Finite Group Databasebeta

← C11×#18288 #14595481

Subgroups — C11×#18288 #14595481

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#539C211yesmaximal, characteristic, complemented
2C11×#3187C211yesmaximal, characteristic, complemented
3C11×#3186C211yesmaximal, characteristic
4C11×#2618C211yesmaximal, characteristic, complemented
5C11×#1609C214yesmaximal, complemented
6C11×#1597C214yesmaximal, complemented
7C11×#1520C211yesmaximal, characteristic, complemented
8C11×#1519C211yesmaximal, characteristic, complemented
9C2×C11×#324C211yesmaximal, characteristic, complemented
10C11×#539—22no—
11C11×#539—22no—
12C11×#539—22no—
13C11×#539C2214yes—
14C2×C11×#126—21no—
15C2×C11×#125—21no—
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×#123—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C22×C11×C4⋊C4C2211yescharacteristic
25C11×#483C2212yescomplemented
26C11×#481—21no—
27C11×#480—21no—
28C11×#480C2212yes—
29C11×#466—22no—
30C11×#465—22no—
31C11×#450C2212yescomplemented
32C11×#448—21no—
33C11×#447—21no—
34C11×#447C2212yes—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#398C2212yescomplemented
38C11×#396—22no—
39C11×#394C2212yescomplemented
40C11×#386—21no—
41C11×#380C2211yescharacteristic
42C11×#328C2214yescomplemented
43C11×#327C2214yes—
44C11×#324C2214yescomplemented
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C2×C11×SD16—22no—
55C2×C11×D8—22no—
56C22×C8×C11—21no—
57C22×C8×C11—21no—
58C11×#126—24no—
59C11×#126—24no—
60C11×#125—24no—
61C11×#125—24no—
62C11×#123—24no—
63C11×#123—24no—
64C11×#123—24no—
65C11×#123—24no—
66C11×#123—44no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8D412yes—
72C11×C22⋊Q8C2312yes—
73C11×#121—21no—
74C11×#121—21no—
75C11×#121—21no—
76C11×#121—21no—
77C11×#121—21no—
78C11×#121—21no—
79C11×#121D412yes—
80C11×#121C2312yes—
81C4×D4×C11—24no—
82C4×D4×C11—24no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4D412yes—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—21no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C42×C11—21no—
108C11×#107—22no—
109C11×#106—22no—
110C11×#103—22no—
111C11×#102—22no—
112C11×#102—22no—
113C11×#102—22no—
114C11×C22⋊C8—21no—
115C11×C22⋊C8—21no—
116C11×C22⋊C8C2312yes—
117C11×C22⋊C8C2312yes—
118C11×#95—22no—
119C11×#95C2312yes—
120#18288C1111yesmaximal, characteristic, direct product factor, Sylow
121C24×C11—21no—
122C24×C11—21no—
123C24×C11C2×D411yescharacteristic
124C2×Q8×C11—21no—
125C2×Q8×C11—81no—
126C2×Q8×C11C2×D412yes—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—42no—
133C2×D4×C11—42no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—81no—
139C2×D4×C11—81no—
140C2×D4×C11C2×D412yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—81no—
154C22×C4×C11—81no—
155C22×C4×C11—82no—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C11×SD16—82no—
165C11×D8—82no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—81no—
169C2×C8×C11—81no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—44no—
184C11×C4⋊C4—81no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4C2×D412yes—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—44no—
195C11×C22⋊C4—42no—
196C11×C22⋊C4—41no—
197C11×C22⋊C4—41no—
198C11×C22⋊C4—82no—
199C42×C11—24no—
200C2×#539C2×C1111yescharacteristic, complemented
201#3187C2×C1111yescharacteristic, complemented
202#3186C2×C1111yescharacteristic
203#2618C2×C1111yescharacteristic, complemented
204#1609C2×C1114yescomplemented
205#1597C2×C1114yescomplemented
206#1520C2×C1111yescharacteristic, complemented
207#1519C2×C1111yescharacteristic, complemented
208C2×#324C2×C1111yescharacteristic, complemented
209C23×C11—22no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11#12011yescharacteristic
221C23×C11#12011yescharacteristic
222C23×C11#13512yes—
223C23×C11AGL(1,ℤ/8)12yes—
224C23×C11C22×D411yescharacteristic
225Q8×C11—42no—
226Q8×C11—81no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—44no—
233D4×C11—81no—
234D4×C11—82no—
235D4×C11—82no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—41no—
262C2×C4×C11—81no—
263C2×C4×C11—84no—
264C2×C4×C11#12011yescharacteristic
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C8×C11—42no—
269C8×C11—42no—
270#539—22no—
271#539—22no—
272#539—22no—
273#539C22×C1114yes—
274C2×#126—21no—
275C2×#125—21no—
276C2×#123—21no—
277C2×#123—21no—
278C2×#123—21no—
279C2×C22⋊Q8—21no—
280C2×C22⋊Q8C22×C1111yescharacteristic
281C2×#121C22×C1111yescharacteristic
282C2×#121C22×C1111yescharacteristic
283C2×C4×D4—21no—
284C22×C4⋊C4C22×C1111yescharacteristic
285#483C22×C1112yescomplemented
286#481—21no—
287#480—21no—
288#480C22×C1112yes—
289#466—22no—
290#465—22no—
291#450C22×C1112yescomplemented
292#448—21no—
293#447—21no—
294#447C22×C1112yes—
295C2×C22⋊C8C22×C1111yescharacteristic
296C2×C22⋊C8C22×C1111yescharacteristic
297#398C22×C1112yescomplemented
298#396—22no—
299#394C22×C1112yescomplemented
300#386—21no—
301#380C22×C1111yescharacteristic
302#328C22×C1114yescomplemented
303#327C22×C1114yes—
304#324C22×C1114yescomplemented
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—21no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—84no—
317C22×C11—82no—
318C22×C11—82no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11#44912yes—
323C22×C11#44912yes—
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×#13511yescharacteristic
326C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—42no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11—82no—
337C4×C11—81no—
338C22×Q8D4×C1111yescharacteristic
339C22×D4—21no—
340C22×D4—21no—
341C22×D4D4×C1111yescharacteristic
342C22×D4C23×C1111yescharacteristic
343C23×C4—21no—
344C23×C4D4×C1111yescharacteristic
345C23×C4D4×C1111yescharacteristic
346C23×C4C23×C1111yescharacteristic
347C2×SD16—22no—
348C2×D8—22no—
349C22×C8—21no—
350C22×C8—21no—
351#126—24no—
352#126—24no—
353#125—24no—
354#125—24no—
355#123—24no—
356#123—24no—
357#123—24no—
358#123—24no—
359#123—44no—
360C22⋊Q8—24no—
361C22⋊Q8—24no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8D4×C1112yes—
365C22⋊Q8C23×C1112yes—
366#121—21no—
367#121—21no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121D4×C1112yes—
373#121C23×C1112yes—
374C4×D4—24no—
375C4×D4—24no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4D4×C1112yes—
387C2×C4⋊C4D4×C1111yescharacteristic
388C2×C4⋊C4D4×C1111yescharacteristic
389C2×C4⋊C4C23×C1111yescharacteristic
390C2×C4⋊C4C23×C1112yes—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C42—21no—
401#107—22no—
402#106—22no—
403#103—22no—
404#102—22no—
405#102—22no—
406#102—22no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8C23×C1112yes—
410C22⋊C8C23×C1112yes—
411#95—22no—
412#95C23×C1112yes—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—22no—
416C2×C11—22no—
417C2×C11—82no—
418C2×C11—161no—
419C2×C11C2×#44911yescharacteristic
420C2×C11#302011yescharacteristic
421C2×C11#302611yescharacteristic
422C24—21no—
423C24—21no—
424C24C2×D4×C1111yescharacteristic
425C2×Q8—21no—
426C2×Q8—81no—
427C2×Q8C2×D4×C1112yes—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—81no—
440C2×D4—81no—
441C2×D4C2×D4×C1112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—82no—
457C22×C4C2×D4×C1112yes—
458C22×C4C2×D4×C1112yes—
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C2×D4×C1111yescharacteristic
464C22×C4C24×C1111yescharacteristic
465SD16—82no—
466D8—82no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—81no—
470C2×C8—81no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—44no—
485C4⋊C4—81no—
486C4⋊C4C2×D4×C1112yes—
487C4⋊C4C2×D4×C1112yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—44no—
496C22⋊C4—42no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—82no—
500C42—24no—
501C11#1828811yescharacteristic, direct product factor, Sylow
502C23—22no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23C11×#12011yescharacteristic
514C23C11×#12011yescharacteristic
515C23C11×#13512yes—
516C23C11×AGL(1,ℤ/8)12yes—
517C23C22×D4×C1111yescharacteristic
518Q8—42no—
519Q8—81no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—42no—
524D4—42no—
525D4—44no—
526D4—81no—
527D4—82no—
528D4—82no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—81no—
556C2×C4—84no—
557C2×C4C11×#12011yescharacteristic
558C2×C4C11×#12011yescharacteristic
559C2×C4C22×D4×C1111yescharacteristic
560C2×C4C22×D4×C1111yescharacteristic
561C8—42no—
562C8—42no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—84no—
575C22—82no—
576C22—82no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C11×#44912yes—
581C22C11×#44912yes—
582C22C2×C11×#12011yescharacteristic
583C22C2×C11×#13511yescharacteristic
584C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—42no—
594C4—82no—
595C4—81no—
596C2—21no—
597C2—21no—
598C2—22no—
599C2—22no—
600C2—82no—
601C2—161no—
602C2C2×C11×#44911yescharacteristic
603C2C11×#302011yescharacteristic
604C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3186C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#539C2semidirect
2. C11×#3187C2semidirect
4. C11×#2618C2semidirect
5. C11×#1609C2semidirect
6. C11×#1597C2semidirect
7. C11×#1520C2semidirect
8. C11×#1519C2semidirect
9. C2×C11×#324C2semidirect
25. C11×#483C22semidirect
31. C11×#450C22semidirect
37. C11×#398C22semidirect
39. C11×#394C22semidirect
42. C11×#328C22semidirect
44. C11×#324C22semidirect
120. #18288C11direct (N × H)
200. C2×#539C2×C11semidirect
201. #3187C2×C11semidirect
203. #2618C2×C11semidirect
204. #1609C2×C11semidirect
205. #1597C2×C11semidirect
206. #1520C2×C11semidirect
207. #1519C2×C11semidirect
208. C2×#324C2×C11semidirect
285. #483C22×C11semidirect
291. #450C22×C11semidirect
297. #398C22×C11semidirect
299. #394C22×C11semidirect
302. #328C22×C11semidirect
304. #324C22×C11semidirect
501. C11#18288direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5392
C11×#31872
C11×#31862
C11×#26182
C11×#16092
C11×#15972
C11×#15202
C11×#15192
C2×C11×#3242
#1828811