Finite Group Databasebeta

← C11×#24249 #14601442

Subgroups — C11×#24249 #14601442

Order 2816.

1488 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
1C2×C11×#547C211yesmaximal, characteristic, complemented
2C2×C11×#461C211yesmaximal, characteristic, complemented
3C2×C11×#449C212yesmaximal, complemented
4C2×C11×#442C211yesmaximal, characteristic, complemented
5C11×#2535C211yesmaximal, characteristic, complemented
6C11×#2035C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1960C211yesmaximal, characteristic, complemented
9C11×#1955C211yesmaximal, characteristic, complemented
10C11×#1804C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C22×C11×SD16C2212yes—
14C22×C11×D8C2211yescharacteristic
15C11×#547—24no—
16C11×#547—24no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121—21no—
21C2×C11×#121C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4—21no—
26C11×#461—24no—
27C11×#449—28no—
28C11×#442—24no—
29C2×C11×#106C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2212yes—
32C2×C11×#103C2212yes—
33C2×C11×#103C2212yes—
34C2×C11×#102C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2212yes—
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C11×#97C2211yescharacteristic
40C11×#397—21no—
41C11×#392—21no—
42C11×#386—22no—
43C11×#382C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41—42no—
52C22×Q8×C11C2312yes—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—22no—
60C23×C4×C11—21no—
61C23×C4×C11C2312yes—
62C2×C11×SD16—24no—
63C2×C11×SD16—24no—
64C2×C11×SD16—42no—
65C2×C11×D8—22no—
66C2×C11×D8—22no—
67C2×C11×D8D414yescomplemented
68C22×C8×C11C2312yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8D414yescomplemented
73C11×#123—216no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—24no—
76C11×#121—28no—
77C11×#121—24no—
78C11×#121—42no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11D414yescomplemented
85C2×C11×C4⋊C4—28no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4D412yes—
99C2×C42×C11C2311yescharacteristic
100C11×#106—22no—
101C11×C4⋊C8—22no—
102C11×#103—24no—
103C11×#103—24no—
104C11×#103—42no—
105C11×#102—22no—
106C11×#102—24no—
107C11×#102—22no—
108C11×C22⋊C8—24no—
109C11×C22⋊C8—42no—
110C11×#97—22no—
111C11×#95—22no—
112C11×#95—21no—
113C11×#95—21no—
114#24249C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C24×C11—21no—
117C24×C11C2×D412yes—
118C11×#41—48no—
119C11×#41—48no—
120C11×#41—48no—
121C11×#41—48no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11C2×D414yes—
128C2×D4×C11—28no—
129C2×D4×C11—22no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—42no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—82no—
144C2×D4×C11C2×D412yes—
145C2×D4×C11C2×D412yes—
146C2×D4×C11C2×D412yes—
147C2×D4×C11#4112yes—
148C22×C4×C11—28no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—44no—
161C22×C4×C11—44no—
162C22×C4×C11—44no—
163C22×C4×C11—42no—
164C22×C4×C11—82no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C11×SD16—48no—
170C11×D8—28no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—22no—
178C2×C8×C11—21no—
179C2×C8×C11C2×D412yes—
180C11×C4⋊C4—28no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2×D412yes—
190C11×C22⋊C4—28no—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—44no—
194C11×C22⋊C4—42no—
195C11×C22⋊C4—82no—
196C42×C11C2×D412yes—
197C42×C11C2×D412yes—
198C2×#547C2×C1111yescharacteristic, complemented
199C2×#461C2×C1111yescharacteristic, complemented
200C2×#449C2×C1112yescomplemented
201C2×#442C2×C1111yescharacteristic, complemented
202#2535C2×C1111yescharacteristic, complemented
203#2035C2×C1112yescomplemented
204#2000C2×C1112yescomplemented
205#1960C2×C1111yescharacteristic, complemented
206#1955C2×C1111yescharacteristic, complemented
207#1804C2×C1111yescharacteristic, complemented
208#1788C2×C1112yescomplemented
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11C22×D411yescharacteristic
227Q8×C11—24no—
228Q8×C11—24no—
229Q8×C11—42no—
230Q8×C11—42no—
231D4×C11—22no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—44no—
237D4×C11—416no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—88no—
241D4×C11#12114yes—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—48no—
250C2×C4×C11—416no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—84no—
264C2×C4×C11#12012yes—
265C2×C4×C11#12012yes—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C8×C11—22no—
273C8×C11—41no—
274C8×C11—42no—
275C22×#41C22×C1112yes—
276C22×SD16C22×C1112yes—
277C22×D8C22×C1111yescharacteristic
278#547—24no—
279#547—24no—
280C2×C4⋊Q8C22×C1111yescharacteristic
281C2×#123—22no—
282C2×C22⋊Q8C22×C1112yes—
283C2×#121—21no—
284C2×#121C22×C1112yes—
285C2×C4×D4C22×C1111yescharacteristic
286C2×C4×D4C22×C1111yescharacteristic
287C2×C4×D4C22×C1111yescharacteristic
288C22×C4⋊C4—21no—
289#461—24no—
290#449—28no—
291#442—24no—
292C2×#106C22×C1111yescharacteristic
293C2×C4⋊C8C22×C1111yescharacteristic
294C2×#103C22×C1112yes—
295C2×#103C22×C1112yes—
296C2×#103C22×C1112yes—
297C2×#102C22×C1112yes—
298C2×#102C22×C1111yescharacteristic
299C2×#102C22×C1111yescharacteristic
300C2×C22⋊C8C22×C1112yes—
301C2×C22⋊C8C22×C1112yes—
302C2×#97C22×C1111yescharacteristic
303#397—21no—
304#392—21no—
305#386—22no—
306#382C22×C1111yescharacteristic
307#380C22×C1112yes—
308#340C22×C1112yes—
309C22×C11—24no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—82no—
326C22×C11C2×#12011yescharacteristic
327C22×C11D4211yescharacteristic
328C22×C11#54611yescharacteristic
329C22×C11#57512yes—
330C22×C11#57712yes—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—42no—
334C4×C11—44no—
335C4×C11—42no—
336C4×C11—81no—
337C4×C11—82no—
338C4×C11C2×#12111yescharacteristic
339C4×C11#53511yescharacteristic
340C4×C11D4211yescharacteristic
341C4×C11#54611yescharacteristic
342C2×#41—24no—
343C2×#41—24no—
344C2×#41—24no—
345C2×#41—24no—
346C2×#41—42no—
347C2×#41—42no—
348C22×Q8C23×C1112yes—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4D4×C1111yescharacteristic
352C22×D4C23×C1111yescharacteristic
353C22×D4C23×C1111yescharacteristic
354C23×C4—21no—
355C23×C4—22no—
356C23×C4—21no—
357C23×C4C23×C1112yes—
358C2×SD16—24no—
359C2×SD16—24no—
360C2×SD16—42no—
361C2×D8—22no—
362C2×D8—22no—
363C2×D8D4×C1114yescomplemented
364C22×C8C23×C1112yes—
365C22×C8C23×C1111yescharacteristic
366C22×C8C23×C1111yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8D4×C1114yescomplemented
369#123—216no—
370C22⋊Q8—24no—
371C22⋊Q8—24no—
372#121—28no—
373#121—24no—
374#121—42no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4D4×C1114yescomplemented
381C2×C4⋊C4—28no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4D4×C1111yescharacteristic
386C2×C4⋊C4C23×C1111yescharacteristic
387C2×C4⋊C4C23×C1112yes—
388C2×C4⋊C4C23×C1111yescharacteristic
389C2×C22⋊C4—22no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4D4×C1112yes—
395C2×C42C23×C1111yescharacteristic
396#106—22no—
397C4⋊C8—22no—
398#103—24no—
399#103—24no—
400#103—42no—
401#102—22no—
402#102—24no—
403#102—22no—
404C22⋊C8—24no—
405C22⋊C8—42no—
406#97—22no—
407#95—22no—
408#95—21no—
409#95—21no—
410C2×C11—44no—
411C2×C11—82no—
412C2×C11—82no—
413C2×C11#240811yescharacteristic
414C2×C11#300511yescharacteristic
415C2×C11#301011yescharacteristic
416C2×C11#326712yes—
417C2×C11#330712yes—
418C24—21no—
419C24—21no—
420C24C2×D4×C1112yes—
421#41—48no—
422#41—48no—
423#41—48no—
424#41—48no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8C2×D4×C1114yes—
431C2×D4—28no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—42no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—82no—
447C2×D4C2×D4×C1112yes—
448C2×D4C2×D4×C1112yes—
449C2×D4C2×D4×C1112yes—
450C2×D4C11×#4112yes—
451C22×C4—28no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—42no—
467C22×C4—82no—
468C22×C4C2×D4×C1112yes—
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C24×C1111yescharacteristic
472SD16—48no—
473D8—28no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—21no—
480C2×C8—22no—
481C2×C8—21no—
482C2×C8C2×D4×C1112yes—
483C4⋊C4—28no—
484C4⋊C4—22no—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4C2×D4×C1112yes—
493C22⋊C4—28no—
494C22⋊C4—24no—
495C22⋊C4—24no—
496C22⋊C4—44no—
497C22⋊C4—42no—
498C22⋊C4—82no—
499C42C2×D4×C1112yes—
500C42C2×D4×C1112yes—
501C11#2424911yescharacteristic, direct product factor, Sylow
502C23—22no—
503C23—22no—
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—42no—
514C23—42no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23C22×D4×C1111yescharacteristic
520Q8—24no—
521Q8—24no—
522Q8—42no—
523Q8—42no—
524D4—22no—
525D4—22no—
526D4—22no—
527D4—22no—
528D4—22no—
529D4—44no—
530D4—416no—
531D4—41no—
532D4—41no—
533D4—88no—
534D4C11×#12114yes—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—48no—
543C2×C4—416no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—84no—
557C2×C4C11×#12012yes—
558C2×C4C11×#12012yes—
559C2×C4C22×D4×C1111yescharacteristic
560C2×C4C22×D4×C1111yescharacteristic
561C2×C4C22×D4×C1111yescharacteristic
562C2×C4C2×C11×#4111yescharacteristic
563C2×C4C11×H(5,𝔽2)11yescharacteristic
564C2×C4C11×H(5,𝔽2)11yescharacteristic
565C8—22no—
566C8—41no—
567C8—42no—
568C22—24no—
569C22—42no—
570C22—42no—
571C22—44no—
572C22—44no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—82no—
585C22C2×C11×#12011yescharacteristic
586C22D42×C1111yescharacteristic
587C22C11×#54611yescharacteristic
588C22C11×#57512yes—
589C22C11×#57712yes—
590C4—22no—
591C4—22no—
592C4—42no—
593C4—44no—
594C4—42no—
595C4—81no—
596C4—82no—
597C4C2×C11×#12111yescharacteristic
598C4C11×#53511yescharacteristic
599C4D42×C1111yescharacteristic
600C4C11×#54611yescharacteristic
601C2—44no—
602C2—82no—
603C2—82no—
604C2C11×#240811yescharacteristic
605C2C11×#300511yescharacteristic
606C2C11×#301011yescharacteristic
607C2C11×#326712yes—
608C2C11×#330712yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#547C2semidirect
2. C2×C11×#461C2semidirect
3. C2×C11×#449C2semidirect
4. C2×C11×#442C2semidirect
5. C11×#2535C2semidirect
6. C11×#2035C2semidirect
7. C11×#2000C2semidirect
8. C11×#1960C2semidirect
9. C11×#1955C2semidirect
10. C11×#1804C2semidirect
11. C11×#1788C2semidirect
67. C2×C11×D8D4semidirect
72. C11×C4⋊Q8D4semidirect
84. C4×D4×C11D4semidirect
114. #24249C11direct (N × H)
198. C2×#547C2×C11semidirect
199. C2×#461C2×C11semidirect
200. C2×#449C2×C11semidirect
201. C2×#442C2×C11semidirect
202. #2535C2×C11semidirect
203. #2035C2×C11semidirect
204. #2000C2×C11semidirect
205. #1960C2×C11semidirect
206. #1955C2×C11semidirect
207. #1804C2×C11semidirect
208. #1788C2×C11semidirect
363. C2×D8D4×C11semidirect
368. C4⋊Q8D4×C11semidirect
380. C4×D4D4×C11semidirect
501. C11#24249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5472
C2×C11×#4612
C2×C11×#4492
C2×C11×#4422
C11×#25352
C11×#20352
C11×#20002
C11×#19602
C11×#19552
C11×#18042
C11×#17882
#2424911