Finite Group Databasebeta

← C11×#18971 #14596164

Subgroups — C11×#18971 #14596164

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3554C211yesmaximal, characteristic
2C11×#3229C211yesmaximal, characteristic, complemented
3C11×#3227C211yesmaximal, characteristic, complemented
4C11×#3218C211yesmaximal, characteristic, complemented
5C11×#1653C212yesmaximal, complemented
6C11×#1651C212yesmaximal, complemented
7C11×#1642C212yesmaximal, complemented
8C11×#1640C212yesmaximal, complemented
9C11×#1553C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1482C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#559—21no—
14C11×#559C2211yescharacteristic
15C11×#557C2211yescharacteristic
16C11×#554—21no—
17C11×#550C2211yescharacteristic
18D4×Q8×C11C2211yescharacteristic
19C11×#548—21no—
20C11×#547—21no—
21C11×#542—21no—
22C11×#542—21no—
23C11×#540—21no—
24C11×#539—22no—
25C11×#536—21no—
26C11×#533C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C2×C11×C4⋊Q8C2211yescharacteristic
29C11×#529C2211yescharacteristic
30C11×#498—21no—
31C11×#498C2212yes—
32C11×#497—21no—
33C11×#491—21no—
34C11×#487—21no—
35C11×#486C2212yes—
36C11×#483—21no—
37C11×#483—21no—
38C11×#481—22no—
39C11×#476—22no—
40C11×#475C2212yes—
41C11×#475C2212yes—
42C11×#462C2212yes—
43C11×#461C2212yes—
44C11×#451—21no—
45C11×#448—21no—
46C11×#432C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#431C2211yescharacteristic
49C11×#332C2212yes—
50C11×#331C2212yes—
51C11×Q8⋊C8C2212yes—
52C11×Q8⋊C8C2212yes—
53C11×Q8⋊C8C2212yes—
54C11×D4⋊C8C2212yes—
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11—21no—
59C2×C11×Q16—22no—
60C2×C11×SD16—22no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8D411yescharacteristic
68C11×C4⋊Q8C2312yes—
69C11×C4⋊Q8C2311yescharacteristic
70C11×#127—21no—
71C11×#127C2311yescharacteristic
72C11×#126—22no—
73C11×#126—21no—
74C11×#125—22no—
75C11×#125—21no—
76C11×#125—21no—
77C11×#125D411yescharacteristic
78C11×#124—22no—
79C11×#124—22no—
80C11×#124—21no—
81C11×#124—21no—
82C11×#124—21no—
83C11×#124D411yescharacteristic
84C11×#123—22no—
85C11×#123—22no—
86C11×#123—22no—
87C11×#123—22no—
88C11×#123—22no—
89C11×#123—22no—
90C11×#123—21no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8D411yescharacteristic
99C11×C22⋊Q8D411yescharacteristic
100C11×C22⋊Q8D411yescharacteristic
101C11×#121—22no—
102C11×#121—22no—
103C11×#121—22no—
104C11×#121—21no—
105C11×#121—21no—
106C11×#121D411yescharacteristic
107C11×#121D412yes—
108C4×Q8×C11—21no—
109C4×Q8×C11—21no—
110C4×Q8×C11—21no—
111C4×Q8×C11C2311yescharacteristic
112C4×Q8×C11C2311yescharacteristic
113C4×Q8×C11C2311yescharacteristic
114C4×D4×C11—22no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11D412yes—
122C4×D4×C11C2311yescharacteristic
123C11×#117—21no—
124C11×#117—21no—
125C2×C11×C4⋊C4—22no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C42×C11C2311yescharacteristic
129C11×#106—22no—
130C11×#106—22no—
131C11×#106—24no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#103—22no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#103—22no—
139C11×#102—24no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C4×C8×C11—21no—
145C4×C8×C11C2312yes—
146#18971C1111yesmaximal, characteristic, direct product factor, Sylow
147C11×#41—82no—
148C11×#41—82no—
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—22no—
153C2×Q8×C11—41no—
154C2×Q8×C11—82no—
155C2×Q8×C11—82no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×Q8×C11C2×D411yescharacteristic
158C2×Q8×C11C2×D411yescharacteristic
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11C2×D411yescharacteristic
166C2×D4×C11C2×D412yes—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—22no—
172C22×C4×C11—41no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C11×Q16—82no—
177C11×SD16—82no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
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—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4—41no—
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D412yes—
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—21no—
220C42×C11—22no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2411yescharacteristic
228#3554C2×C1111yescharacteristic
229#3229C2×C1111yescharacteristic, complemented
230#3227C2×C1111yescharacteristic, complemented
231#3218C2×C1111yescharacteristic, complemented
232#1653C2×C1112yescomplemented
233#1651C2×C1112yescomplemented
234#1642C2×C1112yescomplemented
235#1640C2×C1112yescomplemented
236#1553C2×C1111yescharacteristic, complemented
237#1497C2×C1111yescharacteristic, complemented
238#1482C2×C1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—22no—
241C23×C11#12011yescharacteristic
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—42no—
246Q8×C11—42no—
247Q8×C11—42no—
248Q8×C11—81no—
249Q8×C11—82no—
250Q8×C11—82no—
251D4×C11—22no—
252D4×C11—42no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11—81no—
256D4×C11—82no—
257D4×C11—82no—
258D4×C11—82no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—41no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—82no—
273C2×C4×C11—82no—
274C2×C4×C11—82no—
275C2×C4×C11—82no—
276C2×C4×C11—82no—
277C2×C4×C11#12011yescharacteristic
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C8×C11—42no—
284C8×C11—42no—
285C8×C11—42no—
286#562—22no—
287#559—21no—
288#559C22×C1111yescharacteristic
289#557C22×C1111yescharacteristic
290#554—21no—
291#550C22×C1111yescharacteristic
292D4×Q8C22×C1111yescharacteristic
293#548—21no—
294#547—21no—
295#542—21no—
296#542—21no—
297#540—21no—
298#539—22no—
299#536—21no—
300#533C22×C1111yescharacteristic
301#532C22×C1111yescharacteristic
302C2×C4⋊Q8C22×C1111yescharacteristic
303#529C22×C1111yescharacteristic
304#498—21no—
305#498C22×C1112yes—
306#497—21no—
307#491—21no—
308#487—21no—
309#486C22×C1112yes—
310#483—21no—
311#483—21no—
312#481—22no—
313#476—22no—
314#475C22×C1112yes—
315#475C22×C1112yes—
316#462C22×C1112yes—
317#461C22×C1112yes—
318#451—21no—
319#448—21no—
320#432C22×C1111yescharacteristic
321#431C22×C1111yescharacteristic
322#431C22×C1111yescharacteristic
323#332C22×C1112yes—
324#331C22×C1112yes—
325Q8⋊C8C22×C1112yes—
326Q8⋊C8C22×C1112yes—
327Q8⋊C8C22×C1112yes—
328D4⋊C8C22×C1112yes—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—42no—
334C22×C11—41no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11C2×#12011yescharacteristic
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—82no—
352C4×C11#57712yes—
353C4×C11#57712yes—
354C2×#41—21no—
355C2×#41—21no—
356C22×Q8—21no—
357C22×Q8—21no—
358C2×Q16—22no—
359C2×SD16—22no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8D4×C1111yescharacteristic
366C4⋊Q8D4×C1111yescharacteristic
367C4⋊Q8C23×C1112yes—
368C4⋊Q8C23×C1111yescharacteristic
369#127—21no—
370#127C23×C1111yescharacteristic
371#126—22no—
372#126—21no—
373#125—22no—
374#125—21no—
375#125—21no—
376#125D4×C1111yescharacteristic
377#124—22no—
378#124—22no—
379#124—21no—
380#124—21no—
381#124—21no—
382#124D4×C1111yescharacteristic
383#123—22no—
384#123—22no—
385#123—22no—
386#123—22no—
387#123—22no—
388#123—22no—
389#123—21no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—21no—
397C22⋊Q8D4×C1111yescharacteristic
398C22⋊Q8D4×C1111yescharacteristic
399C22⋊Q8D4×C1111yescharacteristic
400#121—22no—
401#121—22no—
402#121—22no—
403#121—21no—
404#121—21no—
405#121D4×C1111yescharacteristic
406#121D4×C1112yes—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8C23×C1111yescharacteristic
411C4×Q8C23×C1111yescharacteristic
412C4×Q8C23×C1111yescharacteristic
413C4×D4—22no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4D4×C1112yes—
421C4×D4C23×C1111yescharacteristic
422#117—21no—
423#117—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C42C23×C1111yescharacteristic
428#106—22no—
429#106—22no—
430#106—24no—
431C4⋊C8—21no—
432C4⋊C8C23×C1112yes—
433C4⋊C8C23×C1112yes—
434#103—22no—
435#103—22no—
436#103—22no—
437#103—22no—
438#102—24no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442#97—21no—
443C4×C8—21no—
444C4×C8C23×C1112yes—
445C2×C11—41no—
446C2×C11—81no—
447C2×C11—82no—
448C2×C11#300911yescharacteristic
449C2×C11#301011yescharacteristic
450C2×C11#302211yescharacteristic
451#41—82no—
452#41—82no—
453C2×Q8—22no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—41no—
458C2×Q8—82no—
459C2×Q8—82no—
460C2×Q8C2×D4×C1111yescharacteristic
461C2×Q8C2×D4×C1111yescharacteristic
462C2×Q8C2×D4×C1111yescharacteristic
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4C2×D4×C1111yescharacteristic
470C2×D4C2×D4×C1112yes—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—41no—
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480Q16—82no—
481SD16—82no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4C2×D4×C1111yescharacteristic
506C4⋊C4C2×D4×C1111yescharacteristic
507C4⋊C4C2×D4×C1111yescharacteristic
508C4⋊C4C2×D4×C1112yes—
509C4⋊C4C2×D4×C1111yescharacteristic
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C42—22no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42C2×D4×C1111yescharacteristic
529C42C2×D4×C1111yescharacteristic
530C42C2×D4×C1111yescharacteristic
531C42C24×C1111yescharacteristic
532C11#1897111yescharacteristic, direct product factor, Sylow
533C23—21no—
534C23—22no—
535C23C11×#12011yescharacteristic
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543Q8—82no—
544Q8—82no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—42no—
549D4—81no—
550D4—82no—
551D4—82no—
552D4—82no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4C11×#12011yescharacteristic
572C2×C4C11×#12011yescharacteristic
573C2×C4C11×#12011yescharacteristic
574C2×C4C22×D4×C1111yescharacteristic
575C2×C4C22×D4×C1111yescharacteristic
576C2×C4C22×D4×C1111yescharacteristic
577C8—42no—
578C8—42no—
579C8—42no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—41no—
584C22—42no—
585C22—41no—
586C22—42no—
587C22—42no—
588C22—41no—
589C22C2×C11×#12011yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—82no—
603C4C11×#57712yes—
604C4C11×#57712yes—
605C2—41no—
606C2—81no—
607C2—82no—
608C2C11×#300911yescharacteristic
609C2C11×#301011yescharacteristic
610C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3554C2
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
2. C11×#3229C2semidirect
3. C11×#3227C2semidirect
4. C11×#3218C2semidirect
5. C11×#1653C2semidirect
6. C11×#1651C2semidirect
7. C11×#1642C2semidirect
8. C11×#1640C2semidirect
9. C11×#1553C2semidirect
10. C11×#1497C2semidirect
11. C11×#1482C2semidirect
146. #18971C11direct (N × H)
229. #3229C2×C11semidirect
230. #3227C2×C11semidirect
231. #3218C2×C11semidirect
232. #1653C2×C11semidirect
233. #1651C2×C11semidirect
234. #1642C2×C11semidirect
235. #1640C2×C11semidirect
236. #1553C2×C11semidirect
237. #1497C2×C11semidirect
238. #1482C2×C11semidirect
532. C11#18971direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35542
C11×#32292
C11×#32272
C11×#32182
C11×#16532
C11×#16512
C11×#16422
C11×#16402
C11×#15532
C11×#14972
C11×#14822
#1897111