Finite Group Databasebeta

← C11×#23592 #14600785

Subgroups — C11×#23592 #14600785

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 550 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
3C11×#2326C211yesmaximal, characteristic, complemented
4C11×#2060C211yesmaximal, characteristic, complemented
5C11×#2039C211yesmaximal, characteristic, complemented
6C11×#2038C212yesmaximal, complemented
7C11×#2027C211yesmaximal, characteristic, complemented
8C11×#2006C211yesmaximal, characteristic
9C11×#2003C212yesmaximal, complemented
10C11×#1759C212yesmaximal, 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×#385—22no—
41C11×#384C2211yescharacteristic
42C11×#376C2211yescharacteristic
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⋊C4—22no—
93C2×C11×C4⋊C4D412yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—22no—
99C2×C42×C11—22no—
100C2×C42×C11D412yes—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C11×#107—22no—
105C11×#106—22no—
106C11×#104—24no—
107C11×#104—24no—
108C11×#103—22no—
109C11×#102—22no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#101—24no—
113C11×#97—22no—
114C4×C8×C11—22no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—22no—
118#23592C1111yesmaximal, 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—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—42no—
144C22×C4×C11—82no—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C11×SD16—28no—
151C11×D8—28no—
152C11×M16—22no—
153C11×M16—22no—
154C11×M16—22no—
155C11×M16#4114yes—
156C2×C8×C11—22no—
157C2×C8×C11—22no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—82no—
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—41no—
179C11×C22⋊C4—41no—
180C11×C22⋊C4—82no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11—22no—
184C42×C11—22no—
185C42×C11—22no—
186C42×C11—21no—
187C42×C11—22no—
188C42×C11C2×D412yes—
189C42×C11C2×D412yes—
190C42×C11#4112yes—
191#3461C2×C1111yescharacteristic, complemented
192C4×AGL(1,ℤ/8)C2×C1112yescomplemented
193#2326C2×C1111yescharacteristic, complemented
194#2060C2×C1111yescharacteristic, complemented
195#2039C2×C1111yescharacteristic, complemented
196#2038C2×C1112yescomplemented
197#2027C2×C1111yescharacteristic, complemented
198#2006C2×C1111yescharacteristic
199#2003C2×C1112yescomplemented
200#1759C2×C1112yescomplemented
201C4×#101C2×C1111yescharacteristic, complemented
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11C22×D411yescharacteristic
209Q8×C11—22no—
210Q8×C11—22no—
211Q8×C11—42no—
212Q8×C11—42no—
213Q8×C11—82no—
214D4×C11—22no—
215D4×C11—24no—
216D4×C11—22no—
217D4×C11—42no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—82no—
221C2×C4×C11—22no—
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—41no—
230C2×C4×C11—41no—
231C2×C4×C11—44no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—82no—
243C2×C4×C11—84no—
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12012yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4112yes—
250C2×C4×C11C2×#4111yescharacteristic
251C8×C11—24no—
252C8×C11—42no—
253C2×AGL(1,ℤ/8)C22×C1112yes—
254#544C22×C1111yescharacteristic
255#542—22no—
256#541—22no—
257#539—22no—
258#537C22×C1111yescharacteristic
259#536C22×C1112yes—
260#533—22no—
261#529—22no—
262#529—22no—
263C2×#124C22×C1111yescharacteristic
264C4×#41C22×C1112yes—
265C2×C4×Q8C22×C1111yescharacteristic
266C2×C4×D4C22×C1111yescharacteristic
267#442—22no—
268#440—22no—
269C4×SD16—22no—
270C4×D8—22no—
271#428C22×C1112yes—
272C2×#104C22×C1112yes—
273C2×#104C22×C1112yes—
274#418C22×C1112yes—
275#417C22×C1112yes—
276C2×#101C22×C1112yes—
277C4×M16C22×C1112yes—
278#391C22×C1111yescharacteristic
279#390C22×C1111yescharacteristic
280#388—22no—
281#385—22no—
282#384C22×C1111yescharacteristic
283#376C22×C1111yescharacteristic
284#343C22×C1111yescharacteristic
285#343C22×C1111yescharacteristic
286#339C22×C1112yes—
287#339C22×C1112yes—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—44no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—82no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11C2×#12011yescharacteristic
299C22×C11#52511yescharacteristic
300C22×C11#53211yescharacteristic
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—42no—
310C4×C11—81no—
311C4×C11—81no—
312C4×C11#52512yes—
313C4×C11#53212yes—
314C2×#41C23×C1112yes—
315C22×Q8C23×C1111yescharacteristic
316C22×D4C23×C1111yescharacteristic
317C23×C4—21no—
318AGL(1,ℤ/8)—24no—
319AGL(1,ℤ/8)—24no—
320C2×SD16—22no—
321C2×D8—22no—
322C2×M16C23×C1112yes—
323C2×M16C23×C1112yes—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326#126—24no—
327#126—24no—
328#125—22no—
329#125—24no—
330#125—22no—
331#124—22no—
332#124—22no—
333#124—22no—
334#124—22no—
335#123—24no—
336#123—24no—
337C22⋊Q8—24no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342#121—22no—
343#121—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8D4×C1112yes—
348C4×Q8D4×C1112yes—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4D4×C1112yes—
355C4×D4D4×C1112yes—
356#117—24no—
357#117—22no—
358#117C23×C1112yes—
359C2×C4⋊C4—22no—
360C2×C4⋊C4D4×C1112yes—
361C2×C4⋊C4C23×C1111yescharacteristic
362C2×C4⋊C4C23×C1111yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C42—22no—
367C2×C42D4×C1112yes—
368C2×C42C23×C1111yescharacteristic
369C2×C42C23×C1111yescharacteristic
370C2×C42C23×C1111yescharacteristic
371#107—22no—
372#106—22no—
373#104—24no—
374#104—24no—
375#103—22no—
376#102—22no—
377#102—22no—
378#102—22no—
379#101—24no—
380#97—22no—
381C4×C8—22no—
382#95—21no—
383#95—21no—
384#95—22no—
385C2×C11—21no—
386C2×C11—21no—
387C2×C11—82no—
388C2×C11—82no—
389C2×C11#238811yescharacteristic
390C2×C11#302011yescharacteristic
391C2×C11#302111yescharacteristic
392C24—21no—
393#41—22no—
394#41—22no—
395#41—22no—
396#41—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8C2×D4×C1112yes—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4C2×D4×C1112yes—
409C2×D4C11×#4112yes—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—42no—
417C22×C4—82no—
418C22×C4C2×D4×C1112yes—
419C22×C4C2×D4×C1112yes—
420C22×C4C2×D4×C1111yescharacteristic
421C22×C4C2×D4×C1111yescharacteristic
422C22×C4C24×C1111yescharacteristic
423SD16—28no—
424D8—28no—
425M16—22no—
426M16—22no—
427M16—22no—
428M16C11×#4114yes—
429C2×C8—22no—
430C2×C8—22no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—24no—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—82no—
442C4⋊C4C2×D4×C1112yes—
443C4⋊C4C2×D4×C1112yes—
444C22⋊C4—28no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—82no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—22no—
458C42—22no—
459C42—21no—
460C42—22no—
461C42C2×D4×C1112yes—
462C42C2×D4×C1112yes—
463C42C11×#4112yes—
464C11#2359211yescharacteristic, direct product factor, Sylow
465C23—22no—
466C23—22no—
467C23—42no—
468C23—42no—
469C23—41no—
470C23—41no—
471C23C22×D4×C1111yescharacteristic
472Q8—22no—
473Q8—22no—
474Q8—42no—
475Q8—42no—
476Q8—82no—
477D4—22no—
478D4—24no—
479D4—22no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—82no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—44no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—82no—
506C2×C4—84no—
507C2×C4C11×#12011yescharacteristic
508C2×C4C11×#12011yescharacteristic
509C2×C4C11×#12012yes—
510C2×C4C22×D4×C1112yes—
511C2×C4C2×C11×#4111yescharacteristic
512C2×C4C2×C11×#4112yes—
513C2×C4C2×C11×#4111yescharacteristic
514C8—24no—
515C8—42no—
516C22—21no—
517C22—21no—
518C22—44no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—82no—
524C22—81no—
525C22—81no—
526C22C2×C11×#12011yescharacteristic
527C22C11×#52511yescharacteristic
528C22C11×#53211yescharacteristic
529C4—21no—
530C4—21no—
531C4—22no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4—81no—
539C4—81no—
540C4C11×#52512yes—
541C4C11×#53212yes—
542C2—21no—
543C2—21no—
544C2—82no—
545C2—82no—
546C2C11×#238811yescharacteristic
547C2C11×#302011yescharacteristic
548C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#2006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×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. C11×#2326C2semidirect
4. C11×#2060C2semidirect
5. C11×#2039C2semidirect
6. C11×#2038C2semidirect
7. C11×#2027C2semidirect
9. C11×#2003C2semidirect
10. C11×#1759C2semidirect
11. C4×C11×#101C2semidirect
118. #23592C11direct (N × H)
191. #3461C2×C11semidirect
192. C4×AGL(1,ℤ/8)C2×C11semidirect
193. #2326C2×C11semidirect
194. #2060C2×C11semidirect
195. #2039C2×C11semidirect
196. #2038C2×C11semidirect
197. #2027C2×C11semidirect
199. #2003C2×C11semidirect
200. #1759C2×C11semidirect
201. C4×#101C2×C11semidirect
464. C11#23592direct (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
C11×#23262
C11×#20602
C11×#20392
C11×#20382
C11×#20272
C11×#20062
C11×#20032
C11×#17592
C4×C11×#1012
#2359211