Finite Group Databasebeta

← #44534561

Subgroups — #44534561

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#23782906C312yesmaximal, complemented
2#23782889C311yesmaximal, characteristic, complemented
3#23782846C311yesmaximal, characteristic, complemented
4#23782766C312yesmaximal, complemented
5#23782759C312yesmaximal, complemented
6#23782756C312yesmaximal, complemented
7#23782751C311yesmaximal, characteristic, complemented
8#23782746C311yesmaximal, characteristic, complemented
9C43×#6878C311yesmaximal, characteristic, complemented
10#16812526—32no—
11C3×#11923957—31no—
12C3×#11923957C3211yescharacteristic
13H(3,𝔽3)×C43⋊C3—31no—
14#16812515C3212yescomplemented
15#16812513C3211yescharacteristic
16#16812513C3211yescharacteristic
17#16812513C3212yescomplemented
18#16812512—32no—
19#16812511—32no—
20#16812508—32no—
21#16812499—32no—
22#16812499C3212yescomplemented
23C43×#733C3212yescomplemented
24C43×#732C3211yescharacteristic
25C92×C43C3211yescharacteristic, complemented
26C32×C43⋊C3—91no—
27C32×C43⋊C3H(3,𝔽3)11yescharacteristic
28#11923958—32no—
29#11923957—91no—
30#11923957—92no—
31#11923957—93no—
32#11923956—92no—
33C32⋊(C43⋊C3)—32no—
34C32⋊(C43⋊C3)—31no—
35C32⋊(C43⋊C3)—31no—
36C32⋊(C43⋊C3)—92no—
37C3×C43⋊C9—32no—
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—91no—
51C3×C43⋊C3—91no—
52C3×C43⋊C3—273no—
53C9×C43—33no—
54C9×C43—31no—
55C9×C43—92no—
56C43⋊C9—32no—
57C43⋊C9—92no—
58C43⋊C9—92no—
59#6913—432no—
60#6911—431no—
61#6900—431no—
62#6883—432no—
63#6881—432no—
64#6881—432no—
65#6879—431no—
66#6878—431no—
67#6878C43⋊C311yescharacteristic, complemented
68C3×C43—31no—
69C3×C43—271no—
70C3×C43#691111yescharacteristic
71C43⋊C3—91no—
72C43⋊C3—272no—
73C43⋊C3—271no—
74C43⋊C3—271no—
75#737—1292no—
76C3×3−1+2—431no—
77C3×3−1+2—1291no—
78C3×H(3,𝔽3)—1291no—
79#733—432no—
80#733C3×C43⋊C312yescomplemented
81#732—432no—
82#732—431no—
83#732—431no—
84#732—1292no—
85#732C3×C43⋊C311yescharacteristic
86#731—1292no—
87AΣL(1,𝔽27)—1292no—
88C9⋊C9—432no—
89C9⋊C9—1292no—
90C92C3×C43⋊C311yescharacteristic, complemented
91C43#1062485111yescharacteristic, complemented, Sylow
92C33—431no—
93C33—3871no—
943−1+2—32no—
953−1+2—1292no—
963−1+2—3871no—
973−1+2—3873no—
983−1+2—3872no—
993−1+2—3872no—
100H(3,𝔽3)—31no—
101H(3,𝔽3)—1292no—
102H(3,𝔽3)—1291no—
103H(3,𝔽3)—1291no—
104H(3,𝔽3)—3872no—
105C3×C9—31no—
106C3×C9—432no—
107C3×C9—1292no—
108C3×C9—3872no—
109C3×C9C32×C43⋊C311yescharacteristic
110C32—91no—
111C32—1291no—
112C32—3871no—
113C32—3872no—
114C32—3871no—
115C32—3871no—
116C32—11613no—
117C32H(3,𝔽3)×C43⋊C311yescharacteristic
118C9—33no—
119C9—31no—
120C9—92no—
121C9—1292no—
122C9—3872no—
123C9—3872no—
124C3—31no—
125C3—271no—
126C3—3871no—
127C3—11612no—
128C3—11611no—
129C3—11611no—
130C3#2378288911yescharacteristic
subgroupG/H
centerC3#23782889
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6878C3
socleC3×C43#6911
hypercenter#6878C43⋊C3
hypocenterC43#10624851
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6878

Complements

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

NH ≅ G/Ntype
1. #23782906C3semidirect
2. #23782889C3semidirect
3. #23782846C3semidirect
4. #23782766C3semidirect
5. #23782759C3semidirect
6. #23782756C3semidirect
7. #23782751C3semidirect
8. #23782746C3semidirect
9. C43×#6878C3semidirect
14. #16812515C32semidirect
17. #16812513C32semidirect
22. #16812499C32semidirect
23. C43×#733C32semidirect
25. C92×C43C32semidirect
67. #6878C43⋊C3semidirect
80. #733C3×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
#237829063
#237828893
#237828463
#237827663
#237827593
#237827563
#237827513
#237827463
C43×#68783
#1062485143