Finite Group Databasebeta

← #23748596

Subgroups — #23748596

Order 9477.

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

normal subgroups only

This group has 948 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#15691698C311yesmaximal, characteristic, complemented
2#15691697C312yesmaximal, complemented
3C3×#11760454C311yesmaximal, characteristic, complemented
4#15691678C319yesmaximal, complemented
5#15691677C319yesmaximal, complemented
6#15691661C312yesmaximal, complemented
7#15691657C312yesmaximal, complemented
8#15691655C311yesmaximal, characteristic, complemented
9#15691650C319yesmaximal, complemented
10C3×#11760442C312yesmaximal, complemented
11C3×#11760440C311yesmaximal, characteristic, complemented
12C13×#6910C311yesmaximal, characteristic, complemented
13#11760454—33no—
14#11760454—36no—
15#11760454—36no—
16#11760454C32118yescomplemented
17#11760453—36no—
18#11760452—36no—
19#11760452C3219yescomplemented
20C3×#66851—33no—
21C3×#66851C3212yes—
22C3×#66851C3212yes—
23C3×#66851C3211yescharacteristic
24C3×#66848C3213yescomplemented
25C3×#66849C3213yescomplemented
263−1+2×C13⋊C3—36no—
27C3×C32⋊(C13⋊C3)C3211yescharacteristic
28C3×C32⋊(C13⋊C3)C3212yes—
29C32×C13⋊C9C3211yescharacteristic
30C3×C9×C13⋊C3C3213yescomplemented
31#11760442C3216yescomplemented
32#11760442C3216yescomplemented
33#11760442C3216yescomplemented
34#11760440C3213yes—
35#11760440C3213yes—
36#11760440C3213yes—
37#11760438C32118yescomplemented
38#11760436C32118yescomplemented
39#11760434C3219yescomplemented
40C3×C13×3−1+2C3212yes—
41C3×C13×3−1+2C3211yescharacteristic
42C3×C13×H(3,𝔽3)C3211yescharacteristic
43C13×#731C3219yescomplemented
44#10624936—131nomaximal, Sylow
45C33×C13—31no—
46C33×C13C3311yescharacteristic
47C32×C13⋊C3—32no—
48C32×C13⋊C3C3313yes—
49C13×3−1+2—32no—
50C13×3−1+2—32no—
51C13×3−1+2—32no—
52C13×3−1+2—31no—
53C13×3−1+2C3316yes—
54C13×H(3,𝔽3)—32no—
55C13×H(3,𝔽3)C3313yes—
56C3×C9×C13—32no—
57C3×C9×C13C3313yes—
58C32⋊(C13⋊C3)—32no—
59C32⋊(C13⋊C3)—32no—
60C32⋊(C13⋊C3)—31no—
61C32⋊(C13⋊C3)—32no—
62C32⋊(C13⋊C3)C3316yes—
63#66851—32no—
64#66851—32no—
65#66851—32no—
66#66851—32no—
67#66851—318no—
68#66851H(3,𝔽3)13yes—
69#66851H(3,𝔽3)16yes—
70#66851C3316yes—
71#66851C3316yes—
72C3×C13⋊C9—32no—
73C3×C13⋊C9—31no—
74C3×C13⋊C9—32no—
75C3×C13⋊C9—32no—
76C3×C13⋊C9—39no—
77C3×C13⋊C9C3311yescharacteristic
78C3×C13⋊C9C3311yescharacteristic
79C3×C13⋊C9C3311yescharacteristic
80C3×C13⋊C9C3313yes—
81#66849—318no—
82#66849—39no—
83#66848—318no—
84#66848—39no—
85C9×C13⋊C3—39no—
86C9×C13⋊C3—318no—
873−1+4—132no—
883−1+4—131no—
89C3×#737—131no—
90#6913—139no—
91#6913—139no—
92#6910—132no—
93#6910C13⋊C311yescharacteristic, complemented
94#6909—132no—
95#6909—131no—
96#6908—139no—
97C3×#733—132no—
98C3×#732—131no—
99C32×C13—33no—
100C32×C13—91no—
101C32×C13—271no—
102C32×C13C3×H(3,𝔽3)12yes—
103C32×C13C3×H(3,𝔽3)11yescharacteristic
104C32×C13C3411yescharacteristic
105C3×C13⋊C3—33no—
106C3×C13⋊C3—36no—
107C3×C13⋊C3—93no—
108C3×C13⋊C3—272no—
109C9×C13—36no—
110C9×C13—33no—
111C13⋊C9—31no—
112C13⋊C9—36no—
113C13⋊C9—31no—
114C13⋊C9—31no—
115C13⋊C9—36no—
116C13⋊C9C3×H(3,𝔽3)19yes—
117#737—1318no—
118#737—139no—
119#737—396no—
120#737—396no—
121#737—393no—
122#737—396no—
123#737—396no—
124C3×3−1+2—131no—
125C3×3−1+2—133no—
126C3×3−1+2—133no—
127C3×3−1+2—132no—
128C3×3−1+2—132no—
129C3×3−1+2—396no—
130C3×3−1+2—393no—
131C3×3−1+2C3×C13⋊C312yes—
132C3×3−1+2C3×C13⋊C311yescharacteristic
133C3×H(3,𝔽3)—132no—
134C3×H(3,𝔽3)—131no—
135C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic
136C32×C9—131no—
137C32×C9—133no—
138#733—136no—
139#733—136no—
140#733—136no—
141#732—133no—
142#732—133no—
143#732—133no—
144#731—1318no—
145#731C3×C13⋊C319yescomplemented
146AΣL(1,𝔽27)—1318no—
147AΣL(1,𝔽27)—139no—
148C3×C13—31no—
149C3×C13—31no—
150C3×C13—32no—
151C3×C13—93no—
152C3×C13C32×H(3,𝔽3)11yescharacteristic
153C13⋊C3—93no—
154C13⋊C3—96no—
155C33—31no—
156C33—133no—
157C33—392no—
158C33C32×C13⋊C311yescharacteristic
1593−1+2—32no—
1603−1+2—32no—
1613−1+2—32no—
1623−1+2—31no—
1633−1+2—133no—
1643−1+2—136no—
1653−1+2—136no—
1663−1+2—136no—
1673−1+2—399no—
1683−1+2—3918no—
1693−1+2—399no—
1703−1+2—3918no—
1713−1+2—3918no—
1723−1+2—392no—
1733−1+2—392no—
1743−1+2—392no—
1753−1+2—392no—
1763−1+2C32×C13⋊C316yes—
177H(3,𝔽3)—32no—
178H(3,𝔽3)—136no—
179H(3,𝔽3)—392no—
180H(3,𝔽3)—392no—
181H(3,𝔽3)—392no—
182H(3,𝔽3)—391no—
183H(3,𝔽3)C32×C13⋊C313yes—
184C3×C9—32no—
185C3×C9—133no—
186C3×C9—131no—
187C3×C9—131no—
188C3×C9—131no—
189C3×C9—399no—
190C3×C9—3918no—
191C3×C9—399no—
192C3×C9—392no—
193C3×C9—391no—
194C3×C9—392no—
195C3×C9—392no—
196C3×C9C32×C13⋊C313yes—
197C13#1062493611yescharacteristic, complemented, Sylow
198C32—33no—
199C32—91no—
200C32—271no—
201C32—396no—
202C32—393no—
203C32—3512no—
204C32—1173no—
205C32H(3,𝔽3)×C13⋊C312yes—
206C32H(3,𝔽3)×C13⋊C311yescharacteristic
207C32C33×C13⋊C311yescharacteristic
208C9—36no—
209C9—33no—
210C9—139no—
211C9—391no—
212C9—391no—
213C9—391no—
214C9—396no—
215C9—396no—
216C3—31no—
217C3—31no—
218C3—32no—
219C3—93no—
220C3—1176no—
221C3—1173no—
222C3C3×H(3,𝔽3)×C13⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×#6910C3
socleC3×C13C32×H(3,𝔽3)
hypercenter#6910C13⋊C3
hypocenterC13#10624936
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ #6910

Complements

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

NH ≅ G/Ntype
1. #15691698C3semidirect
2. #15691697C3semidirect
3. C3×#11760454C3semidirect
4. #15691678C3semidirect
5. #15691677C3semidirect
6. #15691661C3semidirect
7. #15691657C3semidirect
8. #15691655C3semidirect
9. #15691650C3semidirect
10. C3×#11760442C3semidirect
11. C3×#11760440C3semidirect
12. C13×#6910C3semidirect
16. #11760454C32semidirect
19. #11760452C32semidirect
24. C3×#66848C32semidirect
25. C3×#66849C32semidirect
30. C3×C9×C13⋊C3C32semidirect
31. #11760442C32semidirect
32. #11760442C32semidirect
33. #11760442C32semidirect
37. #11760438C32semidirect
38. #11760436C32semidirect
39. #11760434C32semidirect
43. C13×#731C32semidirect
93. #6910C13⋊C3semidirect
145. #731C3×C13⋊C3semidirect
197. C13#10624936semidirect