Finite Group Databasebeta

← C13⋊C3×#6909 #23748510

Subgroups — C13⋊C3×#6909 #23748510

Order 9477.

1196 conjugacy classes of subgroups; only the 271 normal subgroups are shown.

normal subgroups only

This group has 1196 conjugacy classes of subgroups — too many to draw. Only its 271 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
1C3×3−1+2×C13⋊C3C312yesmaximal, complemented
2C3×H(3,𝔽3)×C13⋊C3C311yesmaximal, characteristic, complemented
3C3×H(3,𝔽3)×C13⋊C3C311yesmaximal, characteristic, complemented
4#15691657C314yesmaximal, complemented
5#15691656C312yesmaximal, complemented
6#15691655C312yesmaximal, complemented
7#15691654C319yesmaximal, complemented
8#15691653C319yesmaximal, complemented
9C13⋊C3×AΣL(1,𝔽27)C319yesmaximal, complemented
10C13×#6909C311yesmaximal, characteristic, complemented
11C33×C13⋊C3—31no—
12C33×C13⋊C3C3211yescharacteristic
13C33×C13⋊C3C3213yescomplemented
14C3×#66851C3214yescomplemented
15C3×#66848—32no—
16C3×#66849—32no—
173−1+2×C13⋊C3—32no—
183−1+2×C13⋊C3—32no—
193−1+2×C13⋊C3—32no—
203−1+2×C13⋊C3—32no—
213−1+2×C13⋊C3—32no—
223−1+2×C13⋊C3—32no—
233−1+2×C13⋊C3C3216yescomplemented
243−1+2×C13⋊C3C3216yescomplemented
253−1+2×C13⋊C3C3216yescomplemented
26C3×C32⋊(C13⋊C3)—32no—
27C3×C32⋊(C13⋊C3)C3213yescomplemented
28C3×C32⋊(C13⋊C3)C3213yescomplemented
29C3×C32⋊(C13⋊C3)C3212yescomplemented
30C3×C32⋊(C13⋊C3)C3212yescomplemented
31H(3,𝔽3)×C13⋊C3—32no—
32H(3,𝔽3)×C13⋊C3—31no—
33H(3,𝔽3)×C13⋊C3—32no—
34H(3,𝔽3)×C13⋊C3—32no—
35H(3,𝔽3)×C13⋊C3—32no—
36H(3,𝔽3)×C13⋊C3—32no—
37H(3,𝔽3)×C13⋊C3—32no—
38H(3,𝔽3)×C13⋊C3—32no—
39H(3,𝔽3)×C13⋊C3C3213yes—
40H(3,𝔽3)×C13⋊C3C3213yescomplemented
41H(3,𝔽3)×C13⋊C3C3213yescomplemented
42C3×C9×C13⋊C3—32no—
43#11760436C32136yescomplemented
44#11760435C32118yescomplemented
45#11760434C32118yescomplemented
46C3×C13×3−1+2C3212yescomplemented
47C3×C13×H(3,𝔽3)C3211yescharacteristic, complemented
48C3×C13×H(3,𝔽3)C3211yescharacteristic, complemented
49C13×AΣL(1,𝔽27)C3219yescomplemented
50C3×#6909—131nomaximal, Sylow
51C33×C13—31no—
52C33×C13C3311yescharacteristic
53C33×C13C3313yescomplemented
54C32×C13⋊C3—32no—
55C32×C13⋊C3—36no—
56C32×C13⋊C3—33no—
57C32×C13⋊C3—33no—
58C32×C13⋊C3—33no—
59C32×C13⋊C3—33no—
60C32×C13⋊C3—93no—
61C32×C13⋊C3—99no—
62C32×C13⋊C3—99no—
63C32×C13⋊C3H(3,𝔽3)12yes—
64C32×C13⋊C3H(3,𝔽3)11yescharacteristic
65C32×C13⋊C3H(3,𝔽3)12yes—
66C32×C13⋊C3H(3,𝔽3)12yes—
67C32×C13⋊C3H(3,𝔽3)12yes—
68C32×C13⋊C3C3311yescharacteristic
69C32×C13⋊C3C3311yescharacteristic
70C32×C13⋊C3C3311yescharacteristic
71C32×C13⋊C3C3316yescomplemented
72C13×3−1+2—32no—
73C13×3−1+2—32no—
74C13×3−1+2C3316yescomplemented
75C13×H(3,𝔽3)—32no—
76C13×H(3,𝔽3)—31no—
77C13×H(3,𝔽3)—32no—
78C13×H(3,𝔽3)C3313yes—
79C3×C9×C13—32no—
80C32⋊(C13⋊C3)—34no—
81C32⋊(C13⋊C3)—32no—
82C32⋊(C13⋊C3)—34no—
83C32⋊(C13⋊C3)—36no—
84C32⋊(C13⋊C3)—36no—
85C32⋊(C13⋊C3)—33no—
86C32⋊(C13⋊C3)—33no—
87C32⋊(C13⋊C3)—36no—
88C32⋊(C13⋊C3)—36no—
89C32⋊(C13⋊C3)—36no—
90C32⋊(C13⋊C3)C3316yes—
91#66851—34no—
92#66851—34no—
93#66851C33112yescomplemented
94C3×C13⋊C9—34no—
95#66849—36no—
96#66849—36no—
97#66849—36no—
98#66848—36no—
99#66848—36no—
100#66848—36no—
101C9×C13⋊C3—36no—
102C9×C13⋊C3—36no—
103C9×C13⋊C3—36no—
104C32×3−1+2—132no—
105C32×H(3,𝔽3)—131no—
106C32×H(3,𝔽3)—131no—
107#6909—134no—
108#6909—132no—
109#6909—132no—
110#6909—139no—
111#6909—139no—
112#6909C13⋊C311yescharacteristic, direct product factor
113C3×AΣL(1,𝔽27)—139no—
114C32×C13—33no—
115C32×C13—33no—
116C32×C13—91no—
117C32×C13—93no—
118C32×C13—93no—
119C32×C13C3×H(3,𝔽3)12yes—
120C32×C13C3×H(3,𝔽3)11yescharacteristic
121C32×C13C3411yescharacteristic
122C3×C13⋊C3—33no—
123C3×C13⋊C3—33no—
124C3×C13⋊C3—36no—
125C3×C13⋊C3—36no—
126C3×C13⋊C3—36no—
127C3×C13⋊C3—92no—
128C3×C13⋊C3—92no—
129C3×C13⋊C3—92no—
130C3×C13⋊C3—91no—
131C3×C13⋊C3—91no—
132C3×C13⋊C3—918no—
133C3×C13⋊C3—99no—
134C3×C13⋊C3—99no—
135C3×C13⋊C3—96no—
136C3×C13⋊C3—99no—
137C3×C13⋊C3—99no—
138C3×C13⋊C3—96no—
139C3×C13⋊C3C3×H(3,𝔽3)12yes—
140C3×C13⋊C3C3×H(3,𝔽3)12yes—
141C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
142C3×C13⋊C3C3×H(3,𝔽3)12yes—
143C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
144C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
145C9×C13—36no—
146C13⋊C9—312no—
147C34—131no—
148C34—133no—
149C34—391no—
150C3×3−1+2—134no—
151C3×3−1+2—136no—
152C3×3−1+2—136no—
153C3×3−1+2—136no—
154C3×3−1+2—392no—
155C3×3−1+2—392no—
156C3×3−1+2—392no—
157C3×3−1+2—392no—
158C3×3−1+2—392no—
159C3×3−1+2—392no—
160C3×3−1+2—392no—
161C3×3−1+2—392no—
162C3×3−1+2C3×C13⋊C312yescomplemented
163C3×H(3,𝔽3)—132no—
164C3×H(3,𝔽3)—133no—
165C3×H(3,𝔽3)—133no—
166C3×H(3,𝔽3)—133no—
167C3×H(3,𝔽3)—132no—
168C3×H(3,𝔽3)—133no—
169C3×H(3,𝔽3)—133no—
170C3×H(3,𝔽3)—392no—
171C3×H(3,𝔽3)—392no—
172C3×H(3,𝔽3)—391no—
173C3×H(3,𝔽3)—392no—
174C3×H(3,𝔽3)—392no—
175C3×H(3,𝔽3)—392no—
176C3×H(3,𝔽3)—392no—
177C3×H(3,𝔽3)—392no—
178C3×H(3,𝔽3)—392no—
179C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic, complemented
180C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic, complemented
181C32×C9—392no—
182AΣL(1,𝔽27)—1318no—
183AΣL(1,𝔽27)—1336no—
184AΣL(1,𝔽27)—1318no—
185AΣL(1,𝔽27)C3×C13⋊C319yescomplemented
186C3×C13—31no—
187C3×C13—31no—
188C3×C13—32no—
189C3×C13—93no—
190C3×C13—93no—
191C3×C13C32×H(3,𝔽3)11yescharacteristic
192C13⋊C3—31no—
193C13⋊C3—31no—
194C13⋊C3—32no—
195C13⋊C3—32no—
196C13⋊C3—32no—
197C13⋊C3—96no—
198C13⋊C3—96no—
199C13⋊C3#690913yesdirect product factor
200C33—31no—
201C33—132no—
202C33—131no—
203C33—131no—
204C33—132no—
205C33—132no—
206C33—132no—
207C33—131no—
208C33—131no—
209C33—136no—
210C33—393no—
211C33—393no—
212C33—393no—
213C33—393no—
214C33—396no—
215C33—392no—
216C33—1173no—
217C33—1179no—
218C33—1179no—
219C33C32×C13⋊C311yescharacteristic
220C33C32×C13⋊C313yescomplemented
2213−1+2—32no—
2223−1+2—32no—
2233−1+2—1312no—
2243−1+2—396no—
2253−1+2—396no—
2263−1+2—396no—
2273−1+2—396no—
2283−1+2—396no—
2293−1+2—396no—
2303−1+2—394no—
2313−1+2—394no—
2323−1+2C32×C13⋊C316yescomplemented
233H(3,𝔽3)—32no—
234H(3,𝔽3)—31no—
235H(3,𝔽3)—32no—
236H(3,𝔽3)—136no—
237H(3,𝔽3)—396no—
238H(3,𝔽3)—396no—
239H(3,𝔽3)—393no—
240H(3,𝔽3)—393no—
241H(3,𝔽3)—396no—
242H(3,𝔽3)—396no—
243H(3,𝔽3)—396no—
244H(3,𝔽3)—394no—
245H(3,𝔽3)—394no—
246H(3,𝔽3)—392no—
247H(3,𝔽3)C32×C13⋊C313yes—
248C3×C9—32no—
249C3×C9—396no—
250C3×C9—396no—
251C3×C9—396no—
252C3×C9—394no—
253C13C3×#690911yescharacteristic, complemented, Sylow
254C32—33no—
255C32—33no—
256C32—91no—
257C32—93no—
258C32—93no—
259C32—131no—
260C32—132no—
261C32—132no—
262C32—131no—
263C32—132no—
264C32—131no—
265C32—393no—
266C32—393no—
267C32—396no—
268C32—396no—
269C32—396no—
270C32—1172no—
271C32—1171no—
272C32—1171no—
273C32—1172no—
274C32—1172no—
275C32—1176no—
276C32—1176no—
277C32—1179no—
278C32—1179no—
279C32—1179no—
280C32—1179no—
281C32—11718no—
282C32H(3,𝔽3)×C13⋊C312yes—
283C32H(3,𝔽3)×C13⋊C311yescharacteristic
284C32C33×C13⋊C311yescharacteristic
285C9—36no—
286C9—3912no—
287C3—31no—
288C3—31no—
289C3—32no—
290C3—93no—
291C3—93no—
292C3—133no—
293C3—391no—
294C3—392no—
295C3—391no—
296C3—392no—
297C3—392no—
298C3—1176no—
299C3—1176no—
300C3C3×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
hypocenterC13C3×#6909
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. C3×3−1+2×C13⋊C3C3semidirect
2. C3×H(3,𝔽3)×C13⋊C3C3semidirect
3. C3×H(3,𝔽3)×C13⋊C3C3semidirect
4. #15691657C3semidirect
5. #15691656C3semidirect
6. #15691655C3semidirect
7. #15691654C3semidirect
8. #15691653C3semidirect
9. C13⋊C3×AΣL(1,𝔽27)C3semidirect
10. C13×#6909C3semidirect
13. C33×C13⋊C3C32semidirect
14. C3×#66851C32semidirect
23. 3−1+2×C13⋊C3C32semidirect
24. 3−1+2×C13⋊C3C32semidirect
25. 3−1+2×C13⋊C3C32semidirect
27. C3×C32⋊(C13⋊C3)C32semidirect
28. C3×C32⋊(C13⋊C3)C32semidirect
29. C3×C32⋊(C13⋊C3)C32semidirect
30. C3×C32⋊(C13⋊C3)C32semidirect
40. H(3,𝔽3)×C13⋊C3C32semidirect
41. H(3,𝔽3)×C13⋊C3C32semidirect
43. #11760436C32semidirect
44. #11760435C32semidirect
45. #11760434C32semidirect
46. C3×C13×3−1+2C32semidirect
47. C3×C13×H(3,𝔽3)C32semidirect
48. C3×C13×H(3,𝔽3)C32semidirect
49. C13×AΣL(1,𝔽27)C32semidirect
53. C33×C13C33semidirect
71. C32×C13⋊C3C33semidirect
74. C13×3−1+2C33semidirect
93. #66851C33semidirect
112. #6909C13⋊C3direct (N × H)
162. C3×3−1+2C3×C13⋊C3semidirect
179. C3×H(3,𝔽3)C3×C13⋊C3semidirect
180. C3×H(3,𝔽3)C3×C13⋊C3semidirect
185. AΣL(1,𝔽27)C3×C13⋊C3semidirect
199. C13⋊C3#6909direct (N × H)
220. C33C32×C13⋊C3semidirect
232. 3−1+2C32×C13⋊C3semidirect
253. C13C3×#6909semidirect