Finite Group Databasebeta

← C11×#18960 #14596153

Subgroups — C11×#18960 #14596153

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3555C211yesmaximal, characteristic, complemented
2C11×#3217C211yesmaximal, characteristic
3C11×#3208C211yesmaximal, characteristic, complemented
4C11×#3208C211yesmaximal, characteristic, complemented
5C11×#1628C212yesmaximal, complemented
6C11×#1626C212yesmaximal, complemented
7C11×#1623C212yesmaximal, complemented
8C11×#1622C212yesmaximal, complemented
9C11×#1554C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1482C211yesmaximal, characteristic, complemented
12C11×#563—22no—
13Q82×C11C2211yescharacteristic, complemented
14C11×#557—21no—
15C11×#557C2211yescharacteristic, complemented
16C11×#556—21no—
17C11×#556—21no—
18C11×#556C2211yescharacteristic, complemented
19C11×#554C2211yescharacteristic, complemented
20C11×#552—21no—
21C11×#544—21no—
22C11×#542—21no—
23C11×#541—21no—
24C11×#541—21no—
25C11×#541—22no—
26C11×#533C2211yescharacteristic
27C11×#533C2211yescharacteristic
28C2×C11×#127C2211yescharacteristic
29C11×#529C2211yescharacteristic
30C11×#496—21no—
31C11×#492—21no—
32C11×#492C2212yes—
33C11×#490—21no—
34C11×#486—21no—
35C11×#486C2212yes—
36C11×#460—22no—
37C11×#460C2212yes—
38C11×#460C2212yes—
39C11×#460C2212yes—
40C11×#459C2212yes—
41C11×#450—22no—
42C11×#450—21no—
43C11×#450—21no—
44C11×#450—21no—
45C11×#447—21no—
46C11×#432C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#431C2211yescharacteristic
49C11×#333C2212yescomplemented
50C11×#332C2212yescomplemented
51C11×Q8⋊C8C2212yescomplemented
52C11×Q8⋊C8C2212yescomplemented
53C11×Q8⋊C8C2212yescomplemented
54C11×D4⋊C8C2212yescomplemented
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C2×C11×SD16—22no—
59C2×C11×SD16—22no—
60C2×C11×SD16—24no—
61C2×C11×SD16—22no—
62C2×C11×D8—22no—
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8D411yescharacteristic
69C11×C4⋊Q8D411yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#127—21no—
73C11×#127—21no—
74C11×#127—21no—
75C11×#127C2312yes—
76C11×#126—22no—
77C11×#126—22no—
78C11×#126—22no—
79C11×#126—22no—
80C11×#126—22no—
81C11×#126—22no—
82C11×#126—21no—
83C11×#125—22no—
84C11×#125—22no—
85C11×#125—22no—
86C11×#125—22no—
87C11×#125—21no—
88C11×#125—22no—
89C11×#125—21no—
90C11×#125—21no—
91C11×#125—21no—
92C11×#125D411yescharacteristic
93C11×#124—22no—
94C11×#124—21no—
95C11×#124D411yescharacteristic
96C11×#123—22no—
97C11×#123—21no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8—21no—
101C11×C22⋊Q8—21no—
102C11×C22⋊Q8—22no—
103C11×C22⋊Q8—21no—
104C11×C22⋊Q8—21no—
105C11×C22⋊Q8D411yescharacteristic
106C11×C22⋊Q8D411yescharacteristic
107C11×C22⋊Q8D411yescharacteristic
108C11×C22⋊Q8D412yes—
109C11×#121D411yescharacteristic
110C4×Q8×C11—22no—
111C4×Q8×C11—21no—
112C4×Q8×C11—21no—
113C4×Q8×C11—21no—
114C4×Q8×C11—21no—
115C4×Q8×C11—21no—
116C4×Q8×C11—21no—
117C4×Q8×C11—21no—
118C4×Q8×C11D412yes—
119C4×Q8×C11C2311yescharacteristic
120C4×Q8×C11C2311yescharacteristic
121C4×Q8×C11C2311yescharacteristic
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11C2311yescharacteristic
125C11×#117—22no—
126C11×#117—21no—
127C11×#117—21no—
128C11×#117—21no—
129C11×#117—21no—
130C2×C11×C4⋊C4—21no—
131C2×C42×C11C2311yescharacteristic
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#102—22no—
136C11×#102—22no—
137C11×#102—24no—
138C11×#102—22no—
139C11×#102—22no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C4×C8×C11—21no—
145C4×C8×C11C2312yes—
146#18960C1111yesmaximal, characteristic, direct product factor, Sylow
147C24×C11—41no—
148C2×Q8×C11—22no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11C2×D411yescharacteristic
152C2×Q8×C11C2×D411yescharacteristic
153C2×Q8×C11C2×D411yescharacteristic
154C2×Q8×C11C2×D412yes—
155C2×D4×C11—21no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11—82no—
163C2×D4×C11—82no—
164C2×D4×C11—82no—
165C2×D4×C11C2×D411yescharacteristic
166C22×C4×C11—22no—
167C22×C4×C11—21no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C11×SD16—82no—
172C11×SD16—82no—
173C11×SD16—82no—
174C11×SD16—84no—
175C11×D8—82no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D412yes—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C42×C11—22no—
220C42×C11—22no—
221C42×C11—22no—
222C42×C11—22no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11C2×D411yescharacteristic
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2411yescharacteristic
230#3555C2×C1111yescharacteristic, complemented
231#3217C2×C1111yescharacteristic
232#3208C2×C1111yescharacteristic, complemented
233#3208C2×C1111yescharacteristic, complemented
234#1628C2×C1112yescomplemented
235#1626C2×C1112yescomplemented
236#1623C2×C1112yescomplemented
237#1622C2×C1112yescomplemented
238#1554C2×C1111yescharacteristic, complemented
239#1497C2×C1111yescharacteristic, complemented
240#1482C2×C1111yescharacteristic, complemented
241C23×C11—21no—
242C23×C11—42no—
243C23×C11—82no—
244C23×C11—82no—
245C23×C11—82no—
246C23×C11#12011yescharacteristic
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—42no—
251Q8×C11—42no—
252Q8×C11—81no—
253Q8×C11—82no—
254D4×C11—22no—
255D4×C11—44no—
256D4×C11—42no—
257D4×C11—42no—
258D4×C11—42no—
259D4×C11—42no—
260D4×C11—82no—
261D4×C11—82no—
262D4×C11—82no—
263D4×C11—81no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—42no—
277C2×C4×C11—82no—
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11#12011yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C8×C11—42no—
285C8×C11—42no—
286C8×C11—42no—
287#563—22no—
288Q82C22×C1111yescharacteristic, complemented
289#557—21no—
290#557C22×C1111yescharacteristic, complemented
291#556—21no—
292#556—21no—
293#556C22×C1111yescharacteristic, complemented
294#554C22×C1111yescharacteristic, complemented
295#552—21no—
296#544—21no—
297#542—21no—
298#541—21no—
299#541—21no—
300#541—22no—
301#533C22×C1111yescharacteristic
302#533C22×C1111yescharacteristic
303C2×#127C22×C1111yescharacteristic
304#529C22×C1111yescharacteristic
305#496—21no—
306#492—21no—
307#492C22×C1112yes—
308#490—21no—
309#486—21no—
310#486C22×C1112yes—
311#460—22no—
312#460C22×C1112yes—
313#460C22×C1112yes—
314#460C22×C1112yes—
315#459C22×C1112yes—
316#450—22no—
317#450—21no—
318#450—21no—
319#450—21no—
320#447—21no—
321#432C22×C1111yescharacteristic
322#431C22×C1111yescharacteristic
323#431C22×C1111yescharacteristic
324#333C22×C1112yescomplemented
325#332C22×C1112yescomplemented
326Q8⋊C8C22×C1112yescomplemented
327Q8⋊C8C22×C1112yescomplemented
328Q8⋊C8C22×C1112yescomplemented
329D4⋊C8C22×C1112yescomplemented
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—82no—
337C22×C11—82no—
338C22×C11—82no—
339C22×C11—164no—
340C22×C11C2×#12011yescharacteristic
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11#57712yes—
355C4×C11#57712yes—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—21no—
359C2×SD16—24no—
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—22no—
363C2×D8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—21no—
366C4⋊Q8—22no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8D4×C1111yescharacteristic
370C4⋊Q8D4×C1111yescharacteristic
371C4⋊Q8C23×C1111yescharacteristic
372C4⋊Q8C23×C1111yescharacteristic
373#127—21no—
374#127—21no—
375#127—21no—
376#127C23×C1112yes—
377#126—22no—
378#126—22no—
379#126—22no—
380#126—22no—
381#126—22no—
382#126—22no—
383#126—21no—
384#125—22no—
385#125—22no—
386#125—22no—
387#125—22no—
388#125—21no—
389#125—22no—
390#125—21no—
391#125—21no—
392#125—21no—
393#125D4×C1111yescharacteristic
394#124—22no—
395#124—21no—
396#124D4×C1111yescharacteristic
397#123—22no—
398#123—21no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—22no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8D4×C1111yescharacteristic
407C22⋊Q8D4×C1111yescharacteristic
408C22⋊Q8D4×C1111yescharacteristic
409C22⋊Q8D4×C1112yes—
410#121D4×C1111yescharacteristic
411C4×Q8—22no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8D4×C1112yes—
420C4×Q8C23×C1111yescharacteristic
421C4×Q8C23×C1111yescharacteristic
422C4×Q8C23×C1111yescharacteristic
423C4×D4—21no—
424C4×D4—21no—
425C4×D4C23×C1111yescharacteristic
426#117—22no—
427#117—21no—
428#117—21no—
429#117—21no—
430#117—21no—
431C2×C4⋊C4—21no—
432C2×C42C23×C1111yescharacteristic
433C4⋊C8—21no—
434C4⋊C8C23×C1112yes—
435C4⋊C8C23×C1112yes—
436#102—22no—
437#102—22no—
438#102—24no—
439#102—22no—
440#102—22no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444#97—21no—
445C4×C8—21no—
446C4×C8C23×C1112yes—
447C2×C11—41no—
448C2×C11—81no—
449C2×C11—162no—
450C2×C11#301011yescharacteristic
451C2×C11#301011yescharacteristic
452C2×C11#302111yescharacteristic
453C24—41no—
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8C2×D4×C1111yescharacteristic
458C2×Q8C2×D4×C1111yescharacteristic
459C2×Q8C2×D4×C1111yescharacteristic
460C2×Q8C2×D4×C1112yes—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—82no—
469C2×D4—82no—
470C2×D4—82no—
471C2×D4C2×D4×C1111yescharacteristic
472C22×C4—22no—
473C22×C4—21no—
474C22×C4C2×D4×C1111yescharacteristic
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1111yescharacteristic
477SD16—82no—
478SD16—82no—
479SD16—82no—
480SD16—84no—
481D8—82no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4C2×D4×C1111yescharacteristic
510C4⋊C4C2×D4×C1111yescharacteristic
511C4⋊C4C2×D4×C1111yescharacteristic
512C4⋊C4C2×D4×C1111yescharacteristic
513C4⋊C4C2×D4×C1112yes—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—22no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—22no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42C2×D4×C1111yescharacteristic
533C42C2×D4×C1111yescharacteristic
534C42C2×D4×C1111yescharacteristic
535C42C24×C1111yescharacteristic
536C11#1896011yescharacteristic, direct product factor, Sylow
537C23—21no—
538C23—42no—
539C23—82no—
540C23—82no—
541C23—82no—
542C23C11×#12011yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—22no—
546Q8—42no—
547Q8—42no—
548Q8—81no—
549Q8—82no—
550D4—22no—
551D4—44no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4—81no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—82no—
574C2×C4C11×#12011yescharacteristic
575C2×C4C11×#12011yescharacteristic
576C2×C4C11×#12011yescharacteristic
577C2×C4C22×D4×C1111yescharacteristic
578C2×C4C22×D4×C1111yescharacteristic
579C2×C4C22×D4×C1111yescharacteristic
580C8—42no—
581C8—42no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—82no—
590C22—82no—
591C22—82no—
592C22—164no—
593C22C2×C11×#12011yescharacteristic
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—42no—
605C4—41no—
606C4—41no—
607C4C11×#57712yes—
608C4C11×#57712yes—
609C2—41no—
610C2—81no—
611C2—162no—
612C2C11×#301011yescharacteristic
613C2C11×#301011yescharacteristic
614C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3217C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3555C2semidirect
3. C11×#3208C2semidirect
4. C11×#3208C2semidirect
5. C11×#1628C2semidirect
6. C11×#1626C2semidirect
7. C11×#1623C2semidirect
8. C11×#1622C2semidirect
9. C11×#1554C2semidirect
10. C11×#1497C2semidirect
11. C11×#1482C2semidirect
13. Q82×C11C22semidirect
15. C11×#557C22semidirect
18. C11×#556C22semidirect
19. C11×#554C22semidirect
49. C11×#333C22semidirect
50. C11×#332C22semidirect
51. C11×Q8⋊C8C22semidirect
52. C11×Q8⋊C8C22semidirect
53. C11×Q8⋊C8C22semidirect
54. C11×D4⋊C8C22semidirect
146. #18960C11direct (N × H)
230. #3555C2×C11semidirect
232. #3208C2×C11semidirect
233. #3208C2×C11semidirect
234. #1628C2×C11semidirect
235. #1626C2×C11semidirect
236. #1623C2×C11semidirect
237. #1622C2×C11semidirect
238. #1554C2×C11semidirect
239. #1497C2×C11semidirect
240. #1482C2×C11semidirect
288. Q82C22×C11semidirect
290. #557C22×C11semidirect
293. #556C22×C11semidirect
294. #554C22×C11semidirect
324. #333C22×C11semidirect
325. #332C22×C11semidirect
326. Q8⋊C8C22×C11semidirect
327. Q8⋊C8C22×C11semidirect
328. Q8⋊C8C22×C11semidirect
329. D4⋊C8C22×C11semidirect
536. C11#18960direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35552
C11×#32172
C11×#32082
C11×#16282
C11×#16262
C11×#16232
C11×#16222
C11×#15542
C11×#14972
C11×#14822
#1896011