Finite Group Databasebeta

← #44534566

Subgroups — #44534566

Order 31347.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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#23782905C312yesmaximal, complemented
2#23782892C311yesmaximal, characteristic, complemented
3#23782767C312yesmaximal, complemented
4#23782757C312yesmaximal, complemented
5#23782757C312yesmaximal, complemented
6#23782751C311yesmaximal, characteristic, complemented
7#23782747C311yesmaximal, characteristic, complemented
8#23782746C311yesmaximal, characteristic, complemented
9C43×#6900C311yesmaximal, characteristic, complemented
10#16812525—32no—
11C3×C32⋊(C43⋊C3)—31no—
12#16812515C3212yescomplemented
13#16812515C3212yescomplemented
14#16812513—32no—
15#16812513C3211yescharacteristic
16#16812513C3211yescharacteristic
17#16812513C3211yescharacteristic
18#16812513C3212yescomplemented
19#16812510—32no—
20#16812507—32no—
21C3×3−1+2×C43—31no—
22C3×3−1+2×C43C3211yescharacteristic
23C43×C9⋊C9—32no—
24C43×C9⋊C9C3212yescomplemented
25C92×C43C3211yescharacteristic, complemented
26C32×C43⋊C3—91no—
27#11923958—32no—
28#11923958—32no—
29#11923957—92no—
30#11923956—92no—
31C32⋊(C43⋊C3)—32no—
32C32⋊(C43⋊C3)—31no—
33C32⋊(C43⋊C3)—31no—
34C32⋊(C43⋊C3)—31no—
35C32⋊(C43⋊C3)—92no—
36C9×C43⋊C3—92no—
37C33×C43H(3,𝔽3)11yescharacteristic
383−1+2×C43—91no—
393−1+2×C43—93no—
40C3×C9×C43—31no—
41C3×C9×C43—32no—
42C3×C9×C43H(3,𝔽3)12yes—
43C3×C9×C43C3311yescharacteristic
44#10624851—431nomaximal, Sylow
45C32×C43—31no—
46C32×C43—91no—
47C32×C43C3×H(3,𝔽3)11yescharacteristic
48C3×C43⋊C3—92no—
49C3×C43⋊C3—91no—
50C3×C43⋊C3—91no—
51C3×C43⋊C3—91no—
52C3×C43⋊C3—273no—
53C9×C43—33no—
54C9×C43—32no—
55C9×C43—31no—
56C9×C43—92no—
57C43⋊C9—92no—
58C43⋊C9—92no—
59#6913—432no—
60#6911—431no—
61#6900C43⋊C311yescharacteristic, complemented
62#6883—432no—
63#6881—432no—
64#6881—432no—
65#6879—431no—
66#6878—431no—
67#6878—431no—
68C3×C43—31no—
69C3×C43—91no—
70C3×C43#691111yescharacteristic
71C43⋊C3—272no—
72C43⋊C3—271no—
73C43⋊C3—271no—
74C43⋊C3—271no—
75#737—1292no—
76C3×3−1+2—31no—
77C3×3−1+2C3×C43⋊C311yescharacteristic
78C3×H(3,𝔽3)—1291no—
79#733—432no—
80#733—432no—
81#732—432no—
82#732—431no—
83#732—431no—
84#732—431no—
85#732—1292no—
86#731—1292no—
87AΣL(1,𝔽27)—1292no—
88C9⋊C9—32no—
89C9⋊C9C3×C43⋊C312yescomplemented
90C92C3×C43⋊C311yescharacteristic, complemented
91C43#1062485111yescharacteristic, complemented, Sylow
92C33—3871no—
93C33C32⋊(C43⋊C3)11yescharacteristic
943−1+2—91no—
953−1+2—93no—
963−1+2—1292no—
973−1+2—1292no—
983−1+2—3872no—
993−1+2—3872no—
100H(3,𝔽3)—1292no—
101H(3,𝔽3)—1291no—
102H(3,𝔽3)—1291no—
103H(3,𝔽3)—1291no—
104H(3,𝔽3)—3872no—
105C3×C9—31no—
106C3×C9—32no—
107C3×C9—3872no—
108C3×C9C32⋊(C43⋊C3)12yes—
109C3×C9C32×C43⋊C311yescharacteristic
110C32—31no—
111C32—91no—
112C32—3872no—
113C32—3871no—
114C32—3871no—
115C32—3871no—
116C32—11613no—
117C32C3×C32⋊(C43⋊C3)11yescharacteristic
118C9—33no—
119C9—32no—
120C9—31no—
121C9—92no—
122C9—3872no—
123C9—3872no—
124C3—31no—
125C3—91no—
126C3—11612no—
127C3—11611no—
128C3—11611no—
129C3—11611no—
130C3#2378289211yescharacteristic
subgroupG/H
centerC3#23782892
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6900C3
socleC3×C43#6911
hypercenter#6900C43⋊C3
hypocenterC43#10624851
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C32 ◁ C3×3−1+2 ◁ #6900

Complements

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

NH ≅ G/Ntype
1. #23782905C3semidirect
2. #23782892C3semidirect
3. #23782767C3semidirect
4. #23782757C3semidirect
5. #23782757C3semidirect
6. #23782751C3semidirect
7. #23782747C3semidirect
8. #23782746C3semidirect
9. C43×#6900C3semidirect
12. #16812515C32semidirect
13. #16812515C32semidirect
18. #16812513C32semidirect
24. C43×C9⋊C9C32semidirect
25. C92×C43C32semidirect
61. #6900C43⋊C3semidirect
89. C9⋊C9C3×C43⋊C3semidirect
90. C92C3×C43⋊C3semidirect
91. C43#10624851semidirect

Maximal subgroups

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

subgroupindex
#237829053
#237828923
#237827673
#237827573
#237827513
#237827473
#237827463
C43×#69003
#1062485143