Finite Group Databasebeta

← #44535409

Subgroups — #44535409

Order 31347.

5490 conjugacy classes of subgroups; only the 2878 normal subgroups are shown.

normal subgroups only

This group has 5490 conjugacy classes of subgroups — too many to draw. Only its 2878 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#23782924C311yesmaximal, characteristic, complemented
2#23782923C3124yesmaximal, complemented
3#23782922C3127yesmaximal, complemented
4#23782921C3127yesmaximal, complemented
5C43⋊H(5,𝔽3)C311yesmaximal, characteristic
6C3×#16812526C3112yesmaximal, complemented
7C3×#16812524C311yesmaximal, characteristic, complemented
8#737×C43⋊C3C3127yesmaximal, complemented
9C43×3−1+4C311yesmaximal, characteristic, complemented
10#16812526C32172yescomplemented
11#16812526C321216yescomplemented
12#16812526C3219yescomplemented
13#16812526C32172yescomplemented
14#16812526C32172yescomplemented
15#16812526C32172yescomplemented
16#16812525C321216yescomplemented
17#16812524C3219yescomplemented
18#16812524C32127yescomplemented
19#16812524C3219yescomplemented
20#16812524C3219yescomplemented
21C3×#11923958C3218yescomplemented
22C3×#11923958C32112yescomplemented
23C3×#11923957C32136yescomplemented
24C3×#11923956C32136yescomplemented
253−1+2×C43⋊C3C321216yescomplemented
26C3×C32⋊(C43⋊C3)C32112yes—
27H(3,𝔽3)×C43⋊C3C32127yes—
28C32×C43⋊C9C3214yescomplemented
29C3×C9×C43⋊C3C32136yescomplemented
30C43×#737C32127yescomplemented
31C3×3−1+2×C43C32112yescomplemented
32C3×H(3,𝔽3)×C43C3211yescharacteristic
33C32×C43⋊C3C33136yes—
34#11923958C33172yes—
35#11923958C33172yes—
36#11923958C3319yes—
37#11923957C331216yes—
38#11923957C33127yes—
39#11923956C331216yes—
40#11923956C33127yes—
41C32⋊(C43⋊C3)C33172yes—
42C32⋊(C43⋊C3)C3319yes—
43C3×C43⋊C9C33112yes—
44C3×C43⋊C9C33136yes—
45C3×C43⋊C9C3311yescharacteristic
46C3×C43⋊C9C33112yes—
47C3×C43⋊C9C33112yes—
48C3×C43⋊C9C3318yes—
49C9×C43⋊C3C33127yes—
50C9×C43⋊C3C331216yes—
51C33×C43C3314yes—
523−1+2×C43C3319yes—
533−1+2×C43C33172yes—
54H(3,𝔽3)×C43C3319yes—
55C3×C9×C43C33136yes—
56#10624943—431nomaximal, Sylow
57C32×C43—94no—
58C32×C43C34112yes—
59C32×C43C3411yescharacteristic
60C3×C43⋊C3—936no—
61C3×C43⋊C3C34127yes—
62C9×C43C34127yes—
63C43⋊C9C3411yescharacteristic
64C43⋊C9C34127yes—
65C43⋊C9C34124yes—
66C43⋊C9C3411yescharacteristic
67C43⋊C9C3411yescharacteristic
683−1+4—4327no—
693−1+4—4327no—
703−1+4—4324no—
713−1+4—431no—
723−1+4C43⋊C311yescharacteristic, complemented
73H(5,𝔽3)—431no—
74C3×#737—4327no—
75C3×#737—4312no—
76C3×#737—431no—
77C3×C43—312no—
78C3×C43—31no—
79C3×C43C3511yescharacteristic
80C43⋊C3—327no—
81#737—4372no—
82#737—439no—
83#737—43216no—
84#737—4372no—
85#737—4372no—
86#737—4372no—
87#737—439no—
88#737—4327no—
89#737—439no—
90#737—439no—
91#737—43216no—
92#737C3×C43⋊C3127yescomplemented
93C3×3−1+2—4312no—
94C3×3−1+2—438no—
95C3×3−1+2—43216no—
96C3×3−1+2—4336no—
97C3×3−1+2—4336no—
98C3×3−1+2C3×C43⋊C3112yescomplemented
99C3×H(3,𝔽3)—4312no—
100C3×H(3,𝔽3)—4327no—
101C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
102C32×C9—434no—
103C32×C9—4336no—
104C43#1062494311yescharacteristic, complemented, Sylow
105C33—4336no—
106C33C32×C43⋊C314yes—
1073−1+2—439no—
1083−1+2—4372no—
1093−1+2—4372no—
1103−1+2—43216no—
1113−1+2—4327no—
1123−1+2—43216no—
1133−1+2—4327no—
1143−1+2C32×C43⋊C3172yes—
1153−1+2C32×C43⋊C319yes—
116H(3,𝔽3)—439no—
117H(3,𝔽3)—4372no—
118H(3,𝔽3)C32×C43⋊C319yes—
119C3×C9—431no—
120C3×C9—4312no—
121C3×C9—438no—
122C3×C9—4312no—
123C3×C9—4312no—
124C3×C9—4336no—
125C3×C9—4327no—
126C3×C9—43216no—
127C3×C9C32×C43⋊C3136yes—
128C32—94no—
129C32—4327no—
130C32—38736no—
131C32C33×C43⋊C311yescharacteristic
132C32C33×C43⋊C3112yes—
133C9—431no—
134C9—4324no—
135C9—4327no—
136C9—431no—
137C9—431no—
138C9C33×C43⋊C3127yes—
139C3—31no—
140C3—312no—
141C3—12927no—
142C3C34×C43⋊C311yescharacteristic
subgroupG/H
center, FrattiniC3C34×C43⋊C3
commutator, socle, cosocleC3×C43C35
FittingC43×3−1+4C3
prime radicalC43⋊H(5,𝔽3)C3
hypercenter3−1+4C43⋊C3
hypocenterC43#10624943
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ 3−1+4

Complements

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

NH ≅ G/Ntype
1. #23782924C3semidirect
2. #23782923C3semidirect
3. #23782922C3semidirect
4. #23782921C3semidirect
6. C3×#16812526C3semidirect
7. C3×#16812524C3semidirect
8. #737×C43⋊C3C3semidirect
9. C43×3−1+4C3semidirect
10. #16812526C32semidirect
11. #16812526C32semidirect
12. #16812526C32semidirect
13. #16812526C32semidirect
14. #16812526C32semidirect
15. #16812526C32semidirect
16. #16812525C32semidirect
17. #16812524C32semidirect
18. #16812524C32semidirect
19. #16812524C32semidirect
20. #16812524C32semidirect
21. C3×#11923958C32semidirect
22. C3×#11923958C32semidirect
23. C3×#11923957C32semidirect
24. C3×#11923956C32semidirect
25. 3−1+2×C43⋊C3C32semidirect
28. C32×C43⋊C9C32semidirect
29. C3×C9×C43⋊C3C32semidirect
30. C43×#737C32semidirect
31. C3×3−1+2×C43C32semidirect
72. 3−1+4C43⋊C3semidirect
92. #737C3×C43⋊C3semidirect
98. C3×3−1+2C3×C43⋊C3semidirect
104. C43#10624943semidirect

Maximal subgroups

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

subgroupindex
#237829243
#237829233
#237829223
#237829213
C43⋊H(5,𝔽3)3
C3×#168125263
C3×#168125243
#737×C43⋊C33
C43×3−1+43
#1062494343