Finite Group Databasebeta

← C3×#737×C43⋊C3 #44535396

Subgroups — C3×#737×C43⋊C3 #44535396

Order 31347.

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×#16812526C3116yesmaximal, complemented
2C3×#16812525C318yesmaximal, complemented
3C3×#16812524C312yesmaximal, complemented
4#737×C43⋊C3C3181yesmaximal, direct product factor
5C3×3−1+2×C43⋊C3C318yesmaximal, complemented
6C3×H(3,𝔽3)×C43⋊C3C311yesmaximal, characteristic
7C32×C9×C43⋊C3C314yesmaximal, complemented
8C3×C43×#737C311yesmaximal, characteristic, complemented
9C33×C43⋊C3C3214yes—
10#16812526C321432yescomplemented
11#16812525C321216yescomplemented
12#16812524C32154yescomplemented
13C3×#11923958C32116yescomplemented
14C3×#11923957C32124yescomplemented
15C3×#11923956C32124yescomplemented
163−1+2×C43⋊C3C321216yescomplemented
17C3×C32⋊(C43⋊C3)C3218yes—
18H(3,𝔽3)×C43⋊C3C32127yes—
19C32×C43⋊C9C3218yescomplemented
20C3×C9×C43⋊C3C3218yes—
21C3×C9×C43⋊C3C3211yescharacteristic
22C3×C9×C43⋊C3C3218yescomplemented
23C3×C9×C43⋊C3C32116yescomplemented
24C3×C9×C43⋊C3C321108yescomplemented
25C43×#737C32127yescomplemented
26C3×3−1+2×C43C3218yescomplemented
27C3×H(3,𝔽3)×C43C3211yescharacteristic
28C32×C9×C43C3214yescomplemented
29C32×C43⋊C3—336no—
30C32×C43⋊C3C33136yes—
31C32×C43⋊C3C3318yes—
32C32×C43⋊C3C3311yescharacteristic
33#11923958C331144yescomplemented
34#11923957C331216yescomplemented
35#11923956C331216yescomplemented
36C32⋊(C43⋊C3)C33172yes—
37C3×C43⋊C9C3312yes—
38C3×C43⋊C9C33116yes—
39C3×C43⋊C9C33172yescomplemented
40C9×C43⋊C3C3319yes—
41C9×C43⋊C3C33172yes—
42C9×C43⋊C3C33172yescomplemented
43C9×C43⋊C3C331144yescomplemented
44C33×C43C3314yes—
453−1+2×C43C33172yescomplemented
46H(3,𝔽3)×C43C3319yes—
47C3×C9×C43C3318yes—
48C3×C9×C43C3311yescharacteristic
49C3×C9×C43C33136yescomplemented
50C32×#737—431nomaximal, Sylow
51C32×C43—312no—
52C32×C43C34112yes—
53C32×C43C3411yescharacteristic
54C3×C43⋊C3—324no—
55C3×C43⋊C3—3108no—
56C3×C43⋊C3#73719yesdirect product factor
57C3×C43⋊C3C34124yes—
58C3×C43⋊C3C3413yes—
59C9×C43C3413yes—
60C9×C43C34124yes—
61C43⋊C9C3416yes—
62C43⋊C9C34148yes—
63C3×#737—4381no—
64C3×#737—4316no—
65C3×#737—432no—
66C3×#737—438no—
67C3×#737C43⋊C311yescharacteristic, direct product factor
68C32×3−1+2—438no—
69C32×H(3,𝔽3)—431no—
70C33×C9—434no—
71C3×C43—312no—
72C3×C43C3×#73713yescomplemented
73C3×C43C3511yescharacteristic
74C43⋊C3—324no—
75C43⋊C3C3×#73719yesdirect product factor
76C34—434no—
77#737—43432no—
78#737—4354no—
79#737—43216no—
80#737C3×C43⋊C3127yesdirect product factor
81C3×3−1+2—4316no—
82C3×3−1+2—43216no—
83C3×3−1+2—4324no—
84C3×3−1+2—4324no—
85C3×3−1+2C3×C43⋊C318yescomplemented
86C3×H(3,𝔽3)—438no—
87C3×H(3,𝔽3)—4327no—
88C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
89C32×C9—438no—
90C32×C9—438no—
91C32×C9—4316no—
92C32×C9—431no—
93C32×C9—438no—
94C32×C9—43108no—
95C32×C9C3×C43⋊C314yescomplemented
96C43C32×#73711yescharacteristic, complemented, Sylow
97C33—431no—
98C33—4336no—
99C33—438no—
100C33—12936no—
101C33C32×C43⋊C314yes—
1023−1+2—43144no—
1033−1+2—43216no—
1043−1+2—43216no—
1053−1+2C32×C43⋊C3172yescomplemented
106H(3,𝔽3)—4372no—
107H(3,𝔽3)C32×C43⋊C319yes—
108C3×C9—432no—
109C3×C9—4316no—
110C3×C9—4372no—
111C3×C9—439no—
112C3×C9—4372no—
113C3×C9—43144no—
114C3×C9—4372no—
115C3×C9C32×C43⋊C318yes—
116C3×C9C32×C43⋊C311yescharacteristic
117C3×C9C32×C43⋊C3136yescomplemented
118C32—312no—
119C32—439no—
120C32—433no—
121C32—4324no—
122C32—129108no—
123C32—12924no—
124C32C33×C43⋊C3112yes—
125C32C33×C43⋊C311yescharacteristic
126C9—436no—
127C9—4348no—
128C9C33×C43⋊C313yes—
129C9C33×C43⋊C3124yes—
130C3—312no—
131C3—439no—
132C3—12924no—
133C3#737×C43⋊C313yesdirect product factor
134C3C34×C43⋊C311yescharacteristic
subgroupG/H
centerC3×C9C32×C43⋊C3
commutator, cosocleC3×C43C35
FrattiniC3C34×C43⋊C3
FittingC3×C43×#737C3
socleC32×C43C34
prime radicalC3×H(3,𝔽3)×C43⋊C3C3
hypercenterC3×#737C43⋊C3
hypocenterC43C32×#737
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C3×C9 ◁ C3×#737

Complements

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

NH ≅ G/Ntype
1. C3×#16812526C3semidirect
2. C3×#16812525C3semidirect
3. C3×#16812524C3semidirect
4. #737×C43⋊C3C3direct (N × H)
5. C3×3−1+2×C43⋊C3C3semidirect
7. C32×C9×C43⋊C3C3semidirect
8. C3×C43×#737C3semidirect
10. #16812526C32semidirect
11. #16812525C32semidirect
12. #16812524C32semidirect
13. C3×#11923958C32semidirect
14. C3×#11923957C32semidirect
15. C3×#11923956C32semidirect
16. 3−1+2×C43⋊C3C32semidirect
19. C32×C43⋊C9C32semidirect
22. C3×C9×C43⋊C3C32semidirect
23. C3×C9×C43⋊C3C32semidirect
24. C3×C9×C43⋊C3C32semidirect
25. C43×#737C32semidirect
26. C3×3−1+2×C43C32semidirect
28. C32×C9×C43C32semidirect
33. #11923958C33semidirect
34. #11923957C33semidirect
35. #11923956C33semidirect
39. C3×C43⋊C9C33semidirect
42. C9×C43⋊C3C33semidirect
43. C9×C43⋊C3C33semidirect
45. 3−1+2×C43C33semidirect
49. C3×C9×C43C33semidirect
56. C3×C43⋊C3#737direct (N × H)
67. C3×#737C43⋊C3direct (N × H)
72. C3×C43C3×#737semidirect
75. C43⋊C3C3×#737direct (N × H)
80. #737C3×C43⋊C3direct (N × H)
85. C3×3−1+2C3×C43⋊C3semidirect
95. C32×C9C3×C43⋊C3semidirect
96. C43C32×#737semidirect
105. 3−1+2C32×C43⋊C3semidirect
117. C3×C9C32×C43⋊C3semidirect
133. C3#737×C43⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#168125263
C3×#168125253
C3×#168125243
#737×C43⋊C33
C3×3−1+2×C43⋊C33
C3×H(3,𝔽3)×C43⋊C33
C32×C9×C43⋊C33
C3×C43×#7373
C32×#73743