Finite Group Databasebeta

← #44535214

Subgroups — #44535214

Order 31347.

596 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 250 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#23782836C314yesmaximal, complemented
2#23782836C314yesmaximal, complemented
3#23782835C311yesmaximal, characteristic, complemented
4#23782834C314yesmaximal, complemented
5#23782834C314yesmaximal, complemented
6#23782828C314yesmaximal, complemented
7#23782827C314yesmaximal, complemented
8#23782826C314yesmaximal, complemented
9#23782826C314yesmaximal, complemented
10#23782825C312yesmaximal, complemented
11#23782797C312yesmaximal
12#23782796C312yesmaximal
13C43×#6898C311yesmaximal, characteristic, complemented
14C33×C43⋊C3C3211yescharacteristic
15C3×#11923957C3212yes—
16C3×#11923957C3214yes—
17C3×#11923956C3212yes—
18C3×#11923956C3214yes—
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)⋊C9C3212yes—
42(C3×C43⋊C3)⋊C9C3214yes—
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—92no—
53C32×C43⋊C3—92no—
54C32×C43⋊C3C3311yescharacteristic
55C32×C43⋊C3C3312yes—
56#11923957—92no—
57#11923957—94no—
58#11923956—92no—
59#11923956—94no—
60C3×C43⋊C9C3314yes—
61C3×C43⋊C9C3314yes—
62C3×C43⋊C9C3314yes—
63C3×C43⋊C9C3314yes—
64C3×C43⋊C9C3314yes—
65C3×C43⋊C9C3314yes—
66C33×C43C3311yescharacteristic
67C3×C9×C43C3312yes—
68C3×C9×C43C3312yes—
69C3×C9×C43C3314yes—
70C3×C9×C43C3314yes—
71#10624913—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—32no—
81C3×C43⋊C3—99no—
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#6898—434no—
95#6898—434no—
96#6898—431no—
97#6898C43⋊C311yescharacteristic, complemented
98#6896—434no—
99#6896—434no—
100#6896—434no—
101#6896—434no—
102#6896—432no—
103#6891—432no—
104#6891—432no—
105C3×C43—91no—
106C3×C433−1+412yes—
107C3×C433−1+412yes—
108C43⋊C3—92no—
109C43⋊C3—91no—
110C34—431no—
111C3×3−1+2—434no—
112C3×3−1+2—432no—
113C3×3−1+2—434no—
114C3×3−1+2—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—434no—
136C32⋊C9—434no—
137C32⋊C9—432no—
138C32⋊C9—432no—
139C32⋊C9—434no—
140C32⋊C9—434no—
141C32⋊C9—432no—
142C32⋊C9—432no—
143C32⋊C9C3×C43⋊C312yes—
144C32⋊C9C3×C43⋊C312yes—
145C92—434no—
146C92—434no—
147C92C3×C43⋊C311yescharacteristic, complemented
148C43#1062491311yescharacteristic, complemented, Sylow
149C33—431no—
150C33—432no—
151C33—3872no—
152C33—3872no—
153C33C32×C43⋊C311yescharacteristic
1543−1+2—3874no—
1553−1+2—3872no—
1563−1+2—3874no—
1573−1+2—3872no—
158C3×C9—434no—
159C3×C9—434no—
160C3×C9—434no—
161C3×C9—434no—
162C3×C9—434no—
163C3×C9—434no—
164C3×C9C32×C43⋊C314yes—
165C3×C9C32×C43⋊C314yes—
166C3×C9C32×C43⋊C312yes—
167C3×C9C32×C43⋊C312yes—
168C32—32no—
169C32—32no—
170C32—1292no—
171C32—1292no—
172C32—1292no—
173C32—1292no—
174C32—1292no—
175C32—1292no—
176C32—3879no—
177C32C33×C43⋊C311yescharacteristic
178C9—34no—
179C9—32no—
180C9—34no—
181C9—32no—
182C9—1294no—
183C9—1294no—
184C9—1294no—
185C9—1294no—
186C9—1294no—
187C9—1294no—
188C3—91no—
189C3—3872no—
190C3—3871no—
191C3#2378292112yes—
192C3#2378292212yes—
subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutator, socle, cosocleC32×C43C34
FittingC43×#6898C3
prime radicalC33×C43⋊C3C32
hypercenter#6898C43⋊C3
hypocenterC43#10624913
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C32 ◁ #6898

Complements

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

NH ≅ G/Ntype
1. #23782836C3semidirect
2. #23782836C3semidirect
3. #23782835C3semidirect
4. #23782834C3semidirect
5. #23782834C3semidirect
6. #23782828C3semidirect
7. #23782827C3semidirect
8. #23782826C3semidirect
9. #23782826C3semidirect
10. #23782825C3semidirect
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
97. #6898C43⋊C3semidirect
131. C9⋊C9C3×C43⋊C3semidirect
132. C9⋊C9C3×C43⋊C3semidirect
147. C92C3×C43⋊C3semidirect
148. C43#10624913semidirect

Maximal subgroups

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

subgroupindex
#237828363
#237828353
#237828343
#237828283
#237828273
#237828263
#237828253
#237827973
#237827963
C43×#68983
#1062491343