Finite Group Databasebeta

← #44534603

Subgroups — #44534603

Order 31347.

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

normal subgroups only

This group has 190 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#23782838C311yesmaximal, 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×C32⋊(C43⋊C3)—31no—
16#16812515C3211yescharacteristic, complemented
17#16812515C3211yescharacteristic, complemented
18#16812513—31no—
19#16812513—31no—
20#16812513C3211yescharacteristic
21#16812513C3211yescharacteristic
22#16812513C3211yescharacteristic
23#16812513C3211yescharacteristic, complemented
24#16812510—31no—
25#16812507—31no—
26#16812500C3211yescharacteristic, complemented
27#16812499C3211yescharacteristic, complemented
28(C43⋊C9)⋊C9—31no—
29(C43⋊C9)⋊C9—31no—
30C32⋊(C43⋊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#11923957—91no—
43#11923956—91no—
44C32⋊(C43⋊C3)—31no—
45C32⋊(C43⋊C3)—31no—
46C32⋊(C43⋊C3)—31no—
47C32⋊(C43⋊C3)—31no—
48C32⋊(C43⋊C3)—92no—
49C3×C43⋊C9—31no—
50C3×C43⋊C9—31no—
51C3×C43⋊C9—31no—
52C9×C43⋊C3—91no—
53C33×C43H(3,𝔽3)11yescharacteristic
543−1+2×C43—31no—
553−1+2×C43—31no—
563−1+2×C43—91no—
573−1+2×C43—92no—
58H(3,𝔽3)×C43—31no—
59C3×C9×C43—91no—
60C3×C9×C43H(3,𝔽3)11yescharacteristic
61C3×C9×C43H(3,𝔽3)11yescharacteristic
62C3×C9×C43C3311yescharacteristic
63#10624853—431nomaximal, Sylow
64C32×C43—31no—
65C32×C43—91no—
66C32×C43—91no—
67C32×C43C3×H(3,𝔽3)11yescharacteristic
68C3×C43⋊C3—91no—
69C3×C43⋊C3—91no—
70C3×C43⋊C3—91no—
71C3×C43⋊C3—91no—
72C3×C43⋊C3—273no—
73C9×C43—31no—
74C9×C43—31no—
75C9×C43—31no—
76C9×C43—91no—
77C9×C43—91no—
78C43⋊C9—91no—
79C43⋊C9—91no—
80C43⋊C9—91no—
81C43⋊C9—91no—
82C43⋊C9—91no—
83#6913—431no—
84#6913C43⋊C311yescharacteristic, complemented
85#6911—431no—
86#6899—431no—
87#6883—431no—
88#6883—431no—
89#6881—431no—
90#6881—431no—
91#6881—431no—
92#6881—431no—
93#6879—431no—
94#6878—431no—
95#6878—431no—
96C3×C43—31no—
97C3×C43—91no—
98C3×C43—271no—
99C3×C43#691111yescharacteristic
100C43⋊C3—271no—
101C43⋊C3—271no—
102C43⋊C3—271no—
103C43⋊C3—271no—
104#737—31no—
105#737—1291no—
106C3×3−1+2C3×C43⋊C311yescharacteristic
107C3×H(3,𝔽3)—1291no—
108#733—431no—
109#733—431no—
110#733C3×C43⋊C311yescharacteristic, complemented
111#733C3×C43⋊C311yescharacteristic, complemented
112#732—431no—
113#732—431no—
114#732—431no—
115#732—431no—
116#732—1291no—
117#732—1291no—
118#732C3×C43⋊C311yescharacteristic, complemented
119#731—31no—
120#731—1291no—
121AΣL(1,𝔽27)—31no—
122AΣL(1,𝔽27)—1291no—
123C9⋊C9—431no—
124C9⋊C9—431no—
125C9⋊C9—1291no—
126C9⋊C9—1291no—
127C32⋊C9—1291no—
128C92—431no—
129C43#1062485311yescharacteristic, complemented, Sylow
130C33—3871no—
131C33C32⋊(C43⋊C3)11yescharacteristic
1323−1+2—31no—
1333−1+2—31no—
1343−1+2—91no—
1353−1+2—92no—
1363−1+2—1291no—
1373−1+2—1291no—
1383−1+2—3871no—
1393−1+2—3871no—
140H(3,𝔽3)—31no—
141H(3,𝔽3)—1291no—
142H(3,𝔽3)—1291no—
143H(3,𝔽3)—1291no—
144H(3,𝔽3)—1291no—
145H(3,𝔽3)—3872no—
146C3×C9—91no—
147C3×C9—1291no—
148C3×C9—1291no—
149C3×C9—1291no—
150C3×C9—3871no—
151C3×C9C32⋊(C43⋊C3)11yescharacteristic
152C3×C9C32⋊(C43⋊C3)11yescharacteristic
153C3×C9C32×C43⋊C311yescharacteristic
154C32—31no—
155C32—91no—
156C32—91no—
157C32—3871no—
158C32—3871no—
159C32—3871no—
160C32—3871no—
161C32—11613no—
162C32C3×C32⋊(C43⋊C3)11yescharacteristic
163C9—31no—
164C9—31no—
165C9—31no—
166C9—91no—
167C9—91no—
168C9—3871no—
169C9—3871no—
170C9—3871no—
171C9—3871no—
172C9—3871no—
173C3—31no—
174C3—91no—
175C3—271no—
176C3—11611no—
177C3—11611no—
178C3—11611no—
179C3—11611no—
180C3#2378289111yescharacteristic
subgroupG/H
centerC3#23782891
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6913C3
socleC3×C43#6911
hypercenter#6913C43⋊C3
hypocenterC43#10624853
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. #23782838C3semidirect
4. #23782766C3semidirect
5. #23782765C3semidirect
6. #23782759C3semidirect
7. #23782758C3semidirect
8. #23782756C3semidirect
9. #23782755C3semidirect
10. #23782750C3semidirect
11. #23782749C3semidirect
12. #23782748C3semidirect
13. C43×#6913C3semidirect
16. #16812515C32semidirect
17. #16812515C32semidirect
23. #16812513C32semidirect
26. #16812500C32semidirect
27. #16812499C32semidirect
31. C9×C43⋊C9C32semidirect
34. C43×#733C32semidirect
35. C43×#733C32semidirect
36. C43×#732C32semidirect
84. #6913C43⋊C3semidirect
110. #733C3×C43⋊C3semidirect
111. #733C3×C43⋊C3semidirect
118. #732C3×C43⋊C3semidirect
129. C43#10624853semidirect

Maximal subgroups

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

subgroupindex
#237829053
#237828923
#237828383
#237827663
#237827653
#237827593
#237827583
#237827563
#237827553
#237827503
#237827493
#237827483
C43×#69133
#1062485343