Finite Group Databasebeta

← C11×#18245 #14595438

Subgroups — C11×#18245 #14595438

Order 2816.

908 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3559C211yesmaximal, characteristic
2C11×#3117C211yesmaximal, characteristic, complemented
3C11×#3103C211yesmaximal, characteristic, complemented
4C11×#2634C211yesmaximal, characteristic, complemented
5C11×#1616C212yesmaximal, complemented
6C11×#1615C212yesmaximal, complemented
7C11×#1604C212yesmaximal, complemented
8C11×#1603C212yesmaximal, complemented
9C11×#1521C211yesmaximal, characteristic, complemented
10C11×#1514C211yesmaximal, characteristic, complemented
11C11×#1470C211yesmaximal, characteristic, complemented
12C11×#563—21no—
13C11×#562—21no—
14C11×#554—21no—
15C11×#553—21no—
16C11×#553—21no—
17C11×#547—22no—
18C11×#547—21no—
19C11×#544—21no—
20C11×#540—21no—
21C11×#539—22no—
22C11×#539C2212yes—
23C11×#537C2212yes—
24C11×#532C2211yescharacteristic
25C11×#529C2211yescharacteristic
26C2×C11×#125C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C11×#484C2211yescharacteristic
29C11×#481C2212yes—
30C11×#481C2211yescharacteristic
31C11×#479—21no—
32C11×#475—21no—
33C11×#464—21no—
34C11×#460—21no—
35C11×#451C2211yescharacteristic
36C11×#448C2212yes—
37C11×#448C2211yescharacteristic
38C11×#441—21no—
39C11×#440—21no—
40C4×C11×SD16—22no—
41C11×#432C2211yescharacteristic
42C11×#431C2211yescharacteristic
43C11×#400—21no—
44C11×#400C2212yes—
45C11×#398—21no—
46C11×#395C2212yes—
47C11×#387—22no—
48C11×#383C2211yescharacteristic
49C11×#328C2212yes—
50C11×#327C2212yes—
51C11×#327C2212yes—
52C11×#327C2212yes—
53C11×#324C2212yes—
54C11×#324C2212yes—
55C2×C11×#41—21no—
56C2×C11×#41—22no—
57C22×Q8×C11C2311yescharacteristic
58C2×C11×Q16—21no—
59C2×C11×SD16—22no—
60C2×C11×SD16—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8D411yescharacteristic
64C11×#127D411yescharacteristic
65C11×#126—22no—
66C11×#126—22no—
67C11×#126—21no—
68C11×#125—21no—
69C11×#125—22no—
70C11×#125—21no—
71C11×#125—21no—
72C11×#125—21no—
73C11×#125—21no—
74C11×#125D411yescharacteristic
75C11×#124—21no—
76C11×#124D411yescharacteristic
77C11×#123—22no—
78C11×#123—22no—
79C11×#123—22no—
80C11×#123—22no—
81C11×#123—22no—
82C11×#123—21no—
83C11×#123—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—22no—
90C11×C22⋊Q8C2311yescharacteristic
91C11×#121—21no—
92C11×#121—22no—
93C11×#121—21no—
94C11×#121—22no—
95C11×#121—22no—
96C11×#121—21no—
97C11×#121—22no—
98C11×#121C2311yescharacteristic
99C11×#121C2312yes—
100C4×Q8×C11—21no—
101C4×Q8×C11—21no—
102C4×Q8×C11—21no—
103C4×Q8×C11—21no—
104C4×Q8×C11D411yescharacteristic
105C4×D4×C11—22no—
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—22no—
110C4×D4×C11—21no—
111C4×D4×C11D411yescharacteristic
112C4×D4×C11D412yes—
113C11×#117—21no—
114C11×#117—21no—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—22no—
119C2×C11×C4⋊C4D412yes—
120C2×C11×C4⋊C4D411yescharacteristic
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2312yes—
124C2×C42×C11—21no—
125C2×C42×C11C2311yescharacteristic
126C11×#107—21no—
127C11×#106—22no—
128C11×#106—21no—
129C11×C4⋊C8—21no—
130C11×C4⋊C8—21no—
131C11×#103—21no—
132C11×#103—22no—
133C11×#103—21no—
134C11×#103—21no—
135C11×#102—22no—
136C11×#102—21no—
137C11×C22⋊C8C2311yescharacteristic
138C11×C22⋊C8C2311yescharacteristic
139C11×C22⋊C8C2312yes—
140C11×#97—21no—
141C4×C8×C11—21no—
142C11×#95—21no—
143C11×#95—21no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95C2312yes—
148#18245C1111yesmaximal, characteristic, direct product factor, Sylow
149C11×#41—82no—
150C11×#41—84no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—42no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—21no—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11C2×D412yes—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C11×Q16—42no—
179C11×SD16—44no—
180C11×SD16—42no—
181C2×C8×C11—22no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—44no—
204C11×C4⋊C4—41no—
205C11×C4⋊C4—41no—
206C11×C4⋊C4C2×D412yes—
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—22no—
221C42×C11—22no—
222C42×C11—21no—
223C42×C11—41no—
224C42×C11—41no—
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229#3559C2×C1111yescharacteristic
230#3117C2×C1111yescharacteristic, complemented
231#3103C2×C1111yescharacteristic, complemented
232#2634C2×C1111yescharacteristic, complemented
233#1616C2×C1112yescomplemented
234#1615C2×C1112yescomplemented
235#1604C2×C1112yescomplemented
236#1603C2×C1112yescomplemented
237#1521C2×C1111yescharacteristic, complemented
238#1514C2×C1111yescharacteristic, complemented
239#1470C2×C1111yescharacteristic, complemented
240C23×C11—21no—
241C23×C11—22no—
242C23×C11C22×D411yescharacteristic
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—41no—
248Q8×C11—81no—
249Q8×C11—82no—
250D4×C11—42no—
251D4×C11—41no—
252D4×C11—42no—
253D4×C11—44no—
254D4×C11—42no—
255D4×C11—81no—
256D4×C11—82no—
257D4×C11—82no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—41no—
277C2×C4×C11—42no—
278C2×C4×C11—82no—
279C2×C4×C11—82no—
280C2×C4×C11—82no—
281C2×C4×C11—82no—
282C2×C4×C11#12011yescharacteristic
283C2×C4×C11#12011yescharacteristic
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C8×C11—42no—
289C8×C11—41no—
290C8×C11—41no—
291#563—21no—
292#562—21no—
293#554—21no—
294#553—21no—
295#553—21no—
296#547—22no—
297#547—21no—
298#544—21no—
299#540—21no—
300#539—22no—
301#539C22×C1112yes—
302#537C22×C1112yes—
303#532C22×C1111yescharacteristic
304#529C22×C1111yescharacteristic
305C2×#125C22×C1111yescharacteristic
306C2×C4×Q8C22×C1111yescharacteristic
307#484C22×C1111yescharacteristic
308#481C22×C1112yes—
309#481C22×C1111yescharacteristic
310#479—21no—
311#475—21no—
312#464—21no—
313#460—21no—
314#451C22×C1111yescharacteristic
315#448C22×C1112yes—
316#448C22×C1111yescharacteristic
317#441—21no—
318#440—21no—
319C4×SD16—22no—
320#432C22×C1111yescharacteristic
321#431C22×C1111yescharacteristic
322#400—21no—
323#400C22×C1112yes—
324#398—21no—
325#395C22×C1112yes—
326#387—22no—
327#383C22×C1111yescharacteristic
328#328C22×C1112yes—
329#327C22×C1112yes—
330#327C22×C1112yes—
331#327C22×C1112yes—
332#324C22×C1112yes—
333#324C22×C1112yes—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—41no—
342C22×C11C2×#12011yescharacteristic
343C22×C11#57712yes—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—82no—
358C4×C11—81no—
359C2×#41—21no—
360C2×#41—22no—
361C22×Q8C23×C1111yescharacteristic
362C2×Q16—21no—
363C2×SD16—22no—
364C2×SD16—21no—
365C4⋊Q8—21no—
366C4⋊Q8—22no—
367C4⋊Q8D4×C1111yescharacteristic
368#127D4×C1111yescharacteristic
369#126—22no—
370#126—22no—
371#126—21no—
372#125—21no—
373#125—22no—
374#125—21no—
375#125—21no—
376#125—21no—
377#125—21no—
378#125D4×C1111yescharacteristic
379#124—21no—
380#124D4×C1111yescharacteristic
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386#123—21no—
387#123—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8C23×C1111yescharacteristic
395#121—21no—
396#121—22no—
397#121—21no—
398#121—22no—
399#121—22no—
400#121—21no—
401#121—22no—
402#121C23×C1111yescharacteristic
403#121C23×C1112yes—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8D4×C1111yescharacteristic
409C4×D4—22no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—22no—
414C4×D4—21no—
415C4×D4D4×C1111yescharacteristic
416C4×D4D4×C1112yes—
417#117—21no—
418#117—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4D4×C1112yes—
424C2×C4⋊C4D4×C1111yescharacteristic
425C2×C4⋊C4D4×C1111yescharacteristic
426C2×C4⋊C4C23×C1111yescharacteristic
427C2×C4⋊C4C23×C1112yes—
428C2×C42—21no—
429C2×C42C23×C1111yescharacteristic
430#107—21no—
431#106—22no—
432#106—21no—
433C4⋊C8—21no—
434C4⋊C8—21no—
435#103—21no—
436#103—22no—
437#103—21no—
438#103—21no—
439#102—22no—
440#102—21no—
441C22⋊C8C23×C1111yescharacteristic
442C22⋊C8C23×C1111yescharacteristic
443C22⋊C8C23×C1112yes—
444#97—21no—
445C4×C8—21no—
446#95—21no—
447#95—21no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95C23×C1112yes—
452C2×C11—22no—
453C2×C11—81no—
454C2×C11—82no—
455C2×C11#300911yescharacteristic
456C2×C11#302011yescharacteristic
457C2×C11#302511yescharacteristic
458#41—82no—
459#41—84no—
460C2×Q8—22no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×Q8C2×D4×C1111yescharacteristic
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4C2×D4×C1111yescharacteristic
473C2×D4C2×D4×C1112yes—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4C2×D4×C1112yes—
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C2×D4×C1112yes—
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C24×C1111yescharacteristic
487Q16—42no—
488SD16—44no—
489SD16—42no—
490C2×C8—22no—
491C2×C8—21no—
492C2×C8—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—44no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C1112yes—
516C4⋊C4C2×D4×C1111yescharacteristic
517C4⋊C4C2×D4×C1111yescharacteristic
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—22no—
528C22⋊C4—21no—
529C22⋊C4—22no—
530C42—22no—
531C42—21no—
532C42—41no—
533C42—41no—
534C42C2×D4×C1111yescharacteristic
535C42C2×D4×C1111yescharacteristic
536C42C2×D4×C1111yescharacteristic
537C42C2×D4×C1111yescharacteristic
538C11#1824511yescharacteristic, direct product factor, Sylow
539C23—21no—
540C23—22no—
541C23C22×D4×C1111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—81no—
548Q8—82no—
549D4—42no—
550D4—41no—
551D4—42no—
552D4—44no—
553D4—42no—
554D4—81no—
555D4—82no—
556D4—82no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4—82no—
581C2×C4C11×#12011yescharacteristic
582C2×C4C11×#12011yescharacteristic
583C2×C4C11×#12011yescharacteristic
584C2×C4C11×#12011yescharacteristic
585C2×C4C22×D4×C1111yescharacteristic
586C2×C4C22×D4×C1111yescharacteristic
587C8—42no—
588C8—41no—
589C8—41no—
590C22—21no—
591C22—21no—
592C22—42no—
593C22—41no—
594C22—41no—
595C22—42no—
596C22—42no—
597C22—41no—
598C22C2×C11×#12011yescharacteristic
599C22C11×#57712yes—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—41no—
609C4—41no—
610C4—42no—
611C4—42no—
612C4—41no—
613C4—82no—
614C4—81no—
615C2—22no—
616C2—81no—
617C2—82no—
618C2C11×#300911yescharacteristic
619C2C11×#302011yescharacteristic
620C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3559C2
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×#3117C2semidirect
3. C11×#3103C2semidirect
4. C11×#2634C2semidirect
5. C11×#1616C2semidirect
6. C11×#1615C2semidirect
7. C11×#1604C2semidirect
8. C11×#1603C2semidirect
9. C11×#1521C2semidirect
10. C11×#1514C2semidirect
11. C11×#1470C2semidirect
148. #18245C11direct (N × H)
230. #3117C2×C11semidirect
231. #3103C2×C11semidirect
232. #2634C2×C11semidirect
233. #1616C2×C11semidirect
234. #1615C2×C11semidirect
235. #1604C2×C11semidirect
236. #1603C2×C11semidirect
237. #1521C2×C11semidirect
238. #1514C2×C11semidirect
239. #1470C2×C11semidirect
538. C11#18245direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35592
C11×#31172
C11×#31032
C11×#26342
C11×#16162
C11×#16152
C11×#16042
C11×#16032
C11×#15212
C11×#15142
C11×#14702
#1824511