Finite Group Databasebeta

← C11×#18395 #14595588

Subgroups — C11×#18395 #14595588

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3496C211yesmaximal, characteristic
2C11×#3227C212yesmaximal, complemented
3C11×#2542C211yesmaximal, characteristic, complemented
4C11×#1613C218yesmaximal, complemented
5C11×#1502C212yesmaximal, complemented
6C11×#1460C211yesmaximal, characteristic, complemented
7C2×C11×H(5,𝔽2)—21no—
8C11×#547—22no—
9C11×#546—24no—
10D42×C11—22no—
11C11×#537—21no—
12C11×#534C2214yes—
13C11×#532C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic, complemented
15C2×C11×C22⋊Q8—22no—
16C2×C11×#121—22no—
17C2×C4×D4×C11C2211yescharacteristic
18C11×#498—22no—
19C11×#486—22no—
20C11×#481C2218yescomplemented
21C11×#476—24no—
22C11×#431C2212yescomplemented
23C11×#399C2214yescomplemented
24C11×#390—21no—
25C11×#384—21no—
26C4×C11×C4⋊C4C2211yescharacteristic, complemented
27C11×#327C2218yescomplemented
28C11×#323C2214yescomplemented
29C11×H(5,𝔽2)—44no—
30C11×H(5,𝔽2)—44no—
31C2×C11×#41—24no—
32C2×C11×#41—22no—
33C22×Q8×C11—21no—
34C22×D4×C11—24no—
35C22×D4×C11—24no—
36C22×D4×C11—22no—
37C22×D4×C11D411yescharacteristic
38C23×C4×C11D412yes—
39C11×C4⋊Q8—22no—
40C11×C4⋊Q8—22no—
41C11×C4⋊Q8D412yes—
42C11×#127D412yes—
43C11×#124—22no—
44C11×#123—28no—
45C11×C22⋊Q8—24no—
46C11×C22⋊Q8—48no—
47C11×#121—24no—
48C11×#121—24no—
49C11×#121—24no—
50C11×#121—22no—
51C11×#121—24no—
52C11×#121C2314yes—
53C11×#120—28no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11D414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4C2312yes—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C11×#106—28no—
70C11×C4⋊C8—22no—
71C11×#102—28no—
72C11×C22⋊C8C2314yes—
73C4×C8×C11—22no—
74C11×#95C2312yes—
75#18395C1111yesmaximal, characteristic, direct product factor, Sylow
76C24×C11—24no—
77C24×C11C2×D412yes—
78C11×#41—416no—
79C11×#41—44no—
80C11×#41—44no—
81C2×Q8×C11—22no—
82C2×Q8×C11—44no—
83C2×Q8×C11—41no—
84C2×Q8×C11—41no—
85C2×D4×C11—28no—
86C2×D4×C11—24no—
87C2×D4×C11—24no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—416no—
93C2×D4×C11—48no—
94C2×D4×C11—48no—
95C2×D4×C11—84no—
96C2×D4×C11SD1614yes—
97C2×D4×C11C2×D414yes—
98C22×C4×C11—24no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—44no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C2×C8×C11—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—24no—
115C11×C4⋊C4—48no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4C2×D414yes—
118C11×C22⋊C4—28no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—48no—
123C42×C11—42no—
124C42×C11C2×D412yes—
125C42×C11C2×D412yes—
126#3496C2×C1111yescharacteristic
127#3227C2×C1112yescomplemented
128#2542C2×C1111yescharacteristic, complemented
129#1613C2×C1118yescomplemented
130#1502C2×C1112yescomplemented
131#1460C2×C1111yescharacteristic, complemented
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—24no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—48no—
138C23×C11—84no—
139C23×C11—84no—
140C23×C11C2×SD1614yes—
141C23×C11C22×D411yescharacteristic
142Q8×C11—44no—
143Q8×C11—82no—
144Q8×C11—82no—
145D4×C11—28no—
146D4×C11—44no—
147D4×C11—416no—
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—44no—
151D4×C11—44no—
152D4×C11—84no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—24no—
157C2×C4×C11—41no—
158C2×C4×C11—42no—
159C2×C4×C11—48no—
160C2×C4×C11—42no—
161C2×C4×C11—48no—
162C2×C4×C11—44no—
163C2×C4×C11—42no—
164C2×C4×C11—44no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12012yes—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11C2×SD1612yes—
171C2×C4×C11AGL(1,ℤ/8)12yes—
172C2×C4×C11C22×D412yes—
173C8×C11—44no—
174C2×H(5,𝔽2)—21no—
175#547—22no—
176#546—24no—
177D42—22no—
178#537—21no—
179#534C22×C1114yes—
180#532C22×C1112yes—
181C2×C4⋊Q8C22×C1111yescharacteristic, complemented
182C2×C22⋊Q8—22no—
183C2×#121—22no—
184C2×C4×D4C22×C1111yescharacteristic
185#498—22no—
186#486—22no—
187#481C22×C1118yescomplemented
188#476—24no—
189#431C22×C1112yescomplemented
190#399C22×C1114yescomplemented
191#390—21no—
192#384—21no—
193C4×C4⋊C4C22×C1111yescharacteristic, complemented
194#327C22×C1118yescomplemented
195#323C22×C1114yescomplemented
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—24no—
199C22×C11—44no—
200C22×C11—42no—
201C22×C11—42no—
202C22×C11—44no—
203C22×C11—44no—
204C22×C11—44no—
205C22×C11—82no—
206C22×C11—168no—
207C22×C11C2×#12011yescharacteristic
208C22×C11C22×SD1611yescharacteristic
209C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
210C4×C11—21no—
211C4×C11—22no—
212C4×C11—44no—
213C4×C11—44no—
214C4×C11—42no—
215C4×C11—82no—
216C4×C11#45014yes—
217C4×C11#45312yes—
218H(5,𝔽2)—44no—
219H(5,𝔽2)—44no—
220C2×#41—24no—
221C2×#41—22no—
222C22×Q8—21no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—22no—
226C22×D4D4×C1111yescharacteristic
227C23×C4D4×C1112yes—
228C4⋊Q8—22no—
229C4⋊Q8—22no—
230C4⋊Q8D4×C1112yes—
231#127D4×C1112yes—
232#124—22no—
233#123—28no—
234C22⋊Q8—24no—
235C22⋊Q8—48no—
236#121—24no—
237#121—24no—
238#121—24no—
239#121—22no—
240#121—24no—
241#121C23×C1114yes—
242#120—28no—
243C4×D4—22no—
244C4×D4—22no—
245C4×D4—22no—
246C4×D4D4×C1114yes—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D4×C1111yescharacteristic
252C2×C4⋊C4C23×C1112yes—
253C2×C22⋊C4—24no—
254C2×C22⋊C4—24no—
255C2×C22⋊C4C23×C1112yes—
256C2×C42—21no—
257C2×C42C23×C1111yescharacteristic
258#106—28no—
259C4⋊C8—22no—
260#102—28no—
261C22⋊C8C23×C1114yes—
262C4×C8—22no—
263#95C23×C1112yes—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11—44no—
267C2×C11—84no—
268C2×C11C2×#45011yescharacteristic
269C2×C11C2×#45311yescharacteristic
270C2×C11#302811yescharacteristic
271C24—24no—
272C24C2×D4×C1112yes—
273#41—416no—
274#41—44no—
275#41—44no—
276C2×Q8—22no—
277C2×Q8—44no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×D4—28no—
281C2×D4—24no—
282C2×D4—24no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—416no—
288C2×D4—48no—
289C2×D4—48no—
290C2×D4—84no—
291C2×D4C11×SD1614yes—
292C2×D4C2×D4×C1114yes—
293C22×C4—24no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—44no—
300C22×C4C2×D4×C1111yescharacteristic
301C22×C4C2×D4×C1112yes—
302C22×C4C2×D4×C1111yescharacteristic
303C22×C4C24×C1111yescharacteristic
304C2×C8—24no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—24no—
310C4⋊C4—48no—
311C4⋊C4—42no—
312C4⋊C4C2×D4×C1114yes—
313C22⋊C4—28no—
314C22⋊C4—24no—
315C22⋊C4—24no—
316C22⋊C4—24no—
317C22⋊C4—48no—
318C42—42no—
319C42C2×D4×C1112yes—
320C42C2×D4×C1112yes—
321C11#1839511yescharacteristic, direct product factor, Sylow
322C23—22no—
323C23—22no—
324C23—24no—
325C23—42no—
326C23—42no—
327C23—48no—
328C23—84no—
329C23—84no—
330C23C2×C11×SD1614yes—
331C23C22×D4×C1111yescharacteristic
332Q8—44no—
333Q8—82no—
334Q8—82no—
335D4—28no—
336D4—44no—
337D4—416no—
338D4—44no—
339D4—44no—
340D4—44no—
341D4—44no—
342D4—84no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—48no—
350C2×C4—42no—
351C2×C4—48no—
352C2×C4—44no—
353C2×C4—42no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4C11×#12011yescharacteristic
358C2×C4C11×#12012yes—
359C2×C4C11×#12011yescharacteristic
360C2×C4C2×C11×SD1612yes—
361C2×C4C11×AGL(1,ℤ/8)12yes—
362C2×C4C22×D4×C1112yes—
363C8—44no—
364C22—21no—
365C22—21no—
366C22—24no—
367C22—44no—
368C22—42no—
369C22—42no—
370C22—44no—
371C22—44no—
372C22—44no—
373C22—82no—
374C22—168no—
375C22C2×C11×#12011yescharacteristic
376C22C22×C11×SD1611yescharacteristic
377C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
378C4—21no—
379C4—22no—
380C4—44no—
381C4—44no—
382C4—42no—
383C4—82no—
384C4C11×#45014yes—
385C4C11×#45312yes—
386C2—21no—
387C2—21no—
388C2—44no—
389C2—84no—
390C2C2×C11×#45011yescharacteristic
391C2C2×C11×#45311yescharacteristic
392C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3496C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#3227C2semidirect
3. C11×#2542C2semidirect
4. C11×#1613C2semidirect
5. C11×#1502C2semidirect
6. C11×#1460C2semidirect
14. C2×C11×C4⋊Q8C22semidirect
20. C11×#481C22semidirect
22. C11×#431C22semidirect
23. C11×#399C22semidirect
26. C4×C11×C4⋊C4C22semidirect
27. C11×#327C22semidirect
28. C11×#323C22semidirect
75. #18395C11direct (N × H)
127. #3227C2×C11semidirect
128. #2542C2×C11semidirect
129. #1613C2×C11semidirect
130. #1502C2×C11semidirect
131. #1460C2×C11semidirect
181. C2×C4⋊Q8C22×C11semidirect
187. #481C22×C11semidirect
189. #431C22×C11semidirect
190. #399C22×C11semidirect
193. C4×C4⋊C4C22×C11semidirect
194. #327C22×C11semidirect
195. #323C22×C11semidirect
321. C11#18395direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C11×#32272
C11×#25422
C11×#16132
C11×#15022
C11×#14602
#1839511