Finite Group Databasebeta

← C11×#19091 #14596284

Subgroups — C11×#19091 #14596284

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3561C211yesmaximal, characteristic
2C11×#3240C211yesmaximal, characteristic, complemented
3C11×#3237C211yesmaximal, characteristic, complemented
4C11×#3215C211yesmaximal, characteristic, complemented
5C11×#1664C212yesmaximal, complemented
6C11×#1662C212yesmaximal, complemented
7C11×#1661C212yesmaximal, complemented
8C11×#1660C212yesmaximal, complemented
9C11×#1537C211yesmaximal, characteristic, complemented
10C11×#1535C211yesmaximal, characteristic, complemented
11C11×#1533C211yesmaximal, characteristic, complemented
12C11×#563C2212yes—
13C11×#562C2212yes—
14C11×#556—21no—
15C11×#551—22no—
16D4×Q8×C11—21no—
17C11×#548—21no—
18C11×#546—21no—
19C11×#543—21no—
20C11×#542—21no—
21C11×#542—22no—
22C11×#538—21no—
23C11×#536—21no—
24C11×#533C2211yescharacteristic
25C11×#533C2211yescharacteristic
26C11×#529C2211yescharacteristic
27C2×C11×#124C2211yescharacteristic
28C11×#501C2211yescharacteristic, complemented
29C11×#501C2212yescomplemented
30C11×#501C2211yescharacteristic, complemented
31C11×#497C2212yes—
32C11×#491C2212yescomplemented
33C11×#489C2212yes—
34C11×#489C2211yescharacteristic, complemented
35C11×#489C2211yescharacteristic, complemented
36C11×#485—21no—
37C11×#485—22no—
38C11×#482—21no—
39C11×#479—21no—
40C11×#478—21no—
41C11×#477—21no—
42C11×#475—21no—
43C11×#464—22no—
44C11×#451—21no—
45C11×#450—21no—
46C11×#432C2211yescharacteristic
47C11×#432C2211yescharacteristic
48C11×#432C2211yescharacteristic
49C11×#330C2212yescomplemented
50C11×#330C2212yescomplemented
51C11×#330C2212yescomplemented
52C11×#329C2212yes—
53C11×#329C2212yes—
54C11×#329C2212yescomplemented
55C2×C11×#41—21no—
56C22×Q8×C11—21no—
57C22×Q8×C11D411yescharacteristic
58C22×D4×C11D411yescharacteristic
59C2×C11×Q16—22no—
60C2×C11×SD16—22no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8D411yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×C4⋊Q8C2311yescharacteristic
67C11×#126—22no—
68C11×#126—22no—
69C11×#126—22no—
70C11×#126—21no—
71C11×#125—21no—
72C11×#125C2312yes—
73C11×#125C2311yescharacteristic
74C11×#124—21no—
75C11×#124—22no—
76C11×#124—22no—
77C11×#124—21no—
78C11×#124—21no—
79C11×#124D412yes—
80C11×#124C2312yes—
81C11×#124C2311yescharacteristic
82C11×#123—22no—
83C11×#123—22no—
84C11×#123—21no—
85C11×#123—22no—
86C11×#123—22no—
87C11×C22⋊Q8—22no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8—21no—
99C11×C22⋊Q8D411yescharacteristic
100C11×#121—21no—
101C11×#121—22no—
102C11×#121—22no—
103C11×#121D411yescharacteristic
104C11×#120—22no—
105C4×Q8×C11—21no—
106C4×Q8×C11—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11—21no—
109C4×Q8×C11—21no—
110C4×Q8×C11D411yescharacteristic
111C4×D4×C11—22no—
112C4×D4×C11—21no—
113C4×D4×C11—22no—
114C4×D4×C11—21no—
115C4×D4×C11D411yescharacteristic
116C11×#117—22no—
117C11×#117—21no—
118C11×#117—21no—
119C11×#117D412yes—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C42×C11C2311yescharacteristic
124C11×#107—22no—
125C11×#107—21no—
126C11×#107—21no—
127C11×#106—22no—
128C11×#106—21no—
129C11×#106—21no—
130C11×C4⋊C8—21no—
131C11×C4⋊C8—21no—
132C11×C4⋊C8—21no—
133C11×#103—22no—
134C11×#103—21no—
135C11×#103—21no—
136C11×#103—22no—
137C11×#103—22no—
138C11×#102—22no—
139C11×#102—21no—
140C11×#102—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×C22⋊C8—21no—
144C11×#97C2312yes—
145C11×#97C2311yescharacteristic
146C11×#97C2311yescharacteristic
147C11×#97C2312yes—
148#19091C1111yesmaximal, characteristic, direct product factor, Sylow
149C24×C11—21no—
150C11×#41—82no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—82no—
158C2×Q8×C11—81no—
159C2×Q8×C11C2×D411yescharacteristic
160C2×Q8×C11C2×D412yes—
161C2×D4×C11—21no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—21no—
165C2×D4×C11—81no—
166C2×D4×C11C2×D411yescharacteristic
167C2×D4×C11C2×D412yes—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C11×Q16—82no—
177C11×SD16—82no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
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—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—41no—
199C11×C4⋊C4—41no—
200C11×C4⋊C4C2×D412yes—
201C11×C4⋊C4C2×D412yes—
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—41no—
220C42×C11—22no—
221C42×C11—22no—
222C42×C11—21no—
223C42×C11—41no—
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2411yescharacteristic
228#3561C2×C1111yescharacteristic
229#3240C2×C1111yescharacteristic, complemented
230#3237C2×C1111yescharacteristic, complemented
231#3215C2×C1111yescharacteristic, complemented
232#1664C2×C1112yescomplemented
233#1662C2×C1112yescomplemented
234#1661C2×C1112yescomplemented
235#1660C2×C1112yescomplemented
236#1537C2×C1111yescharacteristic, complemented
237#1535C2×C1111yescharacteristic, complemented
238#1533C2×C1111yescharacteristic, complemented
239C23×C11—22no—
240C23×C11—21no—
241C23×C11—42no—
242C23×C11—81no—
243C23×C11—81no—
244C23×C11#12011yescharacteristic
245Q8×C11—42no—
246Q8×C11—41no—
247Q8×C11—42no—
248Q8×C11—42no—
249Q8×C11—42no—
250Q8×C11—42no—
251Q8×C11—81no—
252Q8×C11—82no—
253D4×C11—42no—
254D4×C11—41no—
255D4×C11—42no—
256D4×C11—42no—
257D4×C11—82no—
258D4×C11—82no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—81no—
272C2×C4×C11—82no—
273C2×C4×C11—82no—
274C2×C4×C11—82no—
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11#12011yescharacteristic
277C2×C4×C11#12011yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C8×C11—42no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11—42no—
285#563C22×C1112yes—
286#562C22×C1112yes—
287#556—21no—
288#551—22no—
289D4×Q8—21no—
290#548—21no—
291#546—21no—
292#543—21no—
293#542—21no—
294#542—22no—
295#538—21no—
296#536—21no—
297#533C22×C1111yescharacteristic
298#533C22×C1111yescharacteristic
299#529C22×C1111yescharacteristic
300C2×#124C22×C1111yescharacteristic
301#501C22×C1111yescharacteristic, complemented
302#501C22×C1112yescomplemented
303#501C22×C1111yescharacteristic, complemented
304#497C22×C1112yes—
305#491C22×C1112yescomplemented
306#489C22×C1112yes—
307#489C22×C1111yescharacteristic, complemented
308#489C22×C1111yescharacteristic, complemented
309#485—21no—
310#485—22no—
311#482—21no—
312#479—21no—
313#478—21no—
314#477—21no—
315#475—21no—
316#464—22no—
317#451—21no—
318#450—21no—
319#432C22×C1111yescharacteristic
320#432C22×C1111yescharacteristic
321#432C22×C1111yescharacteristic
322#330C22×C1112yescomplemented
323#330C22×C1112yescomplemented
324#330C22×C1112yescomplemented
325#329C22×C1112yes—
326#329C22×C1112yes—
327#329C22×C1112yescomplemented
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—41no—
332C22×C11—42no—
333C22×C11—41no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—41no—
337C22×C11—162no—
338C22×C11C2×#12011yescharacteristic
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—81no—
352C4×C11—81no—
353C2×#41—21no—
354C22×Q8—21no—
355C22×Q8D4×C1111yescharacteristic
356C22×D4D4×C1111yescharacteristic
357C2×Q16—22no—
358C2×SD16—22no—
359C4⋊Q8—21no—
360C4⋊Q8—22no—
361C4⋊Q8D4×C1111yescharacteristic
362C4⋊Q8D4×C1111yescharacteristic
363C4⋊Q8C23×C1111yescharacteristic
364C4⋊Q8C23×C1111yescharacteristic
365#126—22no—
366#126—22no—
367#126—22no—
368#126—21no—
369#125—21no—
370#125C23×C1111yescharacteristic
371#125C23×C1112yes—
372#124—21no—
373#124—22no—
374#124—22no—
375#124—21no—
376#124—21no—
377#124D4×C1112yes—
378#124C23×C1112yes—
379#124C23×C1111yescharacteristic
380#123—22no—
381#123—22no—
382#123—21no—
383#123—22no—
384#123—22no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8D4×C1111yescharacteristic
398#121—21no—
399#121—22no—
400#121—22no—
401#121D4×C1111yescharacteristic
402#120—22no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8D4×C1111yescharacteristic
409C4×D4—22no—
410C4×D4—21no—
411C4×D4—22no—
412C4×D4—21no—
413C4×D4D4×C1111yescharacteristic
414#117—22no—
415#117—21no—
416#117—21no—
417#117D4×C1112yes—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C42C23×C1111yescharacteristic
422#107—22no—
423#107—21no—
424#107—21no—
425#106—22no—
426#106—21no—
427#106—21no—
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431#103—22no—
432#103—21no—
433#103—21no—
434#103—22no—
435#103—22no—
436#102—22no—
437#102—21no—
438#102—21no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442#97C23×C1112yes—
443#97C23×C1111yescharacteristic
444#97C23×C1111yescharacteristic
445#97C23×C1112yes—
446C2×C11—41no—
447C2×C11—81no—
448C2×C11—82no—
449C2×C11#301911yescharacteristic
450C2×C11#302011yescharacteristic
451C2×C11#302211yescharacteristic
452C24—21no—
453#41—82no—
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—82no—
461C2×Q8—81no—
462C2×Q8C2×D4×C1111yescharacteristic
463C2×Q8C2×D4×C1112yes—
464C2×D4—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—81no—
469C2×D4C2×D4×C1111yescharacteristic
470C2×D4C2×D4×C1112yes—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479Q16—82no—
480SD16—82no—
481C2×C8—21no—
482C2×C8—21no—
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—22no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C1112yes—
504C4⋊C4C2×D4×C1112yes—
505C4⋊C4C2×D4×C1111yescharacteristic
506C4⋊C4C2×D4×C1111yescharacteristic
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C42—22no—
524C42—22no—
525C42—21no—
526C42—41no—
527C42C2×D4×C1111yescharacteristic
528C42C2×D4×C1111yescharacteristic
529C42C2×D4×C1111yescharacteristic
530C42C24×C1111yescharacteristic
531C11#1909111yescharacteristic, direct product factor, Sylow
532C23—22no—
533C23—21no—
534C23—42no—
535C23—81no—
536C23—81no—
537C23C11×#12011yescharacteristic
538Q8—42no—
539Q8—41no—
540Q8—42no—
541Q8—42no—
542Q8—42no—
543Q8—42no—
544Q8—81no—
545Q8—82no—
546D4—42no—
547D4—41no—
548D4—42no—
549D4—42no—
550D4—82no—
551D4—82no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—81no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4C11×#12011yescharacteristic
569C2×C4C11×#12011yescharacteristic
570C2×C4C11×#12011yescharacteristic
571C2×C4C22×D4×C1111yescharacteristic
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C22×D4×C1111yescharacteristic
574C8—42no—
575C8—42no—
576C8—41no—
577C8—41no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—41no—
582C22—42no—
583C22—41no—
584C22—42no—
585C22—42no—
586C22—41no—
587C22—162no—
588C22C2×C11×#12011yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—81no—
602C4—81no—
603C2—41no—
604C2—82no—
605C2—81no—
606C2C11×#301911yescharacteristic
607C2C11×#302011yescharacteristic
608C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3561C2
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×#3240C2semidirect
3. C11×#3237C2semidirect
4. C11×#3215C2semidirect
5. C11×#1664C2semidirect
6. C11×#1662C2semidirect
7. C11×#1661C2semidirect
8. C11×#1660C2semidirect
9. C11×#1537C2semidirect
10. C11×#1535C2semidirect
11. C11×#1533C2semidirect
28. C11×#501C22semidirect
29. C11×#501C22semidirect
30. C11×#501C22semidirect
32. C11×#491C22semidirect
34. C11×#489C22semidirect
35. C11×#489C22semidirect
49. C11×#330C22semidirect
50. C11×#330C22semidirect
51. C11×#330C22semidirect
54. C11×#329C22semidirect
148. #19091C11direct (N × H)
229. #3240C2×C11semidirect
230. #3237C2×C11semidirect
231. #3215C2×C11semidirect
232. #1664C2×C11semidirect
233. #1662C2×C11semidirect
234. #1661C2×C11semidirect
235. #1660C2×C11semidirect
236. #1537C2×C11semidirect
237. #1535C2×C11semidirect
238. #1533C2×C11semidirect
301. #501C22×C11semidirect
302. #501C22×C11semidirect
303. #501C22×C11semidirect
305. #491C22×C11semidirect
307. #489C22×C11semidirect
308. #489C22×C11semidirect
322. #330C22×C11semidirect
323. #330C22×C11semidirect
324. #330C22×C11semidirect
327. #329C22×C11semidirect
531. C11#19091direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35612
C11×#32402
C11×#32372
C11×#32152
C11×#16642
C11×#16622
C11×#16612
C11×#16602
C11×#15372
C11×#15352
C11×#15332
#1909111