Finite Group Databasebeta

← #44533731

Subgroups — #44533731

Order 31347.

488 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 61 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#23782923C311yesmaximal, characteristic, complemented
2#23782892C311yesmaximal, characteristic, complemented
3#23782887C312yesmaximal, complemented
4#23782883C312yesmaximal, complemented
5#23782881C312yesmaximal, complemented
6C3×#16812508C312yesmaximal, complemented
7#23782795C311yesmaximal, characteristic, complemented
8(C3×C43⋊C3)⋊H(3,𝔽3)C311yesmaximal, characteristic, complemented
9C43×#6910C311yesmaximal, characteristic, complemented
10C33×C43⋊C3C3211yescharacteristic
11#16812526—36no—
12#16812525—33no—
13C3×#11923958C3212yes—
14C3×#11923958C3212yes—
153−1+2×C43⋊C3—33no—
16C3×C32⋊(C43⋊C3)—33no—
17C3×C32⋊(C43⋊C3)C3211yescharacteristic
18C3×C32⋊(C43⋊C3)C3212yes—
19C3×C32⋊(C43⋊C3)C3211yescharacteristic
20#16812513—33no—
21#16812510—36no—
22#16812508—36no—
23#16812508—36no—
24#16812506—36no—
25(C3×C43⋊C3)⋊C9—33no—
26C3×3−1+2×C43C3212yes—
27C3×3−1+2×C43C3211yescharacteristic
28C3×H(3,𝔽3)×C43C3211yescharacteristic
29C43×#731—33no—
30C32×C43⋊C3—31no—
31C32×C43⋊C3—31no—
32C32×C43⋊C3—32no—
33C32×C43⋊C3—31no—
34C32×C43⋊C3—32no—
35C32×C43⋊C3—93no—
36C32×C43⋊C3H(3,𝔽3)13yes—
37#11923958—32no—
38#11923958—32no—
39#11923958—32no—
40#11923958—32no—
41#11923958—32no—
42#11923958H(3,𝔽3)16yescomplemented
43#11923957—39no—
44#11923956—39no—
45C32⋊(C43⋊C3)—31no—
46C32⋊(C43⋊C3)—32no—
47C32⋊(C43⋊C3)—32no—
48C32⋊(C43⋊C3)—32no—
49C32⋊(C43⋊C3)—32no—
50C32⋊(C43⋊C3)—31no—
51C32⋊(C43⋊C3)—32no—
52C32⋊(C43⋊C3)—99no—
53C3×C43⋊C9—32no—
54C3×C43⋊C9—32no—
55C9×C43⋊C3—39no—
56C33×C43—31no—
57C33×C43C3311yescharacteristic
583−1+2×C43—31no—
593−1+2×C43—32no—
603−1+2×C43—32no—
613−1+2×C43—32no—
623−1+2×C43—32no—
63H(3,𝔽3)×C43—31no—
64H(3,𝔽3)×C43—32no—
65C3×C9×C43—32no—
66C3×C9×C43H(3,𝔽3)13yescomplemented
67#10624749—431nomaximal, Sylow
68C32×C43—91no—
69C32×C43—93no—
70C32×C43—91no—
71C32×C43C3×H(3,𝔽3)12yes—
72C32×C43C3×H(3,𝔽3)11yescharacteristic
73C32×C43C3×H(3,𝔽3)11yescharacteristic
74C3×C43⋊C3—33no—
75C3×C43⋊C3—33no—
76C3×C43⋊C3—33no—
77C3×C43⋊C3—92no—
78C3×C43⋊C3—92no—
79C3×C43⋊C3—91no—
80C3×C43⋊C3—96no—
81C3×C43⋊C3—93no—
82C3×C43⋊C3—93no—
83C3×C43⋊C3—91no—
84C3×C43⋊C3—92no—
85C3×C43⋊C3—272no—
86C9×C43—33no—
87C9×C43—92no—
88C43⋊C9—36no—
89C43⋊C9—92no—
903−1+4—431no—
91#6911—431no—
92#6910—432no—
93#6910C43⋊C311yescharacteristic, complemented
94#6909—432no—
95#6909—432no—
96C3×AΣL(1,𝔽27)—432no—
97#6891—431no—
98C32⋊H(3,𝔽3)—431no—
99C3×C43—31no—
100C3×C43—31no—
101C3×C43—32no—
102C3×C43—271no—
103C3×C43C32⋊H(3,𝔽3)11yescharacteristic
104C43⋊C3—93no—
105C43⋊C3—93no—
106C43⋊C3—271no—
107C43⋊C3—272no—
108C34—431no—
109#737—1296no—
110#737—1293no—
111C3×3−1+2—432no—
112C3×3−1+2—432no—
113C3×3−1+2—1293no—
114C3×3−1+2C3×C43⋊C312yes—
115C3×3−1+2C3×C43⋊C311yescharacteristic
116C3×H(3,𝔽3)—431no—
117C3×H(3,𝔽3)—431no—
118C3×H(3,𝔽3)—432no—
119C3×H(3,𝔽3)—1293no—
120C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
121#732—1293no—
122#731—33no—
123#731—1296no—
124AΣL(1,𝔽27)—1296no—
125AΣL(1,𝔽27)—1296no—
126AΣL(1,𝔽27)—1296no—
127C32⋊C9—1293no—
128C43#1062474911yescharacteristic, complemented, Sylow
129C33—31no—
130C33—433no—
131C33—1291no—
132C33—1291no—
133C33—1292no—
134C33—1291no—
135C33—1292no—
136C33—3873no—
137C33C32×C43⋊C311yescharacteristic
1383−1+2—31no—
1393−1+2—32no—
1403−1+2—32no—
1413−1+2—32no—
1423−1+2—32no—
1433−1+2—436no—
1443−1+2—1299no—
1453−1+2—1299no—
1463−1+2—1292no—
1473−1+2—1292no—
1483−1+2—1292no—
1493−1+2—1292no—
1503−1+2—1292no—
151H(3,𝔽3)—32no—
152H(3,𝔽3)—31no—
153H(3,𝔽3)—1292no—
154H(3,𝔽3)—1291no—
155H(3,𝔽3)—1292no—
156H(3,𝔽3)—1292no—
157H(3,𝔽3)—1292no—
158H(3,𝔽3)—1291no—
159H(3,𝔽3)—1292no—
160H(3,𝔽3)—3879no—
161C3×C9—32no—
162C3×C9—1299no—
163C3×C9—1292no—
164C3×C9—1292no—
165C3×C9C32⋊(C43⋊C3)13yescomplemented
166C32—91no—
167C32—93no—
168C32—91no—
169C32—1293no—
170C32—1293no—
171C32—1293no—
172C32—3873no—
173C32—3876no—
174C32—3872no—
175C32—3872no—
176C32—3873no—
177C32—3871no—
178C32—3871no—
179C32—3872no—
180C32—11612no—
181C32H(3,𝔽3)×C43⋊C312yes—
182C32H(3,𝔽3)×C43⋊C311yescharacteristic
183C32C3×C32⋊(C43⋊C3)11yescharacteristic
184C9—33no—
185C9—92no—
186C9—1296no—
187C9—3872no—
188C3—31no—
189C3—31no—
190C3—32no—
191C3—271no—
192C3—3873no—
193C3—3873no—
194C3—11611no—
195C3—11612no—
196C3(C3×C43⋊C3)⋊H(3,𝔽3)11yescharacteristic
subgroupG/H
centerC3(C3×C43⋊C3)⋊H(3,𝔽3)
commutator, cosocleC33×C43C33
FrattiniC33C32×C43⋊C3
FittingC43×#6910C3
socleC3×C43C32⋊H(3,𝔽3)
hypercenter#6910C43⋊C3
hypocenterC43#10624749
LCSG ▷ C33×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C33 ◁ #6910

Complements

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

NH ≅ G/Ntype
1. #23782923C3semidirect
2. #23782892C3semidirect
3. #23782887C3semidirect
4. #23782883C3semidirect
5. #23782881C3semidirect
6. C3×#16812508C3semidirect
7. #23782795C3semidirect
8. (C3×C43⋊C3)⋊H(3,𝔽3)C3semidirect
9. C43×#6910C3semidirect
42. #11923958H(3,𝔽3)semidirect
66. C3×C9×C43H(3,𝔽3)semidirect
93. #6910C43⋊C3semidirect
128. C43#10624749semidirect
165. 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
#237829233
#237828923
#237828873
#237828833
#237828813
C3×#168125083
#237827953
(C3×C43⋊C3)⋊H(3,𝔽3)3
C43×#69103
#1062474943