Finite Group Databasebeta

← D11×#1701 #14736334

Subgroups — D11×#1701 #14736334

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#486C211yesmaximal, characteristic, complemented
2D11×#461C211yesmaximal, characteristic, complemented
3D11×#459C211yesmaximal, characteristic
4D11×#436C211yesmaximal, characteristic, complemented
5#13068180C211yesmaximal, characteristic, complemented
6#13068179C211yesmaximal, characteristic, complemented
7#13068178C211yesmaximal, characteristic, complemented
8#13068177C211yesmaximal, characteristic, complemented
9#13068176C211yesmaximal, characteristic, complemented
10#13068175C211yesmaximal, characteristic, complemented
11#13068174C211yesmaximal, characteristic, complemented
12D11×#334C211yesmaximal, characteristic, complemented
13D11×#332C211yesmaximal, characteristic, complemented
14D11×#331C211yesmaximal, characteristic, complemented
15C11×#1701C211yesmaximal, characteristic, complemented
16C2×SD16×D11—21no—
17C2×D8×D11—21no—
18C2×M16×D11—21no—
19D11×C4⋊Q8C2211yescharacteristic
20D11×#127C2211yescharacteristic
21C4×D4×D11C2211yescharacteristic
22C11×#486C2211yescharacteristic, complemented
23C11×#461C2211yescharacteristic, complemented
24C11×#459C2211yescharacteristic
25C11×#436C2211yescharacteristic, complemented
26#10622775—21no—
27#10622763—21no—
28#10622741—21no—
29#10622701C2211yescharacteristic, complemented
30#10622696C2211yescharacteristic, complemented
31#10622685C2211yescharacteristic
32#10622683C2211yescharacteristic, complemented
33#10622632C2211yescharacteristic, complemented
34#10622628C2211yescharacteristic
35#10622625C2211yescharacteristic, complemented
36#10622456C2211yescharacteristic
37#10622454C2211yescharacteristic, complemented
38#10622451C2211yescharacteristic, complemented
39D11×C4⋊C8C2211yescharacteristic
40D11×C4⋊C8C2211yescharacteristic
41D11×C4⋊C8C2211yescharacteristic
42#10622431—21no—
43D11×#103—21no—
44#10622399—21no—
45D11×#102—21no—
46D11×#102—21no—
47D11×#102—21no—
48#10622373—21no—
49#10622373—21no—
50#10622342—21no—
51D11×C22⋊C8—21no—
52#10622307C2211yescharacteristic, complemented
53#10622301C2211yescharacteristic, complemented
54C4×C8×D11C2211yescharacteristic
55C11×#334C2211yescharacteristic, complemented
56C11×#332C2211yescharacteristic, complemented
57C11×#331C2211yescharacteristic, complemented
58#10622185C2211yescharacteristic, complemented
59#10622182C2211yescharacteristic, complemented
60#10622124C2211yescharacteristic, complemented
61#10622123C2211yescharacteristic, complemented
62#10622123C2211yescharacteristic, complemented
63#10622120C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622118C2211yescharacteristic, complemented
66#10622095C2211yescharacteristic, complemented
67C2×Q8×D11—21no—
68C2×D4×D11—21no—
69C2×D4×D11—21no—
70C2×D4×D11—21no—
71C2×D4×D11D411yescharacteristic
72C22×C4×D11—21no—
73C2×C11×SD16—21no—
74C2×C11×D8—21no—
75C2×C11×M16—21no—
76C11×C4⋊Q8C2311yescharacteristic
77C11×#127C2311yescharacteristic
78C4×D4×C11C2311yescharacteristic
79#66997—21no—
80C2×#4325—21no—
81#66993—21no—
82#66993—21no—
83#66993—21no—
84D4×Dic11D411yescharacteristic
85C2×#4324—21no—
86C2×#4323—21no—
87C2×#4323—21no—
88C4×C22⋊D11—21no—
89C2×#4318—21no—
90SD16×D11—44no—
91D8×D11—44no—
92M16×D11—44no—
93C2×D88—21no—
94C2×#4314—21no—
95C2×#4313—21no—
96C2×#4313—21no—
97C2×C8×D11—21no—
98C2×C8×D11—21no—
99C2×C8×D11—21no—
100C2×C8×D11D411yescharacteristic
101C2×C8×D11D411yescharacteristic
102#66946D411yescharacteristic
103C4⋊C4×D11—21no—
104C4⋊C4×D11—21no—
105C4⋊C4×D11D411yescharacteristic
106#66941—21no—
107#66941—21no—
108(C22⋊D11)⋊C4—21no—
109C22⋊C4×D11—21no—
110#66927C2311yescharacteristic
111C4×D44C2311yescharacteristic
112C42×D11C2311yescharacteristic
113#66922C2311yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×#103—21no—
118C11×#102—21no—
119C11×#102—21no—
120C11×#102—21no—
121C11×C22⋊C8—21no—
122C4×C8×C11C2311yescharacteristic
123#66899—21no—
124#66896—21no—
125#66896—21no—
126#66896—21no—
127C22⋊(C11⋊C8)—21no—
128#66885—21no—
129#66885—21no—
130#66885—21no—
131(C2×D11)⋊C8—21no—
132(C2×D11)⋊C8—21no—
133#66880—21no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137C8×Dic11D411yescharacteristic
138C8×Dic11D411yescharacteristic
139#66874—21no—
140#66873—21no—
141#66873—21no—
142#66873—21no—
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4⋊(C11⋊C8)C2311yescharacteristic
145C4⋊(C11⋊C8)C2311yescharacteristic
146C4×C11⋊C8C2311yescharacteristic
147C2×#1701—111nomaximal, Sylow
148C23×D11—21no—
149C23×D11—41no—
150C2×Q8×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C2×C22⋊D11—21no—
157C2×C22⋊D11—41no—
158C2×C22⋊D11—41no—
159C2×C22⋊D11—41no—
160C22×Dic11—21no—
161Q8×D11—42no—
162Q8×D11—42no—
163D4×D11—22no—
164D4×D11—22no—
165D4×D11—42no—
166D4×D11—42no—
167D4×D11—42no—
168D4×D11—42no—
169D4×D11—82no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44C2×D411yescharacteristic
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×C4×D11—41no—
180C2×C4×D11C2×D411yescharacteristic
181C2×C4×D11C2×D411yescharacteristic
182C2×C4×D11#4111yescharacteristic
183C2×Dic22—21no—
184C2×Dic22—41no—
185C11×SD16—42no—
186C11×D8—42no—
187C11×M16—42no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11C2×D411yescharacteristic
192C2×C8×C11C2×D411yescharacteristic
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C22⋊C4—21no—
197C42×C11C2411yescharacteristic
198C22⋊Dic11—21no—
199#4325—42no—
200#4324—42no—
201#4323—42no—
202#4323—42no—
203(C2×D11)⋊C4—21no—
204(C2×D11)⋊C4—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11C2×D411yescharacteristic
208Dic11⋊C4—21no—
209Dic11⋊C4—41no—
210Dic11⋊C4—41no—
211C4×Dic11C2×D411yescharacteristic
212C4×Dic11C2×D411yescharacteristic
213C4×Dic11#4111yescharacteristic
214#4318—42no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8C2×D411yescharacteristic
219C2×C11⋊C8C2×D411yescharacteristic
220D88—42no—
221#4314—42no—
222#4313—42no—
223#4313—42no—
224C8×D11—22no—
225C8×D11—22no—
226C8×D11—42no—
227C8×D11—42no—
228C8×D11—42no—
229C2×#486—111no—
230C2×#461—111no—
231C2×#459—111no—
232C2×#436—111no—
233#1701—111no—
234#1701—111no—
235#1701—111no—
236#1701—111no—
237#1701—111no—
238#1701—111no—
239#1701—111no—
240#1701D1111yescharacteristic, direct product factor
241C2×#334—111no—
242C2×#332—111no—
243C2×#331—111no—
244C23×C11—21no—
245C23×C11—41no—
246C22×D11—21no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—41no—
251C22×D11—82no—
252C22×D11—82no—
253C22×D11—82no—
254C22×D11#12111yescharacteristic
255Q8×C11—41no—
256Q8×C11—41no—
257D4×C11—21no—
258D4×C11—21no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—81no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C22⋊D11—42no—
272C22⋊D11—82no—
273C22⋊D11—82no—
274C22⋊D11—82no—
275C2×Dic11—21no—
276C2×Dic11—42no—
277C2×Dic11—41no—
278C2×Dic11#12111yescharacteristic
279C2×Dic11#12111yescharacteristic
280C2×Dic11#12111yescharacteristic
281D44—21no—
282D44—21no—
283D44—41no—
284D44—41no—
285D44—41no—
286D44—41no—
287D44—81no—
288C4×D11—22no—
289C4×D11—42no—
290C4×D11—41no—
291C4×D11—41no—
292C4×D11—42no—
293C4×D11—82no—
294C4×D11#13512yes—
295C4×D11AGL(1,ℤ/8)12yes—
296C4×D11AGL(1,ℤ/8)12yes—
297C4×D11AGL(1,ℤ/8)12yes—
298Dic22—41no—
299Dic22—41no—
300Dic22—82no—
301C8×C11—21no—
302C8×C11—21no—
303C8×C11—41no—
304C8×C11—41no—
305C8×C11—41no—
306C11⋊C8—21no—
307C11⋊C8—21no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C22×SD16—221no—
312C22×D8—221no—
313C22×M16—221no—
314C2×C4⋊Q8—111no—
315C2×#127—111no—
316C2×C4×D4—111no—
317#486—111no—
318#486—111no—
319#486—111no—
320#486—221no—
321#486—221no—
322#486C2×D1111yescharacteristic, complemented
323#461—111no—
324#461—111no—
325#461—111no—
326#461—221no—
327#461—221no—
328#461C2×D1111yescharacteristic, complemented
329#459—111no—
330#459—111no—
331#459—111no—
332#459—221no—
333#459—221no—
334#459C2×D1111yescharacteristic
335#436—111no—
336#436—111no—
337#436—111no—
338#436—221no—
339#436—221no—
340#436C2×D1111yescharacteristic, complemented
341C2×C4⋊C8—111no—
342C2×C4⋊C8—111no—
343C2×C4⋊C8—111no—
344C2×#103—221no—
345C2×#102—221no—
346C2×#102—221no—
347C2×#102—221no—
348C2×C22⋊C8—221no—
349C2×C4×C8—111no—
350#334—111no—
351#334—111no—
352#334—111no—
353#334C2×D1111yescharacteristic, complemented
354#332—111no—
355#332—111no—
356#332—111no—
357#332C2×D1111yescharacteristic, complemented
358#331—111no—
359#331—111no—
360#331—111no—
361#331C2×D1111yescharacteristic, complemented
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11C2×#12111yescharacteristic
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—84no—
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11—164no—
377C2×D11#46312yes—
378C2×D11#46912yes—
379C2×D11#47112yes—
380C4×C11—21no—
381C4×C11—41no—
382C4×C11—81no—
383C4×C11C2×#13511yescharacteristic
384C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
385C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
386C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
387Dic11—21no—
388Dic11—41no—
389Dic11—81no—
390Dic11#46312yes—
391Dic11#46912yes—
392C22×Q8—221no—
393C22×D4—111no—
394C22×D4—221no—
395C22×D4—221no—
396C22×D4—221no—
397C23×C4—221no—
398C2×SD16—21no—
399C2×SD16—221no—
400C2×SD16—221no—
401C2×SD16—221no—
402C2×SD16—444no—
403C2×D8—21no—
404C2×D8—221no—
405C2×D8—221no—
406C2×D8—221no—
407C2×D8—444no—
408C2×M16—21no—
409C2×M16—221no—
410C2×M16—221no—
411C2×M16—221no—
412C2×M16—444no—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8—221no—
416C22×C8—221no—
417C22×C8—221no—
418C4⋊Q8—111no—
419C4⋊Q8—221no—
420C4⋊Q8—221no—
421C4⋊Q8—221no—
422C4⋊Q8C22×D1111yescharacteristic
423#127—111no—
424#127—221no—
425#127—221no—
426#127—221no—
427#127C22×D1111yescharacteristic
428C4×D4—111no—
429C4×D4—111no—
430C4×D4—111no—
431C4×D4—221no—
432C4×D4—221no—
433C4×D4C22×D1111yescharacteristic
434C2×C4⋊C4—111no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C42—111no—
439C4⋊C8—111no—
440C4⋊C8—111no—
441C4⋊C8—111no—
442C4⋊C8—221no—
443C4⋊C8—221no—
444C4⋊C8—221no—
445C4⋊C8C22×D1111yescharacteristic
446C4⋊C8C22×D1111yescharacteristic
447C4⋊C8C22×D1111yescharacteristic
448#103—21no—
449#103—221no—
450#103—221no—
451#103—221no—
452#102—21no—
453#102—21no—
454#102—21no—
455#102—221no—
456#102—221no—
457#102—221no—
458#102—221no—
459#102—221no—
460#102—221no—
461#102—221no—
462#102—221no—
463#102—221no—
464C22⋊C8—21no—
465C22⋊C8—221no—
466C22⋊C8—221no—
467C22⋊C8—221no—
468C4×C8—111no—
469C4×C8—111no—
470C4×C8—111no—
471C4×C8C22×D1111yescharacteristic
472C2×C11—81no—
473C2×C11—161no—
474C2×C11C2×#46311yescharacteristic
475C2×C11C2×#46911yescharacteristic
476C2×C11C2×#47111yescharacteristic
477D11—81no—
478D11—161no—
479D11#170114yesdirect product factor
480C24—221no—
481C24—441no—
482C2×Q8—21no—
483C2×Q8—221no—
484C2×Q8—441no—
485C2×Q8—442no—
486C2×Q8—442no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—111no—
491C2×D4—222no—
492C2×D4—222no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—442no—
498C2×D4—442no—
499C2×D4—442no—
500C2×D4—442no—
501C2×D4—441no—
502C2×D4—441no—
503C2×D4—441no—
504C2×D4—882no—
505C2×D4D4×D1111yescharacteristic
506C22×C4—21no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—441no—
517SD16—42no—
518SD16—442no—
519SD16—442no—
520SD16—442no—
521D8—42no—
522D8—442no—
523D8—442no—
524D8—442no—
525M16—42no—
526M16—442no—
527M16—442no—
528M16—442no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—111no—
533C2×C8—111no—
534C2×C8—222no—
535C2×C8—222no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—442no—
540C2×C8—442no—
541C2×C8—442no—
542C2×C8D4×D1111yescharacteristic
543C2×C8D4×D1111yescharacteristic
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—111no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—441no—
551C4⋊C4—441no—
552C4⋊C4D4×D1111yescharacteristic
553C22⋊C4—21no—
554C22⋊C4—221no—
555C22⋊C4—221no—
556C22⋊C4—221no—
557C42—111no—
558C42—111no—
559C42—111no—
560C42C23×D1111yescharacteristic
561C11C2×#170111yescharacteristic, complemented, Sylow
562C23—21no—
563C23—41no—
564C23—111no—
565C23—221no—
566C23—442no—
567C23—442no—
568C23—442no—
569C23—441no—
570C23—882no—
571C23—882no—
572C23—882no—
573Q8—41no—
574Q8—41no—
575Q8—441no—
576Q8—441no—
577Q8—882no—
578D4—21no—
579D4—21no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—81no—
585D4—221no—
586D4—221no—
587D4—442no—
588D4—441no—
589D4—441no—
590D4—441no—
591D4—441no—
592D4—881no—
593D4—882no—
594D4—882no—
595D4—882no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—111no—
601C2×C4—111no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—112no—
606C2×C4—111no—
607C2×C4—222no—
608C2×C4—221no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—882no—
616C2×C4C2×D4×D1111yescharacteristic
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C8—21no—
620C8—21no—
621C8—41no—
622C8—41no—
623C8—41no—
624C8—221no—
625C8—221no—
626C8—441no—
627C8—441no—
628C8—441no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—112no—
636C22—112no—
637C22—112no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—884no—
642C22—881no—
643C22—881no—
644C22—881no—
645C22—1764no—
646C22D11×#12111yescharacteristic
647C4—21no—
648C4—41no—
649C4—81no—
650C4—112no—
651C4—112no—
652C4—221no—
653C4—441no—
654C4—881no—
655C4D11×#13511yescharacteristic
656C4D11×AGL(1,ℤ/8)11yescharacteristic
657C4D11×AGL(1,ℤ/8)11yescharacteristic
658C4D11×AGL(1,ℤ/8)11yescharacteristic
659C2—81no—
660C2—114no—
661C2—161no—
662C2—881no—
663C2—1761no—
664C2D11×#46311yescharacteristic
665C2D11×#46911yescharacteristic
666C2D11×#47111yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1701C2
socleC22×C11C2×#121
prime radicalD11×#459C2
hypercenter#1701D11
hypocenterC11C2×#1701
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1701

Complements

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

NH ≅ G/Ntype
1. D11×#486C2semidirect
2. D11×#461C2semidirect
4. D11×#436C2semidirect
5. #13068180C2semidirect
6. #13068179C2semidirect
7. #13068178C2semidirect
8. #13068177C2semidirect
9. #13068176C2semidirect
10. #13068175C2semidirect
11. #13068174C2semidirect
12. D11×#334C2semidirect
13. D11×#332C2semidirect
14. D11×#331C2semidirect
15. C11×#1701C2semidirect
22. C11×#486C22semidirect
23. C11×#461C22semidirect
25. C11×#436C22semidirect
29. #10622701C22semidirect
30. #10622696C22semidirect
32. #10622683C22semidirect
33. #10622632C22semidirect
35. #10622625C22semidirect
37. #10622454C22semidirect
38. #10622451C22semidirect
52. #10622307C22semidirect
53. #10622301C22semidirect
55. C11×#334C22semidirect
56. C11×#332C22semidirect
57. C11×#331C22semidirect
58. #10622185C22semidirect
59. #10622182C22semidirect
60. #10622124C22semidirect
61. #10622123C22semidirect
62. #10622123C22semidirect
63. #10622120C22semidirect
64. #10622118C22semidirect
65. #10622118C22semidirect
66. #10622095C22semidirect
240. #1701D11direct (N × H)
322. #486C2×D11semidirect
328. #461C2×D11semidirect
340. #436C2×D11semidirect
353. #334C2×D11semidirect
357. #332C2×D11semidirect
361. #331C2×D11semidirect
479. D11#1701direct (N × H)
561. C11C2×#1701semidirect

Maximal subgroups

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

subgroupindex
D11×#4862
D11×#4612
D11×#4592
D11×#4362
#130681802
#130681792
#130681782
#130681772
#130681762
#130681752
#130681742
D11×#3342
D11×#3322
D11×#3312
C11×#17012
C2×#170111