Finite Group Databasebeta

← C11×#24182 #14601375

Subgroups — C11×#24182 #14601375

Order 2816.

1082 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3506C211yesmaximal, characteristic
2C11×#3078C211yesmaximal, characteristic, complemented
3C11×#3037C211yesmaximal, characteristic, complemented
4C11×#2326C211yesmaximal, characteristic, complemented
5C11×#2037C212yesmaximal, complemented
6C11×#2004C212yesmaximal, complemented
7C11×#1995C211yesmaximal, characteristic, complemented
8C11×#1963C211yesmaximal, characteristic, complemented
9C11×#1882C212yesmaximal, complemented
10C11×#1859C212yesmaximal, complemented
11C11×#1800C211yesmaximal, characteristic, complemented
12C2×C11×#137C2212yes—
13C11×#559—22no—
14C11×#556—21no—
15C11×#555—21no—
16C11×#553—22no—
17C11×#550—21no—
18C11×#547—21no—
19C11×#538—22no—
20C11×#535C2212yes—
21C11×#533C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C11×#525—22no—
25C11×#520C2212yes—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C11×#479—22no—
29C11×#477—21no—
30C11×#475—21no—
31C11×#464—22no—
32C11×#462—21no—
33C11×#460—21no—
34C11×#428C2212yes—
35C11×#423C2211yescharacteristic
36C11×#423C2211yescharacteristic
37C2×C11×#104C2212yes—
38C2×C11×#104C2212yes—
39C11×#419C2212yes—
40C11×#417C2212yes—
41C2×C11×#100C2212yes—
42C11×#391C2211yescharacteristic
43C11×#390C2211yescharacteristic
44C11×#388—22no—
45C11×#385—22no—
46C11×#384C2211yescharacteristic
47C11×#376C2211yescharacteristic
48C11×#343C2212yes—
49C11×#339C2212yes—
50C11×#339C2212yes—
51C2×C11×#41—22no—
52C2×C11×#41C2312yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11D412yes—
56C11×#137—24no—
57C11×#137—42no—
58C2×C11×Q16—22no—
59C2×C11×SD16—22no—
60C2×C11×M16C2312yes—
61C2×C11×M16C2312yes—
62C11×C4⋊Q8D411yescharacteristic
63C11×C4⋊Q8D411yescharacteristic
64C11×C4⋊Q8D411yescharacteristic
65C11×#127—22no—
66C11×#127D411yescharacteristic
67C11×#126—24no—
68C11×#125D412yes—
69C11×#124—24no—
70C11×#124—22no—
71C11×#124—22no—
72C11×#124—22no—
73C11×#124D412yes—
74C11×#123—24no—
75C11×#123—24no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×#121—22no—
80C11×#121—24no—
81C11×#121—21no—
82C11×#121—21no—
83C11×#121—22no—
84C11×#121—22no—
85C11×#120—24no—
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—24no—
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—22no—
103C11×#117—22no—
104C11×#117C2312yes—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—22no—
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—22no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4D412yes—
113C2×C42×C11—21no—
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×#103—22no—
127C11×#103—22no—
128C11×#102—22no—
129C11×#100—42no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95—22no—
133#24182C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11C2×D412yes—
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—84no—
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×Q8×C11#4112yescomplemented
149C2×D4×C11—22no—
150C2×D4×C11—24no—
151C2×D4×C11—24no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11C2×D412yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—24no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—82no—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C11×Q16—44no—
175C11×SD16—44no—
176C11×M16—22no—
177C11×M16—22no—
178C11×M16—22no—
179C11×M16—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—82no—
196C11×C4⋊C4C2×D412yes—
197C11×C4⋊C4C2×D412yes—
198C11×C22⋊C4—28no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—82no—
208C42×C11—24no—
209C42×C11—22no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—41no—
214C42×C11—41no—
215C42×C11C2×D411yescharacteristic
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219C42×C11#4112yescomplemented
220#3506C2×C1111yescharacteristic
221#3078C2×C1111yescharacteristic, complemented
222#3037C2×C1111yescharacteristic, complemented
223#2326C2×C1111yescharacteristic, complemented
224#2037C2×C1112yescomplemented
225#2004C2×C1112yescomplemented
226#1995C2×C1111yescharacteristic, complemented
227#1963C2×C1111yescharacteristic, complemented
228#1882C2×C1112yescomplemented
229#1859C2×C1112yescomplemented
230#1800C2×C1111yescharacteristic, complemented
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11C22×D411yescharacteristic
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—42no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—81no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—81no—
256D4×C11—84no—
257D4×C11—84no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—44no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—41no—
275C2×C4×C11—42no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—82no—
280C2×C4×C11—84no—
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11#12011yescharacteristic
283C2×C4×C11#12011yescharacteristic
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C112−1+411yescharacteristic
291C8×C11—42no—
292C8×C11—42no—
293C2×#137C22×C1112yes—
294#559—22no—
295#556—21no—
296#555—21no—
297#553—22no—
298#550—21no—
299#547—21no—
300#538—22no—
301#535C22×C1112yes—
302#533C22×C1111yescharacteristic
303#532C22×C1111yescharacteristic
304C2×#124C22×C1111yescharacteristic
305#525—22no—
306#520C22×C1112yes—
307C2×C4×Q8C22×C1111yescharacteristic
308C2×C4×D4C22×C1111yescharacteristic
309#479—22no—
310#477—21no—
311#475—21no—
312#464—22no—
313#462—21no—
314#460—21no—
315#428C22×C1112yes—
316#423C22×C1111yescharacteristic
317#423C22×C1111yescharacteristic
318C2×#104C22×C1112yes—
319C2×#104C22×C1112yes—
320#419C22×C1112yes—
321#417C22×C1112yes—
322C2×#100C22×C1112yes—
323#391C22×C1111yescharacteristic
324#390C22×C1111yescharacteristic
325#388—22no—
326#385—22no—
327#384C22×C1111yescharacteristic
328#376C22×C1111yescharacteristic
329#343C22×C1112yes—
330#339C22×C1112yes—
331#339C22×C1112yes—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—44no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—82no—
342C22×C11C2×#12011yescharacteristic
343C22×C11#52511yescharacteristic
344C22×C11#53711yescharacteristic
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#54611yescharacteristic
358C4×C11#54711yescharacteristic
359C4×C11#54811yescharacteristic
360C4×C11#55011yescharacteristic
361C2×#41—22no—
362C2×#41C23×C1112yes—
363C22×Q8C23×C1111yescharacteristic
364C22×D4C23×C1111yescharacteristic
365C23×C4D4×C1112yes—
366#137—24no—
367#137—42no—
368C2×Q16—22no—
369C2×SD16—22no—
370C2×M16C23×C1112yes—
371C2×M16C23×C1112yes—
372C4⋊Q8D4×C1111yescharacteristic
373C4⋊Q8D4×C1111yescharacteristic
374C4⋊Q8D4×C1111yescharacteristic
375#127—22no—
376#127D4×C1111yescharacteristic
377#126—24no—
378#125D4×C1112yes—
379#124—24no—
380#124—22no—
381#124—22no—
382#124—22no—
383#124D4×C1112yes—
384#123—24no—
385#123—24no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389#121—22no—
390#121—24no—
391#121—21no—
392#121—21no—
393#121—22no—
394#121—22no—
395#120—24no—
396C4×Q8—22no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×D4—24no—
404C4×D4—22no—
405C4×D4—24no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412#117—22no—
413#117—22no—
414#117C23×C1112yes—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4C23×C1111yescharacteristic
419C2×C4⋊C4C23×C1111yescharacteristic
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4D4×C1112yes—
423C2×C42—21no—
424C2×C42C23×C1111yescharacteristic
425C2×C42C23×C1111yescharacteristic
426C2×C42C23×C1111yescharacteristic
427#107—22no—
428#106—22no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432C4⋊C8—21no—
433#104—24no—
434#104—42no—
435#103—22no—
436#103—22no—
437#103—22no—
438#102—22no—
439#100—42no—
440#95—21no—
441#95—21no—
442#95—22no—
443C2×C11—21no—
444C2×C11—21no—
445C2×C11—82no—
446C2×C11—82no—
447C2×C11#240711yescharacteristic
448C2×C11#301911yescharacteristic
449C2×C11#302211yescharacteristic
450C24C2×D4×C1112yes—
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—84no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8C2×D4×C1112yes—
464C2×Q8C11×#4112yescomplemented
465C2×D4—22no—
466C2×D4—24no—
467C2×D4—24no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4C2×D4×C1112yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—82no—
486C22×C4C2×D4×C1112yes—
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C24×C1111yescharacteristic
490Q16—44no—
491SD16—44no—
492M16—22no—
493M16—22no—
494M16—22no—
495M16—22no—
496C2×C8—22no—
497C2×C8—22no—
498C4⋊C4—24no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—82no—
512C4⋊C4C2×D4×C1112yes—
513C4⋊C4C2×D4×C1112yes—
514C22⋊C4—28no—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—82no—
524C42—24no—
525C42—22no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—41no—
530C42—41no—
531C42C2×D4×C1111yescharacteristic
532C42C2×D4×C1111yescharacteristic
533C42C2×D4×C1111yescharacteristic
534C42C2×D4×C1111yescharacteristic
535C42C11×#4112yescomplemented
536C11#2418211yescharacteristic, direct product factor, Sylow
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—42no—
542C23—42no—
543C23C22×D4×C1111yescharacteristic
544Q8—22no—
545Q8—22no—
546Q8—22no—
547Q8—22no—
548Q8—42no—
549Q8—41no—
550Q8—41no—
551Q8—81no—
552D4—22no—
553D4—22no—
554D4—42no—
555D4—42no—
556D4—42no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—81no—
562D4—84no—
563D4—84no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—44no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—82no—
586C2×C4—84no—
587C2×C4C11×#12011yescharacteristic
588C2×C4C11×#12011yescharacteristic
589C2×C4C11×#12011yescharacteristic
590C2×C4C11×#12011yescharacteristic
591C2×C4C22×D4×C1111yescharacteristic
592C2×C4C22×D4×C1111yescharacteristic
593C2×C4C2×C11×#4111yescharacteristic
594C2×C4C2×C11×#4111yescharacteristic
595C2×C4C11×H(5,𝔽2)11yescharacteristic
596C2×C4C11×2−1+411yescharacteristic
597C8—42no—
598C8—42no—
599C22—21no—
600C22—21no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—82no—
609C22C2×C11×#12011yescharacteristic
610C22C11×#52511yescharacteristic
611C22C11×#53711yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—42no—
618C4—42no—
619C4—42no—
620C4—42no—
621C4—42no—
622C4—81no—
623C4—81no—
624C4C11×#54611yescharacteristic
625C4C11×#54711yescharacteristic
626C4C11×#54811yescharacteristic
627C4C11×#55011yescharacteristic
628C2—21no—
629C2—21no—
630C2—82no—
631C2—82no—
632C2C11×#240711yescharacteristic
633C2C11×#301911yescharacteristic
634C2C11×#302211yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3506C2
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
2. C11×#3078C2semidirect
3. C11×#3037C2semidirect
4. C11×#2326C2semidirect
5. C11×#2037C2semidirect
6. C11×#2004C2semidirect
7. C11×#1995C2semidirect
8. C11×#1963C2semidirect
9. C11×#1882C2semidirect
10. C11×#1859C2semidirect
11. C11×#1800C2semidirect
133. #24182C11direct (N × H)
148. C2×Q8×C11#41semidirect
219. C42×C11#41semidirect
221. #3078C2×C11semidirect
222. #3037C2×C11semidirect
223. #2326C2×C11semidirect
224. #2037C2×C11semidirect
225. #2004C2×C11semidirect
226. #1995C2×C11semidirect
227. #1963C2×C11semidirect
228. #1882C2×C11semidirect
229. #1859C2×C11semidirect
230. #1800C2×C11semidirect
464. C2×Q8C11×#41semidirect
535. C42C11×#41semidirect
536. C11#24182direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35062
C11×#30782
C11×#30372
C11×#23262
C11×#20372
C11×#20042
C11×#19952
C11×#19632
C11×#18822
C11×#18592
C11×#18002
#2418211