Finite Group Databasebeta

← #23748573

Subgroups — #23748573

Order 9477.

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

normal subgroups only

This group has 980 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#15691696C313yesmaximal, complemented
2C32×#66848C311yesmaximal, characteristic, complemented
3#15691680C314yesmaximal, complemented
4#15691678C316yesmaximal, complemented
5#15691675C312yesmaximal, complemented
6#15691673C316yesmaximal, complemented
7#15691667C312yesmaximal, complemented
8#15691663C311yesmaximal, characteristic, complemented
9#15691659C313yesmaximal, complemented
10#15691651C312yesmaximal, complemented
11#15691647C316yesmaximal, complemented
12C13⋊C3×AΣL(1,𝔽27)C313yesmaximal, complemented
13C13×#6908C311yesmaximal, characteristic, complemented
14C33×C13⋊C3C3211yescharacteristic
15#11760454—312no—
16#11760454C32112yescomplemented
17#11760453—36no—
18#11760453C3216yescomplemented
19#11760452C3216yescomplemented
20C3×#66848—36no—
21C3×#66848—33no—
22C3×#66848—33no—
23C3×#66848C3211yescharacteristic
24C3×#66848C3211yescharacteristic
25C3×#66848C3211yescharacteristic
26C3×#66848C3212yescomplemented
27C3×#66848C3212yescomplemented
28C3×#66848C3212yescomplemented
293−1+2×C13⋊C3—36no—
303−1+2×C13⋊C3C3216yes—
31H(3,𝔽3)×C13⋊C3C3213yes—
32C32×C13⋊C9C3212yescomplemented
33#11760443C3214yescomplemented
34#11760442C32112yescomplemented
35#11760441C3212yescomplemented
36#11760440C3216yescomplemented
37#11760439C32112yescomplemented
38#11760438C3216yescomplemented
39#11760437C3216yescomplemented
40#11760436C32112yescomplemented
41#11760435C3216yescomplemented
42#11760434C3216yescomplemented
43C13×#737C3213yescomplemented
44C32×C9×C13C3211yescharacteristic, complemented
45C13×#733C3212yescomplemented
46C13×#732C3211yescharacteristic, complemented
47C13×#731C3213yescomplemented
48C13×AΣL(1,𝔽27)C3213yescomplemented
49#10624934—131nomaximal, Sylow
50C33×C13C3311yescharacteristic
51C32×C13⋊C3—33no—
52C32×C13⋊C3—33no—
53C32×C13⋊C3—93no—
54C32×C13⋊C3C3312yes—
55C32×C13⋊C3C3311yescharacteristic
56C13×3−1+2—36no—
57C13×3−1+2C3316yes—
58C13×H(3,𝔽3)C3313yes—
59C3×C9×C13—32no—
60C3×C9×C13—31no—
61C3×C9×C13—33no—
62C3×C9×C13C3311yescharacteristic
63C3×C9×C13C3311yescharacteristic
64C3×C9×C13C3311yescharacteristic
65C32⋊(C13⋊C3)—36no—
66C32⋊(C13⋊C3)C3316yes—
67#66851—312no—
68#66851C33112yes—
69C3×C13⋊C9—36no—
70C3×C13⋊C9—36no—
71C3×C13⋊C9C3312yes—
72C3×C13⋊C9C3312yes—
73C3×C13⋊C9C3312yes—
74#66849—36no—
75#66849—36no—
76#66849—312no—
77#66848—36no—
78#66848—33no—
79#66848—33no—
80#66848—34no—
81#66848—32no—
82#66848—36no—
83#66848—36no—
84#66848—36no—
85#66848—312no—
86#66848H(3,𝔽3)16yes—
87#66848H(3,𝔽3)13yes—
88C9×C13⋊C3—36no—
89C9×C13⋊C3—36no—
90C9×C13⋊C3—312no—
913−1+4—133no—
92C32×3−1+2—131no—
93#6913—136no—
94#6913—134no—
95#6913—132no—
96#6913—136no—
97#6912—132no—
98#6911—131no—
99#6910—133no—
100#6908—132no—
101#6908—136no—
102#6908C13⋊C311yescharacteristic, complemented
103C3×AΣL(1,𝔽27)—133no—
104C32×C13—33no—
105C32×C13—31no—
106C32×C13—33no—
107C32×C13C3411yescharacteristic
108C3×C13⋊C3—36no—
109C3×C13⋊C3—32no—
110C3×C13⋊C3—91no—
111C3×C13⋊C3—99no—
112C3×C13⋊C3—92no—
113C3×C13⋊C3—273no—
114C3×C13⋊C3C3×H(3,𝔽3)13yes—
115C9×C13—36no—
116C9×C13—31no—
117C9×C13—31no—
118C9×C13C3×H(3,𝔽3)12yes—
119C9×C13C3×H(3,𝔽3)11yescharacteristic
120C13⋊C9—312no—
121C13⋊C9—32no—
122C13⋊C9—32no—
123C13⋊C9C3×H(3,𝔽3)16yes—
124C34—131no—
125#737—1312no—
126#737—136no—
127#737—136no—
128#737—396no—
129#737—3912no—
130#737C3×C13⋊C313yescomplemented
131C3×3−1+2—131no—
132C3×3−1+2—132no—
133C3×3−1+2—132no—
134C3×3−1+2—131no—
135C3×3−1+2—131no—
136C3×3−1+2—132no—
137C3×3−1+2—136no—
138C3×3−1+2—393no—
139C3×3−1+2—396no—
140C3×3−1+2—393no—
141C3×3−1+2—396no—
142C3×H(3,𝔽3)—133no—
143C32×C9—132no—
144C32×C9C3×C13⋊C311yescharacteristic, complemented
145#733—1312no—
146#733—134no—
147#733C3×C13⋊C312yescomplemented
148#732—136no—
149#732—132no—
150#732C3×C13⋊C311yescharacteristic, complemented
151#731—1312no—
152#731—136no—
153#731—136no—
154#731C3×C13⋊C313yescomplemented
155AΣL(1,𝔽27)—136no—
156AΣL(1,𝔽27)—1312no—
157AΣL(1,𝔽27)—136no—
158AΣL(1,𝔽27)C3×C13⋊C313yescomplemented
159C3×C13—33no—
160C3×C13—31no—
161C3×C13—93no—
162C3×C13C32×H(3,𝔽3)11yescharacteristic
163C13⋊C3—33no—
164C13⋊C3—92no—
165C13⋊C3—96no—
166C33—131no—
167C33—132no—
168C33—393no—
169C33—393no—
170C33—1173no—
171C33C32×C13⋊C311yescharacteristic
1723−1+2—36no—
1733−1+2—133no—
1743−1+2—136no—
1753−1+2—1312no—
1763−1+2—396no—
1773−1+2—396no—
1783−1+2—3912no—
1793−1+2—3912no—
1803−1+2—393no—
1813−1+2—393no—
1823−1+2—396no—
1833−1+2—396no—
1843−1+2—3912no—
1853−1+2—392no—
1863−1+2—394no—
1873−1+2—396no—
1883−1+2—396no—
1893−1+2C32×C13⋊C316yes—
190H(3,𝔽3)—136no—
191H(3,𝔽3)—396no—
192H(3,𝔽3)C32×C13⋊C313yes—
193C3×C9—31no—
194C3×C9—32no—
195C3×C9—33no—
196C3×C9—132no—
197C3×C9—132no—
198C3×C9—132no—
199C3×C9—3912no—
200C3×C9—396no—
201C3×C9—396no—
202C3×C9—396no—
203C3×C9—396no—
204C3×C9C32×C13⋊C311yescharacteristic
205C3×C9C32×C13⋊C311yescharacteristic
206C3×C9C32×C13⋊C311yescharacteristic
207C13#1062493411yescharacteristic, complemented, Sylow
208C32—33no—
209C32—31no—
210C32—33no—
211C32—133no—
212C32—396no—
213C32—392no—
214C32—3513no—
215C32—1171no—
216C32—1179no—
217C32—1172no—
218C32C33×C13⋊C311yescharacteristic
219C9—31no—
220C9—31no—
221C9—36no—
222C9—136no—
223C9—392no—
224C9—392no—
225C9—3912no—
226C9H(3,𝔽3)×C13⋊C311yescharacteristic
227C9H(3,𝔽3)×C13⋊C312yes—
228C3—31no—
229C3—33no—
230C3—93no—
231C3—393no—
232C3—1176no—
233C3—1172no—
234C3C3×H(3,𝔽3)×C13⋊C311yescharacteristic
subgroupG/H
centerC3C3×H(3,𝔽3)×C13⋊C3
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC13×#6908C3
socleC3×C13C32×H(3,𝔽3)
hypercenter#6908C13⋊C3
hypocenterC13#10624934
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C3×C9 ◁ #6908

Complements

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

NH ≅ G/Ntype
1. #15691696C3semidirect
2. C32×#66848C3semidirect
3. #15691680C3semidirect
4. #15691678C3semidirect
5. #15691675C3semidirect
6. #15691673C3semidirect
7. #15691667C3semidirect
8. #15691663C3semidirect
9. #15691659C3semidirect
10. #15691651C3semidirect
11. #15691647C3semidirect
12. C13⋊C3×AΣL(1,𝔽27)C3semidirect
13. C13×#6908C3semidirect
16. #11760454C32semidirect
18. #11760453C32semidirect
19. #11760452C32semidirect
26. C3×#66848C32semidirect
27. C3×#66848C32semidirect
28. C3×#66848C32semidirect
32. C32×C13⋊C9C32semidirect
33. #11760443C32semidirect
34. #11760442C32semidirect
35. #11760441C32semidirect
36. #11760440C32semidirect
37. #11760439C32semidirect
38. #11760438C32semidirect
39. #11760437C32semidirect
40. #11760436C32semidirect
41. #11760435C32semidirect
42. #11760434C32semidirect
43. C13×#737C32semidirect
44. C32×C9×C13C32semidirect
45. C13×#733C32semidirect
46. C13×#732C32semidirect
47. C13×#731C32semidirect
48. C13×AΣL(1,𝔽27)C32semidirect
102. #6908C13⋊C3semidirect
130. #737C3×C13⋊C3semidirect
144. C32×C9C3×C13⋊C3semidirect
147. #733C3×C13⋊C3semidirect
150. #732C3×C13⋊C3semidirect
154. #731C3×C13⋊C3semidirect
158. AΣL(1,𝔽27)C3×C13⋊C3semidirect
207. C13#10624934semidirect