Finite Group Databasebeta

← C11×#24321 #14601514

Subgroups — C11×#24321 #14601514

Order 2816.

1036 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3503C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C4×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C11×#2563C211yesmaximal, characteristic, complemented
5C11×#2061C212yesmaximal, complemented
6C11×#2027C212yesmaximal, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C11×#1986C211yesmaximal, characteristic, complemented
9C11×#1883C212yesmaximal
10C11×#1860C212yesmaximal, complemented
11C11×#1806C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2211yescharacteristic
13Q82×C11—21no—
14C11×#557—21no—
15C11×#554—21no—
16C11×#554—22no—
17D4×Q8×C11—22no—
18D4×Q8×C11—21no—
19C11×#544—22no—
20C11×#544C2212yes—
21C11×#533—21no—
22C11×#533C2211yescharacteristic
23C2×C11×C4⋊Q8—21no—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C11×#520C2212yes—
26C4×C11×#41C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C11×#478—22no—
29C11×#476—21no—
30C11×#474—21no—
31C11×#442—21no—
32C11×#440—21no—
33C4×C11×SD16—21no—
34C4×C11×D8—21no—
35C11×#428C2211yescharacteristic
36C11×#428C2212yes—
37C11×#423C2211yescharacteristic
38C2×C11×#104C2212yes—
39C11×#418C2212yes—
40C11×#418C2211yescharacteristic
41C11×#417C2211yescharacteristic
42C4×C11×M16C2211yescharacteristic
43C11×#393—22no—
44C11×#390C2212yes—
45C11×#382C2212yes—
46C11×#380—22no—
47C4×C11×C4⋊C4C2211yescharacteristic
48C11×#343C2212yes—
49C11×#343C2212yes—
50C11×#339C2212yes—
51C11×#339C2212yes—
52C11×#339C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11D412yes—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C11×AGL(1,ℤ/8)—22no—
59C11×AGL(1,ℤ/8)Q814yescomplemented
60C2×C11×SD16—21no—
61C2×C11×D8—21no—
62C2×C11×M16C2311yescharacteristic
63C2×C11×M16C2312yes—
64C2×C11×M16C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—24no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8D411yescharacteristic
75C11×C4⋊Q8D411yescharacteristic
76C11×#125—24no—
77C11×#125—22no—
78C11×#125—22no—
79C11×#125D412yes—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—24no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—24no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11D411yescharacteristic
93C4×Q8×C11D411yescharacteristic
94C4×D4×C11—22no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—24no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11D411yescharacteristic
103C4×D4×C11D411yescharacteristic
104C11×#117—22no—
105C11×#117—21no—
106C11×#117C2311yescharacteristic
107C11×#117C2312yes—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D412yes—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—24no—
116C2×C42×C11—21no—
117C2×C42×C11C2312yes—
118C2×C42×C11C2311yescharacteristic
119C11×#107—21no—
120C11×#107—22no—
121C11×#106—21no—
122C11×#106—22no—
123C11×C4⋊C8—21no—
124C11×C4⋊C8—21no—
125C11×#104—24no—
126C11×#103—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—22no—
131C11×#102—22no—
132C11×#97—21no—
133C4×C8×C11—21no—
134C11×#95—21no—
135C11×#95—24no—
136#24321C1111yesmaximal, characteristic, direct product factor, Sylow
137C24×C11—21no—
138C11×#41—21no—
139C11×#41—21no—
140C11×#41C2×Q812yes—
141C11×#41#4112yes—
142C2×Q8×C11—24no—
143C2×Q8×C11—21no—
144C2×Q8×C11—22no—
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—82no—
148C2×Q8×C11—84no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11C2×D411yescharacteristic
157C2×D4×C11C2×Q812yescomplemented
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—44no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C11×SD16—24no—
172C11×D8—24no—
173C11×M16—21no—
174C11×M16—22no—
175C11×M16—21no—
176C11×M16—22no—
177C11×M16—21no—
178C11×M16C2×Q812yescomplemented
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—22no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4C2×D412yes—
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D412yes—
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C22⋊C4—24no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—21no—
208C11×C22⋊C4—41no—
209C11×C22⋊C4—41no—
210C11×C22⋊C4—84no—
211C42×C11—24no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—22no—
216C42×C11—22no—
217C42×C11—22no—
218C42×C11C2×D411yescharacteristic
219C42×C11C2×D411yescharacteristic
220C42×C11C2×D411yescharacteristic
221C42×C11C2×D411yescharacteristic
222#3503C2×C1111yescharacteristic, complemented
223#3077C2×C1111yescharacteristic, complemented
224C4×AGL(1,ℤ/8)C2×C1111yescharacteristic
225#2563C2×C1111yescharacteristic, complemented
226#2061C2×C1112yescomplemented
227#2027C2×C1112yescomplemented
228#1997C2×C1111yescharacteristic, complemented
229#1986C2×C1111yescharacteristic, complemented
230#1883C2×C1112yes—
231#1860C2×C1112yescomplemented
232#1806C2×C1111yescharacteristic, complemented
233C23×C11—21no—
234C23×C11—22no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C22×D411yescharacteristic
240Q8×C11—21no—
241Q8×C11—44no—
242Q8×C11—42no—
243Q8×C11—42no—
244Q8×C11—82no—
245Q8×C11—84no—
246Q8×C11C22⋊Q812yes—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—21no—
251D4×C11—22no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11C22⋊Q812yes—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—44no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—82no—
274C2×C4×C11—84no—
275C2×C4×C11—82no—
276C2×C4×C11#12011yescharacteristic
277C2×C4×C11#12011yescharacteristic
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×Q811yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C2×C4×C112−1+411yescharacteristic
286C8×C11—22no—
287C8×C11—41no—
288C8×C11—42no—
289C2×AGL(1,ℤ/8)C22×C1111yescharacteristic
290Q82—21no—
291#557—21no—
292#554—21no—
293#554—22no—
294D4×Q8—22no—
295D4×Q8—21no—
296#544—22no—
297#544C22×C1112yes—
298#533—21no—
299#533C22×C1111yescharacteristic
300C2×C4⋊Q8—21no—
301C2×C4⋊Q8C22×C1111yescharacteristic
302#520C22×C1112yes—
303C4×#41C22×C1111yescharacteristic
304C2×C4×D4C22×C1111yescharacteristic
305#478—22no—
306#476—21no—
307#474—21no—
308#442—21no—
309#440—21no—
310C4×SD16—21no—
311C4×D8—21no—
312#428C22×C1112yes—
313#428C22×C1111yescharacteristic
314#423C22×C1111yescharacteristic
315C2×#104C22×C1112yes—
316#418C22×C1112yes—
317#418C22×C1111yescharacteristic
318#417C22×C1111yescharacteristic
319C4×M16C22×C1111yescharacteristic
320#393—22no—
321#390C22×C1112yes—
322#382C22×C1112yes—
323#380—22no—
324C4×C4⋊C4C22×C1111yescharacteristic
325#343C22×C1112yes—
326#343C22×C1112yes—
327#339C22×C1112yes—
328#339C22×C1112yes—
329#339C22×C1112yes—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—22no—
333C22×C11—44no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—42no—
337C22×C11—82no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11C2×#12011yescharacteristic
341C22×C11#54811yescharacteristic
342C22×C11D4×Q811yescharacteristic
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—41no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11—82no—
353C4×C11—81no—
354C4×C11#45412yes—
355C4×C11C2×C22⋊Q811yescharacteristic
356C4×C11#53611yescharacteristic
357C4×C11#54811yescharacteristic
358C4×C11D4×Q811yescharacteristic
359C2×#41C23×C1111yescharacteristic
360C22×Q8—22no—
361C22×Q8D4×C1112yes—
362C22×D4C23×C1111yescharacteristic
363C23×C4—21no—
364AGL(1,ℤ/8)—22no—
365AGL(1,ℤ/8)Q8×C1114yescomplemented
366C2×SD16—21no—
367C2×D8—21no—
368C2×M16C23×C1111yescharacteristic
369C2×M16C23×C1112yes—
370C2×M16C23×C1111yescharacteristic
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373C4⋊Q8—24no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380C4⋊Q8D4×C1111yescharacteristic
381C4⋊Q8D4×C1111yescharacteristic
382#125—24no—
383#125—22no—
384#125—22no—
385#125D4×C1112yes—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—24no—
389C22⋊Q8—24no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—24no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8D4×C1111yescharacteristic
399C4×Q8D4×C1111yescharacteristic
400C4×D4—22no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—24no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4D4×C1111yescharacteristic
409C4×D4D4×C1111yescharacteristic
410#117—22no—
411#117—21no—
412#117C23×C1111yescharacteristic
413#117C23×C1112yes—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4D4×C1112yes—
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1112yes—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—24no—
422C2×C42—21no—
423C2×C42C23×C1112yes—
424C2×C42C23×C1111yescharacteristic
425#107—21no—
426#107—22no—
427#106—21no—
428#106—22no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431#104—24no—
432#103—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—22no—
437#102—22no—
438#97—21no—
439C4×C8—21no—
440#95—21no—
441#95—24no—
442C2×C11—21no—
443C2×C11—21no—
444C2×C11—42no—
445C2×C11—82no—
446C2×C11#240911yescharacteristic
447C2×C11C2×#45411yescharacteristic
448C2×C11#301911yescharacteristic
449C24—21no—
450#41—21no—
451#41—21no—
452#41C2×Q8×C1112yes—
453#41C11×#4112yes—
454C2×Q8—24no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—21no—
458C2×Q8—22no—
459C2×Q8—82no—
460C2×Q8—84no—
461C2×Q8C2×D4×C1111yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4C2×D4×C1111yescharacteristic
469C2×D4C2×Q8×C1112yescomplemented
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—44no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4C2×D4×C1111yescharacteristic
480C22×C4C2×D4×C1114yes—
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C24×C1111yescharacteristic
483SD16—24no—
484D8—24no—
485M16—21no—
486M16—22no—
487M16—21no—
488M16—21no—
489M16—22no—
490M16C2×Q8×C1112yescomplemented
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—22no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—42no—
511C4⋊C4C2×D4×C1112yes—
512C4⋊C4C2×D4×C1111yescharacteristic
513C4⋊C4C2×D4×C1112yes—
514C4⋊C4C2×D4×C1111yescharacteristic
515C22⋊C4—24no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—84no—
523C42—24no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—22no—
528C42—22no—
529C42—22no—
530C42C2×D4×C1111yescharacteristic
531C42C2×D4×C1111yescharacteristic
532C42C2×D4×C1111yescharacteristic
533C42C2×D4×C1111yescharacteristic
534C11#2432111yescharacteristic, direct product factor, Sylow
535C23—21no—
536C23—22no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—41no—
541C23C22×D4×C1111yescharacteristic
542Q8—21no—
543Q8—44no—
544Q8—42no—
545Q8—42no—
546Q8—82no—
547Q8—84no—
548Q8C11×C22⋊Q812yes—
549D4—22no—
550D4—22no—
551D4—22no—
552D4—21no—
553D4—22no—
554D4—41no—
555D4—41no—
556D4C11×C22⋊Q812yes—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—82no—
576C2×C4—84no—
577C2×C4—82no—
578C2×C4C11×#12011yescharacteristic
579C2×C4C11×#12011yescharacteristic
580C2×C4C11×#12011yescharacteristic
581C2×C4C11×#12011yescharacteristic
582C2×C4C22×D4×C1111yescharacteristic
583C2×C4C22×D4×C1111yescharacteristic
584C2×C4C22×Q8×C1111yescharacteristic
585C2×C4C2×C11×#4111yescharacteristic
586C2×C4C11×2−1+411yescharacteristic
587C2×C4C11×2−1+411yescharacteristic
588C8—22no—
589C8—41no—
590C8—42no—
591C22—21no—
592C22—21no—
593C22—22no—
594C22—44no—
595C22—41no—
596C22—41no—
597C22—42no—
598C22—82no—
599C22—81no—
600C22—81no—
601C22C2×C11×#12011yescharacteristic
602C22C11×#54811yescharacteristic
603C22D4×Q8×C1111yescharacteristic
604C4—22no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—41no—
609C4—42no—
610C4—41no—
611C4—44no—
612C4—42no—
613C4—82no—
614C4—81no—
615C4C11×#45412yes—
616C4C2×C11×C22⋊Q811yescharacteristic
617C4C11×#53611yescharacteristic
618C4C11×#54811yescharacteristic
619C4D4×Q8×C1111yescharacteristic
620C2—21no—
621C2—21no—
622C2—42no—
623C2—82no—
624C2C11×#240911yescharacteristic
625C2C2×C11×#45411yescharacteristic
626C2C11×#301911yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3503C2semidirect
2. C11×#3077C2semidirect
4. C11×#2563C2semidirect
5. C11×#2061C2semidirect
6. C11×#2027C2semidirect
7. C11×#1997C2semidirect
8. C11×#1986C2semidirect
10. C11×#1860C2semidirect
11. C11×#1806C2semidirect
59. C11×AGL(1,ℤ/8)Q8semidirect
136. #24321C11direct (N × H)
157. C2×D4×C11C2×Q8semidirect
178. C11×M16C2×Q8semidirect
222. #3503C2×C11semidirect
223. #3077C2×C11semidirect
225. #2563C2×C11semidirect
226. #2061C2×C11semidirect
227. #2027C2×C11semidirect
228. #1997C2×C11semidirect
229. #1986C2×C11semidirect
231. #1860C2×C11semidirect
232. #1806C2×C11semidirect
365. AGL(1,ℤ/8)Q8×C11semidirect
469. C2×D4C2×Q8×C11semidirect
490. M16C2×Q8×C11semidirect
534. C11#24321direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35032
C11×#30772
C4×C11×AGL(1,ℤ/8)2
C11×#25632
C11×#20612
C11×#20272
C11×#19972
C11×#19862
C11×#18832
C11×#18602
C11×#18062
#2432111