Finite Group Databasebeta

← #23748593

Subgroups — #23748593

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#15691696C313yesmaximal, complemented
2C3×#11760453C311yesmaximal, characteristic, complemented
3#15691677C316yesmaximal, complemented
4#15691673C316yesmaximal, complemented
5#15691672C316yesmaximal, complemented
6#15691658C313yesmaximal, complemented
7#15691654C313yesmaximal, complemented
8#15691652C314yesmaximal, complemented
9#15691651C312yesmaximal, complemented
10#15691649C312yesmaximal, complemented
11C13⋊C3×#733C312yesmaximal, complemented
12C13⋊C3×#732C311yesmaximal, characteristic, complemented
13C13×#6908C311yesmaximal, characteristic, complemented
14#11760454—312no—
15#11760454C32112yescomplemented
16#11760453—32no—
17#11760453—31no—
18#11760453—32no—
19#11760453—34no—
20#11760453—36no—
21#11760453C3216yescomplemented
22#11760452C3216yescomplemented
23C3×#66851C3212yescomplemented
24C3×#66848—33no—
25C3×#66848C3211yescharacteristic
26C3×#66848C3212yescomplemented
27C3×#66849C3211yescharacteristic
28C3×#66849C3212yescomplemented
293−1+2×C13⋊C3—36no—
303−1+2×C13⋊C3C3216yes—
31C3×C32⋊(C13⋊C3)C3211yescharacteristic
32H(3,𝔽3)×C13⋊C3C3213yes—
33C3×C9×C13⋊C3C3211yescharacteristic
34C3×C9×C13⋊C3C3212yescomplemented
35#11760443C3214yescomplemented
36#11760442C32112yescomplemented
37#11760441C3212yes—
38#11760440C3216yes—
39#11760439C32112yescomplemented
40#11760438C3216yescomplemented
41#11760437C3216yescomplemented
42#11760436C32112yescomplemented
43#11760435C3216yescomplemented
44#11760434C3216yescomplemented
45C13×#737C3213yescomplemented
46C32×C9×C13C3211yescharacteristic, complemented
47C13×#733C3212yescomplemented
48C13×#732C3211yescharacteristic
49C13×#731C3213yescomplemented
50C13×AΣL(1,𝔽27)C3213yescomplemented
51#10624936—131nomaximal, Sylow
52C33×C13C3311yescharacteristic
53C32×C13⋊C3—33no—
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)—32no—
67C32⋊(C13⋊C3)—31no—
68C32⋊(C13⋊C3)C3316yes—
69#66851—312no—
70#66851—34no—
71#66851—32no—
72#66851C33112yes—
73C3×C13⋊C9—36no—
74C3×C13⋊C9C3312yes—
75C3×C13⋊C9C3312yes—
76C3×C13⋊C9C3312yes—
77#66849—36no—
78#66849—32no—
79#66849—31no—
80#66849—36no—
81#66849—312no—
82#66849—34no—
83#66849—32no—
84#66848—36no—
85#66848—36no—
86#66848—34no—
87#66848—32no—
88#66848—312no—
89#66848H(3,𝔽3)12yes—
90#66848H(3,𝔽3)11yescharacteristic
91#66848H(3,𝔽3)12yes—
92#66848H(3,𝔽3)14yes—
93C9×C13⋊C3—32no—
94C9×C13⋊C3—31no—
95C9×C13⋊C3—36no—
96C9×C13⋊C3—36no—
97C9×C13⋊C3—34no—
98C9×C13⋊C3—32no—
99C9×C13⋊C3—312no—
1003−1+4—133no—
101C3×#737—131no—
102#6913—136no—
103#6913—136no—
104#6913—136no—
105#6910—133no—
106#6909—133no—
107#6908—132no—
108#6908—134no—
109#6908—132no—
110#6908C13⋊C311yescharacteristic, complemented
111C3×#733—132no—
112C3×#732—131no—
113C32×C13—33no—
114C32×C13—31no—
115C32×C13—91no—
116C32×C13C3411yescharacteristic
117C3×C13⋊C3—32no—
118C3×C13⋊C3—36no—
119C3×C13⋊C3—91no—
120C3×C13⋊C3—92no—
121C3×C13⋊C3—273no—
122C3×C13⋊C3C3×H(3,𝔽3)12yes—
123C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
124C9×C13—31no—
125C9×C13—36no—
126C9×C13—31no—
127C9×C13C3×H(3,𝔽3)12yes—
128C9×C13C3×H(3,𝔽3)11yescharacteristic
129C13⋊C9—312no—
130C13⋊C9—32no—
131C13⋊C9—32no—
132C13⋊C9C3×H(3,𝔽3)14yes—
133C13⋊C9C3×H(3,𝔽3)12yes—
134#737—1312no—
135#737—136no—
136#737—136no—
137#737—391no—
138#737—392no—
139#737—392no—
140#737—394no—
141#737—396no—
142#737—3912no—
143#737C3×C13⋊C313yescomplemented
144C3×3−1+2—132no—
145C3×3−1+2—132no—
146C3×3−1+2—131no—
147C3×3−1+2—131no—
148C3×3−1+2—132no—
149C3×3−1+2—136no—
150C3×3−1+2—393no—
151C3×3−1+2—396no—
152C3×H(3,𝔽3)—133no—
153C3×H(3,𝔽3)—131no—
154C32×C9—131no—
155C32×C9—132no—
156C32×C9C3×C13⋊C311yescharacteristic, complemented
157#733—1312no—
158#733—134no—
159#733C3×C13⋊C312yescomplemented
160#732—136no—
161#732—132no—
162#732C3×C13⋊C311yescharacteristic
163#731—1312no—
164#731—136no—
165#731—136no—
166#731C3×C13⋊C313yescomplemented
167AΣL(1,𝔽27)—136no—
168AΣL(1,𝔽27)—1312no—
169AΣL(1,𝔽27)—136no—
170AΣL(1,𝔽27)C3×C13⋊C313yescomplemented
171C3×C13—31no—
172C3×C13—93no—
173C3×C13—91no—
174C3×C13C32×H(3,𝔽3)11yescharacteristic
175C13⋊C3—31no—
176C13⋊C3—32no—
177C13⋊C3—92no—
178C13⋊C3—96no—
179C33—131no—
180C33—132no—
181C33—393no—
182C33C32×C13⋊C311yescharacteristic
1833−1+2—36no—
1843−1+2—131no—
1853−1+2—132no—
1863−1+2—132no—
1873−1+2—134no—
1883−1+2—1312no—
1893−1+2—3912no—
1903−1+2—394no—
1913−1+2—392no—
1923−1+2—3912no—
1933−1+2—396no—
1943−1+2—392no—
1953−1+2—391no—
1963−1+2—396no—
1973−1+2—394no—
1983−1+2—392no—
1993−1+2—3912no—
2003−1+2—392no—
2013−1+2—394no—
2023−1+2—396no—
2033−1+2—396no—
2043−1+2C32×C13⋊C316yes—
205H(3,𝔽3)—136no—
206H(3,𝔽3)—392no—
207H(3,𝔽3)—391no—
208H(3,𝔽3)—396no—
209H(3,𝔽3)C32×C13⋊C313yes—
210C3×C9—31no—
211C3×C9—32no—
212C3×C9—33no—
213C3×C9—132no—
214C3×C9—132no—
215C3×C9—132no—
216C3×C9—394no—
217C3×C9—392no—
218C3×C9—3912no—
219C3×C9—392no—
220C3×C9—391no—
221C3×C9—396no—
222C3×C9—396no—
223C3×C9—396no—
224C3×C9C32×C13⋊C311yescharacteristic
225C3×C9C32×C13⋊C311yescharacteristic
226C3×C9C32×C13⋊C311yescharacteristic
227C13#1062493611yescharacteristic, complemented, Sylow
228C32—31no—
229C32—33no—
230C32—91no—
231C32—132no—
232C32—131no—
233C32—396no—
234C32—392no—
235C32—3513no—
236C32—1171no—
237C32—1172no—
238C32C33×C13⋊C311yescharacteristic
239C9—31no—
240C9—31no—
241C9—36no—
242C9—134no—
243C9—132no—
244C9—392no—
245C9—392no—
246C9—3912no—
247C9H(3,𝔽3)×C13⋊C311yescharacteristic
248C9H(3,𝔽3)×C13⋊C312yes—
249C3—31no—
250C3—91no—
251C3—93no—
252C3—391no—
253C3—392no—
254C3—1176no—
255C3—1172no—
256C3C3×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#10624936
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. C3×#11760453C3semidirect
3. #15691677C3semidirect
4. #15691673C3semidirect
5. #15691672C3semidirect
6. #15691658C3semidirect
7. #15691654C3semidirect
8. #15691652C3semidirect
9. #15691651C3semidirect
10. #15691649C3semidirect
11. C13⋊C3×#733C3semidirect
12. C13⋊C3×#732C3semidirect
13. C13×#6908C3semidirect
15. #11760454C32semidirect
21. #11760453C32semidirect
22. #11760452C32semidirect
23. C3×#66851C32semidirect
26. C3×#66848C32semidirect
28. C3×#66849C32semidirect
34. C3×C9×C13⋊C3C32semidirect
35. #11760443C32semidirect
36. #11760442C32semidirect
39. #11760439C32semidirect
40. #11760438C32semidirect
41. #11760437C32semidirect
42. #11760436C32semidirect
43. #11760435C32semidirect
44. #11760434C32semidirect
45. C13×#737C32semidirect
46. C32×C9×C13C32semidirect
47. C13×#733C32semidirect
49. C13×#731C32semidirect
50. C13×AΣL(1,𝔽27)C32semidirect
110. #6908C13⋊C3semidirect
143. #737C3×C13⋊C3semidirect
156. C32×C9C3×C13⋊C3semidirect
159. #733C3×C13⋊C3semidirect
166. #731C3×C13⋊C3semidirect
170. AΣL(1,𝔽27)C3×C13⋊C3semidirect
227. C13#10624936semidirect