Finite Group Databasebeta

← C11×#23652 #14600845

Subgroups — C11×#23652 #14600845

Order 2816.

888 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#430C211yesmaximal, characteristic, complemented
2C11×#2896C211yesmaximal, characteristic
3C11×#2896C211yesmaximal, characteristic
4C2×C11×#413C211yesmaximal, characteristic
5C11×#2082C214yesmaximal, complemented
6C11×#2081C214yesmaximal, complemented
7C2×C11×#344C211yesmaximal, characteristic, complemented
8C2×C11×#344C211yesmaximal, characteristic, complemented
9C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C11×#430—22no—
18C11×#430C2214yes—
19C2×C11×#108—22no—
20C11×#419C2212yes—
21C11×#419C2212yes—
22C11×#418C2212yes—
23C11×#418C2212yes—
24C11×#417—22no—
25C11×#417—22no—
26C11×#416—22no—
27C11×#416—22no—
28C11×#413—22no—
29C11×#413—22no—
30C2×C11×#101C2212yes—
31C2×C11×#100C2212yes—
32C11×#344C2214yes—
33C11×#344C2214yes—
34C11×H(3,ℤ/4)C2214yes—
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×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41D412yes—
46C2×C11×#41D412yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
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×M16—21no—
66C2×C11×M16—21no—
67C2×C11×M16—21no—
68C2×C11×M16—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16D412yes—
72C2×C11×M16C2312yes—
73C2×C11×M16C2312yes—
74C2×C11×M16C2312yes—
75C2×C11×M16C2312yes—
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C22×C8×C11—21no—
79C22×C8×C11D412yes—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117—21no—
84C11×#117—21no—
85C11×#117—21no—
86C11×#117C2312yes—
87C11×#117C2312yes—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C42×C11—21no—
93C2×C42×C11—21no—
94C11×#108—28no—
95C11×#103—24no—
96C11×#103—24no—
97C11×#102—24no—
98C11×#102—24no—
99C11×#101—24no—
100C11×#100—24no—
101#23652C1111yesmaximal, characteristic, direct product factor, Sylow
102C24×C11—21no—
103C24×C11#4111yescharacteristic
104C11×#41—22no—
105C11×#41—22no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—22no—
110C11×#41—22no—
111C11×#41—22no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C11×#41—41no—
118C11×#41—41no—
119C11×#41—41no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11C2×D412yes—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—41no—
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
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×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—22no—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—22no—
170C11×M16—22no—
171C11×M16—41no—
172C11×M16—41no—
173C11×M16—41no—
174C11×M16—41no—
175C11×M16—41no—
176C11×M16—41no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C2×C8×C11—41no—
185C2×C8×C11—41no—
186C2×C8×C11—41no—
187C2×C8×C11—41no—
188C2×C8×C11C2×D414yes—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—41no—
196C11×C22⋊C4—41no—
197C42×C11—22no—
198C42×C11—22no—
199C42×C11—41no—
200C42×C11—41no—
201C2×#430C2×C1111yescharacteristic, complemented
202#2896C2×C1111yescharacteristic
203#2896C2×C1111yescharacteristic
204C2×#413C2×C1111yescharacteristic
205#2082C2×C1114yescomplemented
206#2081C2×C1114yescomplemented
207C2×#344C2×C1111yescharacteristic, complemented
208C2×#344C2×C1111yescharacteristic, complemented
209C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
210C23×C11—22no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—81no—
214C23×C11—82no—
215C23×C11#12311yescharacteristic
216C23×C11#12311yescharacteristic
217C23×C11#12411yescharacteristic
218C23×C11#12411yescharacteristic
219C23×C11#12611yescharacteristic
220C23×C11#12611yescharacteristic
221C23×C11C2×#4111yescharacteristic
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11—41no—
225Q8×C11—41no—
226D4×C11—22no—
227D4×C11—22no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232D4×C11—41no—
233D4×C11—41no—
234C2×C4×C11—22no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—82no—
244C2×C4×C11—82no—
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12311yescharacteristic
250C2×C4×C11#12311yescharacteristic
251C2×C4×C11#12311yescharacteristic
252C2×C4×C11#12311yescharacteristic
253C2×C4×C11#12311yescharacteristic
254C2×C4×C11#12311yescharacteristic
255C2×C4×C11#12311yescharacteristic
256C2×C4×C11#12311yescharacteristic
257C2×C4×C11#12311yescharacteristic
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12411yescharacteristic
260C2×C4×C11#12411yescharacteristic
261C2×C4×C11#12611yescharacteristic
262C2×C4×C11#12611yescharacteristic
263C2×C4×C11#12611yescharacteristic
264C2×C4×C11#12611yescharacteristic
265C2×C4×C11#12611yescharacteristic
266C2×C4×C11#12611yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C8×C11—24no—
274C8×C11—42no—
275C8×C11—42no—
276C8×C11—42no—
277C22×#41C22×C1111yescharacteristic
278C22×M16C22×C1111yescharacteristic
279C22×M16C22×C1111yescharacteristic
280C22×M16C22×C1111yescharacteristic
281C22×M16C22×C1111yescharacteristic
282C2×#117C22×C1111yescharacteristic
283C2×#117C22×C1111yescharacteristic
284#430—22no—
285#430C22×C1114yes—
286C2×#108—22no—
287#419C22×C1112yes—
288#419C22×C1112yes—
289#418C22×C1112yes—
290#418C22×C1112yes—
291#417—22no—
292#417—22no—
293#416—22no—
294#416—22no—
295#413—22no—
296#413—22no—
297C2×#101C22×C1112yes—
298C2×#100C22×C1112yes—
299#344C22×C1114yes—
300#344C22×C1114yes—
301H(3,ℤ/4)C22×C1114yes—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—41no—
308C22×C11—41no—
309C22×C11—42no—
310C22×C11—82no—
311C22×C11—82no—
312C22×C11—82no—
313C22×C11#39711yescharacteristic
314C22×C11#39711yescharacteristic
315C22×C11#39711yescharacteristic
316C22×C11#39711yescharacteristic
317C22×C11C2×#12311yescharacteristic
318C22×C11C2×#12411yescharacteristic
319C22×C11C2×#12611yescharacteristic
320C4×C11—42no—
321C4×C11—82no—
322C4×C11—82no—
323C4×C11#39711yescharacteristic
324C4×C11#39711yescharacteristic
325C4×C11#39711yescharacteristic
326C4×C11#39711yescharacteristic
327C4×C11C2×#12111yescharacteristic
328C4×C11C2×#12311yescharacteristic
329C4×C11C2×#12311yescharacteristic
330C4×C11C2×#12611yescharacteristic
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41D4×C1112yes—
342C2×#41D4×C1112yes—
343C22×Q8C23×C1111yescharacteristic
344C22×D4—21no—
345C22×D4C23×C1111yescharacteristic
346C23×C4—21no—
347C23×C4C23×C1111yescharacteristic
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×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16D4×C1112yes—
368C2×M16C23×C1112yes—
369C2×M16C23×C1112yes—
370C2×M16C23×C1112yes—
371C2×M16C23×C1112yes—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8D4×C1112yes—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117C23×C1112yes—
383#117C23×C1112yes—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C42—21no—
389C2×C42—21no—
390#108—28no—
391#103—24no—
392#103—24no—
393#102—24no—
394#102—24no—
395#101—24no—
396#100—24no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—21no—
403C2×C11—21no—
404C2×C11—82no—
405C2×C11C2×#39711yescharacteristic
406C24—21no—
407C24C11×#4111yescharacteristic
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—22no—
415#41—22no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422#41—41no—
423#41—41no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8C2×D4×C1112yes—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4C2×D4×C1112yes—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4C2×D4×C1111yescharacteristic
452C22×C4C2×D4×C1111yescharacteristic
453C22×C4C2×D4×C1111yescharacteristic
454C22×C4C2×D4×C1111yescharacteristic
455C22×C4C11×#4111yescharacteristic
456C22×C4C11×#4111yescharacteristic
457C22×C4C11×#4111yescharacteristic
458C22×C4C11×#4111yescharacteristic
459C22×C4C11×#4111yescharacteristic
460C22×C4C11×#4111yescharacteristic
461C22×C4C11×#4111yescharacteristic
462C22×C4C11×#4111yescharacteristic
463C22×C4C11×#4111yescharacteristic
464C22×C4C24×C1111yescharacteristic
465M16—22no—
466M16—22no—
467M16—22no—
468M16—22no—
469M16—22no—
470M16—22no—
471M16—22no—
472M16—22no—
473M16—22no—
474M16—22no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16—41no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8C2×D4×C1114yes—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C42—22no—
502C42—22no—
503C42—41no—
504C42—41no—
505C11#2365211yescharacteristic, direct product factor, Sylow
506C23—22no—
507C23—41no—
508C23—41no—
509C23—81no—
510C23—82no—
511C23C11×#12311yescharacteristic
512C23C11×#12311yescharacteristic
513C23C11×#12411yescharacteristic
514C23C11×#12411yescharacteristic
515C23C11×#12611yescharacteristic
516C23C11×#12611yescharacteristic
517C23C2×C11×#4111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522D4—22no—
523D4—22no—
524D4—42no—
525D4—42no—
526D4—42no—
527D4—42no—
528D4—41no—
529D4—41no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4C11×#12111yescharacteristic
542C2×C4C11×#12111yescharacteristic
543C2×C4C11×#12111yescharacteristic
544C2×C4C11×#12111yescharacteristic
545C2×C4C11×#12311yescharacteristic
546C2×C4C11×#12311yescharacteristic
547C2×C4C11×#12311yescharacteristic
548C2×C4C11×#12311yescharacteristic
549C2×C4C11×#12311yescharacteristic
550C2×C4C11×#12311yescharacteristic
551C2×C4C11×#12311yescharacteristic
552C2×C4C11×#12311yescharacteristic
553C2×C4C11×#12311yescharacteristic
554C2×C4C11×#12311yescharacteristic
555C2×C4C11×#12411yescharacteristic
556C2×C4C11×#12411yescharacteristic
557C2×C4C11×#12611yescharacteristic
558C2×C4C11×#12611yescharacteristic
559C2×C4C11×#12611yescharacteristic
560C2×C4C11×#12611yescharacteristic
561C2×C4C11×#12611yescharacteristic
562C2×C4C11×#12611yescharacteristic
563C2×C4C22×D4×C1111yescharacteristic
564C2×C4C22×D4×C1111yescharacteristic
565C2×C4C2×C11×#4111yescharacteristic
566C2×C4C2×C11×#4111yescharacteristic
567C2×C4C2×C11×#4111yescharacteristic
568C2×C4C2×C11×#4111yescharacteristic
569C8—24no—
570C8—42no—
571C8—42no—
572C8—42no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22C11×#39711yescharacteristic
585C22C11×#39711yescharacteristic
586C22C11×#39711yescharacteristic
587C22C11×#39711yescharacteristic
588C22C2×C11×#12311yescharacteristic
589C22C2×C11×#12411yescharacteristic
590C22C2×C11×#12611yescharacteristic
591C4—42no—
592C4—82no—
593C4—82no—
594C4C11×#39711yescharacteristic
595C4C11×#39711yescharacteristic
596C4C11×#39711yescharacteristic
597C4C11×#39711yescharacteristic
598C4C2×C11×#12111yescharacteristic
599C4C2×C11×#12311yescharacteristic
600C4C2×C11×#12311yescharacteristic
601C4C2×C11×#12611yescharacteristic
602C2—21no—
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—82no—
610C2C2×C11×#39711yescharacteristic
subgroupG/H
centerC4×C11#397
commutator, Frattini, cosocleC22×C4C24×C11
socleC2×C11C2×#397
prime radicalC22×C11×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#430C2semidirect
5. C11×#2082C2semidirect
6. C11×#2081C2semidirect
7. C2×C11×#344C2semidirect
8. C2×C11×#344C2semidirect
9. C2×C11×H(3,ℤ/4)C2semidirect
101. #23652C11direct (N × H)
201. C2×#430C2×C11semidirect
205. #2082C2×C11semidirect
206. #2081C2×C11semidirect
207. C2×#344C2×C11semidirect
208. C2×#344C2×C11semidirect
209. C2×H(3,ℤ/4)C2×C11semidirect
505. C11#23652direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4302
C11×#28962
C2×C11×#4132
C11×#20822
C11×#20812
C2×C11×#3442
C2×C11×H(3,ℤ/4)2
#2365211