Finite Group Databasebeta

← #44534569

Subgroups — #44534569

Order 31347.

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

normal subgroups only

This group has 200 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#23782905C311yesmaximal, characteristic, complemented
2#23782892C311yesmaximal, characteristic, complemented
3#23782845C311yesmaximal, characteristic, complemented
4#23782766C311yesmaximal, characteristic, complemented
5#23782765C311yesmaximal, characteristic, complemented
6#23782759C311yesmaximal, characteristic, complemented
7#23782758C311yesmaximal, characteristic, complemented
8#23782756C311yesmaximal, characteristic, complemented
9#23782755C311yesmaximal, characteristic, complemented
10#23782750C311yesmaximal, characteristic, complemented
11#23782749C311yesmaximal, characteristic, complemented
12#23782748C311yesmaximal, characteristic, complemented
13C43×#6913C311yesmaximal, characteristic, complemented
14#16812525—31no—
15C3×#11923958—31no—
16C3×C32⋊(C43⋊C3)—31no—
17#16812515C3211yescharacteristic, complemented
18#16812515C3211yescharacteristic, complemented
19#16812513—31no—
20#16812513—31no—
21#16812513C3211yescharacteristic
22#16812513C3211yescharacteristic
23#16812513C3211yescharacteristic
24#16812513C3211yescharacteristic, complemented
25#16812510—31no—
26#16812507—31no—
27#16812500C3211yescharacteristic, complemented
28#16812499C3211yescharacteristic, complemented
29(C43⋊C9)⋊C9—31no—
30(C43⋊C9)⋊C9—31no—
31C9×C43⋊C9C3211yescharacteristic, complemented
32C43×#737—31no—
33C3×3−1+2×C43C3211yescharacteristic
34C43×#733C3211yescharacteristic, complemented
35C43×#733C3211yescharacteristic, complemented
36C43×#732C3211yescharacteristic, complemented
37C43×#731—31no—
38C43×AΣL(1,𝔽27)—31no—
39C32×C43⋊C3—91no—
40#11923958—31no—
41#11923958—31no—
42#11923958—93no—
43#11923957—91no—
44#11923956—91no—
45C32⋊(C43⋊C3)—31no—
46C32⋊(C43⋊C3)—31no—
47C32⋊(C43⋊C3)—31no—
48C32⋊(C43⋊C3)—31no—
49C32⋊(C43⋊C3)—92no—
50C3×C43⋊C9—31no—
51C3×C43⋊C9—31no—
52C3×C43⋊C9—31no—
53C9×C43⋊C3—91no—
54C33×C43H(3,𝔽3)11yescharacteristic
553−1+2×C43—31no—
563−1+2×C43—31no—
573−1+2×C43—91no—
583−1+2×C43—92no—
59H(3,𝔽3)×C43—31no—
60C3×C9×C43—91no—
61C3×C9×C43H(3,𝔽3)11yescharacteristic
62C3×C9×C43H(3,𝔽3)11yescharacteristic
63C3×C9×C43C3311yescharacteristic
64#10624851—431nomaximal, Sylow
65C32×C43—31no—
66C32×C43—91no—
67C32×C43—91no—
68C32×C43C3×H(3,𝔽3)11yescharacteristic
69C3×C43⋊C3—91no—
70C3×C43⋊C3—91no—
71C3×C43⋊C3—91no—
72C3×C43⋊C3—91no—
73C3×C43⋊C3—273no—
74C9×C43—31no—
75C9×C43—31no—
76C9×C43—31no—
77C9×C43—91no—
78C9×C43—91no—
79C43⋊C9—33no—
80C43⋊C9—91no—
81C43⋊C9—91no—
82C43⋊C9—91no—
83C43⋊C9—91no—
84#6913—431no—
85#6913C43⋊C311yescharacteristic, complemented
86#6911—431no—
87#6900—431no—
88#6883—431no—
89#6883—431no—
90#6881—431no—
91#6881—431no—
92#6881—431no—
93#6881—431no—
94#6879—431no—
95#6878—431no—
96#6878—431no—
97C3×C43—31no—
98C3×C43—91no—
99C3×C43—271no—
100C3×C43#691111yescharacteristic
101C43⋊C3—271no—
102C43⋊C3—271no—
103C43⋊C3—271no—
104C43⋊C3—271no—
105#737—31no—
106#737—1291no—
107C3×3−1+2—1291no—
108C3×3−1+2C3×C43⋊C311yescharacteristic
109C3×H(3,𝔽3)—1291no—
110#733—431no—
111#733—431no—
112#733C3×C43⋊C311yescharacteristic, complemented
113#733C3×C43⋊C311yescharacteristic, complemented
114#732—431no—
115#732—431no—
116#732—431no—
117#732—431no—
118#732—1291no—
119#732—1291no—
120#732C3×C43⋊C311yescharacteristic, complemented
121#731—31no—
122#731—1291no—
123AΣL(1,𝔽27)—31no—
124AΣL(1,𝔽27)—1291no—
125C9⋊C9—431no—
126C9⋊C9—431no—
127C9⋊C9—1291no—
128C9⋊C9—1291no—
129C92—431no—
130C43#1062485111yescharacteristic, complemented, Sylow
131C33—3871no—
132C33C32⋊(C43⋊C3)11yescharacteristic
1333−1+2—31no—
1343−1+2—31no—
1353−1+2—91no—
1363−1+2—92no—
1373−1+2—1291no—
1383−1+2—1291no—
1393−1+2—3871no—
1403−1+2—3871no—
1413−1+2—3873no—
142H(3,𝔽3)—31no—
143H(3,𝔽3)—1291no—
144H(3,𝔽3)—1291no—
145H(3,𝔽3)—1291no—
146H(3,𝔽3)—1291no—
147H(3,𝔽3)—3872no—
148C3×C9—91no—
149C3×C9—1291no—
150C3×C9—1291no—
151C3×C9—1291no—
152C3×C9—3871no—
153C3×C9C32⋊(C43⋊C3)11yescharacteristic
154C3×C9C32⋊(C43⋊C3)11yescharacteristic
155C3×C9C32×C43⋊C311yescharacteristic
156C32—31no—
157C32—91no—
158C32—91no—
159C32—3871no—
160C32—3871no—
161C32—3871no—
162C32—3871no—
163C32—11613no—
164C32C3×C32⋊(C43⋊C3)11yescharacteristic
165C9—31no—
166C9—31no—
167C9—31no—
168C9—91no—
169C9—91no—
170C9—1293no—
171C9—3871no—
172C9—3871no—
173C9—3871no—
174C9—3871no—
175C3—31no—
176C3—91no—
177C3—271no—
178C3—11611no—
179C3—11611no—
180C3—11611no—
181C3—11611no—
182C3#2378289111yescharacteristic
subgroupG/H
centerC3#23782891
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6913C3
socleC3×C43#6911
hypercenter#6913C43⋊C3
hypocenterC43#10624851
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C32 ◁ C3×3−1+2 ◁ #6913

Complements

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

NH ≅ G/Ntype
1. #23782905C3semidirect
2. #23782892C3semidirect
3. #23782845C3semidirect
4. #23782766C3semidirect
5. #23782765C3semidirect
6. #23782759C3semidirect
7. #23782758C3semidirect
8. #23782756C3semidirect
9. #23782755C3semidirect
10. #23782750C3semidirect
11. #23782749C3semidirect
12. #23782748C3semidirect
13. C43×#6913C3semidirect
17. #16812515C32semidirect
18. #16812515C32semidirect
24. #16812513C32semidirect
27. #16812500C32semidirect
28. #16812499C32semidirect
31. C9×C43⋊C9C32semidirect
34. C43×#733C32semidirect
35. C43×#733C32semidirect
36. C43×#732C32semidirect
85. #6913C43⋊C3semidirect
112. #733C3×C43⋊C3semidirect
113. #733C3×C43⋊C3semidirect
120. #732C3×C43⋊C3semidirect
130. C43#10624851semidirect

Maximal subgroups

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

subgroupindex
#237829053
#237828923
#237828453
#237827663
#237827653
#237827593
#237827583
#237827563
#237827553
#237827503
#237827493
#237827483
C43×#69133
#1062485143