Finite Group Databasebeta

← #23748554

Subgroups — #23748554

Order 9477.

1118 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 268 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#15691697C312yesmaximal, complemented
2C13⋊H(5,𝔽3)C311yesmaximal, characteristic, complemented
3C32×C32⋊(C13⋊C3)C311yesmaximal, characteristic, complemented
4#15691657C314yesmaximal, complemented
5#15691655C312yesmaximal, complemented
6#15691654C319yesmaximal, complemented
7#15691653C319yesmaximal, complemented
8C3×#11760435C312yesmaximal, complemented
9C13⋊C3×AΣL(1,𝔽27)C319yesmaximal, complemented
10C3×C13×AΣL(1,𝔽27)C311yesmaximal, characteristic, complemented
11C33×C13⋊C3C3213yescomplemented
12#11760454—312no—
13#11760453—36no—
14C3×#66851C3214yescomplemented
153−1+2×C13⋊C3C32118yescomplemented
16C3×C32⋊(C13⋊C3)—36no—
17C3×C32⋊(C13⋊C3)—33no—
18C3×C32⋊(C13⋊C3)—33no—
19C3×C32⋊(C13⋊C3)C3211yescharacteristic
20C3×C32⋊(C13⋊C3)C3213yescomplemented
21C3×C32⋊(C13⋊C3)C3213yescomplemented
22C3×C32⋊(C13⋊C3)C3212yescomplemented
23C3×C32⋊(C13⋊C3)C3212yescomplemented
24H(3,𝔽3)×C13⋊C3—36no—
25H(3,𝔽3)×C13⋊C3C3219yescomplemented
26#11760436C32136yescomplemented
27#11760435C3216yescomplemented
28#11760435C3216yescomplemented
29#11760435C3216yescomplemented
30#11760434C32118yescomplemented
31C34×C13C3211yescharacteristic, complemented
32C3×C13×3−1+2C3212yescomplemented
33C3×C13×H(3,𝔽3)C3211yescharacteristic, complemented
34C13×AΣL(1,𝔽27)C3213yescomplemented
35C13×AΣL(1,𝔽27)C3213yescomplemented
36C13×AΣL(1,𝔽27)C3213yescomplemented
37#10624930—131nomaximal, Sylow
38C33×C13—32no—
39C33×C13—31no—
40C33×C13—31no—
41C33×C13—93no—
42C33×C13C3311yescharacteristic
43C33×C13C3311yescharacteristic
44C33×C13C3311yescharacteristic
45C33×C13C3311yescharacteristic
46C32×C13⋊C3—32no—
47C32×C13⋊C3—39no—
48C32×C13⋊C3—39no—
49C32×C13⋊C3—99no—
50C32×C13⋊C3C3316yes—
51C32×C13⋊C3C3313yes—
52C13×3−1+2—34no—
53C13×3−1+2C3316yes—
54C13×H(3,𝔽3)—32no—
55C13×H(3,𝔽3)C3313yes—
56C3×C9×C13—32no—
57C32⋊(C13⋊C3)—32no—
58C32⋊(C13⋊C3)—34no—
59C32⋊(C13⋊C3)—32no—
60C32⋊(C13⋊C3)—32no—
61C32⋊(C13⋊C3)—318no—
62C32⋊(C13⋊C3)—39no—
63C32⋊(C13⋊C3)—39no—
64C32⋊(C13⋊C3)H(3,𝔽3)16yes—
65C32⋊(C13⋊C3)H(3,𝔽3)13yes—
66C32⋊(C13⋊C3)C3316yes—
67#66851—34no—
68#66851—34no—
69#66851C33112yes—
70C3×C13⋊C9—34no—
71#66849—318no—
72#66848—318no—
73C9×C13⋊C3—318no—
743−1+4—132no—
75H(5,𝔽3)—131no—
76C32×H(3,𝔽3)—131no—
77#6909—134no—
78#6909—132no—
79#6909—139no—
80#6909—139no—
81C3×AΣL(1,𝔽27)—132no—
82C3×AΣL(1,𝔽27)—139no—
83C3×AΣL(1,𝔽27)C13⋊C311yescharacteristic, complemented
84C32×C13—33no—
85C32×C13—31no—
86C32×C13—31no—
87C32×C13—31no—
88C32×C13—33no—
89C32×C13—91no—
90C32×C13—96no—
91C32×C13—93no—
92C32×C13—91no—
93C32×C13—91no—
94C32×C13—271no—
95C32×C13C3×H(3,𝔽3)12yes—
96C32×C13C3×H(3,𝔽3)11yescharacteristic
97C32×C13C3411yescharacteristic
98C3×C13⋊C3—36no—
99C3×C13⋊C3—36no—
100C3×C13⋊C3—93no—
101C3×C13⋊C3—927no—
102C3×C13⋊C3—96no—
103C3×C13⋊C3—279no—
104C3×C13⋊C3—272no—
105C3×C13⋊C3C3×H(3,𝔽3)19yes—
106C9×C13—36no—
107C13⋊C9—312no—
108C34—133no—
109C34C3×C13⋊C311yescharacteristic, complemented
110#737—396no—
111#737—3912no—
112C3×3−1+2—134no—
113C3×3−1+2—1318no—
114C3×3−1+2C3×C13⋊C312yescomplemented
115C3×H(3,𝔽3)—131no—
116C3×H(3,𝔽3)—132no—
117C3×H(3,𝔽3)—139no—
118C3×H(3,𝔽3)—133no—
119C3×H(3,𝔽3)—133no—
120C3×H(3,𝔽3)—132no—
121C3×H(3,𝔽3)—396no—
122C3×H(3,𝔽3)—393no—
123C3×H(3,𝔽3)—396no—
124C3×H(3,𝔽3)—393no—
125C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic, complemented
126AΣL(1,𝔽27)—136no—
127AΣL(1,𝔽27)—136no—
128AΣL(1,𝔽27)—136no—
129AΣL(1,𝔽27)—1336no—
130AΣL(1,𝔽27)—1318no—
131AΣL(1,𝔽27)C3×C13⋊C313yescomplemented
132AΣL(1,𝔽27)C3×C13⋊C313yescomplemented
133AΣL(1,𝔽27)C3×C13⋊C313yescomplemented
134C3×C13—33no—
135C3×C13—31no—
136C3×C13—32no—
137C3×C13—31no—
138C3×C13—93no—
139C3×C13—91no—
140C3×C13—91no—
141C3×C13C32×H(3,𝔽3)11yescharacteristic
142C13⋊C3—39no—
143C13⋊C3—96no—
144C13⋊C3—96no—
145C33—31no—
146C33—32no—
147C33—31no—
148C33—93no—
149C33—133no—
150C33—136no—
151C33—399no—
152C33—399no—
153C33—392no—
154C33—1179no—
155C33C32×C13⋊C311yescharacteristic
156C33C32×C13⋊C311yescharacteristic
157C33C32×C13⋊C311yescharacteristic
158C33C32×C13⋊C311yescharacteristic
1593−1+2—34no—
1603−1+2—1312no—
1613−1+2—3918no—
1623−1+2—3918no—
1633−1+2—394no—
1643−1+2—394no—
1653−1+2C32×C13⋊C316yes—
166H(3,𝔽3)—32no—
167H(3,𝔽3)—133no—
168H(3,𝔽3)—136no—
169H(3,𝔽3)—136no—
170H(3,𝔽3)—3918no—
171H(3,𝔽3)—399no—
172H(3,𝔽3)—399no—
173H(3,𝔽3)—392no—
174H(3,𝔽3)—392no—
175H(3,𝔽3)—392no—
176H(3,𝔽3)—394no—
177H(3,𝔽3)C32×C13⋊C313yes—
178C3×C9—32no—
179C3×C9—3918no—
180C3×C9—394no—
181C13#1062493011yescharacteristic, complemented, Sylow
182C32—33no—
183C32—31no—
184C32—33no—
185C32—31no—
186C32—31no—
187C32—91no—
188C32—93no—
189C32—96no—
190C32—91no—
191C32—91no—
192C32—139no—
193C32—271no—
194C32—396no—
195C32—396no—
196C32—3512no—
197C32—3519no—
198C32—1173no—
199C32—11727no—
200C32—1176no—
201C32H(3,𝔽3)×C13⋊C311yescharacteristic
202C32H(3,𝔽3)×C13⋊C312yes—
203C32C33×C13⋊C311yescharacteristic
204C9—36no—
205C9—3912no—
206C3—31no—
207C3—33no—
208C3—31no—
209C3—32no—
210C3—91no—
211C3—91no—
212C3—93no—
213C3—399no—
214C3—1176no—
215C3—1176no—
216C3C3×H(3,𝔽3)×C13⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC3×C13×AΣL(1,𝔽27)C3
socleC3×C13C32×H(3,𝔽3)
hypercenterC3×AΣL(1,𝔽27)C13⋊C3
hypocenterC13#10624930
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ C3×AΣL(1,𝔽27)

Complements

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

NH ≅ G/Ntype
1. #15691697C3semidirect
2. C13⋊H(5,𝔽3)C3semidirect
3. C32×C32⋊(C13⋊C3)C3semidirect
4. #15691657C3semidirect
5. #15691655C3semidirect
6. #15691654C3semidirect
7. #15691653C3semidirect
8. C3×#11760435C3semidirect
9. C13⋊C3×AΣL(1,𝔽27)C3semidirect
10. C3×C13×AΣL(1,𝔽27)C3semidirect
11. C33×C13⋊C3C32semidirect
14. C3×#66851C32semidirect
15. 3−1+2×C13⋊C3C32semidirect
20. C3×C32⋊(C13⋊C3)C32semidirect
21. C3×C32⋊(C13⋊C3)C32semidirect
22. C3×C32⋊(C13⋊C3)C32semidirect
23. C3×C32⋊(C13⋊C3)C32semidirect
25. H(3,𝔽3)×C13⋊C3C32semidirect
26. #11760436C32semidirect
27. #11760435C32semidirect
28. #11760435C32semidirect
29. #11760435C32semidirect
30. #11760434C32semidirect
31. C34×C13C32semidirect
32. C3×C13×3−1+2C32semidirect
33. C3×C13×H(3,𝔽3)C32semidirect
34. C13×AΣL(1,𝔽27)C32semidirect
35. C13×AΣL(1,𝔽27)C32semidirect
36. C13×AΣL(1,𝔽27)C32semidirect
83. C3×AΣL(1,𝔽27)C13⋊C3semidirect
109. C34C3×C13⋊C3semidirect
114. C3×3−1+2C3×C13⋊C3semidirect
125. C3×H(3,𝔽3)C3×C13⋊C3semidirect
131. AΣL(1,𝔽27)C3×C13⋊C3semidirect
132. AΣL(1,𝔽27)C3×C13⋊C3semidirect
133. AΣL(1,𝔽27)C3×C13⋊C3semidirect
181. C13#10624930semidirect