Finite Group Databasebeta

← C11×#21206 #14598399

Subgroups — C11×#21206 #14598399

Order 2816.

1718 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
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#417C211yesmaximal, characteristic, complemented
3C2×C11×#418C211yesmaximal, characteristic, complemented
4C2×C11×#416C211yesmaximal, characteristic, complemented
5C22×C11×#102C211yesmaximal, characteristic, complemented
6C2×C11×#405C211yesmaximal, characteristic, complemented
7C11×#2317C211yesmaximal, characteristic, complemented
8C11×#1961C212yesmaximal, complemented
9C11×#1959C212yesmaximal, complemented
10C11×#1958C212yesmaximal, complemented
11C11×#1957C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C23×C8×C11C2211yescharacteristic
16C11×#535—24no—
17C11×#535C418yescomplemented
18C2×C11×#127C2212yes—
19C2×C11×#124C2212yes—
20C2×C11×#121—22no—
21C2×C11×#120—22no—
22C2×C11×#117C2211yescharacteristic
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C11×#418—24no—
26C11×#417—24no—
27C11×#416—24no—
28C2×C11×#103C2211yescharacteristic, complemented
29C2×C11×#103C2211yescharacteristic, complemented
30C2×C11×#103C2212yescomplemented
31C2×C11×#102—24no—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×#102C2211yescharacteristic, complemented
37C2×C11×#102C2211yescharacteristic, complemented
38C2×C11×#102C2212yescomplemented
39C11×#405—24no—
40C2×C11×#97C2212yescomplemented
41C2×C4×C8×C11C2212yescomplemented
42C11×#389—22no—
43C11×#385—22no—
44C11×#384C2212yescomplemented
45C11×#382C2212yescomplemented
46C25×C11—21no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41C2×C414yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11—24no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11C2×C414yes—
63C22×D4×C11C2312yes—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16D414yescomplemented
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11D414yescomplemented
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2312yes—
76C22×C8×C11C2311yescharacteristic
77C11×#127—24no—
78C11×#127C2×C418yescomplemented
79C11×#124—24no—
80C11×#124C2×C418yescomplemented
81C11×#121—216no—
82C11×#120—216no—
83C11×#117—22no—
84C11×#117—22no—
85C11×#117C2×C414yes—
86C11×#117D414yes—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—24no—
91C2×C11×C4⋊C4D412yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4D412yes—
98C2×C42×C11—21no—
99C2×C42×C11C2312yes—
100C11×#103—22no—
101C11×#103—22no—
102C11×#103—24no—
103C11×#102—24no—
104C11×#102—24no—
105C11×#102—24no—
106C11×#102—24no—
107C11×#102—22no—
108C11×#102—22no—
109C11×#102—24no—
110C11×#97—24no—
111C4×C8×C11—24no—
112C11×#95—24no—
113#21206C1111yesmaximal, characteristic, direct product factor, Sylow
114C24×C11—22no—
115C24×C11—21no—
116C24×C11—24no—
117C24×C11—42no—
118C24×C11—42no—
119C24×C11—82no—
120C24×C11—82no—
121C24×C11C2×D411yescharacteristic
122C11×#41—28no—
123C11×#41—28no—
124C11×#41—44no—
125C11×#41—44no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11C22×C412yes—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—216no—
135C2×D4×C11—28no—
136C2×D4×C11—28no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—44no—
150C2×D4×C11—44no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11—84no—
154C2×D4×C11—84no—
155C2×D4×C11C22×C414yes—
156C2×D4×C11C22×C412yes—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11—82no—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11#4112yes—
173C22×C4×C11#4112yes—
174C22×C4×C11C2411yescharacteristic
175C11×M16—28no—
176C2×C8×C11—28no—
177C2×C8×C11—21no—
178C2×C8×C11—22no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—22no—
183C2×C8×C11C2×D412yes—
184C2×C8×C11C2×D412yes—
185C2×C8×C11C2×D414yes—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—84no—
194C11×C4⋊C4C22⋊C418yes—
195C11×C22⋊C4—216no—
196C11×C22⋊C4—42no—
197C11×C22⋊C4C22⋊C418yes—
198C42×C11—42no—
199C42×C11C22×C414yes—
200C42×C11C2×D414yes—
201C2×#535C2×C1111yescharacteristic
202C2×#417C2×C1111yescharacteristic, complemented
203C2×#418C2×C1111yescharacteristic, complemented
204C2×#416C2×C1111yescharacteristic, complemented
205C22×#102C2×C1111yescharacteristic, complemented
206C2×#405C2×C1111yescharacteristic, complemented
207#2317C2×C1111yescharacteristic, complemented
208#1961C2×C1112yescomplemented
209#1959C2×C1112yescomplemented
210#1958C2×C1112yescomplemented
211#1957C2×C1112yescomplemented
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—24no—
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—41no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—44no—
222C23×C11—42no—
223C23×C11—44no—
224C23×C11—48no—
225C23×C11—88no—
226C23×C11—88no—
227C23×C11—84no—
228C23×C11—84no—
229C23×C11C2×C22⋊C412yes—
230C23×C11#12412yes—
231C23×C11#12712yes—
232C23×C11C22×D411yescharacteristic
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—41no—
236Q8×C11—41no—
237D4×C11—24no—
238D4×C11—24no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—48no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—48no—
247D4×C11—816no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—48no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—44no—
259C2×C4×C11—42no—
260C2×C4×C11—84no—
261C2×C4×C11C2×C22⋊C418yes—
262C2×C4×C11C2×C22⋊C412yes—
263C2×C4×C11C4×D414yes—
264C2×C4×C11C4×D414yes—
265C2×C4×C11#12114yes—
266C2×C4×C11#12114yes—
267C2×C4×C11#12412yes—
268C2×C4×C11#12712yes—
269C2×C4×C11C23×C411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C8×C11—22no—
276C8×C11—22no—
277C8×C11—24no—
278C22×#41C22×C1111yescharacteristic
279C23×D4C22×C1111yescharacteristic
280C22×M16C22×C1111yescharacteristic
281C23×C8C22×C1111yescharacteristic
282#535—24no—
283#535C4×C1118yescomplemented
284C2×#127C22×C1112yes—
285C2×#124C22×C1112yes—
286C2×#121—22no—
287C2×#120—22no—
288C2×#117C22×C1111yescharacteristic
289C2×#117C22×C1111yescharacteristic
290C22×C4⋊C4C22×C1111yescharacteristic
291#418—24no—
292#417—24no—
293#416—24no—
294C2×#103C22×C1111yescharacteristic, complemented
295C2×#103C22×C1111yescharacteristic, complemented
296C2×#103C22×C1112yescomplemented
297C2×#102—24no—
298C2×#102C22×C1112yes—
299C2×#102C22×C1112yes—
300C2×#102C22×C1112yes—
301C2×#102C22×C1112yes—
302C2×#102C22×C1111yescharacteristic, complemented
303C2×#102C22×C1111yescharacteristic, complemented
304C2×#102C22×C1112yescomplemented
305#405—24no—
306C2×#97C22×C1112yescomplemented
307C2×C4×C8C22×C1112yescomplemented
308#389—22no—
309#385—22no—
310#384C22×C1112yescomplemented
311#382C22×C1112yescomplemented
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—44no—
317C22×C11—48no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—816no—
321C22×C11—82no—
322C22×C11—84no—
323C22×C11—81no—
324C22×C11—82no—
325C22×C11—81no—
326C22×C11—82no—
327C22×C11#39014yes—
328C22×C11C22×C22⋊C411yescharacteristic
329C22×C11C2×#12411yescharacteristic
330C22×C11C2×#12711yescharacteristic
331C22×C11#57612yes—
332C22×C11#57712yes—
333C4×C11—28no—
334C4×C11—42no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—82no—
338C4×C11#39014yes—
339C4×C11C2×C4×D411yescharacteristic
340C4×C11C2×C4×D411yescharacteristic
341C4×C11C2×#12111yescharacteristic
342C4×C11C2×#12111yescharacteristic
343C25—21no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41C2×C4×C1114yes—
350C22×Q8C23×C1111yescharacteristic
351C22×D4—21no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—21no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4C2×C4×C1114yes—
360C22×D4C23×C1112yes—
361C22×D4C23×C1111yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C23×C4C23×C1111yescharacteristic
365C2×M16—22no—
366C2×M16—22no—
367C2×M16D4×C1114yescomplemented
368C22×C8—22no—
369C22×C8—22no—
370C22×C8D4×C1114yescomplemented
371C22×C8C23×C1111yescharacteristic
372C22×C8C23×C1111yescharacteristic
373C22×C8C23×C1112yes—
374#127—24no—
375#127C2×C4×C1118yescomplemented
376#124—24no—
377#124C2×C4×C1118yescomplemented
378#121—216no—
379#120—216no—
380#117—22no—
381#117—22no—
382#117C2×C4×C1114yes—
383#117D4×C1114yes—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4D4×C1112yes—
389C2×C4⋊C4C23×C1112yes—
390C2×C4⋊C4C23×C1111yescharacteristic
391C2×C4⋊C4C23×C1111yescharacteristic
392C2×C22⋊C4—24no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4D4×C1112yes—
395C2×C42—21no—
396C2×C42C23×C1112yes—
397#103—22no—
398#103—22no—
399#103—24no—
400#102—24no—
401#102—24no—
402#102—24no—
403#102—24no—
404#102—22no—
405#102—22no—
406#102—24no—
407#97—24no—
408C4×C8—24no—
409#95—24no—
410C2×C11—24no—
411C2×C11—82no—
412C2×C11—84no—
413C2×C11C2×#39011yescharacteristic
414C2×C11#289712yes—
415C2×C11#313612yes—
416C2×C11#315411yescharacteristic
417C2×C11#315511yescharacteristic
418C24—22no—
419C24—21no—
420C24—24no—
421C24—42no—
422C24—42no—
423C24—82no—
424C24—82no—
425C24C2×D4×C1111yescharacteristic
426#41—28no—
427#41—28no—
428#41—44no—
429#41—44no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C22×C4×C1112yes—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—216no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—84no—
458C2×D4—84no—
459C2×D4C22×C4×C1114yes—
460C2×D4C22×C4×C1112yes—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—82no—
470C22×C4C22×C4×C1112yes—
471C22×C4C2×D4×C1114yes—
472C22×C4C2×D4×C1111yescharacteristic
473C22×C4C2×D4×C1112yes—
474C22×C4C2×D4×C1112yes—
475C22×C4C2×D4×C1112yes—
476C22×C4C11×#4112yes—
477C22×C4C11×#4112yes—
478C22×C4C24×C1111yescharacteristic
479M16—28no—
480C2×C8—28no—
481C2×C8—21no—
482C2×C8—22no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8C2×D4×C1112yes—
488C2×C8C2×D4×C1112yes—
489C2×C8C2×D4×C1114yes—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—84no—
498C4⋊C4C11×C22⋊C418yes—
499C22⋊C4—216no—
500C22⋊C4—42no—
501C22⋊C4C11×C22⋊C418yes—
502C42—42no—
503C42C22×C4×C1114yes—
504C42C2×D4×C1114yes—
505C11#2120611yescharacteristic, direct product factor, Sylow
506C23—22no—
507C23—22no—
508C23—24no—
509C23—22no—
510C23—41no—
511C23—42no—
512C23—48no—
513C23—41no—
514C23—42no—
515C23—42no—
516C23—44no—
517C23—42no—
518C23—44no—
519C23—88no—
520C23—84no—
521C23—84no—
522C23—88no—
523C23C2×C11×C22⋊C412yes—
524C23C11×#12412yes—
525C23C11×#12712yes—
526C23C22×D4×C1111yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—41no—
530Q8—41no—
531D4—24no—
532D4—24no—
533D4—22no—
534D4—22no—
535D4—48no—
536D4—42no—
537D4—42no—
538D4—41no—
539D4—41no—
540D4—48no—
541D4—816no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—48no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—84no—
555C2×C4C2×C11×C22⋊C418yes—
556C2×C4C2×C11×C22⋊C412yes—
557C2×C4C4×D4×C1114yes—
558C2×C4C4×D4×C1114yes—
559C2×C4C11×#12114yes—
560C2×C4C11×#12114yes—
561C2×C4C11×#12412yes—
562C2×C4C11×#12712yes—
563C2×C4C23×C4×C1111yescharacteristic
564C2×C4C22×D4×C1111yescharacteristic
565C2×C4C22×D4×C1111yescharacteristic
566C2×C4C22×D4×C1111yescharacteristic
567C2×C4C2×C11×#4111yescharacteristic
568C2×C4C2×C11×#4111yescharacteristic
569C8—22no—
570C8—22no—
571C8—24no—
572C22—24no—
573C22—22no—
574C22—22no—
575C22—24no—
576C22—44no—
577C22—48no—
578C22—42no—
579C22—44no—
580C22—816no—
581C22—82no—
582C22—81no—
583C22—82no—
584C22—81no—
585C22—84no—
586C22—82no—
587C22C11×#39014yes—
588C22C22×C11×C22⋊C411yescharacteristic
589C22C2×C11×#12411yescharacteristic
590C22C2×C11×#12711yescharacteristic
591C22C11×#57612yes—
592C22C11×#57712yes—
593C4—28no—
594C4—42no—
595C4—81no—
596C4—82no—
597C4—81no—
598C4C11×#39014yes—
599C4C2×C4×D4×C1111yescharacteristic
600C4C2×C4×D4×C1111yescharacteristic
601C4C2×C11×#12111yescharacteristic
602C4C2×C11×#12111yescharacteristic
603C2—24no—
604C2—84no—
605C2—82no—
606C2C2×C11×#39011yescharacteristic
607C2C11×#289712yes—
608C2C11×#313612yes—
609C2C11×#315411yescharacteristic
610C2C11×#315511yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutatorC2×C4C23×C4×C11
Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#417C2semidirect
3. C2×C11×#418C2semidirect
4. C2×C11×#416C2semidirect
5. C22×C11×#102C2semidirect
6. C2×C11×#405C2semidirect
7. C11×#2317C2semidirect
8. C11×#1961C2semidirect
9. C11×#1959C2semidirect
10. C11×#1958C2semidirect
11. C11×#1957C2semidirect
17. C11×#535C4semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#103C22semidirect
36. C2×C11×#102C22semidirect
37. C2×C11×#102C22semidirect
38. C2×C11×#102C22semidirect
40. C2×C11×#97C22semidirect
41. C2×C4×C8×C11C22semidirect
44. C11×#384C22semidirect
45. C11×#382C22semidirect
70. C2×C11×M16D4semidirect
73. C22×C8×C11D4semidirect
78. C11×#127C2×C4semidirect
80. C11×#124C2×C4semidirect
113. #21206C11direct (N × H)
202. C2×#417C2×C11semidirect
203. C2×#418C2×C11semidirect
204. C2×#416C2×C11semidirect
205. C22×#102C2×C11semidirect
206. C2×#405C2×C11semidirect
207. #2317C2×C11semidirect
208. #1961C2×C11semidirect
209. #1959C2×C11semidirect
210. #1958C2×C11semidirect
211. #1957C2×C11semidirect
283. #535C4×C11semidirect
294. C2×#103C22×C11semidirect
295. C2×#103C22×C11semidirect
296. C2×#103C22×C11semidirect
302. C2×#102C22×C11semidirect
303. C2×#102C22×C11semidirect
304. C2×#102C22×C11semidirect
306. C2×#97C22×C11semidirect
307. C2×C4×C8C22×C11semidirect
310. #384C22×C11semidirect
311. #382C22×C11semidirect
367. C2×M16D4×C11semidirect
370. C22×C8D4×C11semidirect
375. #127C2×C4×C11semidirect
377. #124C2×C4×C11semidirect
505. C11#21206direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5352
C2×C11×#4172
C2×C11×#4182
C2×C11×#4162
C22×C11×#1022
C2×C11×#4052
C11×#23172
C11×#19612
C11×#19592
C11×#19582
C11×#19572
#2120611