Finite Group Databasebeta

← #44535097

Subgroups — #44535097

Order 31347.

644 conjugacy classes of subgroups; only the 256 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 256 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#23782834C314yesmaximal, complemented
2#23782834C314yesmaximal, complemented
3#23782832C314yesmaximal, complemented
4#23782832C314yesmaximal, complemented
5#23782831C311yesmaximal, characteristic, complemented
6#23782814C314yesmaximal, complemented
7#23782814C314yesmaximal, complemented
8#23782811C314yesmaximal, complemented
9#23782797C312yesmaximal
10C9×#11923957C312yesmaximal, complemented
11#11923957⋊C9C314yesmaximal, complemented
12C32⋊C9×C43⋊C3C312yesmaximal
13C43×#6898C311yesmaximal, characteristic, complemented
14C33×C43⋊C3C3211yescharacteristic
15C3×#11923957C3214yes—
16C3×#11923957C3212yes—
17C3×C9×C43⋊C3C3214yes—
18C3×C9×C43⋊C3C3212yes—
19#16812500C3214yescomplemented
20#16812500C3214yescomplemented
21#16812499C3214yescomplemented
22#16812499C3214yescomplemented
23(C43⋊C9)⋊C9C3214yescomplemented
24(C43⋊C9)⋊C9C3214yescomplemented
25(C43⋊C9)⋊C9C3214yescomplemented
26(C43⋊C9)⋊C9C3214yescomplemented
27(C43⋊C9)⋊C9C3214yescomplemented
28(C43⋊C9)⋊C9C3214yescomplemented
29(C43⋊C9)⋊C9C3214yescomplemented
30(C43⋊C9)⋊C9C3214yescomplemented
31(C43⋊C9)⋊C9C3214yescomplemented
32(C43⋊C9)⋊C9C3214yescomplemented
33(C43⋊C9)⋊C9C3214yescomplemented
34(C43⋊C9)⋊C9C3214yescomplemented
35C32⋊(C43⋊C9)C3214yes—
36C32⋊(C43⋊C9)C3214yes—
37(C3×C43⋊C3)⋊C9C3212yes—
38(C3×C43⋊C3)⋊C9C3214yes—
39(C3×C43⋊C3)⋊C9C3212yes—
40(C3×C43⋊C3)⋊C9C3214yes—
41(C3×C43⋊C3)⋊C9C3214yes—
42(C3×C43⋊C3)⋊C9C3212yes—
43(C3×C43⋊C3)⋊C9C3212yes—
44(C3×C43⋊C3)⋊C9C3214yes—
45C9×C43⋊C9C3214yescomplemented
46C9×C43⋊C9C3214yescomplemented
47C43×C9⋊C9C3214yescomplemented
48C43×C9⋊C9C3214yescomplemented
49C43×C32⋊C9C3212yes—
50C43×C32⋊C9C3212yes—
51C92×C43C3211yescharacteristic, complemented
52C32×C43⋊C3—36no—
53C32×C43⋊C3—92no—
54C32×C43⋊C3C3311yescharacteristic
55C32×C43⋊C3C3312yes—
56#11923957—312no—
57#11923957—36no—
58C3×C43⋊C9C3314yes—
59C3×C43⋊C9C3314yes—
60C3×C43⋊C9C3314yes—
61C3×C43⋊C9C3314yes—
62C3×C43⋊C9C3314yes—
63C3×C43⋊C9C3314yes—
64C9×C43⋊C3—94no—
65C9×C43⋊C3—92no—
66C33×C43C3311yescharacteristic
67C3×C9×C43C3312yes—
68C3×C9×C43C3312yes—
69C3×C9×C43C3314yes—
70C3×C9×C43C3314yes—
71#10624906—431nomaximal, Sylow
72C32×C43—32no—
73C32×C43—32no—
74C32×C43C3411yescharacteristic
75C3×C43⋊C3—32no—
76C3×C43⋊C3—32no—
77C3×C43⋊C3—32no—
78C3×C43⋊C3—32no—
79C3×C43⋊C3—32no—
80C3×C43⋊C3—99no—
81C3×C43⋊C3#73716yes—
82C9×C43—32no—
83C9×C43—34no—
84C9×C43—32no—
85C9×C43—34no—
86C43⋊C9—34no—
87C43⋊C9—34no—
88C43⋊C9—34no—
89C43⋊C9—34no—
90C43⋊C9—34no—
91C43⋊C9—34no—
92#6898—434no—
93#6898—434no—
94#6898C43⋊C311yescharacteristic, complemented
95#6897—434no—
96#6897—434no—
97#6897—431no—
98#6894—434no—
99#6894—434no—
100#6894—434no—
101#6891—432no—
102C9×3−1+2—434no—
103C9×3−1+2—432no—
104C3×C32⋊C9—432no—
105C3×C43—91no—
106C3×C43C3×#73712yes—
107C3×C433−1+412yes—
108C43⋊C3—36no—
109C43⋊C3—91no—
110C34—431no—
111C3×3−1+2—434no—
112C3×3−1+2—432no—
113C32×C9—434no—
114C32×C9—432no—
115C9⋊C9—434no—
116C9⋊C9—434no—
117C9⋊C9—434no—
118C9⋊C9—434no—
119C9⋊C9—434no—
120C9⋊C9—434no—
121C9⋊C9—434no—
122C9⋊C9—434no—
123C9⋊C9—434no—
124C9⋊C9—434no—
125C9⋊C9—434no—
126C9⋊C9—434no—
127C9⋊C9—434no—
128C9⋊C9—434no—
129C9⋊C9—434no—
130C9⋊C9—434no—
131C9⋊C9C3×C43⋊C314yescomplemented
132C9⋊C9C3×C43⋊C314yescomplemented
133C32⋊C9—434no—
134C32⋊C9—434no—
135C32⋊C9—432no—
136C32⋊C9—434no—
137C32⋊C9—434no—
138C32⋊C9—432no—
139C32⋊C9—434no—
140C32⋊C9—432no—
141C32⋊C9—434no—
142C32⋊C9—432no—
143C32⋊C9C3×C43⋊C312yes—
144C32⋊C9C3×C43⋊C312yes—
145C92—434no—
146C92—434no—
147C92C3×C43⋊C311yescharacteristic, complemented
148C43#1062490611yescharacteristic, complemented, Sylow
149C33—432no—
150C33—431no—
151C33—1296no—
152C33—3872no—
153C33C32×C43⋊C311yescharacteristic
1543−1+2—12912no—
1553−1+2—1296no—
156C3×C9—434no—
157C3×C9—434no—
158C3×C9—434no—
159C3×C9—434no—
160C3×C9—434no—
161C3×C9—434no—
162C3×C9—3872no—
163C3×C9—3874no—
164C3×C9C32×C43⋊C312yes—
165C3×C9C32×C43⋊C314yes—
166C3×C9C32×C43⋊C312yes—
167C3×C9C32×C43⋊C314yes—
168C32—32no—
169C32—32no—
170C32—436no—
171C32—1292no—
172C32—1292no—
173C32—1292no—
174C32—1292no—
175C32—1292no—
176C32—3879no—
177C32C33×C43⋊C311yescharacteristic
178C9—34no—
179C9—32no—
180C9—32no—
181C9—34no—
182C9—1294no—
183C9—1294no—
184C9—1294no—
185C9—1294no—
186C9—1294no—
187C9—1294no—
188C3—91no—
189C3—1296no—
190C3—3871no—
191C3#737×C43⋊C312yes—
192C3#2378292212yes—
subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutator, socle, cosocleC32×C43C34
FittingC43×#6898C3
prime radicalC33×C43⋊C3C32
hypercenter#6898C43⋊C3
hypocenterC43#10624906
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C32 ◁ #6898

Complements

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

NH ≅ G/Ntype
1. #23782834C3semidirect
2. #23782834C3semidirect
3. #23782832C3semidirect
4. #23782832C3semidirect
5. #23782831C3semidirect
6. #23782814C3semidirect
7. #23782814C3semidirect
8. #23782811C3semidirect
10. C9×#11923957C3semidirect
11. #11923957⋊C9C3semidirect
13. C43×#6898C3semidirect
19. #16812500C32semidirect
20. #16812500C32semidirect
21. #16812499C32semidirect
22. #16812499C32semidirect
23. (C43⋊C9)⋊C9C32semidirect
24. (C43⋊C9)⋊C9C32semidirect
25. (C43⋊C9)⋊C9C32semidirect
26. (C43⋊C9)⋊C9C32semidirect
27. (C43⋊C9)⋊C9C32semidirect
28. (C43⋊C9)⋊C9C32semidirect
29. (C43⋊C9)⋊C9C32semidirect
30. (C43⋊C9)⋊C9C32semidirect
31. (C43⋊C9)⋊C9C32semidirect
32. (C43⋊C9)⋊C9C32semidirect
33. (C43⋊C9)⋊C9C32semidirect
34. (C43⋊C9)⋊C9C32semidirect
45. C9×C43⋊C9C32semidirect
46. C9×C43⋊C9C32semidirect
47. C43×C9⋊C9C32semidirect
48. C43×C9⋊C9C32semidirect
51. C92×C43C32semidirect
94. #6898C43⋊C3semidirect
131. C9⋊C9C3×C43⋊C3semidirect
132. C9⋊C9C3×C43⋊C3semidirect
147. C92C3×C43⋊C3semidirect
148. C43#10624906semidirect

Maximal subgroups

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

subgroupindex
#237828343
#237828323
#237828313
#237828143
#237828113
#237827973
C9×#119239573
#11923957⋊C93
C32⋊C9×C43⋊C33
C43×#68983
#1062490643