Finite Group Databasebeta

← C13⋊C3×#6910 #23748516

Subgroups — C13⋊C3×#6910 #23748516

Order 9477.

1088 conjugacy classes of subgroups; only the 271 normal subgroups are shown.

normal subgroups only

This group has 1088 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
2C3×3−1+2×C13⋊C3C311yesmaximal, characteristic, complemented
3C3×H(3,𝔽3)×C13⋊C3C311yesmaximal, characteristic
4#15691662C314yesmaximal, complemented
5#15691661C312yesmaximal, complemented
6#15691660C312yesmaximal, complemented
7#15691659C319yesmaximal, complemented
8#15691658C319yesmaximal, complemented
9C13⋊C3×#731C319yesmaximal, complemented
10C13×#6910C311yesmaximal, characteristic, complemented
11C33×C13⋊C3—31no—
12C33×C13⋊C3C3211yescharacteristic
13C3×#66851C3214yescomplemented
14C3×#66851C3212yescomplemented
15C3×#66848—32no—
16C3×#66848C3213yescomplemented
17C3×#66849—32no—
18C3×#66849C3213yescomplemented
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⋊C3—32no—
243−1+2×C13⋊C3—32no—
253−1+2×C13⋊C3—32no—
263−1+2×C13⋊C3—31no—
273−1+2×C13⋊C3—32no—
283−1+2×C13⋊C3—32no—
293−1+2×C13⋊C3—32no—
303−1+2×C13⋊C3C3216yescomplemented
313−1+2×C13⋊C3C3216yescomplemented
323−1+2×C13⋊C3C3216yescomplemented
33C3×C32⋊(C13⋊C3)—32no—
34C3×C32⋊(C13⋊C3)C3212yes—
35H(3,𝔽3)×C13⋊C3—32no—
36H(3,𝔽3)×C13⋊C3—32no—
37H(3,𝔽3)×C13⋊C3—32no—
38H(3,𝔽3)×C13⋊C3C3213yes—
39H(3,𝔽3)×C13⋊C3C3213yes—
40H(3,𝔽3)×C13⋊C3C3213yes—
41C3×C9×C13⋊C3—32no—
42C3×C9×C13⋊C3C3213yescomplemented
43#11760439C32136yescomplemented
44#11760438C32118yescomplemented
45#11760437C32118yescomplemented
46C3×C13×3−1+2C3212yescomplemented
47C3×C13×3−1+2C3211yescharacteristic, complemented
48C3×C13×H(3,𝔽3)C3211yescharacteristic
49C13×#731C3219yescomplemented
50C3×#6910—131nomaximal, Sylow
51C33×C13—31no—
52C33×C13C3311yescharacteristic
53C32×C13⋊C3—32no—
54C32×C13⋊C3—33no—
55C32×C13⋊C3—33no—
56C32×C13⋊C3—33no—
57C32×C13⋊C3—93no—
58C32×C13⋊C3—99no—
59C32×C13⋊C3H(3,𝔽3)12yes—
60C32×C13⋊C3H(3,𝔽3)11yescharacteristic
61C32×C13⋊C3H(3,𝔽3)12yes—
62C32×C13⋊C3H(3,𝔽3)12yes—
63C32×C13⋊C3H(3,𝔽3)12yes—
64C32×C13⋊C3C3311yescharacteristic
65C32×C13⋊C3C3311yescharacteristic
66C32×C13⋊C3C3311yescharacteristic
67C13×3−1+2—32no—
68C13×3−1+2—32no—
69C13×3−1+2—32no—
70C13×3−1+2—31no—
71C13×3−1+2C3316yescomplemented
72C13×H(3,𝔽3)—32no—
73C13×H(3,𝔽3)C3313yes—
74C3×C9×C13—32no—
75C3×C9×C13C3313yescomplemented
76C32⋊(C13⋊C3)—34no—
77C32⋊(C13⋊C3)—36no—
78C32⋊(C13⋊C3)—36no—
79C32⋊(C13⋊C3)—36no—
80C32⋊(C13⋊C3)C3316yes—
81#66851—34no—
82#66851—34no—
83#66851—34no—
84#66851—32no—
85#66851C33112yescomplemented
86C3×C13⋊C9—34no—
87C3×C13⋊C9C3316yescomplemented
88#66849—36no—
89#66849—33no—
90#66849—36no—
91#66849—36no—
92#66849—36no—
93#66848—36no—
94#66848—33no—
95#66848—36no—
96#66848—36no—
97#66848—36no—
98C9×C13⋊C3—36no—
99C9×C13⋊C3—36no—
100C9×C13⋊C3—36no—
101C9×C13⋊C3—36no—
102C9×C13⋊C3—33no—
103C32×3−1+2—131no—
104C32×3−1+2—132no—
105C32×H(3,𝔽3)—131no—
106#6910—132no—
107#6910—134no—
108#6910—132no—
109#6910—139no—
110#6910—139no—
111#6910C13⋊C311yescharacteristic, direct product factor
112C3×#731—139no—
113C32×C13—33no—
114C32×C13—91no—
115C32×C13—93no—
116C32×C13C3×H(3,𝔽3)12yes—
117C32×C13C3×H(3,𝔽3)11yescharacteristic
118C32×C13C3411yescharacteristic
119C3×C13⋊C3—33no—
120C3×C13⋊C3—36no—
121C3×C13⋊C3—33no—
122C3×C13⋊C3—36no—
123C3×C13⋊C3—92no—
124C3×C13⋊C3—92no—
125C3×C13⋊C3—92no—
126C3×C13⋊C3—91no—
127C3×C13⋊C3—91no—
128C3×C13⋊C3—99no—
129C3×C13⋊C3—99no—
130C3×C13⋊C3—96no—
131C3×C13⋊C3—99no—
132C3×C13⋊C3C3×H(3,𝔽3)12yes—
133C3×C13⋊C3C3×H(3,𝔽3)12yes—
134C3×C13⋊C3C3×H(3,𝔽3)12yes—
135C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
136C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
137C3×C13⋊C3C3×H(3,𝔽3)11yescharacteristic
138C9×C13—36no—
139C9×C13—33no—
140C13⋊C9—312no—
141C13⋊C9—36no—
142C34—131no—
143C34—391no—
144C3×3−1+2—132no—
145C3×3−1+2—133no—
146C3×3−1+2—133no—
147C3×3−1+2—134no—
148C3×3−1+2—136no—
149C3×3−1+2—136no—
150C3×3−1+2—136no—
151C3×3−1+2—392no—
152C3×3−1+2—392no—
153C3×3−1+2—392no—
154C3×3−1+2—391no—
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+2—392no—
163C3×3−1+2—392no—
164C3×3−1+2C3×C13⋊C312yescomplemented
165C3×3−1+2C3×C13⋊C311yescharacteristic, complemented
166C3×H(3,𝔽3)—132no—
167C3×H(3,𝔽3)—133no—
168C3×H(3,𝔽3)—133no—
169C3×H(3,𝔽3)—133no—
170C3×H(3,𝔽3)—392no—
171C3×H(3,𝔽3)—392no—
172C3×H(3,𝔽3)—392no—
173C3×H(3,𝔽3)—392no—
174C3×H(3,𝔽3)C3×C13⋊C311yescharacteristic
175C32×C9—133no—
176C32×C9—392no—
177#731—1336no—
178#731—1318no—
179#731—1318no—
180#731C3×C13⋊C319yescomplemented
181C3×C13—31no—
182C3×C13—32no—
183C3×C13—31no—
184C3×C13—93no—
185C3×C13C32×H(3,𝔽3)11yescharacteristic
186C13⋊C3—31no—
187C13⋊C3—31no—
188C13⋊C3—32no—
189C13⋊C3—32no—
190C13⋊C3—32no—
191C13⋊C3—96no—
192C13⋊C3#691013yesdirect product factor
193C33—31no—
194C33—132no—
195C33—131no—
196C33—131no—
197C33—132no—
198C33—132no—
199C33—132no—
200C33—131no—
201C33—131no—
202C33—393no—
203C33—393no—
204C33—393no—
205C33—392no—
206C33—1173no—
207C33—1179no—
208C33C32×C13⋊C311yescharacteristic
2093−1+2—32no—
2103−1+2—32no—
2113−1+2—32no—
2123−1+2—31no—
2133−1+2—1312no—
2143−1+2—396no—
2153−1+2—396no—
2163−1+2—396no—
2173−1+2—396no—
2183−1+2—393no—
2193−1+2—396no—
2203−1+2—396no—
2213−1+2—396no—
2223−1+2—396no—
2233−1+2—393no—
2243−1+2—394no—
2253−1+2—392no—
2263−1+2—394no—
2273−1+2—394no—
2283−1+2C32×C13⋊C316yescomplemented
229H(3,𝔽3)—32no—
230H(3,𝔽3)—136no—
231H(3,𝔽3)—396no—
232H(3,𝔽3)—396no—
233H(3,𝔽3)—396no—
234H(3,𝔽3)—394no—
235H(3,𝔽3)C32×C13⋊C313yes—
236C3×C9—32no—
237C3×C9—136no—
238C3×C9—393no—
239C3×C9—396no—
240C3×C9—396no—
241C3×C9—396no—
242C3×C9—396no—
243C3×C9—394no—
244C3×C9C32×C13⋊C313yescomplemented
245C13C3×#691011yescharacteristic, complemented, Sylow
246C32—33no—
247C32—91no—
248C32—93no—
249C32—131no—
250C32—132no—
251C32—132no—
252C32—132no—
253C32—131no—
254C32—131no—
255C32—393no—
256C32—396no—
257C32—393no—
258C32—396no—
259C32—1172no—
260C32—1172no—
261C32—1172no—
262C32—1171no—
263C32—1171no—
264C32—1176no—
265C32—1179no—
266C32—1179no—
267C32—1179no—
268C32H(3,𝔽3)×C13⋊C312yes—
269C32H(3,𝔽3)×C13⋊C311yescharacteristic
270C32C33×C13⋊C311yescharacteristic
271C9—36no—
272C9—33no—
273C9—396no—
274C9—3912no—
275C3—31no—
276C3—32no—
277C3—31no—
278C3—93no—
279C3—133no—
280C3—391no—
281C3—391no—
282C3—392no—
283C3—392no—
284C3—392no—
285C3—1176no—
286C3C3×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)
prime radicalC3×H(3,𝔽3)×C13⋊C3C3
hypercenter#6910C13⋊C3
hypocenterC13C3×#6910
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. C3×3−1+2×C13⋊C3C3semidirect
2. C3×3−1+2×C13⋊C3C3semidirect
4. #15691662C3semidirect
5. #15691661C3semidirect
6. #15691660C3semidirect
7. #15691659C3semidirect
8. #15691658C3semidirect
9. C13⋊C3×#731C3semidirect
10. C13×#6910C3semidirect
13. C3×#66851C32semidirect
14. C3×#66851C32semidirect
16. C3×#66848C32semidirect
18. C3×#66849C32semidirect
30. 3−1+2×C13⋊C3C32semidirect
31. 3−1+2×C13⋊C3C32semidirect
32. 3−1+2×C13⋊C3C32semidirect
42. C3×C9×C13⋊C3C32semidirect
43. #11760439C32semidirect
44. #11760438C32semidirect
45. #11760437C32semidirect
46. C3×C13×3−1+2C32semidirect
47. C3×C13×3−1+2C32semidirect
49. C13×#731C32semidirect
71. C13×3−1+2C33semidirect
75. C3×C9×C13C33semidirect
85. #66851C33semidirect
87. C3×C13⋊C9C33semidirect
111. #6910C13⋊C3direct (N × H)
164. C3×3−1+2C3×C13⋊C3semidirect
165. C3×3−1+2C3×C13⋊C3semidirect
180. #731C3×C13⋊C3semidirect
192. C13⋊C3#6910direct (N × H)
228. 3−1+2C32×C13⋊C3semidirect
244. C3×C9C32×C13⋊C3semidirect
245. C13C3×#6910semidirect