Finite Group Databasebeta

← D11×#2071 #14782501

Subgroups — D11×#2071 #14782501

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#102C212yesmaximal
2D11×#390C211yesmaximal, characteristic
3D11×#384C211yesmaximal, characteristic, complemented
4#13070023C212yesmaximal, complemented
5#13070022C212yesmaximal, complemented
6#13070021C211yesmaximal, characteristic, complemented
7#13070020C211yesmaximal, characteristic, complemented
8#13070019C211yesmaximal, characteristic, complemented
9D11×#340C212yesmaximal, complemented
10D11×#336C211yesmaximal, characteristic, complemented
11C11×#2071C211yesmaximal, characteristic, complemented
12C22×D4×D11C2211yescharacteristic
13C22×C8×D11C2212yes—
14C2×C4⋊C4×D11—21no—
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11C2211yescharacteristic
17C2×C4⋊C4×D11C2212yes—
18C2×C22⋊C4×D11—21no—
19C2×C22⋊C4×D11—21no—
20C2×C42×D11C2211yescharacteristic
21C2×C11×#102C2212yes—
22C11×#390C2211yescharacteristic
23C11×#384C2211yescharacteristic, complemented
24#10622834C2211yescharacteristic
25C2×#66896C2212yes—
26C2×#66885C2212yes—
27#10622601C2211yescharacteristic
28#10622589—21no—
29#10622589—21no—
30#10622589C2212yescomplemented
31C2×#66873C2212yes—
32#10622570—21no—
33#10622570—21no—
34#10622552C2211yescharacteristic
35#10622548C2211yescharacteristic, complemented
36D11×#102—28no—
37C11×#340C2212yescomplemented
38C11×#336C2211yescharacteristic, complemented
39#10622189C2212yescomplemented
40#10622188C2212yescomplemented
41#10622167C2212yescomplemented
42#10622167C2212yescomplemented
43#10622162C2211yescharacteristic, complemented
44C24×D11—21no—
45C22×D4×C11C2311yescharacteristic
46C22×C22⋊D11—21no—
47C2×D4×D11—24no—
48C2×D4×D11—24no—
49C2×D4×D11—22no—
50C2×D4×D11D414yes—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×C4×D11—22no—
54C22×C4×D11D411yescharacteristic
55C22×C4×D11D411yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83C2×C8×D11—24no—
84C2×C8×D11—24no—
85C2×C8×D11—24no—
86C4⋊C4×D11—24no—
87C4⋊C4×D11—24no—
88C4⋊C4×D11—24no—
89C4⋊C4×D11—44no—
90C4⋊C4×D11—44no—
91C22⋊C4×D11—44no—
92C22⋊C4×D11—44no—
93C42×D11—24no—
94C11×#102—24no—
95#66896—24no—
96#66885—24no—
97#66873—24no—
98C2×#2071—111nomaximal, Sylow
99C24×C11—21no—
100C23×D11—21no—
101C23×D11—24no—
102C23×D11—42no—
103C23×D11—42no—
104C23×D11—42no—
105C23×D11—42no—
106C23×D11—42no—
107C23×D11—42no—
108C23×D11C2×D411yescharacteristic
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11C2×D412yes—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—24no—
119C2×C22⋊D11—42no—
120C2×C22⋊D11—42no—
121C22×Dic11—22no—
122C22×Dic11—21no—
123C22×Dic11C2×D411yescharacteristic
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126D4×D11—216no—
127D4×D11—48no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44C2×D412yes—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—44no—
137C2×C4×D11—42no—
138C2×C4×D11—42no—
139C2×C4×D11—44no—
140C2×C4×D11—42no—
141C2×C4×D11—44no—
142C2×C4×D11D814yes—
143C2×C4×D11SD1614yes—
144C2×C4×D11C2×D412yes—
145C2×C4×D11#4112yes—
146C2×C4×D11#4114yes—
147C2×C4×D11#4114yes—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—42no—
158C42×C11—22no—
159C22⋊Dic11—42no—
160C22⋊Dic11—42no—
161(C2×D11)⋊C4—42no—
162(C2×D11)⋊C4—42no—
163(C2×D11)⋊C4—42no—
164(C2×D11)⋊C4—42no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—42no—
169C4⋊Dic11—42no—
170Dic11⋊C4—44no—
171Dic11⋊C4—44no—
172Dic11⋊C4—42no—
173Dic11⋊C4—44no—
174C4×Dic11—22no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C8×D11—48no—
181C22×#102—112no—
182C2×#390—111no—
183C2×#384—111no—
184#2071—112no—
185#2071—111no—
186#2071—111no—
187#2071—112no—
188#2071—111no—
189#2071D1111yescharacteristic, direct product factor
190C2×#340—112no—
191C2×#336—111no—
192C23×C11—22no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11C22×D411yescharacteristic
200C22×D11—22no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—48no—
208C22×D11—48no—
209C22×D11—48no—
210C22×D11—84no—
211C22×D11—84no—
212C22×D11—84no—
213C22×D11—84no—
214C22×D11#12112yes—
215C22×D11#12312yes—
216C22×D11#12412yes—
217C22×D11C2×D812yes—
218C22×D11C2×SD1612yes—
219C22×D11AGL(1,ℤ/8)12yes—
220C22×D11#13712yes—
221D4×C11—24no—
222D4×C11—42no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11C2×D812yes—
234C2×C4×C11C2×SD1612yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4112yes—
237C2×C4×C11C2×#4112yes—
238C2×C4×C11C2×#4111yescharacteristic
239C22⋊D11—48no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—42no—
245C2×Dic11—41no—
246C2×Dic11—42no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—42no—
250C2×Dic11#12112yes—
251C2×Dic11#12312yes—
252C2×Dic11#12412yes—
253C2×Dic11C2×D812yes—
254C2×Dic11C2×SD1612yes—
255D44—24no—
256D44—42no—
257C4×D11—28no—
258C4×D11—28no—
259C4×D11—88no—
260C4×D11—84no—
261C4×D11#12318yes—
262C4×D11#12618yes—
263C8×C11—42no—
264C11⋊C8—42no—
265C23×D4—111no—
266C23×C8—112no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—111no—
269C22×C4⋊C4—221no—
270C22×C4⋊C4—221no—
271C22×C22⋊C4—221no—
272C22×C22⋊C4—221no—
273C22×C42—111no—
274C2×#102—112no—
275C2×#102—112no—
276C2×#102—112no—
277C2×#102—228no—
278C2×#102C2×D1112yes—
279#390—111no—
280#390—111no—
281#390—111no—
282#390—221no—
283#390—221no—
284#390C2×D1111yescharacteristic
285#384—112no—
286#384—111no—
287#384—221no—
288#384—221no—
289#384C2×D1111yescharacteristic, complemented
290#340—112no—
291#340—112no—
292#340—112no—
293#340C2×D1112yescomplemented
294#336—112no—
295#336—111no—
296#336C2×D1111yescharacteristic, complemented
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—81no—
304C22×C11C2×#12111yescharacteristic
305C22×C11C2×#12311yescharacteristic
306C22×C11C2×#12411yescharacteristic
307C22×C11C22×D811yescharacteristic
308C22×C11C22×SD1611yescharacteristic
309C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
310C22×C11C2×#13711yescharacteristic
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—81no—
315C2×D11—81no—
316C2×D11—81no—
317C2×D11—81no—
318C2×D11—816no—
319C2×D11#39714yes—
320C2×D11#45914yes—
321C2×D11#46114yes—
322C2×D11#48014yes—
323C2×D11#48114yes—
324C2×D11#48614yes—
325C2×D11#48914yes—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—81no—
329C4×C11—82no—
330C4×C11C2×#12312yes—
331C4×C11C2×#12612yes—
332Dic11—22no—
333Dic11—22no—
334Dic11—81no—
335Dic11—82no—
336Dic11#39714yes—
337C25—221no—
338C22×D4—114no—
339C22×D4—111no—
340C22×D4—224no—
341C22×D4—224no—
342C22×D4—222no—
343C22×D4—221no—
344C22×D4C22×D1111yescharacteristic
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—221no—
349C23×C4—222no—
350C22×C8—112no—
351C22×C8—224no—
352C22×C8—224no—
353C22×C8—224no—
354C22×C8C22×D1112yes—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—224no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—444no—
369C2×C4⋊C4—444no—
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1112yes—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—444no—
381C2×C22⋊C4—444no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—224no—
386C2×C42C22×D1111yescharacteristic
387#102—24no—
388#102—224no—
389#102—224no—
390#102—224no—
391C2×C11—82no—
392C2×C11C2×#39711yescharacteristic
393C2×C11C2×#45911yescharacteristic
394C2×C11C2×#46111yescharacteristic
395C2×C11C2×#48011yescharacteristic
396C2×C11C2×#48111yescharacteristic
397C2×C11C2×#48611yescharacteristic
398C2×C11C2×#48911yescharacteristic
399D11—82no—
400D11#207118yesdirect product factor
401C24—21no—
402C24—111no—
403C24—224no—
404C24—221no—
405C24—442no—
406C24—442no—
407C24—442no—
408C24—442no—
409C24—442no—
410C24—442no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—21no—
414C2×D4—112no—
415C2×D4—2216no—
416C2×D4—224no—
417C2×D4—222no—
418C2×D4—222no—
419C2×D4—221no—
420C2×D4—448no—
421C2×D4—442no—
422C2×D4—442no—
423C2×D4D4×D1112yes—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—111no—
427C22×C4—112no—
428C22×C4—114no—
429C22×C4—112no—
430C22×C4—114no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—114no—
434C22×C4—114no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—221no—
440C22×C4—222no—
441C22×C4—442no—
442C22×C4—442no—
443C22×C4—444no—
444C22×C4—442no—
445C22×C4—444no—
446C22×C4—444no—
447C22×C4D4×D1111yescharacteristic
448C22×C4D4×D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—222no—
454C2×C8—222no—
455C2×C8—222no—
456C2×C8—448no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C4⋊C4—442no—
466C4⋊C4—444no—
467C4⋊C4—442no—
468C4⋊C4—444no—
469C4⋊C4—444no—
470C4⋊C4—442no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—442no—
474C22⋊C4—442no—
475C22⋊C4—442no—
476C22⋊C4—442no—
477C22⋊C4—442no—
478C22⋊C4—442no—
479C42—22no—
480C42—222no—
481C42—222no—
482C42—222no—
483C11C2×#207111yescharacteristic, complemented, Sylow
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—112no—
492C23—112no—
493C23—112no—
494C23—112no—
495C23—112no—
496C23—112no—
497C23—112no—
498C23—222no—
499C23—448no—
500C23—448no—
501C23—448no—
502C23—441no—
503C23—441no—
504C23—441no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—884no—
509C23—884no—
510C23—884no—
511C23—884no—
512C23C2×D4×D1111yescharacteristic
513D4—24no—
514D4—42no—
515D4—224no—
516D4—448no—
517D4—442no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—112no—
529C2×C4—112no—
530C2×C4—112no—
531C2×C4—118no—
532C2×C4—118no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—228no—
536C2×C4—228no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—441no—
542C2×C4—442no—
543C2×C4—441no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—441no—
547C2×C4—888no—
548C2×C4—884no—
549C2×C4D8×D1112yes—
550C2×C4SD16×D1112yes—
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4#41×D1111yescharacteristic
553C2×C4#41×D1112yes—
554C2×C4#41×D1112yes—
555C8—42no—
556C8—442no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—114no—
565C22—114no—
566C22—114no—
567C22—114no—
568C22—114no—
569C22—114no—
570C22—114no—
571C22—442no—
572C22—442no—
573C22—442no—
574C22—8816no—
575C22—881no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22D11×#12111yescharacteristic
580C22D11×#12311yescharacteristic
581C22D11×#12411yescharacteristic
582C22C2×D8×D1111yescharacteristic
583C22C2×SD16×D1111yescharacteristic
584C22D11×AGL(1,ℤ/8)11yescharacteristic
585C22D11×#13711yescharacteristic
586C4—22no—
587C4—22no—
588C4—82no—
589C4—81no—
590C4—114no—
591C4—222no—
592C4—222no—
593C4—882no—
594C4—881no—
595C4D11×#12312yes—
596C4D11×#12612yes—
597C2—82no—
598C2—118no—
599C2—882no—
600C2D11×#39711yescharacteristic
601C2D11×#45911yescharacteristic
602C2D11×#46111yescharacteristic
603C2D11×#48011yescharacteristic
604C2D11×#48111yescharacteristic
605C2D11×#48611yescharacteristic
606C2D11×#48911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2071C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenter#2071D11
hypocenterC11C2×#2071
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
3. D11×#384C2semidirect
4. #13070023C2semidirect
5. #13070022C2semidirect
6. #13070021C2semidirect
7. #13070020C2semidirect
8. #13070019C2semidirect
9. D11×#340C2semidirect
10. D11×#336C2semidirect
11. C11×#2071C2semidirect
23. C11×#384C22semidirect
30. #10622589C22semidirect
35. #10622548C22semidirect
37. C11×#340C22semidirect
38. C11×#336C22semidirect
39. #10622189C22semidirect
40. #10622188C22semidirect
41. #10622167C22semidirect
42. #10622167C22semidirect
43. #10622162C22semidirect
189. #2071D11direct (N × H)
289. #384C2×D11semidirect
293. #340C2×D11semidirect
296. #336C2×D11semidirect
400. D11#2071direct (N × H)
483. C11C2×#2071semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1022
D11×#3902
D11×#3842
#130700232
#130700222
#130700212
#130700202
#130700192
D11×#3402
D11×#3362
C11×#20712
C2×#207111