Finite Group Databasebeta

← C2×C11×#2080 #14600841

Subgroups — C2×C11×#2080 #14600841

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#424C211yesmaximal, characteristic, complemented
2C2×C11×#421C211yesmaximal, characteristic
3C2×C11×#416C211yesmaximal, characteristic
4C2×C11×#413C211yesmaximal, characteristic
5C11×#2080C218yesmaximal, direct product factor
6C2×C11×#344C211yesmaximal, characteristic, complemented
7C2×C11×#341C211yesmaximal, characteristic, complemented
8C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C11×#424—22no—
17C11×#424C2214yescomplemented
18C2×C11×C4⋊C8—22no—
19C11×#421—22no—
20C11×#421C2214yes—
21C2×C11×#104—22no—
22C11×#416—22no—
23C11×#416C2214yes—
24C2×C11×#103—21no—
25C2×C11×#102—21no—
26C11×#413—22no—
27C11×#413C2214yes—
28C2×C11×#101—21no—
29C2×C11×#100—21no—
30C11×#344C2214yescomplemented
31C11×#341C2214yescomplemented
32C11×H(3,ℤ/4)C2214yescomplemented
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41D412yes—
44C2×C11×#41C2312yes—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16—21no—
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16C2312yes—
66C2×C11×M16C2312yes—
67C2×C11×M16C2312yes—
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C22×C8×C11C2312yes—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117D412yes—
84C11×#117C2312yes—
85C11×#117C2312yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C42×C11—21no—
91C2×C42×C11D412yes—
92C11×C4⋊C8—28no—
93C11×#104—28no—
94C11×#103—24no—
95C11×#102—24no—
96C11×#101—24no—
97C11×#100—24no—
98C2×#2080C1111yesmaximal, characteristic, direct product factor, Sylow
99C24×C11—21no—
100C24×C11#4111yescharacteristic
101C11×#41—22no—
102C11×#41—22no—
103C11×#41—22no—
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—41no—
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11C2×D412yes—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C2×D4×C11—41no—
133C2×D4×C11—41no—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—41no—
140C22×C4×C11—41no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×C4×C11#4111yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—41no—
169C11×M16—41no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—41no—
177C2×C8×C11—41no—
178C2×C8×C11—41no—
179C2×C8×C11—41no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C2×C8×C11—41no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—41no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—41no—
194C42×C11—22no—
195C42×C11—22no—
196C42×C11—41no—
197C42×C11C2×D414yes—
198C2×#424C2×C1111yescharacteristic, complemented
199C2×#421C2×C1111yescharacteristic
200C2×#416C2×C1111yescharacteristic
201C2×#413C2×C1111yescharacteristic
202#2080C2×C1118yesdirect product factor
203C2×#344C2×C1111yescharacteristic, complemented
204C2×#341C2×C1111yescharacteristic, complemented
205C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
206C23×C11—22no—
207C23×C11—42no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—82no—
211C23×C11#12311yescharacteristic
212C23×C11#12311yescharacteristic
213C23×C11#12311yescharacteristic
214C23×C11#12311yescharacteristic
215C23×C11#12611yescharacteristic
216C23×C11#12611yescharacteristic
217C23×C11C2×#4111yescharacteristic
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—42no—
225D4×C11—42no—
226D4×C11—42no—
227D4×C11—42no—
228D4×C11—41no—
229D4×C11—41no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—44no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—82no—
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12311yescharacteristic
246C2×C4×C11#12311yescharacteristic
247C2×C4×C11#12311yescharacteristic
248C2×C4×C11#12311yescharacteristic
249C2×C4×C11#12311yescharacteristic
250C2×C4×C11#12311yescharacteristic
251C2×C4×C11#12311yescharacteristic
252C2×C4×C11#12311yescharacteristic
253C2×C4×C11#12411yescharacteristic
254C2×C4×C11#12411yescharacteristic
255C2×C4×C11#12411yescharacteristic
256C2×C4×C11#12411yescharacteristic
257C2×C4×C11#12611yescharacteristic
258C2×C4×C11#12611yescharacteristic
259C2×C4×C11#12611yescharacteristic
260C2×C4×C11#12611yescharacteristic
261C2×C4×C11#12611yescharacteristic
262C2×C4×C11#12611yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C8×C11—42no—
270C8×C11—42no—
271C8×C11—42no—
272C8×C11—42no—
273C22×#41C22×C1111yescharacteristic
274C22×M16C22×C1111yescharacteristic
275C22×M16C22×C1111yescharacteristic
276C22×M16C22×C1111yescharacteristic
277C23×C8C22×C1111yescharacteristic
278C2×#117C22×C1111yescharacteristic
279C2×#117C22×C1111yescharacteristic
280#424—22no—
281#424C22×C1114yescomplemented
282C2×C4⋊C8—22no—
283#421—22no—
284#421C22×C1114yes—
285C2×#104—22no—
286#416—22no—
287#416C22×C1114yes—
288C2×#103—21no—
289C2×#102—21no—
290#413—22no—
291#413C22×C1114yes—
292C2×#101—21no—
293C2×#100—21no—
294#344C22×C1114yescomplemented
295#341C22×C1114yescomplemented
296H(3,ℤ/4)C22×C1114yescomplemented
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—42no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—82no—
308C22×C11#39711yescharacteristic
309C22×C11#39711yescharacteristic
310C22×C11#39711yescharacteristic
311C22×C11#39711yescharacteristic
312C22×C11C2×#12311yescharacteristic
313C22×C11C2×#12311yescharacteristic
314C22×C11C2×#12611yescharacteristic
315C4×C11—44no—
316C4×C11—42no—
317C4×C11—82no—
318C4×C11#39711yescharacteristic
319C4×C11#39711yescharacteristic
320C4×C11#39711yescharacteristic
321C4×C11#39711yescharacteristic
322C4×C11C2×#12111yescharacteristic
323C4×C11C2×#12311yescharacteristic
324C4×C11C2×#12411yescharacteristic
325C4×C11C2×#12611yescharacteristic
326C2×#41—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41D4×C1112yes—
337C2×#41C23×C1112yes—
338C22×Q8D4×C1111yescharacteristic
339C22×D4—21no—
340C22×D4D4×C1111yescharacteristic
341C23×C4—21no—
342C23×C4C23×C1111yescharacteristic
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16C23×C1112yes—
359C2×M16C23×C1112yes—
360C2×M16C23×C1112yes—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8C23×C1112yes—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117D4×C1112yes—
377#117C23×C1112yes—
378#117C23×C1112yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C42—21no—
384C2×C42D4×C1112yes—
385C4⋊C8—28no—
386#104—28no—
387#103—24no—
388#102—24no—
389#101—24no—
390#100—24no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—82no—
398C2×C11#208012yesdirect product factor
399C2×C11C2×#39711yescharacteristic
400C24—21no—
401C24C11×#4111yescharacteristic
402#41—22no—
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—41no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8C2×D4×C1112yes—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4C2×D4×C1112yes—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4C2×D4×C1111yescharacteristic
446C22×C4C2×D4×C1111yescharacteristic
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C11×#4111yescharacteristic
450C22×C4C11×#4111yescharacteristic
451C22×C4C11×#4111yescharacteristic
452C22×C4C11×#4111yescharacteristic
453C22×C4C11×#4111yescharacteristic
454C22×C4C11×#4111yescharacteristic
455C22×C4C11×#4111yescharacteristic
456C22×C4C11×#4111yescharacteristic
457C22×C4C11×#4111yescharacteristic
458C22×C4C24×C1111yescharacteristic
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—41no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—41no—
495C42—22no—
496C42—22no—
497C42—41no—
498C42C2×D4×C1114yes—
499C11C2×#208011yescharacteristic, direct product factor, Sylow
500C23—22no—
501C23—42no—
502C23—41no—
503C23—41no—
504C23—82no—
505C23C11×#12311yescharacteristic
506C23C11×#12311yescharacteristic
507C23C11×#12311yescharacteristic
508C23C11×#12311yescharacteristic
509C23C11×#12611yescharacteristic
510C23C11×#12611yescharacteristic
511C23C2×C11×#4111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—41no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—82no—
535C2×C4C11×#12111yescharacteristic
536C2×C4C11×#12111yescharacteristic
537C2×C4C11×#12111yescharacteristic
538C2×C4C11×#12111yescharacteristic
539C2×C4C11×#12311yescharacteristic
540C2×C4C11×#12311yescharacteristic
541C2×C4C11×#12311yescharacteristic
542C2×C4C11×#12311yescharacteristic
543C2×C4C11×#12311yescharacteristic
544C2×C4C11×#12311yescharacteristic
545C2×C4C11×#12311yescharacteristic
546C2×C4C11×#12311yescharacteristic
547C2×C4C11×#12411yescharacteristic
548C2×C4C11×#12411yescharacteristic
549C2×C4C11×#12411yescharacteristic
550C2×C4C11×#12411yescharacteristic
551C2×C4C11×#12611yescharacteristic
552C2×C4C11×#12611yescharacteristic
553C2×C4C11×#12611yescharacteristic
554C2×C4C11×#12611yescharacteristic
555C2×C4C11×#12611yescharacteristic
556C2×C4C11×#12611yescharacteristic
557C2×C4C22×D4×C1111yescharacteristic
558C2×C4C22×D4×C1111yescharacteristic
559C2×C4C2×C11×#4111yescharacteristic
560C2×C4C2×C11×#4111yescharacteristic
561C2×C4C2×C11×#4111yescharacteristic
562C2×C4C2×C11×#4111yescharacteristic
563C8—42no—
564C8—42no—
565C8—42no—
566C8—42no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22C11×#39711yescharacteristic
579C22C11×#39711yescharacteristic
580C22C11×#39711yescharacteristic
581C22C11×#39711yescharacteristic
582C22C2×C11×#12311yescharacteristic
583C22C2×C11×#12311yescharacteristic
584C22C2×C11×#12611yescharacteristic
585C4—44no—
586C4—42no—
587C4—82no—
588C4C11×#39711yescharacteristic
589C4C11×#39711yescharacteristic
590C4C11×#39711yescharacteristic
591C4C11×#39711yescharacteristic
592C4C2×C11×#12111yescharacteristic
593C4C2×C11×#12311yescharacteristic
594C4C2×C11×#12411yescharacteristic
595C4C2×C11×#12611yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—82no—
603C2C11×#208012yesdirect product factor
604C2C2×C11×#39711yescharacteristic
subgroupG/H
centerC2×C4×C11#124
commutator, Frattini, cosocleC22×C4C24×C11
socleC22×C11#397
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#424C2semidirect
5. C11×#2080C2direct (N × H)
6. C2×C11×#344C2semidirect
7. C2×C11×#341C2semidirect
8. C2×C11×H(3,ℤ/4)C2semidirect
17. C11×#424C22semidirect
30. C11×#344C22semidirect
31. C11×#341C22semidirect
32. C11×H(3,ℤ/4)C22semidirect
98. C2×#2080C11direct (N × H)
198. C2×#424C2×C11semidirect
202. #2080C2×C11direct (N × H)
203. C2×#344C2×C11semidirect
204. C2×#341C2×C11semidirect
205. C2×H(3,ℤ/4)C2×C11semidirect
281. #424C22×C11semidirect
294. #344C22×C11semidirect
295. #341C22×C11semidirect
296. H(3,ℤ/4)C22×C11semidirect
398. C2×C11#2080direct (N × H)
499. C11C2×#2080direct (N × H)
603. C2C11×#2080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4242
C2×C11×#4212
C2×C11×#4162
C2×C11×#4132
C11×#20802
C2×C11×#3442
C2×C11×#3412
C2×C11×H(3,ℤ/4)2
C2×#208011