Finite Group Databasebeta

← #44534629

Subgroups — #44534629

Order 31347.

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

normal subgroups only

This group has 178 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#23782907C311yesmaximal, characteristic, complemented
2#23782907C311yesmaximal, characteristic, complemented
3#23782894C311yesmaximal, characteristic, complemented
4#23782844C311yesmaximal, characteristic, complemented
5#23782766C311yesmaximal, characteristic, complemented
6#23782766C311yesmaximal, characteristic, complemented
7#23782762C311yesmaximal, characteristic, complemented
8#23782761C311yesmaximal, characteristic, complemented
9#23782757C311yesmaximal, characteristic, complemented
10#23782753C311yesmaximal, characteristic, complemented
11#23782749C311yesmaximal, characteristic, complemented
12#23782748C311yesmaximal, characteristic, complemented
13C43×#6882C311yesmaximal, characteristic, complemented
14#16812526—31no—
15#16812526—31no—
16C3×#11923956C3211yescharacteristic
173−1+2×C43⋊C3—31no—
18#16812515C3211yescharacteristic
19#16812515C3211yescharacteristic
20#16812515C3211yescharacteristic
21#16812515C3211yescharacteristic
22#16812514—31no—
23#16812514—31no—
24#16812513C3211yescharacteristic
25#16812513C3211yescharacteristic
26#16812511—31no—
27#16812511—31no—
28#16812508—31no—
29#16812508—31no—
30#16812500—31no—
31#16812499C3211yescharacteristic
32(C43⋊C9)⋊C9—31no—
33(C3×C43⋊C3)⋊C9—31no—
34C9×C43⋊C9C3211yescharacteristic
35C43×#733C3211yescharacteristic
36C43×#733C3211yescharacteristic
37C43×#733C3211yescharacteristic
38C43×C9⋊C9C3211yescharacteristic
39C32×C43⋊C3H(3,𝔽3)11yescharacteristic
40#11923958—31no—
41#11923958—31no—
42#11923958—31no—
43#11923958—31no—
44#11923957—91no—
45#11923957—91no—
46#11923957—91no—
47#11923956—91no—
48#11923956—91no—
49#11923956—91no—
50#11923956—91no—
51C32⋊(C43⋊C3)—31no—
52C32⋊(C43⋊C3)—31no—
53C3×C43⋊C9—31no—
54C3×C43⋊C9—31no—
55C3×C43⋊C9H(3,𝔽3)11yescharacteristic
56C3×C43⋊C9H(3,𝔽3)11yescharacteristic
57C9×C43⋊C3—91no—
58C9×C43⋊C3—91no—
59C9×C43⋊C3—91no—
603−1+2×C43—31no—
613−1+2×C43—31no—
623−1+2×C43—31no—
63C3×C9×C43—31no—
64C3×C9×C43C3311yescharacteristic
65#10624854—431nomaximal, Sylow
66C32×C43C3×H(3,𝔽3)11yescharacteristic
67C3×C43⋊C3—31no—
68C3×C43⋊C3—91no—
69C3×C43⋊C3—91no—
70C3×C43⋊C3—91no—
71C9×C43—31no—
72C9×C43—91no—
73C9×C43—91no—
74C9×C43—91no—
75C9×C43—91no—
76C43⋊C9—31no—
77C43⋊C9—31no—
78C43⋊C9—91no—
79C43⋊C9—91no—
80C43⋊C9—91no—
81C43⋊C9—91no—
82C43⋊C9—91no—
83C43⋊C9—91no—
84#6913—431no—
85#6913—431no—
86#6912—431no—
87#6899—431no—
88#6883—431no—
89#6883—431no—
90#6882—431no—
91#6882—431no—
92#6882C43⋊C311yescharacteristic, complemented
93#6881—431no—
94#6880—431no—
95#6878—431no—
96#6878—431no—
97C3×C43—31no—
98C3×C43#691111yescharacteristic
99C43⋊C3—91no—
100C43⋊C3—271no—
101C43⋊C3—271no—
102#737—1291no—
103#737—1291no—
104C3×3−1+2—431no—
105C3×3−1+2—1291no—
106#733—431no—
107#733—431no—
108#733—431no—
109#733—431no—
110#733—1291no—
111#733—1291no—
112#733C3×C43⋊C311yescharacteristic
113#733C3×C43⋊C311yescharacteristic
114#733C3×C43⋊C311yescharacteristic
115#732—431no—
116#732—431no—
117#731—1291no—
118#731—1291no—
119AΣL(1,𝔽27)—1291no—
120AΣL(1,𝔽27)—1291no—
121C9⋊C9—431no—
122C9⋊C9—1291no—
123C9⋊C9—1291no—
124C9⋊C9C3×C43⋊C311yescharacteristic
125C32⋊C9—1291no—
126C92—431no—
127C43#1062485411yescharacteristic, complemented, Sylow
128C33—431no—
1293−1+2—31no—
1303−1+2—31no—
1313−1+2—31no—
1323−1+2—1291no—
1333−1+2—1291no—
1343−1+2—1291no—
1353−1+2—1291no—
1363−1+2—3871no—
1373−1+2—3871no—
1383−1+2—3871no—
1393−1+2—3871no—
1403−1+2—3871no—
1413−1+2—3871no—
1423−1+2—3871no—
143H(3,𝔽3)—1291no—
144H(3,𝔽3)—1291no—
145C3×C9—31no—
146C3×C9—431no—
147C3×C9—431no—
148C3×C9—1291no—
149C3×C9—1291no—
150C3×C9—3871no—
151C3×C9—3871no—
152C3×C9—3871no—
153C3×C9C32×C43⋊C311yescharacteristic
154C32—1291no—
155C32—3871no—
156C32—3871no—
157C32—3871no—
158C32H(3,𝔽3)×C43⋊C311yescharacteristic
159C9—31no—
160C9—91no—
161C9—91no—
162C9—91no—
163C9—91no—
164C9—1291no—
165C9—1291no—
166C9—3871no—
167C9—3871no—
168C9—3871no—
169C9—3871no—
170C9—3871no—
171C9—3871no—
172C3—31no—
173C3—3871no—
174C3—11611no—
175C3—11611no—
176C3#2378289011yescharacteristic
subgroupG/H
centerC3#23782890
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6882C3
socleC3×C43#6911
hypercenter#6882C43⋊C3
hypocenterC43#10624854
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6882

Complements

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

NH ≅ G/Ntype
1. #23782907C3semidirect
2. #23782907C3semidirect
3. #23782894C3semidirect
4. #23782844C3semidirect
5. #23782766C3semidirect
6. #23782766C3semidirect
7. #23782762C3semidirect
8. #23782761C3semidirect
9. #23782757C3semidirect
10. #23782753C3semidirect
11. #23782749C3semidirect
12. #23782748C3semidirect
13. C43×#6882C3semidirect
92. #6882C43⋊C3semidirect
127. C43#10624854semidirect

Maximal subgroups

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

subgroupindex
#237829073
#237828943
#237828443
#237827663
#237827623
#237827613
#237827573
#237827533
#237827493
#237827483
C43×#68823
#1062485443