Finite Group Databasebeta

← C11×#23472 #14600665

Subgroups — C11×#23472 #14600665

Order 2816.

1148 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3458C211yesmaximal, characteristic, complemented
2C2×C11×#421C211yesmaximal, characteristic
3C2×C11×#421C211yesmaximal, characteristic
4C2×C11×#410C211yesmaximal, characteristic
5C11×#2031C218yesmaximal, complemented
6C2×C11×#344C211yesmaximal, characteristic, complemented
7C11×#1733C211yesmaximal, characteristic, complemented
8C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×C11×#41C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C11×#544—22no—
13C11×#544—22no—
14C11×#544—22no—
15C11×#543—22no—
16C11×#533—22no—
17C11×#533—22no—
18C11×#533C2214yescomplemented
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C11×#421—22no—
24C11×#421—22no—
25C11×#421—22no—
26C11×#421C2214yes—
27C2×C11×#104—22no—
28C2×C11×#104C2214yes—
29C11×#410—22no—
30C11×#410C2214yes—
31C2×C11×#99—22no—
32C11×#344C2214yescomplemented
33C11×#339C2214yescomplemented
34C11×H(3,ℤ/4)C2214yescomplemented
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×#41Q812yescomplemented
46C2×C11×#41C2312yes—
47C22×Q8×C11Q811yescharacteristic, complemented
48C22×D4×C11—21no—
49C22×D4×C11Q811yescharacteristic, complemented
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×M16C2312yes—
63C2×C11×M16C2312yes—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C11×C4⋊Q8—24no—
67C11×C4⋊Q8—24no—
68C11×C4⋊Q8—24no—
69C11×#125—24no—
70C11×#125—24no—
71C11×#125—24no—
72C11×C22⋊Q8—28no—
73C11×C22⋊Q8—28no—
74C11×C22⋊Q8—28no—
75C4×Q8×C11—28no—
76C11×#117—21no—
77C11×#117—21no—
78C11×#117—21no—
79C11×#117—21no—
80C11×#117—21no—
81C11×#117—21no—
82C11×#117—21no—
83C11×#117—21no—
84C11×#117—21no—
85C11×#117D412yes—
86C11×#117D412yes—
87C11×#117D412yes—
88C11×#117D412yes—
89C11×#117C2312yes—
90C11×#117C2312yes—
91C11×#117C2312yes—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4D412yes—
100C2×C42×C11—21no—
101C2×C42×C11—21no—
102C2×C42×C11D412yes—
103C2×C42×C11C2312yes—
104C11×#104—28no—
105C11×#104—28no—
106C11×#99—28no—
107#23472C1111yesmaximal, characteristic, direct product factor, Sylow
108C24×C11—21no—
109C24×C11C2×D411yescharacteristic
110C11×#41—22no—
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—22no—
114C11×#41—22no—
115C11×#41—22no—
116C11×#41—22no—
117C11×#41—22no—
118C11×#41—41no—
119C11×#41—41no—
120C11×#41—41no—
121C11×#41—41no—
122C11×#41—41no—
123C11×#41—41no—
124C11×#41—41no—
125C11×#41—41no—
126C2×Q8×C11—28no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C2×Q812yes—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11C2×Q812yes—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×Q811yescharacteristic
162C22×C4×C11C2×Q811yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11#4111yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—22no—
174C11×M16—41no—
175C11×M16—41no—
176C11×M16—41no—
177C11×M16—41no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C11×C4⋊C4—28no—
185C11×C4⋊C4—28no—
186C11×C4⋊C4—28no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—41no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4C2×D414yes—
203C42×C11—22no—
204C42×C11—22no—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11—22no—
208C42×C11—41no—
209C42×C11C2×D414yes—
210C42×C11C2×D414yes—
211#3458C2×C1111yescharacteristic, complemented
212C2×#421C2×C1111yescharacteristic
213C2×#421C2×C1111yescharacteristic
214C2×#410C2×C1111yescharacteristic
215#2031C2×C1118yescomplemented
216C2×#344C2×C1111yescharacteristic, complemented
217#1733C2×C1111yescharacteristic, complemented
218C2×H(3,ℤ/4)C2×C1111yescharacteristic, complemented
219C23×C11—22no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—81no—
223C23×C11—82no—
224C23×C11#12011yescharacteristic
225C23×C11#12011yescharacteristic
226C23×C11C22⋊Q811yescharacteristic
227C23×C11C22⋊Q811yescharacteristic
228C23×C11#12411yescharacteristic
229C23×C11#12411yescharacteristic
230C23×C11C22×D411yescharacteristic
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—88no—
236D4×C11—22no—
237D4×C11—22no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—42no—
242D4×C11—41no—
243D4×C11—41no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—82no—
256C2×C4×C11—82no—
257C2×C4×C11—82no—
258C2×C4×C11—82no—
259C2×C4×C11#12011yescharacteristic
260C2×C4×C11#12011yescharacteristic
261C2×C4×C11C22⋊Q811yescharacteristic
262C2×C4×C11C22⋊Q811yescharacteristic
263C2×C4×C11C22⋊Q811yescharacteristic
264C2×C4×C11C22⋊Q811yescharacteristic
265C2×C4×C11C22⋊Q811yescharacteristic
266C2×C4×C11C22⋊Q811yescharacteristic
267C2×C4×C11C22⋊Q811yescharacteristic
268C2×C4×C11C22⋊Q811yescharacteristic
269C2×C4×C11C22⋊Q811yescharacteristic
270C2×C4×C11C22⋊Q811yescharacteristic
271C2×C4×C11#12411yescharacteristic
272C2×C4×C11#12411yescharacteristic
273C2×C4×C11#12411yescharacteristic
274C2×C4×C11#12411yescharacteristic
275C2×C4×C11#12411yescharacteristic
276C2×C4×C11#12411yescharacteristic
277C2×C4×C11#12411yescharacteristic
278C2×C4×C11#12411yescharacteristic
279C2×C4×C11#12411yescharacteristic
280C2×C4×C11#12411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×Q811yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C8×C11—42no—
288C8×C11—42no—
289C22×#41C22×C1111yescharacteristic
290C22×M16C22×C1111yescharacteristic
291C22×M16C22×C1111yescharacteristic
292#544—22no—
293#544—22no—
294#544—22no—
295#543—22no—
296#533—22no—
297#533—22no—
298#533C22×C1114yescomplemented
299C2×#117C22×C1111yescharacteristic
300C2×#117C22×C1111yescharacteristic
301C2×#117C22×C1111yescharacteristic
302C2×#117C22×C1111yescharacteristic
303#421—22no—
304#421—22no—
305#421—22no—
306#421C22×C1114yes—
307C2×#104—22no—
308C2×#104C22×C1114yes—
309#410—22no—
310#410C22×C1114yes—
311C2×#99—22no—
312#344C22×C1114yescomplemented
313#339C22×C1114yescomplemented
314H(3,ℤ/4)C22×C1114yescomplemented
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—42no—
323C22×C11—82no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11#39311yescharacteristic
327C22×C11#39311yescharacteristic
328C22×C11#39311yescharacteristic
329C22×C11#39311yescharacteristic
330C22×C11C2×#12011yescharacteristic
331C22×C11C2×C22⋊Q811yescharacteristic
332C22×C11C2×#12411yescharacteristic
333C4×C11—44no—
334C4×C11—44no—
335C4×C11—44no—
336C4×C11—42no—
337C4×C11—82no—
338C4×C11#39311yescharacteristic
339C4×C11#39311yescharacteristic
340C4×C11#39311yescharacteristic
341C4×C11#39311yescharacteristic
342C4×C11C2×C22⋊Q811yescharacteristic
343C4×C11C2×C22⋊Q811yescharacteristic
344C4×C11C2×#12411yescharacteristic
345C4×C11C2×#12411yescharacteristic
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41Q8×C1112yescomplemented
357C2×#41C23×C1112yes—
358C22×Q8Q8×C1111yescharacteristic, complemented
359C22×D4—21no—
360C22×D4Q8×C1111yescharacteristic, complemented
361C23×C4—21no—
362C23×C4C23×C1111yescharacteristic
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16C23×C1112yes—
374C2×M16C23×C1112yes—
375C22×C8—21no—
376C22×C8—21no—
377C4⋊Q8—24no—
378C4⋊Q8—24no—
379C4⋊Q8—24no—
380#125—24no—
381#125—24no—
382#125—24no—
383C22⋊Q8—28no—
384C22⋊Q8—28no—
385C22⋊Q8—28no—
386C4×Q8—28no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117D4×C1112yes—
397#117D4×C1112yes—
398#117D4×C1112yes—
399#117D4×C1112yes—
400#117C23×C1112yes—
401#117C23×C1112yes—
402#117C23×C1112yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4D4×C1112yes—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42D4×C1112yes—
414C2×C42C23×C1112yes—
415#104—28no—
416#104—28no—
417#99—28no—
418C2×C11—21no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11—21no—
424C2×C11—21no—
425C2×C11—82no—
426C2×C11C2×#39311yescharacteristic
427C24—21no—
428C24C2×D4×C1111yescharacteristic
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—22no—
436#41—22no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443#41—41no—
444#41—41no—
445C2×Q8—28no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×Q8×C1112yes—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C2×Q8×C1112yes—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4C2×D4×C1111yescharacteristic
476C22×C4C2×D4×C1111yescharacteristic
477C22×C4C2×D4×C1111yescharacteristic
478C22×C4C2×D4×C1111yescharacteristic
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×Q8×C1111yescharacteristic
481C22×C4C2×Q8×C1111yescharacteristic
482C22×C4C11×#4111yescharacteristic
483C22×C4C11×#4111yescharacteristic
484C22×C4C11×#4111yescharacteristic
485C22×C4C11×#4111yescharacteristic
486C22×C4C11×#4111yescharacteristic
487C22×C4C11×#4111yescharacteristic
488C22×C4C24×C1111yescharacteristic
489M16—22no—
490M16—22no—
491M16—22no—
492M16—22no—
493M16—41no—
494M16—41no—
495M16—41no—
496M16—41no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C4⋊C4—28no—
504C4⋊C4—28no—
505C4⋊C4—28no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—41no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—41no—
521C22⋊C4C2×D4×C1114yes—
522C42—22no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—22no—
527C42—41no—
528C42C2×D4×C1114yes—
529C42C2×D4×C1114yes—
530C11#2347211yescharacteristic, direct product factor, Sylow
531C23—22no—
532C23—41no—
533C23—41no—
534C23—81no—
535C23—82no—
536C23C11×#12011yescharacteristic
537C23C11×#12011yescharacteristic
538C23C11×C22⋊Q811yescharacteristic
539C23C11×C22⋊Q811yescharacteristic
540C23C11×#12411yescharacteristic
541C23C11×#12411yescharacteristic
542C23C22×D4×C1111yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—41no—
546Q8—41no—
547Q8—88no—
548D4—22no—
549D4—22no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—41no—
555D4—41no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—82no—
568C2×C4—82no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4C11×#12011yescharacteristic
572C2×C4C11×#12011yescharacteristic
573C2×C4C11×C22⋊Q811yescharacteristic
574C2×C4C11×C22⋊Q811yescharacteristic
575C2×C4C11×C22⋊Q811yescharacteristic
576C2×C4C11×C22⋊Q811yescharacteristic
577C2×C4C11×C22⋊Q811yescharacteristic
578C2×C4C11×C22⋊Q811yescharacteristic
579C2×C4C11×C22⋊Q811yescharacteristic
580C2×C4C11×C22⋊Q811yescharacteristic
581C2×C4C11×C22⋊Q811yescharacteristic
582C2×C4C11×C22⋊Q811yescharacteristic
583C2×C4C11×#12411yescharacteristic
584C2×C4C11×#12411yescharacteristic
585C2×C4C11×#12411yescharacteristic
586C2×C4C11×#12411yescharacteristic
587C2×C4C11×#12411yescharacteristic
588C2×C4C11×#12411yescharacteristic
589C2×C4C11×#12411yescharacteristic
590C2×C4C11×#12411yescharacteristic
591C2×C4C11×#12411yescharacteristic
592C2×C4C11×#12411yescharacteristic
593C2×C4C22×D4×C1111yescharacteristic
594C2×C4C22×D4×C1111yescharacteristic
595C2×C4C22×Q8×C1111yescharacteristic
596C2×C4C2×C11×#4111yescharacteristic
597C2×C4C2×C11×#4111yescharacteristic
598C2×C4C2×C11×#4111yescharacteristic
599C8—42no—
600C8—42no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22C11×#39311yescharacteristic
613C22C11×#39311yescharacteristic
614C22C11×#39311yescharacteristic
615C22C11×#39311yescharacteristic
616C22C2×C11×#12011yescharacteristic
617C22C2×C11×C22⋊Q811yescharacteristic
618C22C2×C11×#12411yescharacteristic
619C4—44no—
620C4—44no—
621C4—44no—
622C4—42no—
623C4—82no—
624C4C11×#39311yescharacteristic
625C4C11×#39311yescharacteristic
626C4C11×#39311yescharacteristic
627C4C11×#39311yescharacteristic
628C4C2×C11×C22⋊Q811yescharacteristic
629C4C2×C11×C22⋊Q811yescharacteristic
630C4C2×C11×#12411yescharacteristic
631C4C2×C11×#12411yescharacteristic
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—82no—
640C2C2×C11×#39311yescharacteristic
subgroupG/H
centerC4×C11C2×#124
commutator, Frattini, cosocleC22×C4C24×C11
socleC2×C11C2×#393
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. C11×#3458C2semidirect
5. C11×#2031C2semidirect
6. C2×C11×#344C2semidirect
7. C11×#1733C2semidirect
8. C2×C11×H(3,ℤ/4)C2semidirect
18. C11×#533C22semidirect
32. C11×#344C22semidirect
33. C11×#339C22semidirect
34. C11×H(3,ℤ/4)C22semidirect
45. C2×C11×#41Q8semidirect
47. C22×Q8×C11Q8semidirect
49. C22×D4×C11Q8semidirect
107. #23472C11direct (N × H)
211. #3458C2×C11semidirect
215. #2031C2×C11semidirect
216. C2×#344C2×C11semidirect
217. #1733C2×C11semidirect
218. C2×H(3,ℤ/4)C2×C11semidirect
298. #533C22×C11semidirect
312. #344C22×C11semidirect
313. #339C22×C11semidirect
314. H(3,ℤ/4)C22×C11semidirect
356. C2×#41Q8×C11semidirect
358. C22×Q8Q8×C11semidirect
360. C22×D4Q8×C11semidirect
530. C11#23472direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34582
C2×C11×#4212
C2×C11×#4102
C11×#20312
C2×C11×#3442
C11×#17332
C2×C11×H(3,ℤ/4)2
#2347211