Finite Group Databasebeta

← #23748549

Subgroups — #23748549

Order 9477.

960 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 960 conjugacy classes of subgroups — too many to draw. Only its 286 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×#11760453C312yesmaximal, complemented
2C3×#11760453C311yesmaximal, characteristic, complemented
3#15691674C319yesmaximal, complemented
4#15691673C319yesmaximal, complemented
5#15691669C312yesmaximal, complemented
6#15691665C311yesmaximal, characteristic, complemented
7#15691662C312yesmaximal, complemented
8#15691660C311yesmaximal, characteristic, complemented
9#15691657C312yesmaximal, complemented
10#15691655C311yesmaximal, characteristic, complemented
11#15691648C319yesmaximal, complemented
12C3×C13×#737C311yesmaximal, characteristic, complemented
13#11760453—32no—
14#11760453—32no—
15#11760453—32no—
16#11760453—32no—
17#11760453—32no—
18#11760453—32no—
19#11760453—31no—
20#11760453—32no—
21#11760453—32no—
22#11760453—32no—
23#11760453—32no—
24#11760453C3216yescomplemented
25#11760453C3216yescomplemented
26#11760453C3216yescomplemented
27C3×#66851C3212yes—
28C3×#66851C3212yes—
29C3×#66851C3211yescharacteristic
30C3×#66851C3211yescharacteristic
31C3×#66848—32no—
32C3×#66848C3213yescomplemented
33C3×#66849—32no—
34C3×#66849C3213yescomplemented
35C3×C32⋊(C13⋊C3)C3211yescharacteristic
36C3×C32⋊(C13⋊C3)C3212yes—
37C3×C9×C13⋊C3—32no—
38C3×C9×C13⋊C3C3213yescomplemented
39#11760442C32118yescomplemented
40#11760440C3219yes—
41#11760439C32118yescomplemented
42#11760437C3219yescomplemented
43#11760436C32118yescomplemented
44#11760434C3219yescomplemented
45C13×#737—32no—
46C13×#737—32no—
47C13×#737—32no—
48C13×#737C3213yescomplemented
49C13×#737C3213yescomplemented
50C13×#737C3213yescomplemented
51C3×C13×3−1+2—32no—
52C3×C13×3−1+2C3212yes—
53C3×C13×H(3,𝔽3)C3211yescharacteristic
54C32×C9×C13—31no—
55C32×C9×C13C3211yescharacteristic
56#10624929—131nomaximal, Sylow
57C33×C13—31no—
58C33×C13C3311yescharacteristic
59C32×C13⋊C3—32no—
60C32×C13⋊C3C3313yes—
61C13×3−1+2—34no—
62C13×3−1+2—36no—
63C13×3−1+2—36no—
64C13×3−1+2—36no—
65C13×3−1+2C3316yes—
66C13×H(3,𝔽3)—32no—
67C13×H(3,𝔽3)C3313yes—
68C3×C9×C13—32no—
69C3×C9×C13—33no—
70C3×C9×C13—33no—
71C3×C9×C13—33no—
72C3×C9×C13H(3,𝔽3)11yescharacteristic
73C3×C9×C13H(3,𝔽3)12yes—
74C3×C9×C13H(3,𝔽3)12yes—
75C3×C9×C13H(3,𝔽3)12yes—
76C3×C9×C13H(3,𝔽3)12yes—
77C3×C9×C13C3311yescharacteristic
78C3×C9×C13C3311yescharacteristic
79C3×C9×C13C3311yescharacteristic
80C32⋊(C13⋊C3)—32no—
81C32⋊(C13⋊C3)—31no—
82C32⋊(C13⋊C3)—32no—
83C32⋊(C13⋊C3)—32no—
84C32⋊(C13⋊C3)C3316yes—
85#66851—32no—
86#66851—32no—
87#66851—32no—
88#66851—32no—
89#66851—32no—
90#66851—32no—
91#66851—31no—
92#66851—31no—
93#66851C3316yes—
94#66851C3316yes—
95C3×C13⋊C9—32no—
96C3×C13⋊C9—32no—
97C3×C13⋊C9C3313yes—
98C3×C13⋊C9C3313yes—
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—36no—
113C9×C13⋊C3—33no—
114C3×#737—131no—
115C3×#737—132no—
116C3×#737C13⋊C311yescharacteristic, complemented
117#6913—139no—
118#6913—139no—
119#6912—132no—
120#6911—131no—
121#6910—132no—
122#6910—131no—
123#6909—132no—
124#6909—131no—
125#6908—139no—
126C32×C13—33no—
127C32×C13—91no—
128C32×C13—93no—
129C32×C13C3×H(3,𝔽3)12yes—
130C32×C13C3×H(3,𝔽3)11yescharacteristic
131C32×C13C3411yescharacteristic
132C3×C13⋊C3—33no—
133C3×C13⋊C3—36no—
134C3×C13⋊C3—96no—
135C3×C13⋊C3—93no—
136C9×C13—36no—
137C9×C13C3×H(3,𝔽3)12yes—
138C9×C13C3×H(3,𝔽3)12yes—
139C9×C13C3×H(3,𝔽3)12yes—
140C9×C13C3×H(3,𝔽3)11yescharacteristic
141C9×C13C3×H(3,𝔽3)11yescharacteristic
142C9×C13C3×H(3,𝔽3)11yescharacteristic
143C13⋊C9—36no—
144C13⋊C9—36no—
145C13⋊C9—33no—
146C13⋊C9—33no—
147#737—32no—
148#737—32no—
149#737—32no—
150#737—136no—
151#737—136no—
152#737—136no—
153#737—392no—
154#737—392no—
155#737—392no—
156#737—392no—
157#737—392no—
158#737—392no—
159#737—392no—
160#737—391no—
161#737—392no—
162#737—392no—
163#737—392no—
164#737C3×C13⋊C313yescomplemented
165#737C3×C13⋊C313yescomplemented
166#737C3×C13⋊C313yescomplemented
167C3×3−1+2—32no—
168C3×3−1+2—131no—
169C3×3−1+2—131no—
170C3×3−1+2—133no—
171C3×3−1+2—133no—
172C3×3−1+2—132no—
173C3×3−1+2—132no—
174C3×3−1+2—392no—
175C3×3−1+2—392no—
176C3×3−1+2C3×C13⋊C312yes—
177C3×H(3,𝔽3)—132no—
178C3×H(3,𝔽3)—131no—
179C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic
180C32×C9—31no—
181C32×C9—133no—
182C32×C9—392no—
183C32×C9C3×C13⋊C311yescharacteristic
184#733—1318no—
185#732—139no—
186#731—1318no—
187#731—139no—
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—34no—
2023−1+2—36no—
2033−1+2—36no—
2043−1+2—36no—
2053−1+2—136no—
2063−1+2—136no—
2073−1+2—391no—
2083−1+2—391no—
2093−1+2—392no—
2103−1+2—392no—
2113−1+2—392no—
2123−1+2—392no—
2133−1+2—392no—
2143−1+2—392no—
2153−1+2—393no—
2163−1+2—396no—
2173−1+2—396no—
2183−1+2—396no—
2193−1+2—396no—
2203−1+2—393no—
2213−1+2—396no—
2223−1+2—396no—
2233−1+2—396no—
2243−1+2—396no—
2253−1+2C32×C13⋊C316yes—
226H(3,𝔽3)—32no—
227H(3,𝔽3)—136no—
228H(3,𝔽3)—392no—
229H(3,𝔽3)—392no—
230H(3,𝔽3)—391no—
231H(3,𝔽3)—392no—
232H(3,𝔽3)C32×C13⋊C313yes—
233C3×C9—32no—
234C3×C9—33no—
235C3×C9—33no—
236C3×C9—33no—
237C3×C9—133no—
238C3×C9—133no—
239C3×C9—392no—
240C3×C9—392no—
241C3×C9—396no—
242C3×C9—396no—
243C3×C9—396no—
244C3×C9—393no—
245C3×C9—396no—
246C3×C9C32⋊(C13⋊C3)12yes—
247C3×C9C32⋊(C13⋊C3)12yes—
248C3×C9C32⋊(C13⋊C3)12yes—
249C3×C9C32⋊(C13⋊C3)11yescharacteristic
250C3×C9C32⋊(C13⋊C3)12yes—
251C3×C9C32×C13⋊C311yescharacteristic
252C3×C9C32×C13⋊C311yescharacteristic
253C3×C9C32×C13⋊C311yescharacteristic
254C13#1062492911yescharacteristic, complemented, Sylow
255C32—33no—
256C32—91no—
257C32—93no—
258C32—396no—
259C32—393no—
260C32—1173no—
261C32—1176no—
262C32C3×C32⋊(C13⋊C3)11yescharacteristic
263C32C3×C32⋊(C13⋊C3)12yes—
264C32C33×C13⋊C311yescharacteristic
265C9—36no—
266C9—393no—
267C9—393no—
268C9—396no—
269C9—396no—
270C9C3×C32⋊(C13⋊C3)11yescharacteristic
271C9C3×C32⋊(C13⋊C3)11yescharacteristic
272C9C3×C32⋊(C13⋊C3)12yes—
273C9C3×C32⋊(C13⋊C3)12yes—
274C9C3×C32⋊(C13⋊C3)12yes—
275C9C3×C32⋊(C13⋊C3)11yescharacteristic
276C3—31no—
277C3—32no—
278C3—31no—
279C3—93no—
280C3—1176no—
281C3—1173no—
282C3C32×C32⋊(C13⋊C3)11yescharacteristic
subgroupG/H
centerC9C3×C32⋊(C13⋊C3)
commutator, cosocleC32×C13C34
FrattiniC32C33×C13⋊C3
FittingC3×C13×#737C3
socleC3×C13C32×H(3,𝔽3)
hypercenterC3×#737C13⋊C3
hypocenterC13#10624929
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C9 ◁ C32×C9 ◁ C3×#737

Complements

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

NH ≅ G/Ntype
1. C3×#11760453C3semidirect
2. C3×#11760453C3semidirect
3. #15691674C3semidirect
4. #15691673C3semidirect
5. #15691669C3semidirect
6. #15691665C3semidirect
7. #15691662C3semidirect
8. #15691660C3semidirect
9. #15691657C3semidirect
10. #15691655C3semidirect
11. #15691648C3semidirect
12. C3×C13×#737C3semidirect
24. #11760453C32semidirect
25. #11760453C32semidirect
26. #11760453C32semidirect
32. C3×#66848C32semidirect
34. C3×#66849C32semidirect
38. C3×C9×C13⋊C3C32semidirect
39. #11760442C32semidirect
41. #11760439C32semidirect
42. #11760437C32semidirect
43. #11760436C32semidirect
44. #11760434C32semidirect
48. C13×#737C32semidirect
49. C13×#737C32semidirect
50. C13×#737C32semidirect
116. C3×#737C13⋊C3semidirect
164. #737C3×C13⋊C3semidirect
165. #737C3×C13⋊C3semidirect
166. #737C3×C13⋊C3semidirect
254. C13#10624929semidirect