Finite Group Databasebeta

← C11×#24013 #14601206

Subgroups — C11×#24013 #14601206

Order 2816.

1468 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#535C211yesmaximal, characteristic
2C2×C11×#481C211yesmaximal, characteristic, complemented
3C2×C11×#480C211yesmaximal, characteristic, complemented
4C11×#2311C211yesmaximal, characteristic, complemented
5C11×#2034C212yesmaximal, complemented
6C11×#2033C212yesmaximal, complemented
7C11×#1875C211yesmaximal, characteristic, complemented
8C11×#1875C211yesmaximal, characteristic, complemented
9C11×#1854C212yesmaximal, complemented
10C11×#1786C212yesmaximal, complemented
11C11×#1780C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C11×#535—24no—
15C11×#535—24no—
16C2×C11×#127—21no—
17C2×C11×#124—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C11×#120—21no—
23C2×C11×#120—21no—
24C2×C11×#117C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic, complemented
26C22×C11×C4⋊C4C2211yescharacteristic, complemented
27C11×#481—24no—
28C11×#480—24no—
29C2×C11×#107C2212yescomplemented
30C2×C11×#106C2212yescomplemented
31C2×C11×#102C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×C22⋊C8C2212yes—
36C2×C11×C22⋊C8C2211yescharacteristic, complemented
37C2×C11×C22⋊C8C2211yescharacteristic, complemented
38C2×C11×C22⋊C8C2212yescomplemented
39C11×#391—21no—
40C11×#390—21no—
41C11×#386—21no—
42C11×#386—21no—
43C11×#380C2212yes—
44C11×#380C2212yescomplemented
45C11×#340C2212yescomplemented
46C11×#340C2212yescomplemented
47C25×C11—21no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—24no—
51C2×C11×#41—42no—
52C22×Q8×C11D411yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—22no—
58C22×D4×C11—22no—
59C22×D4×C11—21no—
60C22×D4×C11—24no—
61C22×D4×C11—42no—
62C22×D4×C11D411yescharacteristic
63C22×D4×C11D411yescharacteristic
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C22×C8×C11C2312yes—
72C22×C8×C11C2312yes—
73C11×#127—28no—
74C11×#124—28no—
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121D414yes—
82C11×#121D414yes—
83C11×#120—28no—
84C11×#120—28no—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—42no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C42×C11—21no—
104C2×C42×C11—21no—
105C11×#107—24no—
106C11×#106—24no—
107C11×#102—24no—
108C11×#102—24no—
109C11×#102—42no—
110C11×#102—42no—
111C11×C22⋊C8—22no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—24no—
114C11×C22⋊C8—42no—
115C11×#95—22no—
116C11×#95—22no—
117#24013C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—24no—
119C24×C11—21no—
120C24×C11—21no—
121C24×C11—42no—
122C24×C11—42no—
123C24×C11—82no—
124C24×C11—82no—
125C24×C11C2×D411yescharacteristic
126C24×C11C2×D411yescharacteristic
127C24×C11C2×D411yescharacteristic
128C11×#41—48no—
129C11×#41—48no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—41no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—48no—
151C2×D4×C11—48no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11—82no—
158C2×D4×C11—82no—
159C2×D4×C11—82no—
160C2×D4×C11—82no—
161C2×D4×C11C2×D412yes—
162C2×D4×C11C2×D412yes—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—42no—
177C22×C4×C11—82no—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11#4114yes—
184C22×C4×C11C2411yescharacteristic
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4C2×D412yes—
199C11×C4⋊C4C2×D412yes—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C11×C22⋊C4—24no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—82no—
207C11×C22⋊C4—82no—
208C42×C11—24no—
209C42×C11—42no—
210C2×#535C2×C1111yescharacteristic
211C2×#481C2×C1111yescharacteristic, complemented
212C2×#480C2×C1111yescharacteristic, complemented
213#2311C2×C1111yescharacteristic, complemented
214#2034C2×C1112yescomplemented
215#2033C2×C1112yescomplemented
216#1875C2×C1111yescharacteristic, complemented
217#1875C2×C1111yescharacteristic, complemented
218#1854C2×C1112yescomplemented
219#1786C2×C1112yescomplemented
220#1780C2×C1111yescharacteristic, complemented
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—48no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—88no—
246C23×C11—84no—
247C23×C11—84no—
248C23×C11—88no—
249C23×C11#12012yes—
250C23×C11#12312yes—
251C23×C11C22×D411yescharacteristic
252Q8×C11—44no—
253D4×C11—24no—
254D4×C11—24no—
255D4×C11—44no—
256D4×C11—44no—
257D4×C11—48no—
258D4×C11—44no—
259D4×C11—42no—
260D4×C11—42no—
261D4×C11—84no—
262D4×C11—84no—
263D4×C11—84no—
264D4×C11—84no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—84no—
289C2×C4×C11#12012yes—
290C2×C4×C11#12312yes—
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C2×#4112yes—
294C2×C4×C11H(5,𝔽2)12yes—
295C8×C11—42no—
296C8×C11—42no—
297C22×#41C22×C1111yescharacteristic
298C23×D4C22×C1111yescharacteristic
299#535—24no—
300#535—24no—
301C2×#127—21no—
302C2×#124—21no—
303C2×#121C22×C1111yescharacteristic
304C2×#121C22×C1111yescharacteristic
305C2×#121C22×C1111yescharacteristic
306C2×#121C22×C1111yescharacteristic
307C2×#120—21no—
308C2×#120—21no—
309C2×#117C22×C1111yescharacteristic
310C2×#117C22×C1111yescharacteristic, complemented
311C22×C4⋊C4C22×C1111yescharacteristic, complemented
312#481—24no—
313#480—24no—
314C2×#107C22×C1112yescomplemented
315C2×#106C22×C1112yescomplemented
316C2×#102C22×C1112yes—
317C2×#102C22×C1112yes—
318C2×#102C22×C1112yes—
319C2×#102C22×C1112yes—
320C2×C22⋊C8C22×C1112yes—
321C2×C22⋊C8C22×C1111yescharacteristic, complemented
322C2×C22⋊C8C22×C1111yescharacteristic, complemented
323C2×C22⋊C8C22×C1112yescomplemented
324#391—21no—
325#390—21no—
326#386—21no—
327#386—21no—
328#380C22×C1112yes—
329#380C22×C1112yescomplemented
330#340C22×C1112yescomplemented
331#340C22×C1112yescomplemented
332C22×C11—24no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—42no—
343C22×C11—41no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—41no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—41no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—816no—
354C22×C11—82no—
355C22×C11—82no—
356C22×C11—82no—
357C22×C11—82no—
358C22×C11C2×#12011yescharacteristic
359C22×C11C2×#12311yescharacteristic
360C22×C11#53411yescharacteristic
361C22×C11#57612yes—
362C22×C11#57712yes—
363C4×C11—22no—
364C4×C11—22no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—42no—
368C4×C11—82no—
369C4×C11—82no—
370C4×C11#54612yes—
371C4×C11#54612yes—
372C25—21no—
373C2×#41—22no—
374C2×#41—22no—
375C2×#41—24no—
376C2×#41—42no—
377C22×Q8D4×C1111yescharacteristic
378C22×D4—21no—
379C22×D4—21no—
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—22no—
383C22×D4—22no—
384C22×D4—21no—
385C22×D4—24no—
386C22×D4—42no—
387C22×D4D4×C1111yescharacteristic
388C22×D4D4×C1111yescharacteristic
389C22×D4D4×C1111yescharacteristic
390C22×D4C23×C1111yescharacteristic
391C22×D4C23×C1111yescharacteristic
392C23×C4—21no—
393C23×C4C23×C1111yescharacteristic
394C23×C4C23×C1111yescharacteristic
395C23×C4C23×C1111yescharacteristic
396C22×C8C23×C1112yes—
397C22×C8C23×C1112yes—
398#127—28no—
399#124—28no—
400#121—22no—
401#121—22no—
402#121—22no—
403#121—22no—
404#121—22no—
405#121—22no—
406#121D4×C1114yes—
407#121D4×C1114yes—
408#120—28no—
409#120—28no—
410#117—22no—
411#117—22no—
412#117—42no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4C23×C1112yes—
417C2×C4⋊C4C23×C1112yes—
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C42—21no—
429C2×C42—21no—
430#107—24no—
431#106—24no—
432#102—24no—
433#102—24no—
434#102—42no—
435#102—42no—
436C22⋊C8—22no—
437C22⋊C8—22no—
438C22⋊C8—24no—
439C22⋊C8—42no—
440#95—22no—
441#95—22no—
442C2×C11—42no—
443C2×C11—42no—
444C2×C11—81no—
445C2×C11—82no—
446C2×C11—82no—
447C2×C11#240511yescharacteristic
448C2×C11#300811yescharacteristic
449C2×C11#300911yescharacteristic
450C2×C11#309612yes—
451C2×C11#319812yes—
452C24—24no—
453C24—21no—
454C24—21no—
455C24—42no—
456C24—42no—
457C24—82no—
458C24—82no—
459C24C2×D4×C1111yescharacteristic
460C24C2×D4×C1111yescharacteristic
461C24C2×D4×C1111yescharacteristic
462#41—48no—
463#41—48no—
464C2×Q8—22no—
465C2×Q8—22no—
466C2×Q8—41no—
467C2×D4—24no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—24no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—82no—
492C2×D4—82no—
493C2×D4—82no—
494C2×D4—82no—
495C2×D4C2×D4×C1112yes—
496C2×D4C2×D4×C1112yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—42no—
511C22×C4—82no—
512C22×C4C2×D4×C1111yescharacteristic
513C22×C4C2×D4×C1111yescharacteristic
514C22×C4C2×D4×C1112yes—
515C22×C4C2×D4×C1112yes—
516C22×C4C2×D4×C1111yescharacteristic
517C22×C4C11×#4114yes—
518C22×C4C24×C1111yescharacteristic
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—42no—
532C4⋊C4C2×D4×C1112yes—
533C4⋊C4C2×D4×C1112yes—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—42no—
540C22⋊C4—82no—
541C22⋊C4—82no—
542C42—24no—
543C42—42no—
544C11#2401311yescharacteristic, direct product factor, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—22no—
559C23—22no—
560C23—48no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—42no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—88no—
570C23—84no—
571C23—84no—
572C23—88no—
573C23C11×#12012yes—
574C23C11×#12312yes—
575C23C22×D4×C1111yescharacteristic
576Q8—44no—
577D4—24no—
578D4—24no—
579D4—44no—
580D4—44no—
581D4—48no—
582D4—44no—
583D4—42no—
584D4—42no—
585D4—84no—
586D4—84no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—84no—
613C2×C4C11×#12012yes—
614C2×C4C11×#12312yes—
615C2×C4C22×D4×C1111yescharacteristic
616C2×C4C22×D4×C1111yescharacteristic
617C2×C4C2×C11×#4112yes—
618C2×C4C11×H(5,𝔽2)12yes—
619C8—42no—
620C8—42no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—24no—
626C22—42no—
627C22—42no—
628C22—41no—
629C22—41no—
630C22—42no—
631C22—41no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—816no—
643C22—82no—
644C22—82no—
645C22—82no—
646C22—82no—
647C22C2×C11×#12011yescharacteristic
648C22C2×C11×#12311yescharacteristic
649C22C11×#53411yescharacteristic
650C22C11×#57612yes—
651C22C11×#57712yes—
652C4—22no—
653C4—22no—
654C4—41no—
655C4—42no—
656C4—42no—
657C4—82no—
658C4—82no—
659C4C11×#54612yes—
660C4C11×#54612yes—
661C2—42no—
662C2—42no—
663C2—81no—
664C2—82no—
665C2—82no—
666C2C11×#240511yescharacteristic
667C2C11×#300811yescharacteristic
668C2C11×#300911yescharacteristic
669C2C11×#309612yes—
670C2C11×#319812yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#481C2semidirect
3. C2×C11×#480C2semidirect
4. C11×#2311C2semidirect
5. C11×#2034C2semidirect
6. C11×#2033C2semidirect
7. C11×#1875C2semidirect
8. C11×#1875C2semidirect
9. C11×#1854C2semidirect
10. C11×#1786C2semidirect
11. C11×#1780C2semidirect
25. C2×C11×#117C22semidirect
26. C22×C11×C4⋊C4C22semidirect
29. C2×C11×#107C22semidirect
30. C2×C11×#106C22semidirect
36. C2×C11×C22⋊C8C22semidirect
37. C2×C11×C22⋊C8C22semidirect
38. C2×C11×C22⋊C8C22semidirect
44. C11×#380C22semidirect
45. C11×#340C22semidirect
46. C11×#340C22semidirect
117. #24013C11direct (N × H)
211. C2×#481C2×C11semidirect
212. C2×#480C2×C11semidirect
213. #2311C2×C11semidirect
214. #2034C2×C11semidirect
215. #2033C2×C11semidirect
216. #1875C2×C11semidirect
217. #1875C2×C11semidirect
218. #1854C2×C11semidirect
219. #1786C2×C11semidirect
220. #1780C2×C11semidirect
310. C2×#117C22×C11semidirect
311. C22×C4⋊C4C22×C11semidirect
314. C2×#107C22×C11semidirect
315. C2×#106C22×C11semidirect
321. C2×C22⋊C8C22×C11semidirect
322. C2×C22⋊C8C22×C11semidirect
323. C2×C22⋊C8C22×C11semidirect
329. #380C22×C11semidirect
330. #340C22×C11semidirect
331. #340C22×C11semidirect
544. C11#24013direct (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×#4812
C2×C11×#4802
C11×#23112
C11×#20342
C11×#20332
C11×#18752
C11×#18542
C11×#17862
C11×#17802
#2401311