Finite Group Databasebeta

← #23748551

Subgroups — #23748551

Order 9477.

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

normal subgroups only

This group has 960 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
1C3×#11760454C312yesmaximal, complemented
2C3×#11760454C311yesmaximal, characteristic, complemented
3C3×#11760452C311yesmaximal, characteristic, complemented
4#15691678C319yesmaximal, complemented
5#15691677C319yesmaximal, complemented
6#15691669C312yesmaximal, complemented
7#15691665C311yesmaximal, characteristic, complemented
8#15691661C312yesmaximal, complemented
9#15691657C312yesmaximal, complemented
10#15691655C311yesmaximal, characteristic, complemented
11#15691650C319yesmaximal, complemented
12C13×#6910C311yesmaximal, characteristic, complemented
13#11760454—32no—
14#11760454—32no—
15#11760454—32no—
16#11760454—32no—
17#11760454—32no—
18#11760454—32no—
19#11760454—32no—
20#11760454—31no—
21#11760454—32no—
22#11760454—32no—
23#11760454—32no—
24#11760454C3216yescomplemented
25#11760454C3216yescomplemented
26#11760454C3216yescomplemented
27#11760452—32no—
28#11760452—32no—
29#11760452—32no—
30#11760452C3213yescomplemented
31#11760452C3213yescomplemented
32#11760452C3213yescomplemented
33C3×#66851—32no—
34C3×#66851C3212yes—
35C3×#66851C3212yes—
36C3×#66851C3211yescharacteristic
37C3×#66848—32no—
38C3×#66848C3213yescomplemented
39C3×#66849—32no—
40C3×#66849C3213yescomplemented
41C3×C32⋊(C13⋊C3)C3211yescharacteristic
42C3×C32⋊(C13⋊C3)C3212yes—
43C32×C13⋊C9—31no—
44C32×C13⋊C9C3211yescharacteristic
45C3×C9×C13⋊C3—32no—
46C3×C9×C13⋊C3C3213yescomplemented
47#11760442C32118yescomplemented
48#11760440C3219yes—
49#11760438C32118yescomplemented
50#11760436C32118yescomplemented
51#11760434C3219yescomplemented
52C3×C13×3−1+2C3212yes—
53C3×C13×3−1+2C3211yescharacteristic
54C3×C13×H(3,𝔽3)C3211yescharacteristic
55C13×#731C3219yescomplemented
56#10624929—131nomaximal, Sylow
57C33×C13—31no—
58C33×C13C3311yescharacteristic
59C32×C13⋊C3—32no—
60C32×C13⋊C3C3313yes—
61C13×3−1+2—32no—
62C13×3−1+2—32no—
63C13×3−1+2—31no—
64C13×3−1+2—32no—
65C13×3−1+2C3316yes—
66C13×H(3,𝔽3)—32no—
67C13×H(3,𝔽3)C3313yes—
68C3×C9×C13—32no—
69C3×C9×C13C3313yes—
70C32⋊(C13⋊C3)—31no—
71C32⋊(C13⋊C3)—32no—
72C32⋊(C13⋊C3)—32no—
73C32⋊(C13⋊C3)—32no—
74C32⋊(C13⋊C3)C3316yes—
75#66851—34no—
76#66851—32no—
77#66851—32no—
78#66851—31no—
79#66851—32no—
80#66851—36no—
81#66851—36no—
82#66851—36no—
83#66851C3316yes—
84#66851C3316yes—
85C3×C13⋊C9—32no—
86C3×C13⋊C9—32no—
87C3×C13⋊C9—33no—
88C3×C13⋊C9—33no—
89C3×C13⋊C9—33no—
90C3×C13⋊C9H(3,𝔽3)12yes—
91C3×C13⋊C9H(3,𝔽3)11yescharacteristic
92C3×C13⋊C9H(3,𝔽3)12yes—
93C3×C13⋊C9H(3,𝔽3)12yes—
94C3×C13⋊C9H(3,𝔽3)12yes—
95C3×C13⋊C9C3313yes—
96C3×C13⋊C9C3311yescharacteristic
97C3×C13⋊C9C3311yescharacteristic
98C3×C13⋊C9C3311yescharacteristic
99#66849—36no—
100#66849—36no—
101#66849—36no—
102#66849—36no—
103#66849—33no—
104#66848—36no—
105#66848—36no—
106#66848—36no—
107#66848—36no—
108#66848—33no—
109C9×C13⋊C3—36no—
110C9×C13⋊C3—36no—
111C9×C13⋊C3—36no—
112C9×C13⋊C3—33no—
113C9×C13⋊C3—36no—
114C3×#737—131no—
115C3×#737—132no—
116C3×#737—131no—
117#6913—139no—
118#6913—139no—
119#6912—132no—
120#6911—131no—
121#6910—132no—
122#6910C13⋊C311yescharacteristic, complemented
123#6909—132no—
124#6909—131no—
125#6908—139no—
126C32×C13—33no—
127C32×C13—91no—
128C32×C13—93no—
129C32×C13C3×H(3,𝔽3)11yescharacteristic
130C32×C13C3×H(3,𝔽3)12yes—
131C32×C13C3411yescharacteristic
132C3×C13⋊C3—33no—
133C3×C13⋊C3—36no—
134C3×C13⋊C3—96no—
135C3×C13⋊C3—93no—
136C9×C13—36no—
137C9×C13—33no—
138C13⋊C9—36no—
139C13⋊C9—33no—
140C13⋊C9—36no—
141C13⋊C9C3×H(3,𝔽3)11yescharacteristic
142C13⋊C9C3×H(3,𝔽3)12yes—
143C13⋊C9C3×H(3,𝔽3)12yes—
144C13⋊C9C3×H(3,𝔽3)12yes—
145C13⋊C9C3×H(3,𝔽3)11yescharacteristic
146C13⋊C9C3×H(3,𝔽3)11yescharacteristic
147#737—136no—
148#737—136no—
149#737—136no—
150#737—133no—
151#737—133no—
152#737—133no—
153#737—392no—
154#737—392no—
155#737—392no—
156#737—392no—
157#737—391no—
158#737—392no—
159#737—392no—
160#737—392no—
161#737—392no—
162#737—392no—
163#737—392no—
164#737—392no—
165#737—392no—
166#737—392no—
167C3×3−1+2—131no—
168C3×3−1+2—133no—
169C3×3−1+2—133no—
170C3×3−1+2—132no—
171C3×3−1+2—132no—
172C3×3−1+2—392no—
173C3×3−1+2—392no—
174C3×3−1+2—392no—
175C3×3−1+2C3×C13⋊C312yes—
176C3×3−1+2C3×C13⋊C311yescharacteristic
177C3×H(3,𝔽3)—132no—
178C3×H(3,𝔽3)—131no—
179C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic
180C32×C9—131no—
181C32×C9—133no—
182C32×C9—392no—
183C32×C9—391no—
184#733—1318no—
185#732—139no—
186#731—1318no—
187#731C3×C13⋊C319yescomplemented
188AΣL(1,𝔽27)—1318no—
189AΣL(1,𝔽27)—139no—
190C3×C13—32no—
191C3×C13—31no—
192C3×C13—31no—
193C3×C13—93no—
194C3×C13C32×H(3,𝔽3)11yescharacteristic
195C13⋊C3—93no—
196C13⋊C3—96no—
197C33—31no—
198C33—133no—
199C33—392no—
200C33C32×C13⋊C311yescharacteristic
2013−1+2—32no—
2023−1+2—32no—
2033−1+2—32no—
2043−1+2—31no—
2053−1+2—136no—
2063−1+2—136no—
2073−1+2—396no—
2083−1+2—393no—
2093−1+2—396no—
2103−1+2—396no—
2113−1+2—396no—
2123−1+2—396no—
2133−1+2—393no—
2143−1+2—396no—
2153−1+2—396no—
2163−1+2—396no—
2173−1+2—396no—
2183−1+2—396no—
2193−1+2—396no—
2203−1+2—392no—
2213−1+2—391no—
2223−1+2—394no—
2233−1+2—392no—
2243−1+2—392no—
2253−1+2C32×C13⋊C316yes—
226H(3,𝔽3)—32no—
227H(3,𝔽3)—136no—
228H(3,𝔽3)—392no—
229H(3,𝔽3)—392no—
230H(3,𝔽3)—392no—
231H(3,𝔽3)—391no—
232H(3,𝔽3)C32×C13⋊C313yes—
233C3×C9—32no—
234C3×C9—132no—
235C3×C9—131no—
236C3×C9—132no—
237C3×C9—132no—
238C3×C9—132no—
239C3×C9—131no—
240C3×C9—131no—
241C3×C9—131no—
242C3×C9—133no—
243C3×C9—393no—
244C3×C9—396no—
245C3×C9—396no—
246C3×C9—396no—
247C3×C9—396no—
248C3×C9—393no—
249C3×C9—393no—
250C3×C9—393no—
251C3×C9—392no—
252C3×C9—392no—
253C3×C9C32×C13⋊C313yes—
254C13#1062492911yescharacteristic, complemented, Sylow
255C32—33no—
256C32—91no—
257C32—93no—
258C32—396no—
259C32—393no—
260C32—1173no—
261C32—1176no—
262C32H(3,𝔽3)×C13⋊C312yes—
263C32H(3,𝔽3)×C13⋊C311yescharacteristic
264C32C33×C13⋊C311yescharacteristic
265C9—36no—
266C9—33no—
267C9—131no—
268C9—132no—
269C9—132no—
270C9—131no—
271C9—131no—
272C9—132no—
273C9—393no—
274C9—396no—
275C9—396no—
276C3—31no—
277C3—32no—
278C3—31no—
279C3—93no—
280C3—1176no—
281C3—1173no—
282C3C3×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#10624929
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. C3×#11760454C3semidirect
2. C3×#11760454C3semidirect
3. C3×#11760452C3semidirect
4. #15691678C3semidirect
5. #15691677C3semidirect
6. #15691669C3semidirect
7. #15691665C3semidirect
8. #15691661C3semidirect
9. #15691657C3semidirect
10. #15691655C3semidirect
11. #15691650C3semidirect
12. C13×#6910C3semidirect
24. #11760454C32semidirect
25. #11760454C32semidirect
26. #11760454C32semidirect
30. #11760452C32semidirect
31. #11760452C32semidirect
32. #11760452C32semidirect
38. C3×#66848C32semidirect
40. C3×#66849C32semidirect
46. C3×C9×C13⋊C3C32semidirect
47. #11760442C32semidirect
49. #11760438C32semidirect
50. #11760436C32semidirect
51. #11760434C32semidirect
55. C13×#731C32semidirect
122. #6910C13⋊C3semidirect
187. #731C3×C13⋊C3semidirect
254. C13#10624929semidirect