Finite Group Databasebeta

← C11×#18279 #14595472

Subgroups — C11×#18279 #14595472

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3563C211yesmaximal, characteristic
2C11×#3113C211yesmaximal, characteristic, complemented
3C11×#3108C211yesmaximal, characteristic
4C11×#2584C211yesmaximal, characteristic, complemented
5C11×#1611C212yesmaximal, complemented
6C11×#1609C212yesmaximal
7C11×#1605C212yesmaximal, complemented
8C11×#1603C212yesmaximal
9C11×#1509C211yesmaximal, characteristic
10C11×#1503C211yesmaximal, characteristic, complemented
11C11×#1470C211yesmaximal, characteristic, complemented
12C11×#564—21no—
13C11×#563—21no—
14C11×#557—21no—
15C11×#554—21no—
16C11×#552—21no—
17C11×#552—22no—
18C11×#552—21no—
19C11×#544—21no—
20C11×#544C2212yes—
21C11×#541—21no—
22C11×#541—22no—
23C11×#539C2212yes—
24C11×#533C2211yescharacteristic
25C11×#529C2211yescharacteristic
26C2×C11×#125C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C11×#483C2211yescharacteristic
29C11×#483C2212yes—
30C11×#480C2211yescharacteristic
31C11×#479—21no—
32C11×#475—21no—
33C11×#464—21no—
34C11×#462—21no—
35C11×#451C2211yescharacteristic
36C11×#451C2212yes—
37C11×#448C2211yescharacteristic
38C11×#441—22no—
39C4×C11×Q16—21no—
40C4×C11×SD16—21no—
41C11×#432C2211yescharacteristic
42C11×#431C2211yescharacteristic
43C11×#398C2212yes—
44C11×#395C2212yes—
45C11×#389—21no—
46C11×#389—22no—
47C11×#389—21no—
48C4×C11×C4⋊C4C2211yescharacteristic
49C11×#328C2212yes—
50C11×#328C2212yes—
51C11×#328C2212yes—
52C11×#327C2212yes—
53C11×#324C2212yes—
54C11×#324C2212yes—
55C22×Q8×C11C2311yescharacteristic
56C2×C11×Q16—21no—
57C2×C11×Q16—22no—
58C2×C11×SD16—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8D411yescharacteristic
64C11×#126—22no—
65C11×#126—22no—
66C11×#126—22no—
67C11×#126—22no—
68C11×#126—21no—
69C11×#125—22no—
70C11×#125—22no—
71C11×#125—22no—
72C11×#125—22no—
73C11×#125—21no—
74C11×#125—22no—
75C11×#125—22no—
76C11×#125—22no—
77C11×#125—22no—
78C11×#125—21no—
79C11×#125—21no—
80C11×#125—21no—
81C11×#125—21no—
82C11×#125—21no—
83C11×#125D411yescharacteristic
84C11×#124D411yescharacteristic
85C11×#123—22no—
86C11×#123—21no—
87C11×#123—22no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8C2311yescharacteristic
96C11×C22⋊Q8C2312yes—
97C11×#121C2311yescharacteristic
98C4×Q8×C11—21no—
99C4×Q8×C11—22no—
100C4×Q8×C11—21no—
101C4×Q8×C11—21no—
102C4×Q8×C11—21no—
103C4×Q8×C11—21no—
104C4×Q8×C11—21no—
105C4×Q8×C11—21no—
106C4×Q8×C11D411yescharacteristic
107C4×Q8×C11D412yes—
108C4×D4×C11—21no—
109C4×D4×C11—22no—
110C4×D4×C11D411yescharacteristic
111C11×#117—22no—
112C11×#117—21no—
113C11×#117—21no—
114C11×#117—22no—
115C11×#117—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4—22no—
120C2×C11×C4⋊C4—22no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C4⋊C4D412yes—
123C2×C11×C4⋊C4D411yescharacteristic
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2312yes—
126C2×C42×C11—21no—
127C2×C42×C11—21no—
128C2×C42×C11C2311yescharacteristic
129C11×#107—21no—
130C11×#106—21no—
131C11×#106—22no—
132C11×C4⋊C8—21no—
133C11×C4⋊C8—21no—
134C11×#103—21no—
135C11×#103—22no—
136C11×#103—21no—
137C11×#103—21no—
138C11×#103—22no—
139C11×#102—21no—
140C11×C22⋊C8C2312yes—
141C11×C22⋊C8C2311yescharacteristic
142C11×C22⋊C8C2311yescharacteristic
143C11×#97—21no—
144C4×C8×C11—21no—
145C11×#95—22no—
146C11×#95—22no—
147C11×#95C2312yes—
148#18279C1111yesmaximal, characteristic, direct product factor, Sylow
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—42no—
154C2×Q8×C11C2×D412yes—
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11C2×D411yescharacteristic
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2411yescharacteristic
168C11×Q16—42no—
169C11×Q16—44no—
170C11×SD16—42no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
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—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—44no—
203C11×C4⋊C4—41no—
204C11×C4⋊C4—41no—
205C11×C4⋊C4—82no—
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D412yes—
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C42×C11—22no—
219C42×C11—22no—
220C42×C11—22no—
221C42×C11—22no—
222C42×C11—21no—
223C42×C11—41no—
224C42×C11—41no—
225C42×C11—81no—
226C42×C11C2×D411yescharacteristic
227C42×C11C2×D411yescharacteristic
228C42×C11C2×D411yescharacteristic
229C42×C11C2×D411yescharacteristic
230#3563C2×C1111yescharacteristic
231#3113C2×C1111yescharacteristic, complemented
232#3108C2×C1111yescharacteristic
233#2584C2×C1111yescharacteristic, complemented
234#1611C2×C1112yescomplemented
235#1609C2×C1112yes—
236#1605C2×C1112yescomplemented
237#1603C2×C1112yes—
238#1509C2×C1111yescharacteristic
239#1503C2×C1111yescharacteristic, complemented
240#1470C2×C1111yescharacteristic, complemented
241C23×C11—21no—
242C23×C11C22×D411yescharacteristic
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—41no—
246Q8×C11—42no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11—42no—
250Q8×C11—82no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
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—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—82no—
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11#12011yescharacteristic
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11#12011yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C8×C11—41no—
286C8×C11—41no—
287C8×C11—42no—
288#564—21no—
289#563—21no—
290#557—21no—
291#554—21no—
292#552—21no—
293#552—22no—
294#552—21no—
295#544—21no—
296#544C22×C1112yes—
297#541—21no—
298#541—22no—
299#539C22×C1112yes—
300#533C22×C1111yescharacteristic
301#529C22×C1111yescharacteristic
302C2×#125C22×C1111yescharacteristic
303C2×C4×Q8C22×C1111yescharacteristic
304#483C22×C1111yescharacteristic
305#483C22×C1112yes—
306#480C22×C1111yescharacteristic
307#479—21no—
308#475—21no—
309#464—21no—
310#462—21no—
311#451C22×C1111yescharacteristic
312#451C22×C1112yes—
313#448C22×C1111yescharacteristic
314#441—22no—
315C4×Q16—21no—
316C4×SD16—21no—
317#432C22×C1111yescharacteristic
318#431C22×C1111yescharacteristic
319#398C22×C1112yes—
320#395C22×C1112yes—
321#389—21no—
322#389—22no—
323#389—21no—
324C4×C4⋊C4C22×C1111yescharacteristic
325#328C22×C1112yes—
326#328C22×C1112yes—
327#328C22×C1112yes—
328#327C22×C1112yes—
329#324C22×C1112yes—
330#324C22×C1112yes—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×#12011yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—44no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—81no—
354C4×C11#45612yes—
355C22×Q8C23×C1111yescharacteristic
356C2×Q16—21no—
357C2×Q16—22no—
358C2×SD16—21no—
359C4⋊Q8—21no—
360C4⋊Q8—22no—
361C4⋊Q8—22no—
362C4⋊Q8D4×C1111yescharacteristic
363C4⋊Q8D4×C1111yescharacteristic
364#126—22no—
365#126—22no—
366#126—22no—
367#126—22no—
368#126—21no—
369#125—22no—
370#125—22no—
371#125—22no—
372#125—22no—
373#125—21no—
374#125—22no—
375#125—22no—
376#125—22no—
377#125—22no—
378#125—21no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125D4×C1111yescharacteristic
384#124D4×C1111yescharacteristic
385#123—22no—
386#123—21no—
387#123—22no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8—22no—
395C22⋊Q8C23×C1111yescharacteristic
396C22⋊Q8C23×C1112yes—
397#121C23×C1111yescharacteristic
398C4×Q8—21no—
399C4×Q8—22no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8D4×C1111yescharacteristic
407C4×Q8D4×C1112yes—
408C4×D4—21no—
409C4×D4—22no—
410C4×D4D4×C1111yescharacteristic
411#117—22no—
412#117—21no—
413#117—21no—
414#117—22no—
415#117—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4D4×C1111yescharacteristic
422C2×C4⋊C4D4×C1112yes—
423C2×C4⋊C4D4×C1111yescharacteristic
424C2×C4⋊C4C23×C1111yescharacteristic
425C2×C4⋊C4C23×C1112yes—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42C23×C1111yescharacteristic
429#107—21no—
430#106—21no—
431#106—22no—
432C4⋊C8—21no—
433C4⋊C8—21no—
434#103—21no—
435#103—22no—
436#103—21no—
437#103—21no—
438#103—22no—
439#102—21no—
440C22⋊C8C23×C1112yes—
441C22⋊C8C23×C1111yescharacteristic
442C22⋊C8C23×C1111yescharacteristic
443#97—21no—
444C4×C8—21no—
445#95—22no—
446#95—22no—
447#95C23×C1112yes—
448C2×C11—21no—
449C2×C11—21no—
450C2×C11—81no—
451C2×C11#301311yescharacteristic
452C2×C11C2×#45611yescharacteristic
453C2×C11#302511yescharacteristic
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—42no—
459C2×Q8C2×D4×C1112yes—
460C2×Q8C2×D4×C1111yescharacteristic
461C2×D4—21no—
462C2×D4C2×D4×C1111yescharacteristic
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4C2×D4×C1112yes—
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C2×D4×C1112yes—
472C22×C4C24×C1111yescharacteristic
473Q16—42no—
474Q16—44no—
475SD16—42no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—22no—
479C4⋊C4—22no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—44no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—82no—
511C4⋊C4C2×D4×C1111yescharacteristic
512C4⋊C4C2×D4×C1112yes—
513C4⋊C4C2×D4×C1111yescharacteristic
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—21no—
528C42—41no—
529C42—41no—
530C42—81no—
531C42C2×D4×C1111yescharacteristic
532C42C2×D4×C1111yescharacteristic
533C42C2×D4×C1111yescharacteristic
534C42C2×D4×C1111yescharacteristic
535C11#1827911yescharacteristic, direct product factor, Sylow
536C23—21no—
537C23C22×D4×C1111yescharacteristic
538Q8—22no—
539Q8—22no—
540Q8—41no—
541Q8—42no—
542Q8—41no—
543Q8—41no—
544Q8—42no—
545Q8—82no—
546D4—41no—
547D4—41no—
548D4—41no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—82no—
574C2×C4C11×#12011yescharacteristic
575C2×C4C11×#12011yescharacteristic
576C2×C4C11×#12011yescharacteristic
577C2×C4C11×#12011yescharacteristic
578C2×C4C22×D4×C1111yescharacteristic
579C2×C4C22×D4×C1111yescharacteristic
580C8—41no—
581C8—41no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22C2×C11×#12011yescharacteristic
589C22C11×#57711yescharacteristic
590C22C11×#57811yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—44no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—42no—
604C4—41no—
605C4—81no—
606C4C11×#45612yes—
607C2—21no—
608C2—21no—
609C2—81no—
610C2C11×#301311yescharacteristic
611C2C2×C11×#45611yescharacteristic
612C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#121C23
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×#3113C2semidirect
4. C11×#2584C2semidirect
5. C11×#1611C2semidirect
7. C11×#1605C2semidirect
10. C11×#1503C2semidirect
11. C11×#1470C2semidirect
148. #18279C11direct (N × H)
231. #3113C2×C11semidirect
233. #2584C2×C11semidirect
234. #1611C2×C11semidirect
236. #1605C2×C11semidirect
239. #1503C2×C11semidirect
240. #1470C2×C11semidirect
535. C11#18279direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35632
C11×#31132
C11×#31082
C11×#25842
C11×#16112
C11×#16092
C11×#16052
C11×#16032
C11×#15092
C11×#15032
C11×#14702
#1827911