Finite Group Databasebeta

← #23748559

Subgroups — #23748559

Order 9477.

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

normal subgroups only

This group has 978 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
3C3×#11760453C311yesmaximal, characteristic, complemented
4#15691662C314yesmaximal, complemented
5#15691660C312yesmaximal, complemented
6#15691659C319yesmaximal, complemented
7#15691658C319yesmaximal, complemented
8C3×#11760438C312yesmaximal, complemented
9C13⋊C3×#731C319yesmaximal, complemented
10C3×C13×#731C311yesmaximal, characteristic, complemented
11#11760454—312no—
12#11760453—36no—
13#11760453—33no—
14#11760453—36no—
15C3×#66851C3214yescomplemented
16C3×#66851C3212yescomplemented
17C3×#66848C3213yescomplemented
18C3×#66849C3213yescomplemented
193−1+2×C13⋊C3C32118yescomplemented
20C3×C32⋊(C13⋊C3)—33no—
21C3×C32⋊(C13⋊C3)C3212yes—
22C3×C32⋊(C13⋊C3)C3211yescharacteristic
23H(3,𝔽3)×C13⋊C3—36no—
24H(3,𝔽3)×C13⋊C3C3219yes—
25C3×C9×C13⋊C3C3213yescomplemented
26#11760439C32136yescomplemented
27#11760438C3216yescomplemented
28#11760438C3216yescomplemented
29#11760438C3216yescomplemented
30#11760437C32118yescomplemented
31C3×C13×3−1+2C3212yescomplemented
32C3×C13×H(3,𝔽3)C3211yescharacteristic
33C32×C9×C13C3211yescharacteristic, complemented
34C13×#731C3213yescomplemented
35C13×#731C3213yescomplemented
36C13×#731C3213yescomplemented
37#10624931—131nomaximal, Sylow
38C33×C13—31no—
39C33×C13C3311yescharacteristic
40C32×C13⋊C3—32no—
41C32×C13⋊C3—39no—
42C32×C13⋊C3C3313yes—
43C13×3−1+2—34no—
44C13×3−1+2C3316yes—
45C13×H(3,𝔽3)—32no—
46C13×H(3,𝔽3)C3313yes—
47C3×C9×C13—32no—
48C3×C9×C13—31no—
49C3×C9×C13—32no—
50C3×C9×C13C3311yescharacteristic
51C3×C9×C13C3311yescharacteristic
52C3×C9×C13C3311yescharacteristic
53C32⋊(C13⋊C3)—32no—
54C32⋊(C13⋊C3)—32no—
55C32⋊(C13⋊C3)—318no—
56C32⋊(C13⋊C3)H(3,𝔽3)16yes—
57C32⋊(C13⋊C3)H(3,𝔽3)13yes—
58C32⋊(C13⋊C3)C3316yes—
59#66851—34no—
60#66851—34no—
61#66851—32no—
62#66851—34no—
63#66851C33112yes—
64C3×C13⋊C9—34no—
65C3×C13⋊C9C3316yes—
66#66849—318no—
67#66849—39no—
68#66848—318no—
69#66848—39no—
70C9×C13⋊C3—39no—
71C9×C13⋊C3—318no—
723−1+4—132no—
73H(5,𝔽3)—131no—
74C3×#737—131no—
75#6910—134no—
76#6910—132no—
77#6910—139no—
78#6910—139no—
79C3×#731—132no—
80C3×#731—139no—
81C3×#731C13⋊C311yescharacteristic, complemented
82C32×C13—33no—
83C32×C13—91no—
84C32×C13—271no—
85C32×C13C3×H(3,𝔽3)12yes—
86C32×C13C3×H(3,𝔽3)11yescharacteristic
87C32×C13C3411yescharacteristic
88C3×C13⋊C3—36no—
89C3×C13⋊C3—93no—
90C3×C13⋊C3—279no—
91C3×C13⋊C3—272no—
92C3×C13⋊C3C3×H(3,𝔽3)19yes—
93C9×C13—31no—
94C9×C13—36no—
95C9×C13—31no—
96C9×C13—31no—
97C13⋊C9—312no—
98C13⋊C9—36no—
99#737—393no—
100#737—396no—
101#737—396no—
102#737—3912no—
103C3×3−1+2—132no—
104C3×3−1+2—133no—
105C3×3−1+2—133no—
106C3×3−1+2—134no—
107C3×3−1+2—1318no—
108C3×3−1+2C3×C13⋊C312yescomplemented
109C3×H(3,𝔽3)—131no—
110C3×H(3,𝔽3)—132no—
111C3×H(3,𝔽3)—139no—
112C3×H(3,𝔽3)—396no—
113C3×H(3,𝔽3)—393no—
114C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic
115C32×C9—133no—
116C32×C9C3×C13⋊C311yescharacteristic, complemented
117#731—1336no—
118#731—1318no—
119#731—136no—
120#731—136no—
121#731—136no—
122#731C3×C13⋊C313yescomplemented
123#731C3×C13⋊C313yescomplemented
124#731C3×C13⋊C313yescomplemented
125C3×C13—31no—
126C3×C13—32no—
127C3×C13—31no—
128C3×C13—93no—
129C3×C13C32×H(3,𝔽3)11yescharacteristic
130C13⋊C3—39no—
131C13⋊C3—96no—
132C33—31no—
133C33—133no—
134C33—399no—
135C33—392no—
136C33C32×C13⋊C311yescharacteristic
1373−1+2—34no—
1383−1+2—1312no—
1393−1+2—399no—
1403−1+2—3918no—
1413−1+2—399no—
1423−1+2—3918no—
1433−1+2—392no—
1443−1+2—394no—
1453−1+2—394no—
1463−1+2—394no—
1473−1+2C32×C13⋊C316yes—
148H(3,𝔽3)—32no—
149H(3,𝔽3)—133no—
150H(3,𝔽3)—136no—
151H(3,𝔽3)—136no—
152H(3,𝔽3)—3918no—
153H(3,𝔽3)—392no—
154H(3,𝔽3)—392no—
155H(3,𝔽3)C32×C13⋊C313yes—
156C3×C9—31no—
157C3×C9—32no—
158C3×C9—32no—
159C3×C9—136no—
160C3×C9—399no—
161C3×C9—3918no—
162C3×C9—394no—
163C3×C9C32×C13⋊C311yescharacteristic
164C3×C9C32×C13⋊C311yescharacteristic
165C3×C9C32×C13⋊C311yescharacteristic
166C13#1062493111yescharacteristic, complemented, Sylow
167C32—33no—
168C32—91no—
169C32—139no—
170C32—271no—
171C32—396no—
172C32—3512no—
173C32—3519no—
174C32—1173no—
175C32H(3,𝔽3)×C13⋊C311yescharacteristic
176C32H(3,𝔽3)×C13⋊C312yes—
177C32C33×C13⋊C311yescharacteristic
178C9—31no—
179C9—31no—
180C9—31no—
181C9—36no—
182C9—396no—
183C9—3912no—
184C3—31no—
185C3—32no—
186C3—31no—
187C3—93no—
188C3—399no—
189C3—1176no—
190C3C3×H(3,𝔽3)×C13⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC3×C13×#731C3
socleC3×C13C32×H(3,𝔽3)
prime radicalC13⋊H(5,𝔽3)C3
hypercenterC3×#731C13⋊C3
hypocenterC13#10624931
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ C3×#731

Complements

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

NH ≅ G/Ntype
1. #15691697C3semidirect
3. C3×#11760453C3semidirect
4. #15691662C3semidirect
5. #15691660C3semidirect
6. #15691659C3semidirect
7. #15691658C3semidirect
8. C3×#11760438C3semidirect
9. C13⋊C3×#731C3semidirect
10. C3×C13×#731C3semidirect
15. C3×#66851C32semidirect
16. C3×#66851C32semidirect
17. C3×#66848C32semidirect
18. C3×#66849C32semidirect
19. 3−1+2×C13⋊C3C32semidirect
25. C3×C9×C13⋊C3C32semidirect
26. #11760439C32semidirect
27. #11760438C32semidirect
28. #11760438C32semidirect
29. #11760438C32semidirect
30. #11760437C32semidirect
31. C3×C13×3−1+2C32semidirect
33. C32×C9×C13C32semidirect
34. C13×#731C32semidirect
35. C13×#731C32semidirect
36. C13×#731C32semidirect
81. C3×#731C13⋊C3semidirect
108. C3×3−1+2C3×C13⋊C3semidirect
116. C32×C9C3×C13⋊C3semidirect
122. #731C3×C13⋊C3semidirect
123. #731C3×C13⋊C3semidirect
124. #731C3×C13⋊C3semidirect
166. C13#10624931semidirect