Finite Group Databasebeta

← C11×#33557 #14610750

Subgroups — C11×#33557 #14610750

Order 2816.

1258 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3543C211yesmaximal, characteristic, complemented
2C11×#3026C212yesmaximal, complemented
3C2×C11×#453C211yesmaximal, characteristic, complemented
4C11×#2200C214yesmaximal, complemented
5C11×#2198C212yesmaximal, complemented
6C11×#2196C212yesmaximal, complemented
7C2×C11×#353C211yesmaximal, characteristic, complemented
8C11×#2121C212yesmaximal, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic, complemented
10C2×C11×AGL(1,ℤ/8)—21no—
11C11×#560—21no—
12C11×#560C2212yescomplemented
13C11×#559C2211yescharacteristic, complemented
14C11×#550—21no—
15C11×#546—22no—
16D42×C11—22no—
17D42×C11C2211yescharacteristic, complemented
18C11×#540—22no—
19C11×#535—22no—
20C11×#534—21no—
21C11×#534—22no—
22C11×#534C2212yes—
23C2×C11×#127C2211yescharacteristic
24C11×#529—21no—
25C11×#458—22no—
26C11×#458C2214yescomplemented
27C11×B(4,𝔽2)—22no—
28C11×B(4,𝔽2)C2214yescomplemented
29C11×#453—21no—
30C11×#453—21no—
31C11×#453C2212yes—
32C11×#453C2212yescomplemented
33C2×C11×#104—21no—
34C2×C11×#100C2211yescharacteristic, complemented
35C2×C11×#99—22no—
36C2×C11×#99C2212yescomplemented
37C11×#353C2212yescomplemented
38C11×#353C2212yescomplemented
39C11×#352C2214yescomplemented
40C11×AΣL(1,𝔽16)C2214yescomplemented
41C11×H(5,𝔽2)—22no—
42C11×H(5,𝔽2)—21no—
43C11×H(5,𝔽2)—42no—
44C11×H(5,𝔽2)C2312yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C2×C11×#41—41no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—41no—
53C22×D4×C11D412yescomplemented
54C22×D4×C11D411yescharacteristic, complemented
55C22×D4×C11C2311yescharacteristic
56C11×AGL(1,ℤ/8)—22no—
57C11×AGL(1,ℤ/8)—22no—
58C11×AGL(1,ℤ/8)—42no—
59C2×C11×SD16—41no—
60C2×C11×D8—41no—
61C2×C11×M16—21no—
62C11×#127—22no—
63C11×#127—22no—
64C11×#127D411yescharacteristic, complemented
65C11×#127D411yescharacteristic, complemented
66C11×#127C2311yescharacteristic
67C11×#127C2311yescharacteristic
68C11×#126—22no—
69C11×#125—21no—
70C11×#124—21no—
71C11×#124—22no—
72C11×#123—21no—
73C11×#123—22no—
74C11×#123—21no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—24no—
78C11×#123—42no—
79C11×#123D412yescomplemented
80C11×#123C2312yes—
81C11×C22⋊Q8—21no—
82C11×#121—21no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#121—22no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121—22no—
90C11×#121—22no—
91C11×#121—22no—
92C11×#121—22no—
93C11×#121—44no—
94C11×#120—21no—
95C11×#120—22no—
96C11×#120—22no—
97C11×#120—22no—
98C11×#120—22no—
99C11×#120—21no—
100C11×#120—24no—
101C11×#120—42no—
102C11×#120D412yescomplemented
103C11×#120C2312yes—
104C4×Q8×C11—21no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11—22no—
108C4×D4×C11—21no—
109C11×#117—22no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4D412yescomplemented
113C2×C42×C11D411yescharacteristic, complemented
114C11×#104—22no—
115C11×#104—22no—
116C11×#100—21no—
117C11×#100C2312yes—
118C11×#99—22no—
119C11×#99—24no—
120C11×#99—24no—
121C11×#99C2314yes—
122#33557C1111yesmaximal, characteristic, direct product factor, Sylow
123C24×C11—22no—
124C24×C11—21no—
125C24×C11—21no—
126C24×C11C2×D412yes—
127C24×C11C2×D412yes—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41—42no—
131C11×#41—41no—
132C11×#41—44no—
133C11×#41—42no—
134C11×#41—41no—
135C11×#41—84no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11—41no—
156C2×D4×C11—41no—
157C2×D4×C11—41no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—44no—
163C2×D4×C11—42no—
164C2×D4×C11—41no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—44no—
168C2×D4×C11—84no—
169C2×D4×C11—84no—
170C2×D4×C11—81no—
171C2×D4×C11—81no—
172C2×D4×C11C2×D412yes—
173C2×D4×C11C2×D411yescharacteristic
174C2×D4×C11C2×D411yescharacteristic
175C2×D4×C11C2×D411yescharacteristic
176C2×D4×C11C2411yescharacteristic
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—21no—
180C22×C4×C11—22no—
181C22×C4×C11—21no—
182C22×C4×C11—22no—
183C22×C4×C11—41no—
184C22×C4×C11—42no—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C11×SD16—42no—
188C11×SD16—42no—
189C11×D8—42no—
190C11×D8—42no—
191C11×M16—22no—
192C11×M16—41no—
193C2×C8×C11—41no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—44no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—44no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—44no—
216C11×C22⋊C4C2×D412yes—
217C11×C22⋊C4C2×D412yes—
218C42×C11—22no—
219C42×C11—21no—
220C42×C11C2×D411yescharacteristic
221C42×C11C2×D411yescharacteristic
222#3543C2×C1111yescharacteristic, complemented
223#3026C2×C1112yescomplemented
224C2×#453C2×C1111yescharacteristic, complemented
225#2200C2×C1114yescomplemented
226#2198C2×C1112yescomplemented
227#2196C2×C1112yescomplemented
228C2×#353C2×C1111yescharacteristic, complemented
229#2121C2×C1112yescomplemented
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—82no—
242C23×C11—82no—
243C23×C11—82no—
244C23×C11—82no—
245C23×C11—81no—
246C23×C11—162no—
247C23×C11#12012yes—
248C23×C11#12011yescharacteristic
249C23×C11C22×D412yes—
250Q8×C11—22no—
251Q8×C11—41no—
252Q8×C11—42no—
253D4×C11—22no—
254D4×C11—42no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—44no—
261D4×C11—42no—
262D4×C11—44no—
263D4×C11—44no—
264D4×C11—44no—
265D4×C11—42no—
266D4×C11—42no—
267D4×C11—42no—
268D4×C11—42no—
269D4×C11—81no—
270D4×C11—82no—
271D4×C11—82no—
272D4×C11—82no—
273D4×C11—82no—
274D4×C11—82no—
275D4×C11—82no—
276D4×C11—82no—
277D4×C11—82no—
278D4×C11—164no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—24no—
283C2×C4×C11—21no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—42no—
288C2×C4×C11—44no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—41no—
293C2×C4×C11—42no—
294C2×C4×C11—44no—
295C2×C4×C11—81no—
296C2×C4×C11—82no—
297C2×C4×C11—82no—
298C2×C4×C11—162no—
299C2×C4×C11#12011yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C8×C11—42no—
302C2×H(5,𝔽2)C22×C1111yescharacteristic, complemented
303C2×AGL(1,ℤ/8)—21no—
304#560—21no—
305#560C22×C1112yescomplemented
306#559C22×C1111yescharacteristic, complemented
307#550—21no—
308#546—22no—
309D42—22no—
310D42C22×C1111yescharacteristic, complemented
311#540—22no—
312#535—22no—
313#534—21no—
314#534—22no—
315#534C22×C1112yes—
316C2×#127C22×C1111yescharacteristic
317#529—21no—
318#458—22no—
319#458C22×C1114yescomplemented
320B(4,𝔽2)—22no—
321B(4,𝔽2)C22×C1114yescomplemented
322#453—21no—
323#453—21no—
324#453C22×C1112yes—
325#453C22×C1112yescomplemented
326C2×#104—21no—
327C2×#100C22×C1111yescharacteristic, complemented
328C2×#99—22no—
329C2×#99C22×C1112yescomplemented
330#353C22×C1112yescomplemented
331#353C22×C1112yescomplemented
332#352C22×C1114yescomplemented
333AΣL(1,𝔽16)C22×C1114yescomplemented
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—41no—
345C22×C11—42no—
346C22×C11—41no—
347C22×C11—82no—
348C22×C11—82no—
349C22×C11—82no—
350C22×C11—84no—
351C22×C11—84no—
352C22×C11—161no—
353C22×C11—161no—
354C22×C11—162no—
355C22×C11—162no—
356C22×C11B(4,𝔽2)11yescharacteristic
357C22×C11B(4,𝔽2)11yescharacteristic
358C22×C11C2×#12011yescharacteristic
359C4×C11—22no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11—84no—
368H(5,𝔽2)—22no—
369H(5,𝔽2)—21no—
370H(5,𝔽2)—42no—
371H(5,𝔽2)C23×C1112yes—
372C2×#41—22no—
373C2×#41—21no—
374C2×#41—41no—
375C22×D4—22no—
376C22×D4—21no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—41no—
380C22×D4D4×C1112yescomplemented
381C22×D4D4×C1111yescharacteristic, complemented
382C22×D4C23×C1111yescharacteristic
383AGL(1,ℤ/8)—22no—
384AGL(1,ℤ/8)—22no—
385AGL(1,ℤ/8)—42no—
386C2×SD16—41no—
387C2×D8—41no—
388C2×M16—21no—
389#127—22no—
390#127—22no—
391#127D4×C1111yescharacteristic, complemented
392#127D4×C1111yescharacteristic, complemented
393#127C23×C1111yescharacteristic
394#127C23×C1111yescharacteristic
395#126—22no—
396#125—21no—
397#124—21no—
398#124—22no—
399#123—21no—
400#123—22no—
401#123—21no—
402#123—22no—
403#123—22no—
404#123—24no—
405#123—42no—
406#123D4×C1112yescomplemented
407#123C23×C1112yes—
408C22⋊Q8—21no—
409#121—21no—
410#121—22no—
411#121—22no—
412#121—22no—
413#121—22no—
414#121—22no—
415#121—22no—
416#121—22no—
417#121—22no—
418#121—22no—
419#121—22no—
420#121—44no—
421#120—21no—
422#120—22no—
423#120—22no—
424#120—22no—
425#120—22no—
426#120—21no—
427#120—24no—
428#120—42no—
429#120D4×C1112yescomplemented
430#120C23×C1112yes—
431C4×Q8—21no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—21no—
436#117—22no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4D4×C1112yescomplemented
440C2×C42D4×C1111yescharacteristic, complemented
441#104—22no—
442#104—22no—
443#100—21no—
444#100C23×C1112yes—
445#99—22no—
446#99—24no—
447#99—24no—
448#99C23×C1114yes—
449C2×C11—21no—
450C2×C11—21no—
451C2×C11—21no—
452C2×C11—42no—
453C2×C11—42no—
454C2×C11—82no—
455C2×C11—81no—
456C2×C11—81no—
457C2×C11—82no—
458C2×C11C2×B(4,𝔽2)11yescharacteristic
459C24—22no—
460C24—21no—
461C24—21no—
462C24C2×D4×C1112yes—
463C24C2×D4×C1112yes—
464#41—22no—
465#41—22no—
466#41—42no—
467#41—41no—
468#41—44no—
469#41—42no—
470#41—41no—
471#41—84no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—24no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—24no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—41no—
491C2×D4—41no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—44no—
499C2×D4—41no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—44no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4C2×D4×C1112yes—
509C2×D4C2×D4×C1111yescharacteristic
510C2×D4C2×D4×C1111yescharacteristic
511C2×D4C2×D4×C1111yescharacteristic
512C2×D4C24×C1111yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4C2×D4×C1111yescharacteristic
522C22×C4C2×D4×C1112yes—
523SD16—42no—
524SD16—42no—
525D8—42no—
526D8—42no—
527M16—22no—
528M16—41no—
529C2×C8—41no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—44no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—24no—
549C22⋊C4—44no—
550C22⋊C4—42no—
551C22⋊C4—44no—
552C22⋊C4C2×D4×C1112yes—
553C22⋊C4C2×D4×C1112yes—
554C42—22no—
555C42—21no—
556C42C2×D4×C1111yescharacteristic
557C42C2×D4×C1111yescharacteristic
558C11#3355711yescharacteristic, direct product factor, Sylow
559C23—22no—
560C23—22no—
561C23—24no—
562C23—22no—
563C23—21no—
564C23—21no—
565C23—42no—
566C23—42no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—82no—
571C23—82no—
572C23—82no—
573C23—82no—
574C23—81no—
575C23—162no—
576C23C11×#12012yes—
577C23C11×#12011yescharacteristic
578C23C22×D4×C1112yes—
579Q8—22no—
580Q8—41no—
581Q8—42no—
582D4—22no—
583D4—41no—
584D4—42no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—44no—
590D4—42no—
591D4—44no—
592D4—44no—
593D4—44no—
594D4—42no—
595D4—42no—
596D4—42no—
597D4—42no—
598D4—81no—
599D4—82no—
600D4—82no—
601D4—82no—
602D4—82no—
603D4—82no—
604D4—82no—
605D4—82no—
606D4—82no—
607D4—164no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—24no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—42no—
617C2×C4—44no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—44no—
624C2×C4—81no—
625C2×C4—82no—
626C2×C4—82no—
627C2×C4—162no—
628C2×C4C11×#12011yescharacteristic
629C2×C4C22×D4×C1111yescharacteristic
630C8—42no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—41no—
642C22—42no—
643C22—41no—
644C22—82no—
645C22—82no—
646C22—82no—
647C22—84no—
648C22—84no—
649C22—161no—
650C22—161no—
651C22—162no—
652C22—162no—
653C22C11×B(4,𝔽2)11yescharacteristic
654C22C11×B(4,𝔽2)11yescharacteristic
655C22C2×C11×#12011yescharacteristic
656C4—22no—
657C4—21no—
658C4—21no—
659C4—42no—
660C4—41no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—84no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—42no—
669C2—42no—
670C2—82no—
671C2—81no—
672C2—81no—
673C2—82no—
674C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C11C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C11
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C23×C11 ◁ C22×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3543C2semidirect
2. C11×#3026C2semidirect
3. C2×C11×#453C2semidirect
4. C11×#2200C2semidirect
5. C11×#2198C2semidirect
6. C11×#2196C2semidirect
7. C2×C11×#353C2semidirect
8. C11×#2121C2semidirect
9. C2×C11×H(5,𝔽2)C22semidirect
12. C11×#560C22semidirect
13. C11×#559C22semidirect
17. D42×C11C22semidirect
26. C11×#458C22semidirect
28. C11×B(4,𝔽2)C22semidirect
32. C11×#453C22semidirect
34. C2×C11×#100C22semidirect
36. C2×C11×#99C22semidirect
37. C11×#353C22semidirect
38. C11×#353C22semidirect
39. C11×#352C22semidirect
40. C11×AΣL(1,𝔽16)C22semidirect
53. C22×D4×C11D4semidirect
54. C22×D4×C11D4semidirect
64. C11×#127D4semidirect
65. C11×#127D4semidirect
79. C11×#123D4semidirect
102. C11×#120D4semidirect
112. C2×C11×C22⋊C4D4semidirect
113. C2×C42×C11D4semidirect
122. #33557C11direct (N × H)
222. #3543C2×C11semidirect
223. #3026C2×C11semidirect
224. C2×#453C2×C11semidirect
225. #2200C2×C11semidirect
226. #2198C2×C11semidirect
227. #2196C2×C11semidirect
228. C2×#353C2×C11semidirect
229. #2121C2×C11semidirect
302. C2×H(5,𝔽2)C22×C11semidirect
305. #560C22×C11semidirect
306. #559C22×C11semidirect
310. D42C22×C11semidirect
319. #458C22×C11semidirect
321. B(4,𝔽2)C22×C11semidirect
325. #453C22×C11semidirect
327. C2×#100C22×C11semidirect
329. C2×#99C22×C11semidirect
330. #353C22×C11semidirect
331. #353C22×C11semidirect
332. #352C22×C11semidirect
333. AΣL(1,𝔽16)C22×C11semidirect
380. C22×D4D4×C11semidirect
381. C22×D4D4×C11semidirect
391. #127D4×C11semidirect
392. #127D4×C11semidirect
406. #123D4×C11semidirect
429. #120D4×C11semidirect
439. C2×C22⋊C4D4×C11semidirect
440. C2×C42D4×C11semidirect
558. C11#33557direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35432
C11×#30262
C2×C11×#4532
C11×#22002
C11×#21982
C11×#21962
C2×C11×#3532
C11×#21212
#3355711