Finite Group Databasebeta

← C43⋊C3×#6911 #44535308

Subgroups — C43⋊C3×#6911 #44535308

Order 31347.

1304 conjugacy classes of subgroups; only the 271 normal subgroups are shown.

normal subgroups only

This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 271 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
1C3×3−1+2×C43⋊C3C311yesmaximal, characteristic, complemented
2C3×H(3,𝔽3)×C43⋊C3C313yesmaximal, complemented
3#23782892C312yesmaximal, complemented
4#23782891C316yesmaximal, complemented
5#23782890C319yesmaximal, complemented
6#23782889C319yesmaximal, complemented
7#732×C43⋊C3C319yesmaximal, complemented
8C43×#6911C311yesmaximal, characteristic, complemented
9C33×C43⋊C3—33no—
10C33×C43⋊C3C3211yescharacteristic
11C3×#11923958C3212yescomplemented
12C3×#11923957C3213yescomplemented
13C3×#11923956C3213yescomplemented
143−1+2×C43⋊C3—33no—
153−1+2×C43⋊C3—36no—
16C3×C32⋊(C43⋊C3)—36no—
17C3×C32⋊(C43⋊C3)C3216yescomplemented
18H(3,𝔽3)×C43⋊C3—36no—
19H(3,𝔽3)×C43⋊C3—36no—
20H(3,𝔽3)×C43⋊C3—36no—
21H(3,𝔽3)×C43⋊C3C3219yescomplemented
22H(3,𝔽3)×C43⋊C3C3219yescomplemented
23H(3,𝔽3)×C43⋊C3C3219yescomplemented
24C3×C9×C43⋊C3C3213yescomplemented
25#16812513C32118yescomplemented
26#16812512C32154yescomplemented
27C3×3−1+2×C43C3211yescharacteristic, complemented
28C3×H(3,𝔽3)×C43C3213yescomplemented
29C43×#732C3219yescomplemented
30C32×C43⋊C3—36no—
31C32×C43⋊C3—39no—
32C32×C43⋊C3—39no—
33C32×C43⋊C3—39no—
34C32×C43⋊C3—93no—
35C32×C43⋊C3—927no—
36C32×C43⋊C3H(3,𝔽3)13yes—
37C32×C43⋊C3H(3,𝔽3)16yes—
38C32×C43⋊C3C3311yescharacteristic
39C32×C43⋊C3C3311yescharacteristic
40C32×C43⋊C3C3311yescharacteristic
41#11923958—36no—
42#11923957—39no—
43#11923956—39no—
44C32⋊(C43⋊C3)—312no—
45C32⋊(C43⋊C3)—318no—
46C32⋊(C43⋊C3)—318no—
47C32⋊(C43⋊C3)—318no—
48C32⋊(C43⋊C3)C33118yescomplemented
49C3×C43⋊C9C3316yescomplemented
50C9×C43⋊C3—36no—
51C9×C43⋊C3—33no—
52C33×C43—33no—
53C33×C43C3311yescharacteristic
543−1+2×C43—33no—
55H(3,𝔽3)×C43—36no—
56H(3,𝔽3)×C43C3319yescomplemented
57C3×C9×C43C3313yescomplemented
58C3×#6911—431nomaximal, Sylow
59C32×C43—39no—
60C32×C43—91no—
61C32×C43—99no—
62C32×C43C3×H(3,𝔽3)13yes—
63C32×C43C3411yescharacteristic
64C3×C43⋊C3—39no—
65C3×C43⋊C3—33no—
66C3×C43⋊C3—318no—
67C3×C43⋊C3—96no—
68C3×C43⋊C3—91no—
69C3×C43⋊C3—91no—
70C3×C43⋊C3—927no—
71C3×C43⋊C3—927no—
72C3×C43⋊C3—918no—
73C3×C43⋊C3—927no—
74C3×C43⋊C3C3×H(3,𝔽3)12yes—
75C3×C43⋊C3C3×H(3,𝔽3)13yes—
76C3×C43⋊C3C3×H(3,𝔽3)13yes—
77C3×C43⋊C3C3×H(3,𝔽3)11yescharacteristic
78C9×C43—33no—
79C43⋊C9—36no—
80C32×3−1+2—431no—
81C32×H(3,𝔽3)—433no—
82#6911—432no—
83#6911—436no—
84#6911—439no—
85#6911—439no—
86#6911C43⋊C311yescharacteristic, direct product factor
87C3×#732—439no—
88C3×C43—33no—
89C3×C43—31no—
90C3×C43—99no—
91C3×C43C32×H(3,𝔽3)11yescharacteristic
92C43⋊C3—33no—
93C43⋊C3—33no—
94C43⋊C3—32no—
95C43⋊C3—918no—
96C43⋊C3#691113yesdirect product factor
97C34—431no—
98C34—1293no—
99C3×3−1+2—432no—
100C3×3−1+2—433no—
101C3×3−1+2—433no—
102C3×3−1+2—1293no—
103C3×3−1+2—1296no—
104C3×3−1+2C3×C43⋊C311yescharacteristic, complemented
105C3×H(3,𝔽3)—436no—
106C3×H(3,𝔽3)—439no—
107C3×H(3,𝔽3)—439no—
108C3×H(3,𝔽3)—439no—
109C3×H(3,𝔽3)—1296no—
110C3×H(3,𝔽3)—1296no—
111C3×H(3,𝔽3)—1296no—
112C3×H(3,𝔽3)—1296no—
113C3×H(3,𝔽3)C3×C43⋊C313yescomplemented
114C32×C9—433no—
115#732—4354no—
116#732—4318no—
117#732C3×C43⋊C319yescomplemented
118C43C3×#691111yescharacteristic, complemented, Sylow
119C33—33no—
120C33—433no—
121C33—431no—
122C33—436no—
123C33—431no—
124C33—431no—
125C33—1299no—
126C33—1299no—
127C33—1299no—
128C33—1296no—
129C33—3873no—
130C33—38727no—
131C33C32×C43⋊C311yescharacteristic
1323−1+2—33no—
1333−1+2—1299no—
1343−1+2—1299no—
1353−1+2—1296no—
136H(3,𝔽3)—36no—
137H(3,𝔽3)—4318no—
138H(3,𝔽3)—12918no—
139H(3,𝔽3)—12918no—
140H(3,𝔽3)—12918no—
141H(3,𝔽3)—12912no—
142H(3,𝔽3)C32×C43⋊C319yescomplemented
143C3×C9—436no—
144C3×C9—1293no—
145C3×C9—1296no—
146C3×C9C32×C43⋊C313yescomplemented
147C32—39no—
148C32—91no—
149C32—99no—
150C32—431no—
151C32—432no—
152C32—433no—
153C32—433no—
154C32—1293no—
155C32—1299no—
156C32—12918no—
157C32—3876no—
158C32—3871no—
159C32—3871no—
160C32—38718no—
161C32—38727no—
162C32—38727no—
163C32—38727no—
164C32H(3,𝔽3)×C43⋊C313yes—
165C32C33×C43⋊C311yescharacteristic
166C9—33no—
167C9—1296no—
168C3—33no—
169C3—31no—
170C3—99no—
171C3—433no—
172C3—1292no—
173C3—1293no—
174C3—1293no—
175C3—38718no—
176C3C3×H(3,𝔽3)×C43⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C43⋊C3
commutator, cosocleC32×C43C34
FrattiniC32C33×C43⋊C3
FittingC43×#6911C3
socleC3×C43C32×H(3,𝔽3)
hypercenter#6911C43⋊C3
hypocenterC43C3×#6911
LCSG ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C33 ◁ #6911

Complements

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

NH ≅ G/Ntype
1. C3×3−1+2×C43⋊C3C3semidirect
2. C3×H(3,𝔽3)×C43⋊C3C3semidirect
3. #23782892C3semidirect
4. #23782891C3semidirect
5. #23782890C3semidirect
6. #23782889C3semidirect
7. #732×C43⋊C3C3semidirect
8. C43×#6911C3semidirect
11. C3×#11923958C32semidirect
12. C3×#11923957C32semidirect
13. C3×#11923956C32semidirect
17. C3×C32⋊(C43⋊C3)C32semidirect
21. H(3,𝔽3)×C43⋊C3C32semidirect
22. H(3,𝔽3)×C43⋊C3C32semidirect
23. H(3,𝔽3)×C43⋊C3C32semidirect
24. C3×C9×C43⋊C3C32semidirect
25. #16812513C32semidirect
26. #16812512C32semidirect
27. C3×3−1+2×C43C32semidirect
28. C3×H(3,𝔽3)×C43C32semidirect
29. C43×#732C32semidirect
48. C32⋊(C43⋊C3)C33semidirect
49. C3×C43⋊C9C33semidirect
56. H(3,𝔽3)×C43C33semidirect
57. C3×C9×C43C33semidirect
86. #6911C43⋊C3direct (N × H)
96. C43⋊C3#6911direct (N × H)
104. C3×3−1+2C3×C43⋊C3semidirect
113. C3×H(3,𝔽3)C3×C43⋊C3semidirect
117. #732C3×C43⋊C3semidirect
118. C43C3×#6911semidirect
142. H(3,𝔽3)C32×C43⋊C3semidirect
146. C3×C9C32×C43⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×3−1+2×C43⋊C33
C3×H(3,𝔽3)×C43⋊C33
#237828923
#237828913
#237828903
#237828893
#732×C43⋊C33
C43×#69113
C3×#691143