Finite Group Databasebeta

← C43×#10624907 #44531844

Subgroups — C43×#10624907 #44531844

Order 31347.

622 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#6899C313yesmaximal, complemented
2C43×#6899C313yesmaximal, complemented
3C43×#6898C313yesmaximal, complemented
4C43×#6897C313yesmaximal, complemented
5C43×#6897C313yesmaximal, complemented
6C43×#6896C313yesmaximal, complemented
7C43×#6895C313yesmaximal, complemented
8C43×#6895C311yesmaximal, characteristic, complemented
9C43×#6894C313yesmaximal, complemented
10C43×#6894C311yesmaximal, characteristic, complemented
11C43×#6894C311yesmaximal, characteristic, complemented
12C43×#6894C311yesmaximal, characteristic, complemented
13C43×#6894C311yesmaximal, characteristic, complemented
14C43×#6893C311yesmaximal, characteristic
15C43×C9⋊H(3,𝔽3)C311yesmaximal, characteristic
16C43×C9⋊H(3,𝔽3)C311yesmaximal, characteristic
17C9×3−1+2×C43C311yesmaximal, characteristic, complemented
18C9×3−1+2×C43C313yesmaximal, complemented
19C9×3−1+2×C43C311yesmaximal, characteristic, complemented
20C9×H(3,𝔽3)×C43C311yesmaximal, characteristic
21C43×#6887C311yesmaximal, characteristic, complemented
22C3×C43×C9⋊C9C311yesmaximal, characteristic, complemented
23C3×3−1+2×C43C3211yescharacteristic
24C3×3−1+2×C43C3211yescharacteristic
25C3×3−1+2×C43C3213yes—
26C3×3−1+2×C43C3213yes—
27C3×H(3,𝔽3)×C43C3211yescharacteristic
28C32×C9×C43C3211yescharacteristic
29C32×C9×C43C3211yescharacteristic
30C32×C9×C43C3211yescharacteristic
31C32×C9×C43C3213yes—
32C32×C9×C43C3211yescharacteristic
33C43×C9⋊C9C3211yescharacteristic
34C43×C9⋊C9C3213yes—
35C43×C9⋊C9C3213yes—
36C43×C9⋊C9C3213yes—
37C43×C9⋊C9C3213yes—
38C43×C9⋊C9C3213yes—
39C43×C9⋊C9C3213yes—
40C43×C9⋊C9C3213yes—
41C43×C9⋊C9C3213yes—
42C43×C9⋊C9C3213yes—
43C43×C9⋊C9C3213yes—
44C43×C9⋊C9C3213yes—
45C43×C9⋊C9C3213yes—
46C43×C9⋊C9C3213yes—
47C43×C9⋊C9C3213yes—
48C43×C9⋊C9C3213yes—
49C43×C9⋊C9C3213yes—
50C43×C9⋊C9C3211yescharacteristic
51C43×C9⋊C9C3213yes—
52C43×C9⋊C9C3213yes—
53C43×C9⋊C9C3213yes—
54C43×C9⋊C9C3213yes—
55C43×C9⋊C9C3213yes—
56C43×C9⋊C9C3211yescharacteristic
57C43×C9⋊C9C3211yescharacteristic
58C43×C9⋊C9C3211yescharacteristic
59C43×C9⋊C9C3211yescharacteristic
60C43×C9⋊C9C3211yescharacteristic
61C43×C9⋊C9C3211yescharacteristic
62C43×C9⋊C9C3211yescharacteristic
63C43×C32⋊C9C3213yes—
64C43×C32⋊C9C3213yes—
65C43×C32⋊C9C3213yes—
66C43×C32⋊C9C3211yescharacteristic
67C43×C32⋊C9C3211yescharacteristic
68C43×C32⋊C9C3211yescharacteristic
69C43×C32⋊C9C3211yescharacteristic
70C43×C32⋊C9C3211yescharacteristic
71C43×C32⋊C9C3213yes—
72C43×C32⋊C9C3213yes—
73C43×C32⋊C9C3213yes—
74C43×C32⋊C9C3213yes—
75C43×C32⋊C9C3213yes—
76C43×C32⋊C9C3213yes—
77C43×C32⋊C9C3211yescharacteristic
78C92×C43C3213yes—
79C92×C43C3213yes—
80C92×C43C3213yes—
81C33×C43C3313yes—
82C33×C43C3311yescharacteristic
833−1+2×C43—33no—
843−1+2×C43—33no—
853−1+2×C43—39no—
863−1+2×C43—93no—
87H(3,𝔽3)×C43—33no—
88C3×C9×C43—33no—
89C3×C9×C43—33no—
90C3×C9×C43—91no—
91C3×C9×C43—93no—
92C3×C9×C43—91no—
93C3×C9×C43C3311yescharacteristic
94C3×C9×C43C3313yes—
95C3×C9×C43C3311yescharacteristic
96C3×C9×C43C3313yes—
97C3×C9×C43C3313yes—
98C3×C9×C43C3313yes—
99C3×C9×C43C3313yes—
100C3×C9×C43C3313yes—
101C3×C9×C43C3313yes—
102C3×C9×C43C3311yescharacteristic
103C3×C9×C43C3311yescharacteristic
104C3×C9×C43C3311yescharacteristic
105C3×C9×C43C3311yescharacteristic
106C3×C9×C43C3313yes—
107C3×C9×C43C3311yescharacteristic
108C3×C9×C43C3311yescharacteristic
109C3×C9×C43C3311yescharacteristic
110C3×C9×C43C3311yescharacteristic
111C3×C9×C43C3311yescharacteristic
112C3×C9×C43C3311yescharacteristic
113#10624907C4311yesmaximal, characteristic, direct product factor, Sylow
114C32×C43—31no—
115C32×C43—31no—
116C32×C43—31no—
117C32×C43—33no—
118C32×C43—33no—
119C32×C43—33no—
120C32×C43—33no—
121C32×C43#73713yes—
122C32×C43C3411yescharacteristic
123C9×C43—31no—
124C9×C43—31no—
125C9×C43—31no—
126C9×C43—31no—
127C9×C43—31no—
128C9×C43—33no—
129C9×C43—33no—
130C9×C43—33no—
131C9×C43—33no—
132C9×C43—31no—
133C9×C43—33no—
134C9×C43—31no—
135C9×C43—31no—
136C9×C43—31no—
137C9×C43—33no—
138C9×C43—31no—
139C9×C43—31no—
140C9×C43—33no—
141C9×C43—33no—
142C9×C43#73713yes—
143#6899C3×C4313yescomplemented
144#6899C3×C4313yescomplemented
145#6898C3×C4313yescomplemented
146#6897C3×C4313yescomplemented
147#6897C3×C4313yescomplemented
148#6896C3×C4313yescomplemented
149#6895C3×C4311yescharacteristic, complemented
150#6895C3×C4313yescomplemented
151#6894C3×C4311yescharacteristic, complemented
152#6894C3×C4311yescharacteristic, complemented
153#6894C3×C4311yescharacteristic, complemented
154#6894C3×C4311yescharacteristic, complemented
155#6894C3×C4313yescomplemented
156#6893C3×C4311yescharacteristic
157C9⋊H(3,𝔽3)C3×C4311yescharacteristic
158C9⋊H(3,𝔽3)C3×C4311yescharacteristic
159C9×3−1+2C3×C4313yescomplemented
160C9×3−1+2C3×C4311yescharacteristic, complemented
161C9×3−1+2C3×C4311yescharacteristic, complemented
162C9×H(3,𝔽3)C3×C4311yescharacteristic
163#6887C3×C4311yescharacteristic, complemented
164C3×C9⋊C9C3×C4311yescharacteristic, complemented
165C3×C43—33no—
166C3×C43—93no—
167C3×C43C3×#73711yescharacteristic
168C3×C43C3×#73711yescharacteristic
169C3×C433−1+411yescharacteristic
170C3×C433−1+411yescharacteristic
171C3×3−1+2C32×C4313yes—
172C3×3−1+2C32×C4311yescharacteristic
173C3×3−1+2C32×C4311yescharacteristic
174C3×3−1+2C32×C4313yes—
175C3×H(3,𝔽3)C32×C4311yescharacteristic
176C32×C9C32×C4311yescharacteristic
177C32×C9C32×C4311yescharacteristic
178C32×C9C32×C4311yescharacteristic
179C32×C9C32×C4311yescharacteristic
180C32×C9C32×C4313yes—
181C9⋊C9C32×C4311yescharacteristic
182C9⋊C9C32×C4311yescharacteristic
183C9⋊C9C32×C4311yescharacteristic
184C9⋊C9C32×C4311yescharacteristic
185C9⋊C9C32×C4311yescharacteristic
186C9⋊C9C32×C4311yescharacteristic
187C9⋊C9C32×C4311yescharacteristic
188C9⋊C9C32×C4311yescharacteristic
189C9⋊C9C32×C4311yescharacteristic
190C9⋊C9C32×C4313yes—
191C9⋊C9C32×C4313yes—
192C9⋊C9C32×C4313yes—
193C9⋊C9C32×C4313yes—
194C9⋊C9C32×C4313yes—
195C9⋊C9C32×C4313yes—
196C9⋊C9C32×C4313yes—
197C9⋊C9C32×C4313yes—
198C9⋊C9C32×C4313yes—
199C9⋊C9C32×C4313yes—
200C9⋊C9C32×C4313yes—
201C9⋊C9C32×C4313yes—
202C9⋊C9C32×C4313yes—
203C9⋊C9C32×C4313yes—
204C9⋊C9C32×C4313yes—
205C9⋊C9C32×C4313yes—
206C9⋊C9C32×C4313yes—
207C9⋊C9C32×C4313yes—
208C9⋊C9C32×C4313yes—
209C9⋊C9C32×C4313yes—
210C9⋊C9C32×C4313yes—
211C32⋊C9C32×C4311yescharacteristic
212C32⋊C9C32×C4311yescharacteristic
213C32⋊C9C32×C4311yescharacteristic
214C32⋊C9C32×C4311yescharacteristic
215C32⋊C9C32×C4313yes—
216C32⋊C9C32×C4313yes—
217C32⋊C9C32×C4311yescharacteristic
218C32⋊C9C32×C4311yescharacteristic
219C32⋊C9C32×C4313yes—
220C32⋊C9C32×C4313yes—
221C32⋊C9C32×C4313yes—
222C32⋊C9C32×C4313yes—
223C32⋊C9C32×C4313yes—
224C32⋊C9C32×C4313yes—
225C32⋊C9C32×C4313yes—
226C92C32×C4313yes—
227C92C32×C4313yes—
228C92C32×C4313yes—
229C43#1062490711yescharacteristic, direct product factor, Sylow
230C33C33×C4313yes—
231C33C33×C4311yescharacteristic
2323−1+2—33no—
2333−1+2—33no—
2343−1+2—39no—
2353−1+2—93no—
236H(3,𝔽3)—33no—
237C3×C9—33no—
238C3×C9—33no—
239C3×C9—91no—
240C3×C9—93no—
241C3×C9—91no—
242C3×C9C33×C4311yescharacteristic
243C3×C9C33×C4313yes—
244C3×C9C33×C4311yescharacteristic
245C3×C9C33×C4313yes—
246C3×C9C33×C4313yes—
247C3×C9C33×C4313yes—
248C3×C9C33×C4313yes—
249C3×C9C33×C4313yes—
250C3×C9C33×C4313yes—
251C3×C9C33×C4311yescharacteristic
252C3×C9C33×C4311yescharacteristic
253C3×C9C33×C4311yescharacteristic
254C3×C9C33×C4311yescharacteristic
255C3×C9C33×C4313yes—
256C3×C9C33×C4311yescharacteristic
257C3×C9C33×C4311yescharacteristic
258C3×C9C33×C4311yescharacteristic
259C3×C9C33×C4311yescharacteristic
260C3×C9C33×C4311yescharacteristic
261C3×C9C33×C4311yescharacteristic
262C32—31no—
263C32—31no—
264C32—31no—
265C32—33no—
266C32—33no—
267C32—33no—
268C32—33no—
269C32C43×#73713yes—
270C32C34×C4311yescharacteristic
271C9—31no—
272C9—31no—
273C9—31no—
274C9—31no—
275C9—31no—
276C9—33no—
277C9—33no—
278C9—33no—
279C9—33no—
280C9—31no—
281C9—33no—
282C9—31no—
283C9—31no—
284C9—31no—
285C9—33no—
286C9—31no—
287C9—31no—
288C9—33no—
289C9—33no—
290C9C43×#73713yes—
291C3—33no—
292C3—93no—
293C3C3×C43×#73711yescharacteristic
294C3C3×C43×#73711yescharacteristic
295C3C43×3−1+411yescharacteristic
296C3C43×3−1+411yescharacteristic
subgroupG/H
center, socleC32×C43C34
commutator, Frattini, cosocleC32C34×C43
prime radicalC3×H(3,𝔽3)×C43C32
LCSG ▷ C32 ▷ C1
UCSC1 ◁ C32×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#6899C3semidirect
2. C43×#6899C3semidirect
3. C43×#6898C3semidirect
4. C43×#6897C3semidirect
5. C43×#6897C3semidirect
6. C43×#6896C3semidirect
7. C43×#6895C3semidirect
8. C43×#6895C3semidirect
9. C43×#6894C3semidirect
10. C43×#6894C3semidirect
11. C43×#6894C3semidirect
12. C43×#6894C3semidirect
13. C43×#6894C3semidirect
17. C9×3−1+2×C43C3semidirect
18. C9×3−1+2×C43C3semidirect
19. C9×3−1+2×C43C3semidirect
21. C43×#6887C3semidirect
22. C3×C43×C9⋊C9C3semidirect
113. #10624907C43direct (N × H)
143. #6899C3×C43semidirect
144. #6899C3×C43semidirect
145. #6898C3×C43semidirect
146. #6897C3×C43semidirect
147. #6897C3×C43semidirect
148. #6896C3×C43semidirect
149. #6895C3×C43semidirect
150. #6895C3×C43semidirect
151. #6894C3×C43semidirect
152. #6894C3×C43semidirect
153. #6894C3×C43semidirect
154. #6894C3×C43semidirect
155. #6894C3×C43semidirect
159. C9×3−1+2C3×C43semidirect
160. C9×3−1+2C3×C43semidirect
161. C9×3−1+2C3×C43semidirect
163. #6887C3×C43semidirect
164. C3×C9⋊C9C3×C43semidirect
229. C43#10624907direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C43×#68993
C43×#68983
C43×#68973
C43×#68963
C43×#68953
C43×#68943
C43×#68933
C43×C9⋊H(3,𝔽3)3
C9×3−1+2×C433
C9×H(3,𝔽3)×C433
C43×#68873
C3×C43×C9⋊C93
#1062490743