Finite Group Databasebeta

← #44534531

Subgroups — #44534531

Order 31347.

210 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 46 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#733×C43⋊C3C311yesmaximal, characteristic, complemented
2#732×C43⋊C3C311yesmaximal, characteristic, complemented
3#732×C43⋊C3C311yesmaximal, characteristic, complemented
4#23782781C311yesmaximal, characteristic, complemented
5#23782759C311yesmaximal, characteristic, complemented
6#23782758C311yesmaximal, characteristic, complemented
7#23782757C311yesmaximal, characteristic, complemented
8#23782757C311yesmaximal, characteristic, complemented
9#23782756C311yesmaximal, characteristic, complemented
10#23782756C311yesmaximal, characteristic, complemented
11#23782755C311yesmaximal, characteristic, complemented
12#23782755C311yesmaximal, characteristic, complemented
13C43×#6881C311yesmaximal, characteristic, complemented
143−1+2×C43⋊C3—31no—
15H(3,𝔽3)×C43⋊C3—31no—
16H(3,𝔽3)×C43⋊C3—31no—
17C3×C9×C43⋊C3C3211yescharacteristic
18#16812515C3211yescharacteristic, complemented
19#16812515C3211yescharacteristic, complemented
20#16812514—31no—
21#16812514—31no—
22#16812513C3211yescharacteristic, complemented
23#16812513C3211yescharacteristic, complemented
24#16812513C3211yescharacteristic, complemented
25#16812513C3211yescharacteristic, complemented
26#16812512—31no—
27#16812512—31no—
28#16812512—31no—
29#16812512—31no—
30#16812500C3211yescharacteristic, complemented
31#16812499C3211yescharacteristic, complemented
32(C43⋊C9)⋊C9—31no—
33(C3×C43⋊C3)⋊C9—31no—
34C9×C43⋊C9—31no—
35C43×#733C3211yescharacteristic, complemented
36C43×#732C3211yescharacteristic, complemented
37C43×#732C3211yescharacteristic, complemented
38C43×C9⋊C9C3211yescharacteristic, complemented
39C32×C43⋊C3—91no—
40C32×C43⋊C3—91no—
41C32×C43⋊C3H(3,𝔽3)11yescharacteristic
42#11923958—31no—
43#11923958—31no—
44#11923957—91no—
45#11923956—91no—
46C32⋊(C43⋊C3)—31no—
47C32⋊(C43⋊C3)—31no—
48C32⋊(C43⋊C3)—31no—
49C32⋊(C43⋊C3)—31no—
50C32⋊(C43⋊C3)—91no—
51C32⋊(C43⋊C3)—91no—
52C32⋊(C43⋊C3)—91no—
53C32⋊(C43⋊C3)—91no—
54C3×C43⋊C9—31no—
55C3×C43⋊C9—31no—
56C3×C43⋊C9H(3,𝔽3)11yescharacteristic
57C3×C43⋊C9H(3,𝔽3)11yescharacteristic
58C9×C43⋊C3—31no—
59C9×C43⋊C3—31no—
60C9×C43⋊C3—31no—
61C9×C43⋊C3—91no—
623−1+2×C43—31no—
63H(3,𝔽3)×C43—31no—
64H(3,𝔽3)×C43—31no—
65C3×C9×C43—31no—
66C3×C9×C43C3311yescharacteristic
67#10624846—431nomaximal, Sylow
68C32×C43—91no—
69C32×C43—91no—
70C32×C43C3×H(3,𝔽3)11yescharacteristic
71C3×C43⋊C3—91no—
72C3×C43⋊C3—91no—
73C3×C43⋊C3—91no—
74C3×C43⋊C3—91no—
75C3×C43⋊C3—91no—
76C3×C43⋊C3—273no—
77C3×C43⋊C3—273no—
78C3×C43⋊C3#73211yescharacteristic
79C3×C43⋊C3#73211yescharacteristic
80C3×C43⋊C3#73211yescharacteristic
81C9×C43—31no—
82C9×C43—91no—
83C9×C43—91no—
84C43⋊C9—31no—
85C43⋊C9—31no—
86C43⋊C9—91no—
87C43⋊C9—91no—
88C43⋊C9—91no—
89C43⋊C9—91no—
90C3×#733—431no—
91C3×#732—431no—
92C3×#732—431no—
93#6887—431no—
94#6881—431no—
95#6881—431no—
96#6881—431no—
97#6881—431no—
98#6881—431no—
99#6881—431no—
100#6881—431no—
101#6881—431no—
102#6881C43⋊C311yescharacteristic, complemented
103C3×C43—31no—
104C3×C43—271no—
105C3×C43—271no—
106C3×C43C3×#73211yescharacteristic
107C43⋊C3—31no—
108C43⋊C3—31no—
109C43⋊C3—31no—
110C43⋊C3—271no—
111C43⋊C3—271no—
112C43⋊C3—271no—
113C43⋊C3—271no—
114C3×3−1+2—1291no—
115C3×H(3,𝔽3)—1291no—
116C3×H(3,𝔽3)—1291no—
117C32×C9—431no—
118#733—431no—
119#733—431no—
120#733—1291no—
121#733—1291no—
122#733C3×C43⋊C311yescharacteristic, complemented
123#732—431no—
124#732—431no—
125#732—431no—
126#732—431no—
127#732—1291no—
128#732—1291no—
129#732—1291no—
130#732—1291no—
131#732C3×C43⋊C311yescharacteristic, complemented
132#732C3×C43⋊C311yescharacteristic, complemented
133C9⋊C9—431no—
134C9⋊C9—431no—
135C9⋊C9—1291no—
136C9⋊C9C3×C43⋊C311yescharacteristic, complemented
137C32⋊C9—1291no—
138C92—1291no—
139C43#1062484611yescharacteristic, complemented, Sylow
140C33—431no—
141C33—3871no—
142C33—3871no—
1433−1+2—31no—
1443−1+2—1291no—
1453−1+2—1291no—
1463−1+2—3871no—
1473−1+2—3871no—
148H(3,𝔽3)—31no—
149H(3,𝔽3)—31no—
150H(3,𝔽3)—1291no—
151H(3,𝔽3)—1291no—
152H(3,𝔽3)—1291no—
153H(3,𝔽3)—1291no—
154H(3,𝔽3)—3871no—
155H(3,𝔽3)—3871no—
156H(3,𝔽3)—3871no—
157H(3,𝔽3)—3871no—
158C3×C9—31no—
159C3×C9—431no—
160C3×C9—431no—
161C3×C9—1291no—
162C3×C9—1291no—
163C3×C9—1291no—
164C3×C9—1291no—
165C3×C9—1291no—
166C3×C9—3871no—
167C3×C9C32×C43⋊C311yescharacteristic
168C32—91no—
169C32—91no—
170C32—431no—
171C32—431no—
172C32—431no—
173C32—3871no—
174C32—3871no—
175C32—3871no—
176C32—3871no—
177C32—3871no—
178C32—11613no—
179C32—11613no—
180C32H(3,𝔽3)×C43⋊C311yescharacteristic
181C9—31no—
182C9—91no—
183C9—91no—
184C9—1291no—
185C9—1291no—
186C9—3871no—
187C9—3871no—
188C9—3871no—
189C9—3871no—
190C3—31no—
191C3—271no—
192C3—271no—
193C3—1291no—
194C3—1291no—
195C3—1291no—
196C3—11611no—
197C3—11611no—
198C3—11611no—
199C3—11611no—
200C3#732×C43⋊C311yescharacteristic
subgroupG/H
centerC3#732×C43⋊C3
commutator, cosocleC3×C9×C43C33
FrattiniC3×C9C32×C43⋊C3
FittingC43×#6881C3
socleC3×C43C3×#732
hypercenter#6881C43⋊C3
hypocenterC43#10624846
LCSG ▷ C3×C9×C43 ▷ C32×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6881

Complements

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

NH ≅ G/Ntype
1. #733×C43⋊C3C3semidirect
2. #732×C43⋊C3C3semidirect
3. #732×C43⋊C3C3semidirect
4. #23782781C3semidirect
5. #23782759C3semidirect
6. #23782758C3semidirect
7. #23782757C3semidirect
8. #23782757C3semidirect
9. #23782756C3semidirect
10. #23782756C3semidirect
11. #23782755C3semidirect
12. #23782755C3semidirect
13. C43×#6881C3semidirect
18. #16812515C32semidirect
19. #16812515C32semidirect
22. #16812513C32semidirect
23. #16812513C32semidirect
24. #16812513C32semidirect
25. #16812513C32semidirect
30. #16812500C32semidirect
31. #16812499C32semidirect
35. C43×#733C32semidirect
36. C43×#732C32semidirect
37. C43×#732C32semidirect
38. C43×C9⋊C9C32semidirect
102. #6881C43⋊C3semidirect
122. #733C3×C43⋊C3semidirect
131. #732C3×C43⋊C3semidirect
132. #732C3×C43⋊C3semidirect
136. C9⋊C9C3×C43⋊C3semidirect
139. C43#10624846semidirect

Maximal subgroups

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

subgroupindex
#733×C43⋊C33
#732×C43⋊C33
#237827813
#237827593
#237827583
#237827573
#237827563
#237827553
C43×#68813
#1062484643