Finite Group Databasebeta

← #44534977

Subgroups — #44534977

Order 31347.

836 conjugacy classes of subgroups; only the 298 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 298 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⋊C3C312yesmaximal
2#23782849C314yesmaximal, complemented
3#23782849C314yesmaximal, complemented
4#23782846C311yesmaximal, characteristic, complemented
5#23782824C314yesmaximal, complemented
6#23782823C314yesmaximal, complemented
7#23782813C318yesmaximal, complemented
8#23782810C314yesmaximal, complemented
9#23782797C312yesmaximal
10C9×#11923956C312yesmaximal, complemented
11#11923956⋊C9C314yesmaximal, complemented
12C43×#6896C311yesmaximal, characteristic, complemented
13C33×C43⋊C3C3211yescharacteristic
14C3×#11923958C3214yes—
15C3×#11923957C3212yes—
16C3×#11923957C3214yes—
17C3×#11923957C3212yes—
18C3×#11923957C3214yes—
19C3×#11923956C3214yes—
20C3×#11923956C3212yes—
213−1+2×C43⋊C3—318no—
22C3×C9×C43⋊C3C3214yes—
23C3×C9×C43⋊C3C3212yes—
24#16812500C3214yescomplemented
25#16812500C3214yescomplemented
26#16812499C3214yescomplemented
27#16812499C3214yescomplemented
28(C43⋊C9)⋊C9C3218yescomplemented
29(C43⋊C9)⋊C9C3218yescomplemented
30(C43⋊C9)⋊C9C3218yescomplemented
31(C43⋊C9)⋊C9C3218yescomplemented
32(C43⋊C9)⋊C9C3218yescomplemented
33(C43⋊C9)⋊C9C3218yescomplemented
34C32⋊(C43⋊C9)C3214yes—
35(C3×C43⋊C3)⋊C9C3218yes—
36(C3×C43⋊C3)⋊C9C3214yes—
37C9×C43⋊C9C3214yescomplemented
38C9×C43⋊C9C3214yescomplemented
39C3×3−1+2×C43C3212yes—
40C43×C9⋊C9C3214yescomplemented
41C43×C9⋊C9C3214yescomplemented
42C43×C32⋊C9C3212yes—
43C92×C43C3211yescharacteristic, complemented
44C32×C43⋊C3—36no—
45C32×C43⋊C3—92no—
46C32×C43⋊C3C3311yescharacteristic
47C32×C43⋊C3C3312yes—
48#11923958—312no—
49#11923957—36no—
50#11923957—312no—
51#11923957—92no—
52#11923957—94no—
53#11923956—312no—
54#119239563−1+2118yescomplemented
55C3×C43⋊C9C3318yes—
56C3×C43⋊C9C3314yes—
57C3×C43⋊C9C3314yes—
58C3×C43⋊C9C3314yes—
59C3×C43⋊C9C3314yes—
60C9×C43⋊C3—36no—
61C9×C43⋊C3—312no—
62C33×C43C3311yescharacteristic
633−1+2×C43—36no—
64C3×C9×C43C3312yes—
65C3×C9×C43C3314yes—
66C3×C9×C43C3314yes—
67C3×C9×C43C3312yes—
683−1+22—431nomaximal, Sylow
69C32×C43—32no—
70C32×C43—32no—
71C32×C43C3411yescharacteristic
72C3×C43⋊C3—32no—
73C3×C43⋊C3—34no—
74C3×C43⋊C3—32no—
75C3×C43⋊C3—32no—
76C3×C43⋊C3—99no—
77C3×C43⋊C3C3×3−1+216yes—
78C9×C43—34no—
79C9×C43—32no—
80C9×C43—34no—
81C9×C43C3×3−1+216yescomplemented
82C43⋊C9—34no—
83C43⋊C9—34no—
84C43⋊C9—38no—
85C43⋊C9—34no—
86C43⋊C9C3×3−1+2112yescomplemented
87C32×3−1+2—432no—
88#6900—434no—
89#6900—434no—
90#6900—431no—
91#6896—434no—
92#6896—434no—
93#6896C43⋊C311yescharacteristic, complemented
94#6894—434no—
95#6894—438no—
96#6891—432no—
97C9×3−1+2—434no—
98C9×3−1+2—432no—
99C3×C43—91no—
100C3×C43C32×3−1+212yes—
101C3×C433−1+412yes—
102C43⋊C3—36no—
103C43⋊C3—91no—
104C34—431no—
105C3×3−1+2—434no—
106C3×3−1+2—432no—
107C3×3−1+2—434no—
108C3×3−1+2—434no—
109C3×3−1+2—432no—
110C3×3−1+2—434no—
111C3×3−1+2—432no—
112C3×3−1+2—12918no—
113C3×3−1+2C3×C43⋊C312yes—
114C32×C9—434no—
115C32×C9—432no—
116C9⋊C9—438no—
117C9⋊C9—438no—
118C9⋊C9—438no—
119C9⋊C9—438no—
120C9⋊C9—438no—
121C9⋊C9—438no—
122C9⋊C9—434no—
123C9⋊C9—434no—
124C9⋊C9—434no—
125C9⋊C9—434no—
126C9⋊C9C3×C43⋊C314yescomplemented
127C9⋊C9C3×C43⋊C314yescomplemented
128C32⋊C9—434no—
129C32⋊C9—438no—
130C32⋊C9—434no—
131C32⋊C9C3×C43⋊C312yes—
132C92—434no—
133C92—434no—
134C92C3×C43⋊C311yescharacteristic, complemented
135C433−1+2211yescharacteristic, complemented, Sylow
136C33—432no—
137C33—431no—
138C33—1296no—
139C33—3872no—
140C33C32×C43⋊C311yescharacteristic
1413−1+2—36no—
1423−1+2—4318no—
1433−1+2—12912no—
1443−1+2—12912no—
1453−1+2—12912no—
1463−1+2—1296no—
1473−1+2—3874no—
1483−1+2—3872no—
149C3×C9—434no—
150C3×C9—438no—
151C3×C9—434no—
152C3×C9—434no—
153C3×C9—434no—
154C3×C9—12912no—
155C3×C9—1296no—
156C3×C9C32×C43⋊C314yes—
157C3×C9C32×C43⋊C312yes—
158C3×C9C32×C43⋊C314yes—
159C3×C9C32×C43⋊C312yes—
160C32—32no—
161C32—32no—
162C32—436no—
163C32—1292no—
164C32—1294no—
165C32—1292no—
166C32—1292no—
167C32—3879no—
168C32C33×C43⋊C311yescharacteristic
169C9—34no—
170C9—34no—
171C9—32no—
172C9—4312no—
173C9—1294no—
174C9—1294no—
175C9—1298no—
176C9—1294no—
177C93−1+2×C43⋊C316yescomplemented
178C3—91no—
179C3—1296no—
180C3—3871no—
181C3C3×3−1+2×C43⋊C312yes—
182C3#2378292212yes—
subgroupG/H
center, FrattiniC32C33×C43⋊C3
commutator, socle, cosocleC32×C43C34
FittingC43×#6896C3
prime radicalC33×C43⋊C3C32
hypercenter#6896C43⋊C3
hypocenterC433−1+22
LCSG ▷ C32×C43 ▷ C43
UCSC1 ◁ C32 ◁ #6896

Complements

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

NH ≅ G/Ntype
2. #23782849C3semidirect
3. #23782849C3semidirect
4. #23782846C3semidirect
5. #23782824C3semidirect
6. #23782823C3semidirect
7. #23782813C3semidirect
8. #23782810C3semidirect
10. C9×#11923956C3semidirect
11. #11923956⋊C9C3semidirect
12. C43×#6896C3semidirect
24. #16812500C32semidirect
25. #16812500C32semidirect
26. #16812499C32semidirect
27. #16812499C32semidirect
28. (C43⋊C9)⋊C9C32semidirect
29. (C43⋊C9)⋊C9C32semidirect
30. (C43⋊C9)⋊C9C32semidirect
31. (C43⋊C9)⋊C9C32semidirect
32. (C43⋊C9)⋊C9C32semidirect
33. (C43⋊C9)⋊C9C32semidirect
37. C9×C43⋊C9C32semidirect
38. C9×C43⋊C9C32semidirect
40. C43×C9⋊C9C32semidirect
41. C43×C9⋊C9C32semidirect
43. C92×C43C32semidirect
54. #119239563−1+2semidirect
81. C9×C43C3×3−1+2semidirect
86. C43⋊C9C3×3−1+2semidirect
93. #6896C43⋊C3semidirect
126. C9⋊C9C3×C43⋊C3semidirect
127. C9⋊C9C3×C43⋊C3semidirect
134. C92C3×C43⋊C3semidirect
135. C433−1+22semidirect
177. C93−1+2×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
#237828493
#237828463
#237828243
#237828233
#237828133
#237828103
#237827973
C9×#119239563
#11923956⋊C93
C43×#68963
3−1+2243