Finite Group Databasebeta

← C11×#10624907 #22548430

Subgroups — C11×#10624907 #22548430

Order 8019.

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
1C11×#6899C313yesmaximal, complemented
2C11×#6899C313yesmaximal, complemented
3C11×#6898C313yesmaximal, complemented
4C11×#6897C313yesmaximal, complemented
5C11×#6897C313yesmaximal, complemented
6C11×#6896C313yesmaximal, complemented
7C11×#6895C311yesmaximal, characteristic, complemented
8C11×#6895C313yesmaximal, complemented
9C11×#6894C311yesmaximal, characteristic, complemented
10C11×#6894C311yesmaximal, characteristic, complemented
11C11×#6894C311yesmaximal, characteristic, complemented
12C11×#6894C311yesmaximal, characteristic, complemented
13C11×#6894C313yesmaximal, complemented
14C11×#6893C311yesmaximal, characteristic
15C11×C9⋊H(3,𝔽3)C311yesmaximal, characteristic
16C11×C9⋊H(3,𝔽3)C311yesmaximal, characteristic
17C9×C11×3−1+2C313yesmaximal, complemented
18C9×C11×3−1+2C311yesmaximal, characteristic, complemented
19C9×C11×3−1+2C311yesmaximal, characteristic, complemented
20C9×C11×H(3,𝔽3)C311yesmaximal, characteristic
21C11×#6887C311yesmaximal, characteristic, complemented
22C3×C11×C9⋊C9C311yesmaximal, characteristic, complemented
23C3×C11×3−1+2C3213yes—
24C3×C11×3−1+2C3211yescharacteristic
25C3×C11×3−1+2C3211yescharacteristic
26C3×C11×3−1+2C3213yes—
27C3×C11×H(3,𝔽3)C3211yescharacteristic
28C32×C9×C11C3211yescharacteristic
29C32×C9×C11C3211yescharacteristic
30C32×C9×C11C3211yescharacteristic
31C32×C9×C11C3211yescharacteristic
32C32×C9×C11C3213yes—
33C11×C9⋊C9C3211yescharacteristic
34C11×C9⋊C9C3211yescharacteristic
35C11×C9⋊C9C3211yescharacteristic
36C11×C9⋊C9C3211yescharacteristic
37C11×C9⋊C9C3211yescharacteristic
38C11×C9⋊C9C3211yescharacteristic
39C11×C9⋊C9C3211yescharacteristic
40C11×C9⋊C9C3211yescharacteristic
41C11×C9⋊C9C3211yescharacteristic
42C11×C9⋊C9C3213yes—
43C11×C9⋊C9C3213yes—
44C11×C9⋊C9C3213yes—
45C11×C9⋊C9C3213yes—
46C11×C9⋊C9C3213yes—
47C11×C9⋊C9C3213yes—
48C11×C9⋊C9C3213yes—
49C11×C9⋊C9C3213yes—
50C11×C9⋊C9C3213yes—
51C11×C9⋊C9C3213yes—
52C11×C9⋊C9C3213yes—
53C11×C9⋊C9C3213yes—
54C11×C9⋊C9C3213yes—
55C11×C9⋊C9C3213yes—
56C11×C9⋊C9C3213yes—
57C11×C9⋊C9C3213yes—
58C11×C9⋊C9C3213yes—
59C11×C9⋊C9C3213yes—
60C11×C9⋊C9C3213yes—
61C11×C9⋊C9C3213yes—
62C11×C9⋊C9C3213yes—
63C11×C32⋊C9C3211yescharacteristic
64C11×C32⋊C9C3211yescharacteristic
65C11×C32⋊C9C3211yescharacteristic
66C11×C32⋊C9C3211yescharacteristic
67C11×C32⋊C9C3213yes—
68C11×C32⋊C9C3213yes—
69C11×C32⋊C9C3211yescharacteristic
70C11×C32⋊C9C3211yescharacteristic
71C11×C32⋊C9C3213yes—
72C11×C32⋊C9C3213yes—
73C11×C32⋊C9C3213yes—
74C11×C32⋊C9C3213yes—
75C11×C32⋊C9C3213yes—
76C11×C32⋊C9C3213yes—
77C11×C32⋊C9C3213yes—
78C92×C11C3213yes—
79C92×C11C3213yes—
80C92×C11C3213yes—
81#10624907C1111yesmaximal, characteristic, direct product factor, Sylow
82C33×C11C3313yes—
83C33×C11C3311yescharacteristic
84C11×3−1+2—33no—
85C11×3−1+2—33no—
86C11×3−1+2—39no—
87C11×3−1+2—93no—
88C11×H(3,𝔽3)—33no—
89C3×C9×C11—33no—
90C3×C9×C11—33no—
91C3×C9×C11—91no—
92C3×C9×C11—93no—
93C3×C9×C11—91no—
94C3×C9×C11C3311yescharacteristic
95C3×C9×C11C3313yes—
96C3×C9×C11C3311yescharacteristic
97C3×C9×C11C3313yes—
98C3×C9×C11C3313yes—
99C3×C9×C11C3313yes—
100C3×C9×C11C3313yes—
101C3×C9×C11C3313yes—
102C3×C9×C11C3313yes—
103C3×C9×C11C3311yescharacteristic
104C3×C9×C11C3311yescharacteristic
105C3×C9×C11C3311yescharacteristic
106C3×C9×C11C3311yescharacteristic
107C3×C9×C11C3313yes—
108C3×C9×C11C3311yescharacteristic
109C3×C9×C11C3311yescharacteristic
110C3×C9×C11C3311yescharacteristic
111C3×C9×C11C3311yescharacteristic
112C3×C9×C11C3311yescharacteristic
113C3×C9×C11C3311yescharacteristic
114#6899C3×C1113yescomplemented
115#6899C3×C1113yescomplemented
116#6898C3×C1113yescomplemented
117#6897C3×C1113yescomplemented
118#6897C3×C1113yescomplemented
119#6896C3×C1113yescomplemented
120#6895C3×C1111yescharacteristic, complemented
121#6895C3×C1113yescomplemented
122#6894C3×C1111yescharacteristic, complemented
123#6894C3×C1111yescharacteristic, complemented
124#6894C3×C1111yescharacteristic, complemented
125#6894C3×C1111yescharacteristic, complemented
126#6894C3×C1113yescomplemented
127#6893C3×C1111yescharacteristic
128C9⋊H(3,𝔽3)C3×C1111yescharacteristic
129C9⋊H(3,𝔽3)C3×C1111yescharacteristic
130C9×3−1+2C3×C1113yescomplemented
131C9×3−1+2C3×C1111yescharacteristic, complemented
132C9×3−1+2C3×C1111yescharacteristic, complemented
133C9×H(3,𝔽3)C3×C1111yescharacteristic
134#6887C3×C1111yescharacteristic, complemented
135C3×C9⋊C9C3×C1111yescharacteristic, complemented
136C32×C11—31no—
137C32×C11—31no—
138C32×C11—31no—
139C32×C11—33no—
140C32×C11—33no—
141C32×C11—33no—
142C32×C11—33no—
143C32×C11#73713yes—
144C32×C11C3411yescharacteristic
145C9×C11—31no—
146C9×C11—31no—
147C9×C11—31no—
148C9×C11—31no—
149C9×C11—31no—
150C9×C11—33no—
151C9×C11—33no—
152C9×C11—33no—
153C9×C11—33no—
154C9×C11—31no—
155C9×C11—33no—
156C9×C11—31no—
157C9×C11—31no—
158C9×C11—31no—
159C9×C11—33no—
160C9×C11—31no—
161C9×C11—31no—
162C9×C11—33no—
163C9×C11—33no—
164C9×C11#73713yes—
165C3×3−1+2C32×C1113yes—
166C3×3−1+2C32×C1111yescharacteristic
167C3×3−1+2C32×C1111yescharacteristic
168C3×3−1+2C32×C1113yes—
169C3×H(3,𝔽3)C32×C1111yescharacteristic
170C32×C9C32×C1111yescharacteristic
171C32×C9C32×C1111yescharacteristic
172C32×C9C32×C1111yescharacteristic
173C32×C9C32×C1111yescharacteristic
174C32×C9C32×C1113yes—
175C9⋊C9C32×C1111yescharacteristic
176C9⋊C9C32×C1111yescharacteristic
177C9⋊C9C32×C1111yescharacteristic
178C9⋊C9C32×C1111yescharacteristic
179C9⋊C9C32×C1111yescharacteristic
180C9⋊C9C32×C1111yescharacteristic
181C9⋊C9C32×C1111yescharacteristic
182C9⋊C9C32×C1111yescharacteristic
183C9⋊C9C32×C1111yescharacteristic
184C9⋊C9C32×C1113yes—
185C9⋊C9C32×C1113yes—
186C9⋊C9C32×C1113yes—
187C9⋊C9C32×C1113yes—
188C9⋊C9C32×C1113yes—
189C9⋊C9C32×C1113yes—
190C9⋊C9C32×C1113yes—
191C9⋊C9C32×C1113yes—
192C9⋊C9C32×C1113yes—
193C9⋊C9C32×C1113yes—
194C9⋊C9C32×C1113yes—
195C9⋊C9C32×C1113yes—
196C9⋊C9C32×C1113yes—
197C9⋊C9C32×C1113yes—
198C9⋊C9C32×C1113yes—
199C9⋊C9C32×C1113yes—
200C9⋊C9C32×C1113yes—
201C9⋊C9C32×C1113yes—
202C9⋊C9C32×C1113yes—
203C9⋊C9C32×C1113yes—
204C9⋊C9C32×C1113yes—
205C32⋊C9C32×C1111yescharacteristic
206C32⋊C9C32×C1111yescharacteristic
207C32⋊C9C32×C1111yescharacteristic
208C32⋊C9C32×C1111yescharacteristic
209C32⋊C9C32×C1113yes—
210C32⋊C9C32×C1113yes—
211C32⋊C9C32×C1111yescharacteristic
212C32⋊C9C32×C1111yescharacteristic
213C32⋊C9C32×C1113yes—
214C32⋊C9C32×C1113yes—
215C32⋊C9C32×C1113yes—
216C32⋊C9C32×C1113yes—
217C32⋊C9C32×C1113yes—
218C32⋊C9C32×C1113yes—
219C32⋊C9C32×C1113yes—
220C92C32×C1113yes—
221C92C32×C1113yes—
222C92C32×C1113yes—
223C3×C11—33no—
224C3×C11—93no—
225C3×C11C3×#73711yescharacteristic
226C3×C11C3×#73711yescharacteristic
227C3×C113−1+411yescharacteristic
228C3×C113−1+411yescharacteristic
229C33C33×C1113yes—
230C33C33×C1111yescharacteristic
2313−1+2—33no—
2323−1+2—33no—
2333−1+2—39no—
2343−1+2—93no—
235H(3,𝔽3)—33no—
236C3×C9—33no—
237C3×C9—33no—
238C3×C9—91no—
239C3×C9—93no—
240C3×C9—91no—
241C3×C9C33×C1111yescharacteristic
242C3×C9C33×C1113yes—
243C3×C9C33×C1111yescharacteristic
244C3×C9C33×C1113yes—
245C3×C9C33×C1113yes—
246C3×C9C33×C1113yes—
247C3×C9C33×C1113yes—
248C3×C9C33×C1113yes—
249C3×C9C33×C1113yes—
250C3×C9C33×C1111yescharacteristic
251C3×C9C33×C1111yescharacteristic
252C3×C9C33×C1111yescharacteristic
253C3×C9C33×C1111yescharacteristic
254C3×C9C33×C1113yes—
255C3×C9C33×C1111yescharacteristic
256C3×C9C33×C1111yescharacteristic
257C3×C9C33×C1111yescharacteristic
258C3×C9C33×C1111yescharacteristic
259C3×C9C33×C1111yescharacteristic
260C3×C9C33×C1111yescharacteristic
261C11#1062490711yescharacteristic, direct product factor, Sylow
262C32—31no—
263C32—31no—
264C32—31no—
265C32—33no—
266C32—33no—
267C32—33no—
268C32—33no—
269C32C11×#73713yes—
270C32C34×C1111yescharacteristic
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—
290C9C11×#73713yes—
291C3—33no—
292C3—93no—
293C3C3×C11×#73711yescharacteristic
294C3C3×C11×#73711yescharacteristic
295C3C11×3−1+411yescharacteristic
296C3C11×3−1+411yescharacteristic
subgroupG/H
center, socleC32×C11C34
commutator, FrattiniC32C34×C11
LCSG ▷ C32 ▷ C1
UCSC1 ◁ C32×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#6899C3semidirect
2. C11×#6899C3semidirect
3. C11×#6898C3semidirect
4. C11×#6897C3semidirect
5. C11×#6897C3semidirect
6. C11×#6896C3semidirect
7. C11×#6895C3semidirect
8. C11×#6895C3semidirect
9. C11×#6894C3semidirect
10. C11×#6894C3semidirect
11. C11×#6894C3semidirect
12. C11×#6894C3semidirect
13. C11×#6894C3semidirect
17. C9×C11×3−1+2C3semidirect
18. C9×C11×3−1+2C3semidirect
19. C9×C11×3−1+2C3semidirect
21. C11×#6887C3semidirect
22. C3×C11×C9⋊C9C3semidirect
81. #10624907C11direct (N × H)
114. #6899C3×C11semidirect
115. #6899C3×C11semidirect
116. #6898C3×C11semidirect
117. #6897C3×C11semidirect
118. #6897C3×C11semidirect
119. #6896C3×C11semidirect
120. #6895C3×C11semidirect
121. #6895C3×C11semidirect
122. #6894C3×C11semidirect
123. #6894C3×C11semidirect
124. #6894C3×C11semidirect
125. #6894C3×C11semidirect
126. #6894C3×C11semidirect
130. C9×3−1+2C3×C11semidirect
131. C9×3−1+2C3×C11semidirect
132. C9×3−1+2C3×C11semidirect
134. #6887C3×C11semidirect
135. C3×C9⋊C9C3×C11semidirect
261. C11#10624907direct (N × H)