Finite Group Databasebeta

← #23748556

Subgroups — #23748556

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
3C3×H(3,𝔽3)×C13⋊C3C311yesmaximal, characteristic, complemented
4#15691657C312yesmaximal, complemented
5#15691656C312yesmaximal, complemented
6#15691655C311yesmaximal, characteristic, complemented
7#15691654C319yesmaximal, complemented
8#15691653C319yesmaximal, complemented
9C3×#11760436C312yesmaximal, complemented
10C3×#11760434C311yesmaximal, characteristic, complemented
11C13⋊C3×AΣL(1,𝔽27)C319yesmaximal, complemented
12C13×#6909C311yesmaximal, characteristic, complemented
13C33×C13⋊C3C3213yescomplemented
14C33×C13⋊C3C3211yescharacteristic, complemented
15#11760454—36no—
16#11760454—36no—
17#11760453—36no—
18C3×#66851C3212yescomplemented
19C3×#66851C3212yescomplemented
203−1+2×C13⋊C3C32118yescomplemented
21C3×C32⋊(C13⋊C3)—33no—
22C3×C32⋊(C13⋊C3)C3211yescharacteristic
23C3×C32⋊(C13⋊C3)C3213yescomplemented
24C3×C32⋊(C13⋊C3)C3213yescomplemented
25C3×C32⋊(C13⋊C3)C3211yescharacteristic, complemented
26C3×C32⋊(C13⋊C3)C3212yescomplemented
27H(3,𝔽3)×C13⋊C3—36no—
28H(3,𝔽3)×C13⋊C3—33no—
29H(3,𝔽3)×C13⋊C3—36no—
30H(3,𝔽3)×C13⋊C3C3219yescomplemented
31#11760436C3216yescomplemented
32#11760436C32118yescomplemented
33#11760436C3216yescomplemented
34#11760436C3216yescomplemented
35#11760435C32118yescomplemented
36#11760434C3213yescomplemented
37#11760434C3219yescomplemented
38#11760434C3213yescomplemented
39#11760434C3213yescomplemented
40C3×C13×3−1+2C3212yescomplemented
41C3×C13×H(3,𝔽3)C3211yescharacteristic, complemented
42C3×C13×H(3,𝔽3)C3211yescharacteristic, complemented
43C13×AΣL(1,𝔽27)C3219yescomplemented
44#10624930—131nomaximal, Sylow
45C33×C13—31no—
46C33×C13C3313yes—
47C33×C13C3311yescharacteristic
48C32×C13⋊C3—31no—
49C32×C13⋊C3—32no—
50C32×C13⋊C3—32no—
51C32×C13⋊C3—39no—
52C32×C13⋊C3—39no—
53C32×C13⋊C3—99no—
54C32×C13⋊C3—93no—
55C32×C13⋊C3C3311yescharacteristic
56C32×C13⋊C3C3313yes—
57C32×C13⋊C3C3311yescharacteristic
58C32×C13⋊C3C3311yescharacteristic
59C32×C13⋊C3C3313yes—
60C13×3−1+2—32no—
61C13×3−1+2—32no—
62C13×3−1+2C3316yes—
63C13×H(3,𝔽3)—31no—
64C13×H(3,𝔽3)—32no—
65C13×H(3,𝔽3)—32no—
66C13×H(3,𝔽3)C3313yes—
67C3×C9×C13—32no—
68C32⋊(C13⋊C3)—31no—
69C32⋊(C13⋊C3)—32no—
70C32⋊(C13⋊C3)—32no—
71C32⋊(C13⋊C3)—32no—
72C32⋊(C13⋊C3)—39no—
73C32⋊(C13⋊C3)—39no—
74C32⋊(C13⋊C3)—318no—
75C32⋊(C13⋊C3)H(3,𝔽3)16yes—
76C32⋊(C13⋊C3)H(3,𝔽3)13yes—
77C32⋊(C13⋊C3)C3316yes—
78#66851—32no—
79#66851—32no—
80#66851—32no—
81#66851—32no—
82#66851C3316yes—
83#66851C3316yes—
84C3×C13⋊C9—32no—
85C3×C13⋊C9—32no—
86#66849—318no—
87#66848—318no—
88C9×C13⋊C3—318no—
893−1+4—132no—
90H(5,𝔽3)—131no—
91C32×H(3,𝔽3)—131no—
92#6909—132no—
93#6909—131no—
94#6909—132no—
95#6909—139no—
96#6909—139no—
97#6909C13⋊C311yescharacteristic, complemented
98C3×AΣL(1,𝔽27)—132no—
99C3×AΣL(1,𝔽27)—131no—
100C3×AΣL(1,𝔽27)—139no—
101C32×C13—33no—
102C32×C13—33no—
103C32×C13—91no—
104C32×C13—93no—
105C32×C13—271no—
106C32×C13C3×H(3,𝔽3)11yescharacteristic
107C32×C13C3×H(3,𝔽3)12yes—
108C32×C13C3411yescharacteristic
109C3×C13⋊C3—31no—
110C3×C13⋊C3—33no—
111C3×C13⋊C3—33no—
112C3×C13⋊C3—31no—
113C3×C13⋊C3—31no—
114C3×C13⋊C3—36no—
115C3×C13⋊C3—93no—
116C3×C13⋊C3—927no—
117C3×C13⋊C3—96no—
118C3×C13⋊C3—93no—
119C3×C13⋊C3—93no—
120C3×C13⋊C3—91no—
121C3×C13⋊C3—91no—
122C3×C13⋊C3—279no—
123C3×C13⋊C3—272no—
124C3×C13⋊C3C3×H(3,𝔽3)19yes—
125C9×C13—36no—
126C13⋊C9—36no—
127C13⋊C9—36no—
128C34—133no—
129C34—131no—
130#737—396no—
131#737—396no—
132#737—396no—
133C3×3−1+2—132no—
134C3×3−1+2—132no—
135C3×3−1+2—1318no—
136C3×3−1+2C3×C13⋊C312yescomplemented
137C3×H(3,𝔽3)—131no—
138C3×H(3,𝔽3)—132no—
139C3×H(3,𝔽3)—139no—
140C3×H(3,𝔽3)—133no—
141C3×H(3,𝔽3)—133no—
142C3×H(3,𝔽3)—131no—
143C3×H(3,𝔽3)—396no—
144C3×H(3,𝔽3)—393no—
145C3×H(3,𝔽3)—396no—
146C3×H(3,𝔽3)—393no—
147C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic, complemented
148C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic, complemented
149AΣL(1,𝔽27)—1318no—
150AΣL(1,𝔽27)—136no—
151AΣL(1,𝔽27)—1318no—
152AΣL(1,𝔽27)—136no—
153AΣL(1,𝔽27)—136no—
154AΣL(1,𝔽27)—133no—
155AΣL(1,𝔽27)—139no—
156AΣL(1,𝔽27)—133no—
157AΣL(1,𝔽27)—133no—
158AΣL(1,𝔽27)C3×C13⋊C319yescomplemented
159C3×C13—31no—
160C3×C13—32no—
161C3×C13—31no—
162C3×C13—93no—
163C3×C13—93no—
164C3×C13C32×H(3,𝔽3)11yescharacteristic
165C13⋊C3—33no—
166C13⋊C3—39no—
167C13⋊C3—93no—
168C13⋊C3—91no—
169C13⋊C3—91no—
170C13⋊C3—96no—
171C33—31no—
172C33—133no—
173C33—131no—
174C33—131no—
175C33—131no—
176C33—133no—
177C33—399no—
178C33—399no—
179C33—392no—
180C33—392no—
181C33—391no—
182C33—1173no—
183C33—1179no—
184C33C32×C13⋊C313yes—
185C33C32×C13⋊C311yescharacteristic
1863−1+2—32no—
1873−1+2—32no—
1883−1+2—136no—
1893−1+2—136no—
1903−1+2—3918no—
1913−1+2—3918no—
1923−1+2—392no—
1933−1+2—392no—
1943−1+2—392no—
1953−1+2—392no—
1963−1+2C32×C13⋊C316yes—
197H(3,𝔽3)—32no—
198H(3,𝔽3)—31no—
199H(3,𝔽3)—32no—
200H(3,𝔽3)—136no—
201H(3,𝔽3)—133no—
202H(3,𝔽3)—136no—
203H(3,𝔽3)—399no—
204H(3,𝔽3)—399no—
205H(3,𝔽3)—3918no—
206H(3,𝔽3)—392no—
207H(3,𝔽3)—392no—
208H(3,𝔽3)—392no—
209H(3,𝔽3)—391no—
210H(3,𝔽3)C32×C13⋊C313yes—
211C3×C9—32no—
212C3×C9—3918no—
213C3×C9—392no—
214C3×C9—392no—
215C13#1062493011yescharacteristic, complemented, Sylow
216C32—33no—
217C32—33no—
218C32—91no—
219C32—93no—
220C32—139no—
221C32—271no—
222C32—393no—
223C32—391no—
224C32—396no—
225C32—391no—
226C32—391no—
227C32—393no—
228C32—3512no—
229C32—3519no—
230C32—1173no—
231C32—1173no—
232C32—1176no—
233C32—1171no—
234C32—1171no—
235C32—1173no—
236C32—11727no—
237C32H(3,𝔽3)×C13⋊C312yes—
238C32H(3,𝔽3)×C13⋊C311yescharacteristic
239C32C33×C13⋊C311yescharacteristic
240C9—36no—
241C9—396no—
242C9—396no—
243C3—31no—
244C3—31no—
245C3—32no—
246C3—93no—
247C3—93no—
248C3—399no—
249C3—393no—
250C3—1176no—
251C3—1171no—
252C3—1171no—
253C3—1173no—
254C3C3×H(3,𝔽3)×C13⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×#6909C3
socleC3×C13C32×H(3,𝔽3)
hypercenter#6909C13⋊C3
hypocenterC13#10624930
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ #6909

Complements

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

NH ≅ G/Ntype
1. #15691697C3semidirect
2. C13⋊H(5,𝔽3)C3semidirect
3. C3×H(3,𝔽3)×C13⋊C3C3semidirect
4. #15691657C3semidirect
5. #15691656C3semidirect
6. #15691655C3semidirect
7. #15691654C3semidirect
8. #15691653C3semidirect
9. C3×#11760436C3semidirect
10. C3×#11760434C3semidirect
11. C13⋊C3×AΣL(1,𝔽27)C3semidirect
12. C13×#6909C3semidirect
13. C33×C13⋊C3C32semidirect
14. C33×C13⋊C3C32semidirect
18. C3×#66851C32semidirect
19. C3×#66851C32semidirect
20. 3−1+2×C13⋊C3C32semidirect
23. C3×C32⋊(C13⋊C3)C32semidirect
24. C3×C32⋊(C13⋊C3)C32semidirect
25. C3×C32⋊(C13⋊C3)C32semidirect
26. C3×C32⋊(C13⋊C3)C32semidirect
30. H(3,𝔽3)×C13⋊C3C32semidirect
31. #11760436C32semidirect
32. #11760436C32semidirect
33. #11760436C32semidirect
34. #11760436C32semidirect
35. #11760435C32semidirect
36. #11760434C32semidirect
37. #11760434C32semidirect
38. #11760434C32semidirect
39. #11760434C32semidirect
40. C3×C13×3−1+2C32semidirect
41. C3×C13×H(3,𝔽3)C32semidirect
42. C3×C13×H(3,𝔽3)C32semidirect
43. C13×AΣL(1,𝔽27)C32semidirect
97. #6909C13⋊C3semidirect
136. C3×3−1+2C3×C13⋊C3semidirect
147. C3×H(3,𝔽3)C3×C13⋊C3semidirect
148. C3×H(3,𝔽3)C3×C13⋊C3semidirect
158. AΣL(1,𝔽27)C3×C13⋊C3semidirect
215. C13#10624930semidirect