Finite Group Databasebeta

← C11×#18206 #14595399

Subgroups — C11×#18206 #14595399

Order 2816.

1028 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3505C211yesmaximal, characteristic
2C2×C11×#483C211yesmaximal, characteristic, complemented
3C2×C11×#480C211yesmaximal, characteristic, complemented
4C11×#2486C211yesmaximal, characteristic, complemented
5C11×#1612C214yesmaximal, complemented
6C11×#1609C214yesmaximal, complemented
7C11×#1520C211yesmaximal, characteristic, complemented
8C11×#1519C211yesmaximal, characteristic, complemented
9C11×#1459C211yesmaximal, characteristic, complemented
10C11×#553—22no—
11C11×#553—21no—
12C11×#552—21no—
13C11×#551—22no—
14C11×#548—21no—
15C11×#546—21no—
16C11×#539C2212yes—
17C11×#538C2212yes—
18C11×#534—21no—
19C11×#529—21no—
20C11×#525—21no—
21C2×C11×#123—21no—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C11×#518—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#483—22no—
28C11×#483C2214yescomplemented
29C11×#480—22no—
30C11×#480C2214yes—
31C2×C11×#107—21no—
32C2×C11×#106—21no—
33C2×C11×#103—21no—
34C2×C11×#102—21no—
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C11×#398C2212yescomplemented
38C11×#397C2212yescomplemented
39C11×#389—21no—
40C11×#381—21no—
41C11×#380—21no—
42C11×#380C2211yescharacteristic
43C11×#328C2214yescomplemented
44C11×#327C2214yes—
45C11×#324C2212yescomplemented
46C11×#323C2212yescomplemented
47C2×C11×#41—21no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C8×C11—21no—
56C22×C8×C11—21no—
57C11×#126—22no—
58C11×#126—22no—
59C11×#126—22no—
60C11×#125—21no—
61C11×#125—22no—
62C11×#124—21no—
63C11×#124—22no—
64C11×#123—22no—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—44no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8D412yes—
75C11×C22⋊Q8C2312yes—
76C11×#121—21no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121—21no—
81C11×#121—21no—
82C11×#121D412yes—
83C11×#121C2312yes—
84C11×#120—22no—
85C11×#120—22no—
86C4×Q8×C11—21no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C11×#117—22no—
98C11×#117—21no—
99C11×#117—22no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4D411yescharacteristic
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4D411yescharacteristic
118C2×C11×C22⋊C4C2311yescharacteristic
119C2×C42×C11D411yescharacteristic
120C11×#107—24no—
121C11×#106—24no—
122C11×#103—24no—
123C11×#102—24no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—21no—
126C11×C22⋊C8C2312yes—
127C11×C22⋊C8C2312yes—
128C11×#95—22no—
129C11×#95—22no—
130C11×#95C2312yes—
131#18206C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D411yescharacteristic
135C11×#41—82no—
136C2×Q8×C11—21no—
137C2×Q8×C11—42no—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11C2×D412yes—
152C22×C4×C11—21no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—42no—
179C2×C8×C11—42no—
180C11×C4⋊C4—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—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—44no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4C2×D412yes—
197C11×C4⋊C4C2×D412yes—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—44no—
213C11×C22⋊C4—42no—
214C42×C11—22no—
215C42×C11—22no—
216C42×C11—21no—
217C42×C11—21no—
218#3505C2×C1111yescharacteristic
219C2×#483C2×C1111yescharacteristic, complemented
220C2×#480C2×C1111yescharacteristic, complemented
221#2486C2×C1111yescharacteristic, complemented
222#1612C2×C1114yescomplemented
223#1609C2×C1114yescomplemented
224#1520C2×C1111yescharacteristic, complemented
225#1519C2×C1111yescharacteristic, complemented
226#1459C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—42no—
236C23×C11—81no—
237C23×C11—81no—
238C23×C11#12011yescharacteristic
239C23×C11#12011yescharacteristic
240C23×C11#13512yes—
241C23×C11AGL(1,ℤ/8)12yes—
242C23×C11C22×D411yescharacteristic
243Q8×C11—42no—
244Q8×C11—42no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—44no—
251D4×C11—42no—
252D4×C11—82no—
253D4×C11—82no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
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—42no—
277C2×C4×C11—42no—
278C2×C4×C11—81no—
279C2×C4×C11—81no—
280C2×C4×C11—81no—
281C2×C4×C11—82no—
282C2×C4×C11—82no—
283C2×C4×C11—82no—
284C2×C4×C11—82no—
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C8×C11—42no—
290C8×C11—42no—
291#553—22no—
292#553—21no—
293#552—21no—
294#551—22no—
295#548—21no—
296#546—21no—
297#539C22×C1112yes—
298#538C22×C1112yes—
299#534—21no—
300#529—21no—
301#525—21no—
302C2×#123—21no—
303C2×C22⋊Q8C22×C1111yescharacteristic
304C2×#121C22×C1111yescharacteristic
305#518—21no—
306C2×C4×D4C22×C1111yescharacteristic
307C22×C4⋊C4C22×C1111yescharacteristic
308#483—22no—
309#483C22×C1114yescomplemented
310#480—22no—
311#480C22×C1114yes—
312C2×#107—21no—
313C2×#106—21no—
314C2×#103—21no—
315C2×#102—21no—
316C2×C22⋊C8C22×C1111yescharacteristic
317C2×C22⋊C8C22×C1111yescharacteristic
318#398C22×C1112yescomplemented
319#397C22×C1112yescomplemented
320#389—21no—
321#381—21no—
322#380—21no—
323#380C22×C1111yescharacteristic
324#328C22×C1114yescomplemented
325#327C22×C1114yes—
326#324C22×C1112yescomplemented
327#323C22×C1112yescomplemented
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—42no—
343C22×C11—81no—
344C22×C11—162no—
345C22×C11#44912yes—
346C22×C11#44912yes—
347C22×C11C2×#12011yescharacteristic
348C22×C11C2×#13511yescharacteristic
349C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—82no—
360C4×C11—82no—
361C4×C11#45812yes—
362C2×#41—21no—
363C22×Q8D4×C1111yescharacteristic
364C22×D4—21no—
365C22×D4D4×C1111yescharacteristic
366C22×D4D4×C1111yescharacteristic
367C23×C4—21no—
368C23×C4D4×C1111yescharacteristic
369C23×C4C23×C1111yescharacteristic
370C22×C8—21no—
371C22×C8—21no—
372#126—22no—
373#126—22no—
374#126—22no—
375#125—21no—
376#125—22no—
377#124—21no—
378#124—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—44no—
385C22⋊Q8—21no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8D4×C1112yes—
390C22⋊Q8C23×C1112yes—
391#121—21no—
392#121—22no—
393#121—22no—
394#121—22no—
395#121—21no—
396#121—21no—
397#121D4×C1112yes—
398#121C23×C1112yes—
399#120—22no—
400#120—22no—
401C4×Q8—21no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—22no—
411C4×D4—22no—
412#117—22no—
413#117—21no—
414#117—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4D4×C1111yescharacteristic
424C2×C4⋊C4D4×C1111yescharacteristic
425C2×C4⋊C4C23×C1112yes—
426C2×C4⋊C4C23×C1111yescharacteristic
427C2×C22⋊C4—22no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4D4×C1111yescharacteristic
433C2×C22⋊C4C23×C1111yescharacteristic
434C2×C42D4×C1111yescharacteristic
435#107—24no—
436#106—24no—
437#103—24no—
438#102—24no—
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8C23×C1112yes—
442C22⋊C8C23×C1112yes—
443#95—22no—
444#95—22no—
445#95C23×C1112yes—
446C2×C11—21no—
447C2×C11—21no—
448C2×C11—22no—
449C2×C11—22no—
450C2×C11—81no—
451C2×C11—82no—
452C2×C11C2×#44911yescharacteristic
453C2×C11#302211yescharacteristic
454C2×C11C2×#45811yescharacteristic
455C24—21no—
456C24C2×D4×C1111yescharacteristic
457C24C2×D4×C1111yescharacteristic
458#41—82no—
459C2×Q8—21no—
460C2×Q8—42no—
461C2×Q8C2×D4×C1112yes—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4C2×D4×C1112yes—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C2×D4×C1111yescharacteristic
496C22×C4C2×D4×C1111yescharacteristic
497C22×C4C2×D4×C1111yescharacteristic
498C22×C4C24×C1111yescharacteristic
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—42no—
502C2×C8—42no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—44no—
516C4⋊C4—42no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4C2×D4×C1112yes—
520C4⋊C4C2×D4×C1112yes—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—21no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—44no—
536C22⋊C4—42no—
537C42—22no—
538C42—22no—
539C42—21no—
540C42—21no—
541C11#1820611yescharacteristic, direct product factor, Sylow
542C23—21no—
543C23—22no—
544C23—21no—
545C23—21no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—42no—
551C23—81no—
552C23—81no—
553C23C11×#12011yescharacteristic
554C23C11×#12011yescharacteristic
555C23C11×#13512yes—
556C23C11×AGL(1,ℤ/8)12yes—
557C23C22×D4×C1111yescharacteristic
558Q8—42no—
559Q8—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563D4—42no—
564D4—42no—
565D4—44no—
566D4—42no—
567D4—82no—
568D4—82no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4C11×#12011yescharacteristic
601C2×C4C11×#12011yescharacteristic
602C2×C4C22×D4×C1111yescharacteristic
603C2×C4C22×D4×C1111yescharacteristic
604C8—42no—
605C8—42no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—81no—
622C22—162no—
623C22C11×#44912yes—
624C22C11×#44912yes—
625C22C2×C11×#12011yescharacteristic
626C22C2×C11×#13511yescharacteristic
627C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—42no—
637C4—82no—
638C4—82no—
639C4C11×#45812yes—
640C2—21no—
641C2—21no—
642C2—22no—
643C2—22no—
644C2—81no—
645C2—82no—
646C2C2×C11×#44911yescharacteristic
647C2C11×#302211yescharacteristic
648C2C2×C11×#45811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3505C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#483C2semidirect
3. C2×C11×#480C2semidirect
4. C11×#2486C2semidirect
5. C11×#1612C2semidirect
6. C11×#1609C2semidirect
7. C11×#1520C2semidirect
8. C11×#1519C2semidirect
9. C11×#1459C2semidirect
28. C11×#483C22semidirect
37. C11×#398C22semidirect
38. C11×#397C22semidirect
43. C11×#328C22semidirect
45. C11×#324C22semidirect
46. C11×#323C22semidirect
131. #18206C11direct (N × H)
219. C2×#483C2×C11semidirect
220. C2×#480C2×C11semidirect
221. #2486C2×C11semidirect
222. #1612C2×C11semidirect
223. #1609C2×C11semidirect
224. #1520C2×C11semidirect
225. #1519C2×C11semidirect
226. #1459C2×C11semidirect
309. #483C22×C11semidirect
318. #398C22×C11semidirect
319. #397C22×C11semidirect
324. #328C22×C11semidirect
326. #324C22×C11semidirect
327. #323C22×C11semidirect
541. C11#18206direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35052
C2×C11×#4832
C2×C11×#4802
C11×#24862
C11×#16122
C11×#16092
C11×#15202
C11×#15192
C11×#14592
#1820611