Finite Group Databasebeta

← C11×#24046 #14601239

Subgroups — C11×#24046 #14601239

Order 2816.

1390 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
1C2×C11×#550C211yesmaximal, characteristic
2C2×C11×#480C211yesmaximal, characteristic, complemented
3C2×C11×#417C211yesmaximal, characteristic, complemented
4C11×#2487C211yesmaximal, characteristic, complemented
5C11×#2041C212yesmaximal, complemented
6C11×#2033C212yesmaximal, complemented
7C11×#1895C211yesmaximal, characteristic, complemented
8C11×#1870C211yesmaximal, characteristic, complemented
9C11×#1863C212yesmaximal, complemented
10C11×#1788C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×#41C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C11×#550—24no—
16C11×#550—24no—
17C2×C11×#127—21no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#121—21no—
20C2×C11×#121—21no—
21C2×C11×#121C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C22×C11×C4⋊C4C2211yescharacteristic
27C11×#480—24no—
28C2×C11×#107C2212yes—
29C11×#417—24no—
30C2×C11×#103C2212yes—
31C2×C11×#103C2212yes—
32C2×C11×#102C2212yes—
33C2×C11×#102C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×C11×C22⋊C8C2212yes—
38C11×#400—21no—
39C11×#399—21no—
40C11×#389C2212yes—
41C11×#386—21no—
42C11×#385—21no—
43C11×#380C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C11×#336C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—24no—
51C2×C11×#41—24no—
52C2×C11×#41—42no—
53C2×C11×#41—42no—
54C2×C11×#41D414yes—
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11D411yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11—21no—
67C23×C4×C11—21no—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C2×C11×M16—22no—
71C2×C11×M16—42no—
72C22×C8×C11C2312yes—
73C22×C8×C11C2312yes—
74C11×#127—28no—
75C11×#127—22no—
76C11×#127—22no—
77C11×#121—28no—
78C11×#121—28no—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121—22no—
82C11×#121D414yes—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×D4×C11—28no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C11×#107—24no—
106C11×#103—24no—
107C11×#103—24no—
108C11×#102—24no—
109C11×#102—24no—
110C11×#102—42no—
111C11×#102—42no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—42no—
114C11×#95—22no—
115C11×#95—21no—
116C11×#95—22no—
117#24046C1111yesmaximal, characteristic, direct product factor, Sylow
118C24×C11—21no—
119C24×C11—21no—
120C24×C11C2×D411yescharacteristic
121C24×C11C2×D411yescharacteristic
122C11×#41—28no—
123C11×#41—44no—
124C11×#41—48no—
125C11×#41—48no—
126C11×#41—44no—
127C11×#41—44no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11C2×D412yes—
131C2×Q8×C11#4114yes—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—22no—
135C2×D4×C11—24no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—41no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—82no—
152C2×D4×C11—82no—
153C2×D4×C11—82no—
154C2×D4×C11C2×D412yes—
155C2×D4×C11C2×D412yes—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—24no—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—44no—
169C22×C4×C11—44no—
170C22×C4×C11—42no—
171C22×C4×C11—82no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C11×M16—44no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—22no—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4—82no—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—82no—
202C42×C11—24no—
203C42×C11—21no—
204C42×C11—21no—
205C2×#550C2×C1111yescharacteristic
206C2×#480C2×C1111yescharacteristic, complemented
207C2×#417C2×C1111yescharacteristic, complemented
208#2487C2×C1111yescharacteristic, complemented
209#2041C2×C1112yescomplemented
210#2033C2×C1112yescomplemented
211#1895C2×C1111yescharacteristic, complemented
212#1870C2×C1111yescharacteristic, complemented
213#1863C2×C1112yescomplemented
214#1788C2×C1112yescomplemented
215#1788C2×C1111yescharacteristic, complemented
216C23×C11—22no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—22no—
220C23×C11—21no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11#12012yes—
236C23×C11C22×D411yescharacteristic
237Q8×C11—22no—
238Q8×C11—24no—
239Q8×C11#12314yes—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—24no—
243D4×C11—44no—
244D4×C11—48no—
245D4×C11—48no—
246D4×C11—48no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—42no—
250D4×C11—84no—
251D4×C11—84no—
252D4×C11—84no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—48no—
267C2×C4×C11—48no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—84no—
279C2×C4×C11#12012yes—
280C2×C4×C11#13712yes—
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4112yes—
284C2×C4×C11H(5,𝔽2)12yes—
285C8×C11—42no—
286C8×C11—42no—
287C22×#41C22×C1111yescharacteristic
288C22×#41C22×C1111yescharacteristic
289C22×M16C22×C1111yescharacteristic
290#550—24no—
291#550—24no—
292C2×#127—21no—
293C2×#127C22×C1111yescharacteristic
294C2×#121—21no—
295C2×#121—21no—
296C2×#121C22×C1111yescharacteristic
297C2×#121C22×C1111yescharacteristic
298C2×C4×Q8C22×C1111yescharacteristic
299C2×C4×D4—21no—
300C2×C4×D4C22×C1111yescharacteristic
301C22×C4⋊C4C22×C1111yescharacteristic
302#480—24no—
303C2×#107C22×C1112yes—
304#417—24no—
305C2×#103C22×C1112yes—
306C2×#103C22×C1112yes—
307C2×#102C22×C1112yes—
308C2×#102C22×C1112yes—
309C2×#102C22×C1112yes—
310C2×#102C22×C1112yes—
311C2×C22⋊C8C22×C1111yescharacteristic
312C2×C22⋊C8C22×C1112yes—
313#400—21no—
314#399—21no—
315#389C22×C1112yes—
316#386—21no—
317#385—21no—
318#380C22×C1111yescharacteristic
319#380C22×C1112yes—
320#340C22×C1112yes—
321#336C22×C1112yes—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—41no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—82no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11C2×#12011yescharacteristic
343C22×C11#54612yes—
344C22×C11C2×#13711yescharacteristic
345C22×C11#57511yescharacteristic
346C22×C11#57612yes—
347C4×C11—22no—
348C4×C11—24no—
349C4×C11—22no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—82no—
354C4×C11—82no—
355C4×C11C2×#12311yescharacteristic
356C4×C11#53411yescharacteristic
357C4×C11#54612yes—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—24no—
362C2×#41—24no—
363C2×#41—42no—
364C2×#41—42no—
365C2×#41D4×C1114yes—
366C22×Q8C23×C1111yescharacteristic
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—21no—
373C22×D4D4×C1111yescharacteristic
374C22×D4C23×C1111yescharacteristic
375C22×D4C23×C1111yescharacteristic
376C23×C4—21no—
377C23×C4—21no—
378C23×C4—21no—
379C23×C4C23×C1111yescharacteristic
380C23×C4C23×C1111yescharacteristic
381C2×M16—22no—
382C2×M16—42no—
383C22×C8C23×C1112yes—
384C22×C8C23×C1112yes—
385#127—28no—
386#127—22no—
387#127—22no—
388#121—28no—
389#121—28no—
390#121—22no—
391#121—22no—
392#121—22no—
393#121D4×C1114yes—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×D4—28no—
397C4×D4—22no—
398C4×D4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4D4×C1111yescharacteristic
405C2×C4⋊C4C23×C1112yes—
406C2×C4⋊C4C23×C1112yes—
407C2×C4⋊C4C23×C1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4D4×C1111yescharacteristic
413C2×C22⋊C4D4×C1111yescharacteristic
414C2×C42—21no—
415C2×C42C23×C1111yescharacteristic
416#107—24no—
417#103—24no—
418#103—24no—
419#102—24no—
420#102—24no—
421#102—42no—
422#102—42no—
423C22⋊C8—22no—
424C22⋊C8—42no—
425#95—22no—
426#95—21no—
427#95—22no—
428C2×C11—42no—
429C2×C11—81no—
430C2×C11—82no—
431C2×C11—82no—
432C2×C11#240511yescharacteristic
433C2×C11#300711yescharacteristic
434C2×C11#300811yescharacteristic
435C2×C11#330912yes—
436C2×C11#333312yes—
437C24—21no—
438C24—21no—
439C24C2×D4×C1111yescharacteristic
440C24C2×D4×C1111yescharacteristic
441#41—28no—
442#41—44no—
443#41—48no—
444#41—48no—
445#41—44no—
446#41—44no—
447C2×Q8—21no—
448C2×Q8—22no—
449C2×Q8C2×D4×C1112yes—
450C2×Q8C11×#4114yes—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—22no—
454C2×D4—24no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—41no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—82no—
471C2×D4—82no—
472C2×D4—82no—
473C2×D4C2×D4×C1112yes—
474C2×D4C2×D4×C1112yes—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—42no—
490C22×C4—82no—
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C2×D4×C1112yes—
495C22×C4C2×D4×C1112yes—
496C22×C4C2×D4×C1111yescharacteristic
497C22×C4C24×C1111yescharacteristic
498M16—44no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C4⋊C4—24no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—42no—
513C4⋊C4—82no—
514C4⋊C4C2×D4×C1112yes—
515C22⋊C4—24no—
516C22⋊C4—22no—
517C22⋊C4—24no—
518C22⋊C4—22no—
519C22⋊C4—42no—
520C22⋊C4—82no—
521C42—24no—
522C42—21no—
523C42—21no—
524C11#2404611yescharacteristic, direct product factor, Sylow
525C23—22no—
526C23—21no—
527C23—21no—
528C23—22no—
529C23—21no—
530C23—22no—
531C23—22no—
532C23—22no—
533C23—21no—
534C23—21no—
535C23—22no—
536C23—42no—
537C23—42no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—42no—
543C23—42no—
544C23C11×#12012yes—
545C23C22×D4×C1111yescharacteristic
546Q8—22no—
547Q8—24no—
548Q8C11×#12314yes—
549D4—22no—
550D4—22no—
551D4—24no—
552D4—44no—
553D4—48no—
554D4—48no—
555D4—48no—
556D4—41no—
557D4—41no—
558D4—42no—
559D4—84no—
560D4—84no—
561D4—84no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—48no—
576C2×C4—48no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—84no—
588C2×C4C11×#12012yes—
589C2×C4C11×#13712yes—
590C2×C4C22×D4×C1111yescharacteristic
591C2×C4C22×D4×C1111yescharacteristic
592C2×C4C2×C11×#4112yes—
593C2×C4C11×H(5,𝔽2)12yes—
594C8—42no—
595C8—42no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—41no—
604C22—41no—
605C22—42no—
606C22—42no—
607C22—41no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—82no—
616C22C2×C11×#12011yescharacteristic
617C22C11×#54612yes—
618C22C2×C11×#13711yescharacteristic
619C22C11×#57511yescharacteristic
620C22C11×#57612yes—
621C4—22no—
622C4—24no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—82no—
628C4—82no—
629C4C2×C11×#12311yescharacteristic
630C4C11×#53411yescharacteristic
631C4C11×#54612yes—
632C2—42no—
633C2—81no—
634C2—82no—
635C2—82no—
636C2C11×#240511yescharacteristic
637C2C11×#300711yescharacteristic
638C2C11×#300811yescharacteristic
639C2C11×#330912yes—
640C2C11×#333312yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC2×C11×#550C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C4×D4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#480C2semidirect
3. C2×C11×#417C2semidirect
4. C11×#2487C2semidirect
5. C11×#2041C2semidirect
6. C11×#2033C2semidirect
7. C11×#1895C2semidirect
8. C11×#1870C2semidirect
9. C11×#1863C2semidirect
10. C11×#1788C2semidirect
11. C11×#1788C2semidirect
117. #24046C11direct (N × H)
206. C2×#480C2×C11semidirect
207. C2×#417C2×C11semidirect
208. #2487C2×C11semidirect
209. #2041C2×C11semidirect
210. #2033C2×C11semidirect
211. #1895C2×C11semidirect
212. #1870C2×C11semidirect
213. #1863C2×C11semidirect
214. #1788C2×C11semidirect
215. #1788C2×C11semidirect
524. C11#24046direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5502
C2×C11×#4802
C2×C11×#4172
C11×#24872
C11×#20412
C11×#20332
C11×#18952
C11×#18702
C11×#18632
C11×#17882
#2404611