Finite Group Databasebeta

← #44534571

Subgroups — #44534571

Order 31347.

200 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 43 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#23782907C312yesmaximal, complemented
2#23782890C311yesmaximal, characteristic, complemented
3#23782848C311yesmaximal, characteristic, complemented
4#23782769C311yesmaximal, characteristic, complemented
5#23782759C312yesmaximal, complemented
6#23782757C312yesmaximal, complemented
7#23782750C311yesmaximal, characteristic, complemented
8#23782749C312yesmaximal, complemented
9C43×#6883C311yesmaximal, characteristic, complemented
10#16812526—32no—
11C3×#11923956—31no—
12C3×#11923956C3211yescharacteristic
13H(3,𝔽3)×C43⋊C3—31no—
14#16812515C3212yescomplemented
15#16812513C3212yes—
16#16812513C3212yescomplemented
17#16812512—32no—
18#16812511—32no—
19#16812508—32no—
20#16812499C3211yescharacteristic, complemented
21(C43⋊C9)⋊C9—32no—
22C9×C43⋊C9C3211yescharacteristic, complemented
23C43×#733C3212yescomplemented
24C43×#732C3211yescharacteristic
25C43×C9⋊C9C3211yescharacteristic, complemented
26C32×C43⋊C3—91no—
27C32×C43⋊C3H(3,𝔽3)11yescharacteristic
28#11923958—32no—
29#11923957—92no—
30#11923956—91no—
31#11923956—93no—
32#11923956—92no—
33C32⋊(C43⋊C3)—32no—
34C32⋊(C43⋊C3)—32no—
35C32⋊(C43⋊C3)—92no—
36C3×C43⋊C9—31no—
37C3×C43⋊C9—31no—
38C3×C43⋊C9H(3,𝔽3)12yes—
39C9×C43⋊C3—92no—
403−1+2×C43—32no—
41H(3,𝔽3)×C43—31no—
42C3×C9×C43—31no—
43C3×C9×C43C3311yescharacteristic
44#10624851—431nomaximal, Sylow
45C32×C43—91no—
46C32×C43C3×H(3,𝔽3)11yescharacteristic
47C3×C43⋊C3—31no—
48C3×C43⋊C3—91no—
49C3×C43⋊C3—92no—
50C3×C43⋊C3—92no—
51C3×C43⋊C3—273no—
52C9×C43—31no—
53C9×C43—91no—
54C9×C43—92no—
55C43⋊C9—33no—
56C43⋊C9—32no—
57C43⋊C9—91no—
58C43⋊C9—92no—
59#6913—432no—
60#6911—431no—
61#6900—431no—
62#6883—431no—
63#6883C43⋊C311yescharacteristic, complemented
64#6881—432no—
65#6881—432no—
66#6879—431no—
67#6878—432no—
68C3×C43—31no—
69C3×C43—271no—
70C3×C43#691111yescharacteristic
71C43⋊C3—91no—
72C43⋊C3—272no—
73C43⋊C3—272no—
74#737—1292no—
75C3×3−1+2—431no—
76C3×3−1+2—1291no—
77C3×H(3,𝔽3)—1291no—
78#733—432no—
79#733C3×C43⋊C312yescomplemented
80#732—432no—
81#732—432no—
82#732—1292no—
83#732C3×C43⋊C311yescharacteristic
84#731—1292no—
85AΣL(1,𝔽27)—1292no—
86C9⋊C9—431no—
87C9⋊C9—1292no—
88C9⋊C9C3×C43⋊C311yescharacteristic, complemented
89C92—431no—
90C43#1062485111yescharacteristic, complemented, Sylow
91C33—431no—
92C33—3871no—
933−1+2—32no—
943−1+2—1292no—
953−1+2—3871no—
963−1+2—3873no—
973−1+2—3872no—
983−1+2—3872no—
99H(3,𝔽3)—31no—
100H(3,𝔽3)—1292no—
101H(3,𝔽3)—1292no—
102H(3,𝔽3)—3872no—
103C3×C9—31no—
104C3×C9—432no—
105C3×C9—1291no—
106C3×C9—1291no—
107C3×C9—3872no—
108C3×C9C32×C43⋊C311yescharacteristic
109C32—91no—
110C32—1291no—
111C32—3871no—
112C32—3872no—
113C32—3872no—
114C32—11613no—
115C32H(3,𝔽3)×C43⋊C311yescharacteristic
116C9—31no—
117C9—91no—
118C9—92no—
119C9—1293no—
120C9—1292no—
121C9—3871no—
122C9—3872no—
123C3—31no—
124C3—271no—
125C3—3871no—
126C3—11612no—
127C3—11612no—
128C3#2378289011yescharacteristic
subgroupG/H
centerC3#23782890
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6883C3
socleC3×C43#6911
hypercenter#6883C43⋊C3
hypocenterC43#10624851
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6883

Complements

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

NH ≅ G/Ntype
1. #23782907C3semidirect
2. #23782890C3semidirect
3. #23782848C3semidirect
4. #23782769C3semidirect
5. #23782759C3semidirect
6. #23782757C3semidirect
7. #23782750C3semidirect
8. #23782749C3semidirect
9. C43×#6883C3semidirect
14. #16812515C32semidirect
16. #16812513C32semidirect
20. #16812499C32semidirect
22. C9×C43⋊C9C32semidirect
23. C43×#733C32semidirect
25. C43×C9⋊C9C32semidirect
63. #6883C43⋊C3semidirect
79. #733C3×C43⋊C3semidirect
88. C9⋊C9C3×C43⋊C3semidirect
90. C43#10624851semidirect

Maximal subgroups

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

subgroupindex
#237829073
#237828903
#237828483
#237827693
#237827593
#237827573
#237827503
#237827493
C43×#68833
#1062485143