Finite Group Databasebeta

← #44534543

Subgroups — #44534543

Order 31347.

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

normal subgroups only

This group has 198 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#733×C43⋊C3C311yesmaximal, characteristic, complemented
2#733×C43⋊C3C311yesmaximal, characteristic, complemented
3#732×C43⋊C3C311yesmaximal, characteristic
4#23782781C311yesmaximal, characteristic, complemented
5#23782769C311yesmaximal, characteristic, complemented
6#23782768C311yesmaximal, characteristic, complemented
7#23782767C311yesmaximal, characteristic, complemented
8#23782767C311yesmaximal, characteristic, complemented
9#23782766C311yesmaximal, characteristic, complemented
10#23782766C311yesmaximal, characteristic, complemented
11#23782765C311yesmaximal, characteristic, complemented
12#23782765C311yesmaximal, characteristic, complemented
13C43×#6883C311yesmaximal, characteristic, complemented
143−1+2×C43⋊C3—31no—
153−1+2×C43⋊C3—31no—
16H(3,𝔽3)×C43⋊C3—31no—
17C3×C9×C43⋊C3C3211yescharacteristic
18#16812515C3211yescharacteristic, complemented
19#16812515C3211yescharacteristic, complemented
20#16812515C3211yescharacteristic, complemented
21#16812515C3211yescharacteristic, complemented
22#16812514—31no—
23#16812514—31no—
24#16812514—31no—
25#16812514—31no—
26#16812513C3211yescharacteristic
27#16812513C3211yescharacteristic
28#16812512—31no—
29#16812512—31no—
30#16812500C3211yescharacteristic, complemented
31#16812499C3211yescharacteristic, complemented
32(C43⋊C9)⋊C9—31no—
33(C3×C43⋊C3)⋊C9—31no—
34C9×C43⋊C9—31no—
35C43×#733C3211yescharacteristic, complemented
36C43×#733C3211yescharacteristic, complemented
37C43×#732C3211yescharacteristic
38C43×C9⋊C9C3211yescharacteristic, complemented
39C32×C43⋊C3—91no—
40C32×C43⋊C3H(3,𝔽3)11yescharacteristic
41#11923958—31no—
42#11923958—31no—
43#11923958—31no—
44#11923958—31no—
45#11923957—91no—
46#11923957—91no—
47#11923956—91no—
48#11923956—91no—
49C32⋊(C43⋊C3)—31no—
50C32⋊(C43⋊C3)—31no—
51C32⋊(C43⋊C3)—91no—
52C32⋊(C43⋊C3)—91no—
53C3×C43⋊C9—31no—
54C3×C43⋊C9—31no—
55C3×C43⋊C9H(3,𝔽3)11yescharacteristic
56C3×C43⋊C9H(3,𝔽3)11yescharacteristic
57C9×C43⋊C3—31no—
58C9×C43⋊C3—31no—
59C9×C43⋊C3—31no—
60C9×C43⋊C3—91no—
61C9×C43⋊C3—91no—
623−1+2×C43—31no—
633−1+2×C43—31no—
64H(3,𝔽3)×C43—31no—
65C3×C9×C43—31no—
66C3×C9×C43C3311yescharacteristic
67#10624848—431nomaximal, Sylow
68C32×C43—91no—
69C32×C43C3×H(3,𝔽3)11yescharacteristic
70C3×C43⋊C3—91no—
71C3×C43⋊C3—91no—
72C3×C43⋊C3—91no—
73C3×C43⋊C3—273no—
74C3×C43⋊C3#73211yescharacteristic
75C3×C43⋊C3#73211yescharacteristic
76C3×C43⋊C3#73211yescharacteristic
77C9×C43—31no—
78C9×C43—91no—
79C9×C43—91no—
80C9×C43—91no—
81C43⋊C9—31no—
82C43⋊C9—31no—
83C43⋊C9—91no—
84C43⋊C9—91no—
85C43⋊C9—91no—
86C43⋊C9—91no—
87C43⋊C9—91no—
88C43⋊C9—91no—
89C3×#733—431no—
90C3×#733—431no—
91C3×#732—431no—
92#6887—431no—
93#6883—431no—
94#6883—431no—
95#6883—431no—
96#6883—431no—
97#6883—431no—
98#6883—431no—
99#6883—431no—
100#6883—431no—
101#6883C43⋊C311yescharacteristic, complemented
102C3×C43—31no—
103C3×C43—271no—
104C3×C43C3×#73211yescharacteristic
105C43⋊C3—31no—
106C43⋊C3—31no—
107C43⋊C3—31no—
108C43⋊C3—271no—
109C43⋊C3—271no—
110C3×3−1+2—1291no—
111C3×3−1+2—1291no—
112C3×H(3,𝔽3)—1291no—
113C32×C9—431no—
114#733—431no—
115#733—431no—
116#733—431no—
117#733—431no—
118#733—1291no—
119#733—1291no—
120#733—1291no—
121#733—1291no—
122#733C3×C43⋊C311yescharacteristic, complemented
123#733C3×C43⋊C311yescharacteristic, complemented
124#732—431no—
125#732—431no—
126#732—1291no—
127#732—1291no—
128#732C3×C43⋊C311yescharacteristic
129C9⋊C9—431no—
130C9⋊C9—431no—
131C9⋊C9—1291no—
132C9⋊C9C3×C43⋊C311yescharacteristic, complemented
133C32⋊C9—1291no—
134C92—1291no—
135C43#1062484811yescharacteristic, complemented, Sylow
136C33—431no—
137C33—3871no—
1383−1+2—31no—
1393−1+2—31no—
1403−1+2—1291no—
1413−1+2—1291no—
1423−1+2—1291no—
1433−1+2—1291no—
1443−1+2—3871no—
1453−1+2—3871no—
1463−1+2—3871no—
1473−1+2—3871no—
148H(3,𝔽3)—31no—
149H(3,𝔽3)—1291no—
150H(3,𝔽3)—1291no—
151H(3,𝔽3)—3871no—
152H(3,𝔽3)—3871no—
153C3×C9—31no—
154C3×C9—431no—
155C3×C9—431no—
156C3×C9—1291no—
157C3×C9—1291no—
158C3×C9—1291no—
159C3×C9—1291no—
160C3×C9—1291no—
161C3×C9—3871no—
162C3×C9—3871no—
163C3×C9C32×C43⋊C311yescharacteristic
164C32—91no—
165C32—431no—
166C32—431no—
167C32—431no—
168C32—3871no—
169C32—3871no—
170C32—3871no—
171C32—11613no—
172C32H(3,𝔽3)×C43⋊C311yescharacteristic
173C9—31no—
174C9—91no—
175C9—91no—
176C9—91no—
177C9—1291no—
178C9—1291no—
179C9—3871no—
180C9—3871no—
181C9—3871no—
182C9—3871no—
183C9—3871no—
184C9—3871no—
185C3—31no—
186C3—271no—
187C3—1291no—
188C3—1291no—
189C3—1291no—
190C3—11611no—
191C3—11611no—
192C3#732×C43⋊C311yescharacteristic
subgroupG/H
centerC3#732×C43⋊C3
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6883C3
socleC3×C43C3×#732
prime radical#732×C43⋊C3C3
hypercenter#6883C43⋊C3
hypocenterC43#10624848
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. #733×C43⋊C3C3semidirect
2. #733×C43⋊C3C3semidirect
4. #23782781C3semidirect
5. #23782769C3semidirect
6. #23782768C3semidirect
7. #23782767C3semidirect
8. #23782767C3semidirect
9. #23782766C3semidirect
10. #23782766C3semidirect
11. #23782765C3semidirect
12. #23782765C3semidirect
13. C43×#6883C3semidirect
18. #16812515C32semidirect
19. #16812515C32semidirect
20. #16812515C32semidirect
21. #16812515C32semidirect
30. #16812500C32semidirect
31. #16812499C32semidirect
35. C43×#733C32semidirect
36. C43×#733C32semidirect
38. C43×C9⋊C9C32semidirect
101. #6883C43⋊C3semidirect
122. #733C3×C43⋊C3semidirect
123. #733C3×C43⋊C3semidirect
132. C9⋊C9C3×C43⋊C3semidirect
135. C43#10624848semidirect

Maximal subgroups

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

subgroupindex
#733×C43⋊C33
#732×C43⋊C33
#237827813
#237827693
#237827683
#237827673
#237827663
#237827653
C43×#68833
#1062484843