no—
84C3×3−1+2C3×C13⋊C318yescomplemented
85C3×H(3,𝔽3)—138no—
86C3×H(3,𝔽3)—1327no—
87C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic
88C32×C9—138no—
89C32×C9—1324no—
90C32×C9C3×C13⋊C314yescomplemented
91C3×C13—312no—
92C3×C133−1+413yescomplemented
93C3×C13C3511yescharacteristic
94C13⋊C3—33no—
95C13⋊C3—324no—
96C33—138no—
97C33—131no—
98C33—1336no—
99C33—11712no—
100C33C32×C13⋊C314yes—
1013−1+2—13144no—
1023−1+2—13216no—
1033−1+2—1372no—
1043−1+2—139no—
1053−1+2—13144no—
1063−1+2—1372no—
1073−1+2C32×C13⋊C3172yescomplemented
108H(3,𝔽3)—1372no—
109H(3,𝔽3)C32×C13⋊C319yes—
110C3×C9—1372no—
111C3×C9—1316no—
112C3×C9—132no—
113C3×C9—13216no—
114C3×C9C32×C13⋊C318yes—
115C3×C9C32×C13⋊C311yescharacteristic
116C3×C9C32×C13⋊C3136yescomplemented
117C13C3×3−1+411yescharacteristic, complemented, Sylow
118C32—312no—
119C32—1324no—
120C32—133no—
121C32—393no—
122C32—3924no—
123C32—11736no—
124C32C33×C13⋊C3112yes—
125C32C33×C13⋊C311yescharacteristic
126C9—136no—
127C9—1348no—
128C9C33×C13⋊C3124yes—
129C9C33×C13⋊C313yes—
130C3—312no—
131C3—393no—
132C3—3924no—
133C3#1569169513yesdirect product factor
134C3C34×C13⋊C311yescharacteristic
subgroupG/H
centerC32C33×C13⋊C3
commutator, cosocleC3×C13C35
FrattiniC3C34×C13⋊C3
FittingC3×C13×#737C3
socleC32×C13C34
prime radicalC3×H(3,𝔽3)×C13⋊C3C3
hypercenterC3×#737C13⋊C3
hypocenterC13C3×3−1+4
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C32 ◁ C3×#737

Complements

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

NH ≅ G/Ntype
1. #15691695C3direct (N × H)
2. C3×#11760454C3semidirect
3. C3×#11760453C3semidirect
4. C3×#11760452C3semidirect
5. C32×#66849C3semidirect
6. C3×3−1+2×C13⋊C3C3semidirect
8. C3×C13×#737C3semidirect
10. #11760454C32semidirect
11. #11760453C32semidirect
12. #11760452C32semidirect
13. C3×#66851C32semidirect
14. C3×#66848C32semidirect
17. C3×#66849C32semidirect
18. C3×#66849C32semidirect
19. C3×#66849C32semidirect
20. 3−1+2×C13⋊C3C32semidirect
23. C32×C13⋊C9C32semidirect
24. C3×C9×C13⋊C3C32semidirect
25. C13×#737C32semidirect
26. C3×C13×3−1+2C32semidirect
28. C32×C9×C13C32semidirect
35. C13×3−1+2C33semidirect
39. C3×C9×C13C33semidirect
41. #66851C33semidirect
44. C3×C13⋊C9C33semidirect
47. #66849C33semidirect
48. #66849C33semidirect
49. #66848C33semidirect
50. C9×C13⋊C3C33semidirect
55. C3×#737C13⋊C3semidirect
75. #737C3×C13⋊C3semidirect
84. C3×3−1+2C3×C13⋊C3semidirect
90. C32×C9C3×C13⋊C3semidirect
92. C3×C133−1+4semidirect
107. 3−1+2C32×C13⋊C3semidirect
116. C3×C9C32×C13⋊C3semidirect
117. C13C3×3−1+4semidirect
133. C3#15691695direct (N × H)