Finite Group Databasebeta

← #44534502

Subgroups — #44534502

Order 31347.

188 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 52 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#23782877C312yesmaximal, complemented
2#23782782C311yesmaximal, characteristic, complemented
3#23782753C311yesmaximal, characteristic, complemented
4#23782752C311yesmaximal, characteristic, complemented
5#23782750C311yesmaximal, characteristic, complemented
6#23782749C312yesmaximal, complemented
7#23782748C312yesmaximal, complemented
8#23782745C312yesmaximal, complemented
9C43×#6908C311yesmaximal, characteristic, complemented
10#16812525—32no—
11#16812515C3212yes—
12#16812515C3212yes—
13#16812513C3212yes—
14#16812510—32no—
15#16812507—32no—
16#16812500—31no—
17#16812499—31no—
18C32⋊(C43⋊C9)—31no—
19C9×C43⋊C9C3212yes—
20C9×C43⋊C9C3211yescharacteristic
21C43×#737—31no—
22C32×C9×C43C3211yescharacteristic
23C43×#733C3211yescharacteristic
24C43×#733C3211yescharacteristic
25C43×#732C3211yescharacteristic
26C43×#731—31no—
27C43×AΣL(1,𝔽27)—31no—
28#11923958—32no—
29#11923958—32no—
30#11923957—92no—
31#11923956—92no—
32C32⋊(C43⋊C3)—32no—
33C3×C43⋊C9—32no—
34C3×C43⋊C9—31no—
35C9×C43⋊C3—92no—
36C33×C43H(3,𝔽3)11yescharacteristic
373−1+2×C43—31no—
383−1+2×C43—31no—
393−1+2×C43—92no—
40H(3,𝔽3)×C43—31no—
41C3×C9×C43—31no—
42C3×C9×C43—32no—
43C3×C9×C43—91no—
44C3×C9×C43H(3,𝔽3)11yescharacteristic
45C3×C9×C43H(3,𝔽3)11yescharacteristic
46C3×C9×C43C3311yescharacteristic
47#10624841—431nomaximal, Sylow
48C32×C43—31no—
49C32×C43—91no—
50C32×C43—91no—
51C32×C43C3×H(3,𝔽3)11yescharacteristic
52C3×C43⋊C3—92no—
53C9×C43—31no—
54C9×C43—31no—
55C9×C43—91no—
56C9×C43—91no—
57C9×C43#73211yescharacteristic
58C9×C43#73212yes—
59C43⋊C9—92no—
60C43⋊C9—91no—
61C43⋊C9—92no—
62C43⋊C9—92no—
63#6908—432no—
64#6908C43⋊C311yescharacteristic, complemented
65#6887—431no—
66#6880—431no—
67#6880—431no—
68#6879—431no—
69#6878—432no—
70#6878—432no—
71#6878—432no—
72C3×C43—31no—
73C3×C43—91no—
74C3×C43—271no—
75C3×C43C3×#73211yescharacteristic
76C43⋊C3—272no—
77#737—31no—
78#737—1292no—
79C32×C9C3×C43⋊C311yescharacteristic
80#733—432no—
81#733—432no—
82#733C3×C43⋊C311yescharacteristic
83#733C3×C43⋊C311yescharacteristic
84#732—432no—
85#732C3×C43⋊C311yescharacteristic
86#731—31no—
87#731—1292no—
88AΣL(1,𝔽27)—31no—
89AΣL(1,𝔽27)—1292no—
90C9⋊C9—1291no—
91C9⋊C9—1291no—
92C32⋊C9—1291no—
93C92—432no—
94C92—431no—
95C43#1062484111yescharacteristic, complemented, Sylow
96C33C32⋊(C43⋊C3)11yescharacteristic
973−1+2—31no—
983−1+2—31no—
993−1+2—92no—
1003−1+2—1292no—
1013−1+2—1292no—
1023−1+2—3872no—
1033−1+2—3872no—
104H(3,𝔽3)—31no—
105H(3,𝔽3)—1292no—
106C3×C9—31no—
107C3×C9—32no—
108C3×C9—91no—
109C3×C9—1292no—
110C3×C9—1291no—
111C3×C9—3872no—
112C3×C9C32⋊(C43⋊C3)11yescharacteristic
113C3×C9C32⋊(C43⋊C3)11yescharacteristic
114C3×C9C32×C43⋊C311yescharacteristic
115C32—31no—
116C32—91no—
117C32—91no—
118C32—3872no—
119C32C3×C32⋊(C43⋊C3)11yescharacteristic
120C9—31no—
121C9—31no—
122C9—91no—
123C9—91no—
124C9—3872no—
125C9—3871no—
126C9—3872no—
127C9—3872no—
128C9#1681251211yescharacteristic
129C9#1681251212yes—
130C3—31no—
131C3—91no—
132C3—271no—
133C3—11612no—
134C3C3×#1681251211yescharacteristic
subgroupG/H
centerC3C3×#16812512
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6908C3
socleC3×C43C3×#732
hypercenter#6908C43⋊C3
hypocenterC43#10624841
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C3×C9 ◁ C32×C9 ◁ #6908

Complements

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

NH ≅ G/Ntype
1. #23782877C3semidirect
2. #23782782C3semidirect
3. #23782753C3semidirect
4. #23782752C3semidirect
5. #23782750C3semidirect
6. #23782749C3semidirect
7. #23782748C3semidirect
8. #23782745C3semidirect
9. C43×#6908C3semidirect
64. #6908C43⋊C3semidirect
95. C43#10624841semidirect

Maximal subgroups

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

subgroupindex
#237828773
#237827823
#237827533
#237827523
#237827503
#237827493
#237827483
#237827453
C43×#69083
#1062484143