Finite Group Databasebeta

← #44534581

Subgroups — #44534581

Order 31347.

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

normal subgroups only

This group has 188 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#23782893C311yesmaximal, characteristic, complemented
3#23782846C311yesmaximal, characteristic, complemented
4#23782766C312yesmaximal, complemented
5#23782764C311yesmaximal, characteristic, complemented
6#23782761C312yesmaximal, complemented
7#23782759C311yesmaximal, characteristic, complemented
8#23782747C312yesmaximal, complemented
9C43×#6880C311yesmaximal, characteristic, complemented
10#16812526—32no—
11C3×#11923957—31no—
12C3×#11923957C3211yescharacteristic
133−1+2×C43⋊C3—31no—
14#16812515C3212yes—
15#16812515C3212yes—
16#16812514—32no—
17#16812513C3212yes—
18#16812511—32no—
19#16812508—32no—
20#16812499—32no—
21#16812499C3211yescharacteristic
22#16812499C3211yescharacteristic
23C43×#733C3211yescharacteristic
24C43×#733C3212yes—
25C92×C43C3211yescharacteristic
26C32×C43⋊C3H(3,𝔽3)11yescharacteristic
27#11923958—32no—
28#11923958—32no—
29#11923957—91no—
30#11923957—92no—
31#11923957—93no—
32#11923957—91no—
33#11923956—92no—
34#11923956—91no—
35C32⋊(C43⋊C3)—32no—
36C3×C43⋊C9—31no—
37C3×C43⋊C9—31no—
38C3×C43⋊C9H(3,𝔽3)12yes—
39C9×C43⋊C3—92no—
40C9×C43⋊C3—91no—
413−1+2×C43—32no—
423−1+2×C43—31no—
43C3×C9×C43—31no—
44C3×C9×C43C3311yescharacteristic
45#10624852—431nomaximal, Sylow
46C32×C43C3×H(3,𝔽3)11yescharacteristic
47C3×C43⋊C3—31no—
48C3×C43⋊C3—91no—
49C3×C43⋊C3—92no—
50C9×C43—33no—
51C9×C43—31no—
52C9×C43—92no—
53C9×C43—91no—
54C43⋊C9—32no—
55C43⋊C9—91no—
56C43⋊C9—91no—
57C43⋊C9—92no—
58C43⋊C9—92no—
59#6913—432no—
60#6912—431no—
61#6900—431no—
62#6883—432no—
63#6882—432no—
64#6882—431no—
65#6881—431no—
66#6880C43⋊C311yescharacteristic, complemented
67#6878—432no—
68C3×C43—31no—
69C3×C43#691111yescharacteristic
70C43⋊C3—91no—
71C43⋊C3—272no—
72#737—1292no—
73C3×3−1+2—431no—
74C3×3−1+2—1291no—
75C3×3−1+2—1291no—
76#733—432no—
77#733—432no—
78#733—1292no—
79#733C3×C43⋊C311yescharacteristic
80#733C3×C43⋊C312yes—
81#732—432no—
82#731—1292no—
83AΣL(1,𝔽27)—1292no—
84C9⋊C9—431no—
85C9⋊C9—431no—
86C9⋊C9—1292no—
87C92C3×C43⋊C311yescharacteristic
88C43#1062485211yescharacteristic, complemented, Sylow
89C33—431no—
903−1+2—32no—
913−1+2—31no—
923−1+2—1292no—
933−1+2—1292no—
943−1+2—3871no—
953−1+2—3873no—
963−1+2—3872no—
973−1+2—3872no—
983−1+2—3871no—
993−1+2—3871no—
100H(3,𝔽3)—1292no—
101C3×C9—31no—
102C3×C9—432no—
103C3×C9—1291no—
104C3×C9—1291no—
105C3×C9—3872no—
106C3×C9—3871no—
107C3×C9C32×C43⋊C311yescharacteristic
108C32—1291no—
109C32—3871no—
110C32—3872no—
111C32H(3,𝔽3)×C43⋊C311yescharacteristic
112C9—33no—
113C9—31no—
114C9—92no—
115C9—91no—
116C9—1292no—
117C9—3871no—
118C9—3871no—
119C9—3872no—
120C9—3872no—
121C3—31no—
122C3—3871no—
123C3—11612no—
124C3#2378288911yescharacteristic
subgroupG/H
centerC3#23782889
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6880C3
socleC3×C43#6911
hypercenter#6880C43⋊C3
hypocenterC43#10624852
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6880

Complements

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

NH ≅ G/Ntype
1. #23782906C3semidirect
2. #23782893C3semidirect
3. #23782846C3semidirect
4. #23782766C3semidirect
5. #23782764C3semidirect
6. #23782761C3semidirect
7. #23782759C3semidirect
8. #23782747C3semidirect
9. C43×#6880C3semidirect
66. #6880C43⋊C3semidirect
88. C43#10624852semidirect

Maximal subgroups

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

subgroupindex
#237829063
#237828933
#237828463
#237827663
#237827643
#237827613
#237827593
#237827473
C43×#68803
#1062485243