Finite Group Databasebeta

← #44533734

Subgroups — #44533734

Order 31347.

488 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 70 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#23782892C311yesmaximal, characteristic, complemented
2#23782888C312yesmaximal, complemented
3#23782887C311yesmaximal, characteristic, complemented
4#23782883C312yesmaximal, complemented
5#23782882C312yesmaximal, complemented
6C3×#16812508C312yesmaximal, complemented
7#23782795C311yesmaximal, characteristic, complemented
8(C3×C43⋊C3)⋊H(3,𝔽3)C311yesmaximal, characteristic, complemented
9C43×3−1+4C311yesmaximal, characteristic, complemented
10C33×C43⋊C3C3211yescharacteristic
11C3×#11923958C3212yes—
12C3×#11923958C3212yes—
13C3×C32⋊(C43⋊C3)—33no—
14C3×C32⋊(C43⋊C3)C3211yescharacteristic
15C3×C32⋊(C43⋊C3)C3211yescharacteristic
16C3×C32⋊(C43⋊C3)C3212yes—
17#16812513—33no—
18#16812511—36no—
19#16812510—33no—
20#16812508—36no—
21#16812508—36no—
22#16812507—36no—
23(C3×C43⋊C3)⋊C9—33no—
24C43×#737—36no—
25C43×#737—33no—
26C3×3−1+2×C43—33no—
27C3×3−1+2×C43C3212yes—
28C3×3−1+2×C43C3211yescharacteristic
29C3×H(3,𝔽3)×C43C3211yescharacteristic
30C32×C43⋊C3—31no—
31C32×C43⋊C3—31no—
32C32×C43⋊C3—32no—
33C32×C43⋊C3—31no—
34C32×C43⋊C3—31no—
35C32×C43⋊C3—32no—
36C32×C43⋊C3—93no—
37#11923958—32no—
38#11923958—32no—
39#11923958—32no—
40#11923958—32no—
41#11923958—32no—
42#11923958—32no—
43C32⋊(C43⋊C3)—32no—
44C32⋊(C43⋊C3)—32no—
45C32⋊(C43⋊C3)—32no—
46C32⋊(C43⋊C3)—31no—
47C32⋊(C43⋊C3)—32no—
48C32⋊(C43⋊C3)—31no—
49C32⋊(C43⋊C3)—32no—
50C32⋊(C43⋊C3)—99no—
51C3×C43⋊C9—32no—
52C3×C43⋊C9—32no—
53C33×C43H(3,𝔽3)13yes—
54C33×C43C3311yescharacteristic
553−1+2×C43—318no—
563−1+2×C43—32no—
573−1+2×C43—31no—
583−1+2×C43—32no—
593−1+2×C43—32no—
603−1+2×C43H(3,𝔽3)16yescomplemented
61H(3,𝔽3)×C43—32no—
62H(3,𝔽3)×C43—31no—
63C3×C9×C43—39no—
64C3×C9×C43—32no—
65C3×C9×C43H(3,𝔽3)13yescomplemented
66#10624749—431nomaximal, Sylow
67C32×C43—33no—
68C32×C43—91no—
69C32×C43—93no—
70C32×C43C3×H(3,𝔽3)12yes—
71C32×C43C3×H(3,𝔽3)11yescharacteristic
72C32×C43C3×H(3,𝔽3)11yescharacteristic
73C3×C43⋊C3—33no—
74C3×C43⋊C3—33no—
75C3×C43⋊C3—92no—
76C3×C43⋊C3—92no—
77C3×C43⋊C3—91no—
78C3×C43⋊C3—96no—
79C3×C43⋊C3—93no—
80C3×C43⋊C3—93no—
81C3×C43⋊C3—91no—
82C3×C43⋊C3—91no—
83C3×C43⋊C3—92no—
84C3×C43⋊C3—272no—
85C9×C43—36no—
86C9×C43—33no—
87C43⋊C9—92no—
88C43⋊C9—92no—
893−1+4C43⋊C311yescharacteristic, complemented
90#6911—431no—
91#6910—431no—
92#6910—432no—
93#6909—432no—
94#6909—432no—
95C3×AΣL(1,𝔽27)—432no—
96#6891—431no—
97C32⋊H(3,𝔽3)—431no—
98C3×C43—31no—
99C3×C43—31no—
100C3×C43—32no—
101C3×C43—93no—
102C3×C43C32⋊H(3,𝔽3)11yescharacteristic
103C43⋊C3—93no—
104C43⋊C3—271no—
105C43⋊C3—271no—
106C43⋊C3—272no—
107C34—431no—
108#737—36no—
109#737—33no—
110C3×3−1+2—33no—
111C3×3−1+2—432no—
112C3×3−1+2—432no—
113C3×3−1+2C3×C43⋊C312yes—
114C3×3−1+2C3×C43⋊C311yescharacteristic
115C3×H(3,𝔽3)—431no—
116C3×H(3,𝔽3)—431no—
117C3×H(3,𝔽3)—432no—
118C3×H(3,𝔽3)—1293no—
119C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
120#732—1293no—
121#731—1296no—
122#731—1293no—
123AΣL(1,𝔽27)—1296no—
124AΣL(1,𝔽27)—1296no—
125AΣL(1,𝔽27)—1296no—
126C32⋊C9—1293no—
127C43#1062474911yescharacteristic, complemented, Sylow
128C33—1291no—
129C33—1291no—
130C33—1292no—
131C33—1291no—
132C33—1291no—
133C33—1292no—
134C33—3873no—
135C33C32⋊(C43⋊C3)13yes—
136C33C32×C43⋊C311yescharacteristic
1373−1+2—318no—
1383−1+2—32no—
1393−1+2—31no—
1403−1+2—32no—
1413−1+2—32no—
1423−1+2—1292no—
1433−1+2—1292no—
1443−1+2—1292no—
1453−1+2—1292no—
1463−1+2—1292no—
1473−1+2—1292no—
1483−1+2C32⋊(C43⋊C3)16yescomplemented
149H(3,𝔽3)—32no—
150H(3,𝔽3)—31no—
151H(3,𝔽3)—1292no—
152H(3,𝔽3)—1292no—
153H(3,𝔽3)—1292no—
154H(3,𝔽3)—1292no—
155H(3,𝔽3)—1291no—
156H(3,𝔽3)—1291no—
157H(3,𝔽3)—1292no—
158H(3,𝔽3)—3879no—
159C3×C9—39no—
160C3×C9—32no—
161C3×C9—1292no—
162C3×C9—1292no—
163C3×C9C32⋊(C43⋊C3)13yescomplemented
164C32—33no—
165C32—91no—
166C32—93no—
167C32—1293no—
168C32—1293no—
169C32—3876no—
170C32—3872no—
171C32—3872no—
172C32—3873no—
173C32—3873no—
174C32—3871no—
175C32—3871no—
176C32—3871no—
177C32—3872no—
178C32—11612no—
179C32C3×C32⋊(C43⋊C3)12yes—
180C32C3×C32⋊(C43⋊C3)11yescharacteristic
181C32C3×C32⋊(C43⋊C3)11yescharacteristic
182C9—36no—
183C9—33no—
184C9—3872no—
185C9—3872no—
186C3—31no—
187C3—31no—
188C3—32no—
189C3—93no—
190C3—3873no—
191C3—11611no—
192C3—11611no—
193C3—11612no—
194C3#2378279411yescharacteristic
subgroupG/H
centerC3#23782794
commutator, cosocleC33×C43C33
FrattiniC33C32×C43⋊C3
FittingC43×3−1+4C3
socleC3×C43C32⋊H(3,𝔽3)
hypercenter3−1+4C43⋊C3
hypocenterC43#10624749
LCSG ▷ C33×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C33 ◁ 3−1+4

Complements

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

NH ≅ G/Ntype
1. #23782892C3semidirect
2. #23782888C3semidirect
3. #23782887C3semidirect
4. #23782883C3semidirect
5. #23782882C3semidirect
6. C3×#16812508C3semidirect
7. #23782795C3semidirect
8. (C3×C43⋊C3)⋊H(3,𝔽3)C3semidirect
9. C43×3−1+4C3semidirect
60. 3−1+2×C43H(3,𝔽3)semidirect
65. C3×C9×C43H(3,𝔽3)semidirect
89. 3−1+4C43⋊C3semidirect
127. C43#10624749semidirect
148. 3−1+2C32⋊(C43⋊C3)semidirect
163. C3×C9C32⋊(C43⋊C3)semidirect

Maximal subgroups

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

subgroupindex
#237828923
#237828883
#237828873
#237828833
#237828823
C3×#168125083
#237827953
(C3×C43⋊C3)⋊H(3,𝔽3)3
C43×3−1+43
#1062474943