Finite Group Databasebeta

← C11×#23588 #14600781

Subgroups — C11×#23588 #14600781

Order 2816.

1106 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3461C211yesmaximal, characteristic, complemented
2C4×C11×AGL(1,ℤ/8)C212yesmaximal, complemented
3C4×C11×#124C211yesmaximal, characteristic, complemented
4C11×#2061C211yesmaximal, characteristic, complemented
5C11×#2040C211yesmaximal, characteristic, complemented
6C11×#2038C212yesmaximal, complemented
7C11×#2027C211yesmaximal, characteristic, complemented
8C11×#2006C211yesmaximal, characteristic
9C11×#2003C212yesmaximal, complemented
10C4×C11×#104C212yesmaximal, complemented
11C4×C11×#101C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2212yes—
13C11×#544C2211yescharacteristic
14C11×#542—22no—
15C11×#541—22no—
16C11×#539—22no—
17C11×#537C2211yescharacteristic
18C11×#536C2212yes—
19C11×#533—22no—
20C11×#529—22no—
21C11×#529—22no—
22C2×C11×#124C2211yescharacteristic
23C4×C11×#41C2212yes—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C11×#442—22no—
27C11×#440—22no—
28C4×C11×SD16—22no—
29C4×C11×D8—22no—
30C11×#428C2212yes—
31C2×C11×#104C2212yes—
32C2×C11×#104C2212yes—
33C11×#418C2212yes—
34C11×#417C2212yes—
35C2×C11×#101C2212yes—
36C4×C11×M16C2212yes—
37C11×#391C2211yescharacteristic
38C11×#390C2211yescharacteristic
39C11×#388—22no—
40C11×#382C2211yescharacteristic
41C4×C11×C22⋊C4—22no—
42C43×C11C2211yescharacteristic
43C11×#343C2211yescharacteristic
44C11×#343C2211yescharacteristic
45C11×#339C2212yes—
46C11×#339C2212yes—
47C2×C11×#41C2312yes—
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C11×AGL(1,ℤ/8)—24no—
52C11×AGL(1,ℤ/8)—24no—
53C2×C11×SD16—22no—
54C2×C11×D8—22no—
55C2×C11×M16C2312yes—
56C2×C11×M16C2312yes—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×#126—24no—
60C11×#126—24no—
61C11×#125—22no—
62C11×#125—24no—
63C11×#125—22no—
64C11×#124—22no—
65C11×#124—22no—
66C11×#124—22no—
67C11×#124—22no—
68C11×#123—24no—
69C11×#123—24no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×#121—22no—
76C11×#121—22no—
77C4×Q8×C11—22no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11D412yes—
81C4×Q8×C11D412yes—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—22no—
87C4×D4×C11D412yes—
88C4×D4×C11D412yes—
89C11×#117—24no—
90C11×#117—22no—
91C11×#117C2312yes—
92C2×C11×C4⋊C4D412yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11—22no—
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11D412yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C11×#107—22no—
106C11×#106—22no—
107C11×#104—24no—
108C11×#104—24no—
109C11×#103—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#101—24no—
114C11×#97—22no—
115C4×C8×C11—22no—
116C11×#95—22no—
117C11×#95—22no—
118#23588C1111yesmaximal, characteristic, direct product factor, Sylow
119C24×C11—21no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11C2×D412yes—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11C2×D412yes—
136C2×D4×C11#4112yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—44no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C11×SD16—28no—
152C11×D8—28no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16—22no—
156C11×M16#4114yes—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—44no—
179C11×C22⋊C4—42no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—21no—
186C42×C11—22no—
187C42×C11—42no—
188C42×C11—42no—
189C42×C11C2×D412yes—
190C42×C11C2×D412yes—
191C42×C11#4112yes—
192#3461C2×C1111yescharacteristic, complemented
193C4×AGL(1,ℤ/8)C2×C1112yescomplemented
194C4×#124C2×C1111yescharacteristic, complemented
195#2061C2×C1111yescharacteristic, complemented
196#2040C2×C1111yescharacteristic, complemented
197#2038C2×C1112yescomplemented
198#2027C2×C1111yescharacteristic, complemented
199#2006C2×C1111yescharacteristic
200#2003C2×C1112yescomplemented
201C4×#104C2×C1112yescomplemented
202C4×#101C2×C1111yescharacteristic, complemented
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11C22×D411yescharacteristic
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—42no—
213Q8×C11—42no—
214Q8×C11—82no—
215D4×C11—22no—
216D4×C11—24no—
217D4×C11—22no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—42no—
221D4×C11—82no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—82no—
244C2×C4×C11—82no—
245C2×C4×C11—82no—
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12012yes—
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11C22×D412yes—
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4112yes—
252C2×C4×C11C2×#4111yescharacteristic
253C8×C11—24no—
254C8×C11—42no—
255C2×AGL(1,ℤ/8)C22×C1112yes—
256#544C22×C1111yescharacteristic
257#542—22no—
258#541—22no—
259#539—22no—
260#537C22×C1111yescharacteristic
261#536C22×C1112yes—
262#533—22no—
263#529—22no—
264#529—22no—
265C2×#124C22×C1111yescharacteristic
266C4×#41C22×C1112yes—
267C2×C4×Q8C22×C1111yescharacteristic
268C2×C4×D4C22×C1111yescharacteristic
269#442—22no—
270#440—22no—
271C4×SD16—22no—
272C4×D8—22no—
273#428C22×C1112yes—
274C2×#104C22×C1112yes—
275C2×#104C22×C1112yes—
276#418C22×C1112yes—
277#417C22×C1112yes—
278C2×#101C22×C1112yes—
279C4×M16C22×C1112yes—
280#391C22×C1111yescharacteristic
281#390C22×C1111yescharacteristic
282#388—22no—
283#382C22×C1111yescharacteristic
284C4×C22⋊C4—22no—
285C43C22×C1111yescharacteristic
286#343C22×C1111yescharacteristic
287#343C22×C1111yescharacteristic
288#339C22×C1112yes—
289#339C22×C1112yes—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—44no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—82no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11C2×#12011yescharacteristic
301C22×C11#52511yescharacteristic
302C22×C11#53211yescharacteristic
303C4×C11—21no—
304C4×C11—22no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—81no—
313C4×C11#45412yes—
314C4×C11#52512yes—
315C4×C11#53212yes—
316C2×#41C23×C1112yes—
317C22×Q8C23×C1111yescharacteristic
318C22×D4C23×C1111yescharacteristic
319C23×C4—21no—
320AGL(1,ℤ/8)—24no—
321AGL(1,ℤ/8)—24no—
322C2×SD16—22no—
323C2×D8—22no—
324C2×M16C23×C1112yes—
325C2×M16C23×C1112yes—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328#126—24no—
329#126—24no—
330#125—22no—
331#125—24no—
332#125—22no—
333#124—22no—
334#124—22no—
335#124—22no—
336#124—22no—
337#123—24no—
338#123—24no—
339C22⋊Q8—24no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344#121—22no—
345#121—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8D4×C1112yes—
350C4×Q8D4×C1112yes—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4D4×C1112yes—
357C4×D4D4×C1112yes—
358#117—24no—
359#117—22no—
360#117C23×C1112yes—
361C2×C4⋊C4D4×C1112yes—
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C4⋊C4C23×C1111yescharacteristic
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C42—22no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42D4×C1112yes—
371C2×C42C23×C1111yescharacteristic
372C2×C42C23×C1111yescharacteristic
373C2×C42C23×C1111yescharacteristic
374#107—22no—
375#106—22no—
376#104—24no—
377#104—24no—
378#103—22no—
379#102—22no—
380#102—22no—
381#102—22no—
382#101—24no—
383#97—22no—
384C4×C8—22no—
385#95—22no—
386#95—22no—
387C2×C11—21no—
388C2×C11—21no—
389C2×C11—82no—
390C2×C11—82no—
391C2×C11#238811yescharacteristic
392C2×C11C2×#45411yescharacteristic
393C2×C11#301811yescharacteristic
394C24—21no—
395#41—22no—
396#41—22no—
397#41—22no—
398#41—22no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8C2×D4×C1112yes—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4C2×D4×C1112yes—
411C2×D4C11×#4112yes—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—44no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4C2×D4×C1112yes—
422C22×C4C2×D4×C1111yescharacteristic
423C22×C4C2×D4×C1112yes—
424C22×C4C2×D4×C1111yescharacteristic
425C22×C4C24×C1111yescharacteristic
426SD16—28no—
427D8—28no—
428M16—22no—
429M16—22no—
430M16—22no—
431M16C11×#4114yes—
432C2×C8—22no—
433C2×C8—22no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4C2×D4×C1112yes—
445C4⋊C4C2×D4×C1112yes—
446C22⋊C4—28no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C42—22no—
456C42—22no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—21no—
461C42—22no—
462C42—42no—
463C42—42no—
464C42C2×D4×C1112yes—
465C42C2×D4×C1112yes—
466C42C11×#4112yes—
467C11#2358811yescharacteristic, direct product factor, Sylow
468C23—22no—
469C23—22no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—41no—
474C23C22×D4×C1111yescharacteristic
475Q8—22no—
476Q8—22no—
477Q8—42no—
478Q8—42no—
479Q8—82no—
480D4—22no—
481D4—24no—
482D4—22no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—82no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—82no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4C11×#12011yescharacteristic
512C2×C4C11×#12012yes—
513C2×C4C11×#12011yescharacteristic
514C2×C4C22×D4×C1112yes—
515C2×C4C2×C11×#4111yescharacteristic
516C2×C4C2×C11×#4112yes—
517C2×C4C2×C11×#4111yescharacteristic
518C8—24no—
519C8—42no—
520C22—21no—
521C22—21no—
522C22—44no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—82no—
528C22—81no—
529C22—81no—
530C22C2×C11×#12011yescharacteristic
531C22C11×#52511yescharacteristic
532C22C11×#53211yescharacteristic
533C4—21no—
534C4—22no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4—42no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—81no—
543C4C11×#45412yes—
544C4C11×#52512yes—
545C4C11×#53212yes—
546C2—21no—
547C2—21no—
548C2—82no—
549C2—82no—
550C2C11×#238811yescharacteristic
551C2C2×C11×#45411yescharacteristic
552C2C11×#301811yescharacteristic
subgroupG/H
centerC2×C4×C11#120
commutator, Frattini, cosocleC22×C4C24×C11
socleC22×C11C2×#120
prime radicalC11×#2006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3461C2semidirect
2. C4×C11×AGL(1,ℤ/8)C2semidirect
3. C4×C11×#124C2semidirect
4. C11×#2061C2semidirect
5. C11×#2040C2semidirect
6. C11×#2038C2semidirect
7. C11×#2027C2semidirect
9. C11×#2003C2semidirect
10. C4×C11×#104C2semidirect
11. C4×C11×#101C2semidirect
118. #23588C11direct (N × H)
192. #3461C2×C11semidirect
193. C4×AGL(1,ℤ/8)C2×C11semidirect
194. C4×#124C2×C11semidirect
195. #2061C2×C11semidirect
196. #2040C2×C11semidirect
197. #2038C2×C11semidirect
198. #2027C2×C11semidirect
200. #2003C2×C11semidirect
201. C4×#104C2×C11semidirect
202. C4×#101C2×C11semidirect
467. C11#23588direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34612
C4×C11×AGL(1,ℤ/8)2
C4×C11×#1242
C11×#20612
C11×#20402
C11×#20382
C11×#20272
C11×#20062
C11×#20032
C4×C11×#1042
C4×C11×#1012
#2358811