Finite Group Databasebeta

← C11×#24181 #14601374

Subgroups — C11×#24181 #14601374

Order 2816.

1050 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3507C211yesmaximal, characteristic, complemented
2C11×#3077C211yesmaximal, characteristic, complemented
3C11×#3036C211yesmaximal, characteristic
4C11×#2326C211yesmaximal, characteristic, complemented
5C11×#2038C212yesmaximal, complemented
6C11×#2003C212yesmaximal, complemented
7C11×#1995C211yesmaximal, characteristic, complemented
8C11×#1963C211yesmaximal, characteristic, complemented
9C11×#1883C212yesmaximal, complemented
10C11×#1859C212yesmaximal, complemented
11C11×#1801C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)C2212yes—
13C11×#559—21no—
14C11×#557—21no—
15C11×#556—21no—
16C11×#556—22no—
17C11×#554—21no—
18C11×#552—22no—
19C11×#539—22no—
20C11×#536C2212yes—
21C11×#533C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C11×#529—22no—
24C2×C11×#124C2211yescharacteristic
25C11×#520C2212yes—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C11×#478—22no—
29C11×#476—21no—
30C11×#474—21no—
31C11×#463—22no—
32C11×#461—21no—
33C11×#459—21no—
34C11×#428C2212yes—
35C11×#423C2211yescharacteristic
36C11×#423C2211yescharacteristic
37C2×C11×#104C2212yes—
38C2×C11×#104C2212yes—
39C11×#418C2212yes—
40C11×#417C2212yes—
41C2×C11×#101C2212yes—
42C11×#391C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#388—22no—
45C11×#385—22no—
46C11×#384C2211yescharacteristic
47C11×#376C2211yescharacteristic
48C11×#343C2212yes—
49C11×#339C2212yes—
50C11×#339C2212yes—
51C2×C11×#41C2312yes—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C11×AGL(1,ℤ/8)—24no—
56C11×AGL(1,ℤ/8)—42no—
57C2×C11×SD16—22no—
58C2×C11×D8—22no—
59C2×C11×M16C2312yes—
60C2×C11×M16C2312yes—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8D411yescharacteristic
65C11×#127D411yescharacteristic
66C11×#126—24no—
67C11×#126—24no—
68C11×#125—22no—
69C11×#125—24no—
70C11×#125D412yes—
71C11×#124—22no—
72C11×#124—22no—
73C11×#124—22no—
74C11×#124—22no—
75C11×#124D412yes—
76C11×#123—24no—
77C11×#123—24no—
78C11×C22⋊Q8—24no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C11×#121—21no—
84C11×#121—21no—
85C4×Q8×C11—22no—
86C4×Q8×C11—22no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—24no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C11×#117—24no—
103C11×#117—22no—
104C11×#117C2312yes—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4D412yes—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—22no—
113C2×C42×C11D412yes—
114C2×C42×C11C2311yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C2×C42×C11C2311yescharacteristic
117C11×#107—22no—
118C11×#106—22no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8—21no—
123C11×#104—24no—
124C11×#104—42no—
125C11×#103—22no—
126C11×#102—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×#101—42no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—22no—
133#24181C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11—21no—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D412yes—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
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×D412yes—
157C2×D4×C11#4112yes—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—82no—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C11×SD16—44no—
172C11×D8—44no—
173C11×M16—22no—
174C11×M16—22no—
175C11×M16—22no—
176C11×M16—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—82no—
195C11×C4⋊C4C2×D412yes—
196C11×C4⋊C4C2×D412yes—
197C11×C22⋊C4—28no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—82no—
207C42×C11—24no—
208C42×C11—22no—
209C42×C11—22no—
210C42×C11—22no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—21no—
214C42×C11C2×D411yescharacteristic
215C42×C11C2×D411yescharacteristic
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11#4112yes—
219#3507C2×C1111yescharacteristic, complemented
220#3077C2×C1111yescharacteristic, complemented
221#3036C2×C1111yescharacteristic
222#2326C2×C1111yescharacteristic, complemented
223#2038C2×C1112yescomplemented
224#2003C2×C1112yescomplemented
225#1995C2×C1111yescharacteristic, complemented
226#1963C2×C1111yescharacteristic, complemented
227#1883C2×C1112yescomplemented
228#1859C2×C1112yescomplemented
229#1801C2×C1111yescharacteristic, complemented
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C22×D411yescharacteristic
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—42no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—81no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—81no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—82no—
276C2×C4×C11—82no—
277C2×C4×C11—84no—
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11#12011yescharacteristic
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C8×C11—42no—
289C8×C11—42no—
290C2×AGL(1,ℤ/8)C22×C1112yes—
291#559—21no—
292#557—21no—
293#556—21no—
294#556—22no—
295#554—21no—
296#552—22no—
297#539—22no—
298#536C22×C1112yes—
299#533C22×C1111yescharacteristic
300#532C22×C1111yescharacteristic
301#529—22no—
302C2×#124C22×C1111yescharacteristic
303#520C22×C1112yes—
304C2×C4×Q8C22×C1111yescharacteristic
305C2×C4×D4C22×C1111yescharacteristic
306#478—22no—
307#476—21no—
308#474—21no—
309#463—22no—
310#461—21no—
311#459—21no—
312#428C22×C1112yes—
313#423C22×C1111yescharacteristic
314#423C22×C1111yescharacteristic
315C2×#104C22×C1112yes—
316C2×#104C22×C1112yes—
317#418C22×C1112yes—
318#417C22×C1112yes—
319C2×#101C22×C1112yes—
320#391C22×C1111yescharacteristic
321#390C22×C1111yescharacteristic
322#388—22no—
323#385—22no—
324#384C22×C1111yescharacteristic
325#376C22×C1111yescharacteristic
326#343C22×C1112yes—
327#339C22×C1112yes—
328#339C22×C1112yes—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—44no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—82no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11C2×#12011yescharacteristic
340C22×C11#52511yescharacteristic
341C22×C11#53711yescharacteristic
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11#54611yescharacteristic
355C4×C11#54711yescharacteristic
356C4×C11#54811yescharacteristic
357C4×C11#55011yescharacteristic
358C2×#41C23×C1112yes—
359C22×Q8C23×C1111yescharacteristic
360C22×D4C23×C1111yescharacteristic
361C23×C4—21no—
362AGL(1,ℤ/8)—24no—
363AGL(1,ℤ/8)—42no—
364C2×SD16—22no—
365C2×D8—22no—
366C2×M16C23×C1112yes—
367C2×M16C23×C1112yes—
368C4⋊Q8—22no—
369C4⋊Q8D4×C1111yescharacteristic
370C4⋊Q8D4×C1111yescharacteristic
371C4⋊Q8D4×C1111yescharacteristic
372#127D4×C1111yescharacteristic
373#126—24no—
374#126—24no—
375#125—22no—
376#125—24no—
377#125D4×C1112yes—
378#124—22no—
379#124—22no—
380#124—22no—
381#124—22no—
382#124D4×C1112yes—
383#123—24no—
384#123—24no—
385C22⋊Q8—24no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390#121—21no—
391#121—21no—
392C4×Q8—22no—
393C4×Q8—22no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—24no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409#117—24no—
410#117—22no—
411#117C23×C1112yes—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4D4×C1112yes—
415C2×C4⋊C4C23×C1111yescharacteristic
416C2×C4⋊C4C23×C1111yescharacteristic
417C2×C22⋊C4—22no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—22no—
420C2×C42D4×C1112yes—
421C2×C42C23×C1111yescharacteristic
422C2×C42C23×C1111yescharacteristic
423C2×C42C23×C1111yescharacteristic
424#107—22no—
425#106—22no—
426C4⋊C8—21no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—21no—
430#104—24no—
431#104—42no—
432#103—22no—
433#102—22no—
434#102—22no—
435#102—22no—
436#101—42no—
437#95—21no—
438#95—21no—
439#95—22no—
440C2×C11—21no—
441C2×C11—21no—
442C2×C11—82no—
443C2×C11—82no—
444C2×C11#240711yescharacteristic
445C2×C11#302011yescharacteristic
446C2×C11#302111yescharacteristic
447C24—21no—
448#41—22no—
449#41—22no—
450#41—22no—
451#41—22no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×D4×C1112yes—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4C2×D4×C1112yes—
470C2×D4C11×#4112yes—
471C22×C4—21no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—82no—
479C22×C4C2×D4×C1112yes—
480C22×C4C2×D4×C1112yes—
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C24×C1111yescharacteristic
484SD16—44no—
485D8—44no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490C2×C8—22no—
491C2×C8—22no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—82no—
508C4⋊C4C2×D4×C1112yes—
509C4⋊C4C2×D4×C1112yes—
510C22⋊C4—28no—
511C22⋊C4—24no—
512C22⋊C4—24no—
513C22⋊C4—24no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—82no—
520C42—24no—
521C42—22no—
522C42—22no—
523C42—22no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42C2×D4×C1111yescharacteristic
528C42C2×D4×C1111yescharacteristic
529C42C2×D4×C1111yescharacteristic
530C42C2×D4×C1111yescharacteristic
531C42C11×#4112yes—
532C11#2418111yescharacteristic, direct product factor, Sylow
533C23—22no—
534C23—22no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—41no—
539C23C22×D4×C1111yescharacteristic
540Q8—22no—
541Q8—22no—
542Q8—42no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—81no—
548D4—22no—
549D4—22no—
550D4—22no—
551D4—22no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—41no—
556D4—41no—
557D4—81no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4—84no—
581C2×C4C11×#12011yescharacteristic
582C2×C4C11×#12011yescharacteristic
583C2×C4C11×#12011yescharacteristic
584C2×C4C11×#12011yescharacteristic
585C2×C4C22×D4×C1111yescharacteristic
586C2×C4C22×D4×C1111yescharacteristic
587C2×C4C2×C11×#4111yescharacteristic
588C2×C4C2×C11×#4111yescharacteristic
589C2×C4C11×H(5,𝔽2)11yescharacteristic
590C2×C4C11×2−1+411yescharacteristic
591C8—42no—
592C8—42no—
593C22—21no—
594C22—21no—
595C22—44no—
596C22—42no—
597C22—42no—
598C22—42no—
599C22—42no—
600C22—82no—
601C22—81no—
602C22—81no—
603C22C2×C11×#12011yescharacteristic
604C22C11×#52511yescharacteristic
605C22C11×#53711yescharacteristic
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4—81no—
617C4—81no—
618C4C11×#54611yescharacteristic
619C4C11×#54711yescharacteristic
620C4C11×#54811yescharacteristic
621C4C11×#55011yescharacteristic
622C2—21no—
623C2—21no—
624C2—82no—
625C2—82no—
626C2C11×#240711yescharacteristic
627C2C11×#302011yescharacteristic
628C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3036C2
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×#3507C2semidirect
2. C11×#3077C2semidirect
4. C11×#2326C2semidirect
5. C11×#2038C2semidirect
6. C11×#2003C2semidirect
7. C11×#1995C2semidirect
8. C11×#1963C2semidirect
9. C11×#1883C2semidirect
10. C11×#1859C2semidirect
11. C11×#1801C2semidirect
133. #24181C11direct (N × H)
219. #3507C2×C11semidirect
220. #3077C2×C11semidirect
222. #2326C2×C11semidirect
223. #2038C2×C11semidirect
224. #2003C2×C11semidirect
225. #1995C2×C11semidirect
226. #1963C2×C11semidirect
227. #1883C2×C11semidirect
228. #1859C2×C11semidirect
229. #1801C2×C11semidirect
532. C11#24181direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35072
C11×#30772
C11×#30362
C11×#23262
C11×#20382
C11×#20032
C11×#19952
C11×#19632
C11×#18832
C11×#18592
C11×#18012
#2418111