Finite Group Databasebeta

← C11×#24242 #14601435

Subgroups — C11×#24242 #14601435

Order 2816.

1490 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
1C2×C11×#550C211yesmaximal, characteristic
2C2×C11×#460C211yesmaximal, characteristic, complemented
3C2×C11×#452C212yesmaximal, complemented
4C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
5C11×#2538C211yesmaximal, characteristic, complemented
6C11×#2033C212yesmaximal, complemented
7C11×#2000C212yesmaximal, complemented
8C11×#1957C211yesmaximal, characteristic, complemented
9C11×#1954C211yesmaximal, characteristic, complemented
10C11×#1803C211yesmaximal, characteristic, complemented
11C11×#1788C212yesmaximal, complemented
12C22×C11×#41C2212yes—
13C22×C11×Q16C2211yescharacteristic
14C22×C11×SD16C2212yes—
15C11×#550—24no—
16C11×#550—24no—
17C2×C11×#127—21no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#121—22no—
21C2×C11×#121C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C11×#460—24no—
27C11×#452—28no—
28C4×C11×Q16—24no—
29C2×C11×#107C2211yescharacteristic
30C2×C11×C4⋊C8C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C2×C11×#103C2211yescharacteristic
33C2×C11×#103C2212yes—
34C2×C11×#102C2212yes—
35C2×C11×#102C2212yes—
36C2×C11×#102C2212yes—
37C2×C11×C22⋊C8C2212yes—
38C2×C11×C22⋊C8C2212yes—
39C2×C4×C8×C11C2211yescharacteristic
40C11×#396—22no—
41C11×#390—21no—
42C11×#389—21no—
43C11×#384C2211yescharacteristic
44C11×#380C2212yes—
45C11×#340C2212yes—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41—42no—
52C22×Q8×C11C2311yescharacteristic
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11D411yescharacteristic
59C22×D4×C11C2312yes—
60C23×C4×C11—22no—
61C23×C4×C11C2312yes—
62C2×C11×Q16—22no—
63C2×C11×Q16—22no—
64C2×C11×Q16D414yescomplemented
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—42no—
68C22×C8×C11C2312yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#127—28no—
72C11×#127—22no—
73C11×#127D414yes—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—42no—
76C11×#121—216no—
77C11×#121—24no—
78C11×#121—24no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11D414yes—
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4D412yes—
99C2×C42×C11—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C11×#107—22no—
103C11×C4⋊C8—22no—
104C11×#103—22no—
105C11×#103—24no—
106C11×#103—22no—
107C11×#102—24no—
108C11×#102—24no—
109C11×#102—42no—
110C11×C22⋊C8—24no—
111C11×C22⋊C8—42no—
112C4×C8×C11—22no—
113C11×#95—22no—
114#24242C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—22no—
116C24×C11C2×D412yes—
117C11×#41—48no—
118C11×#41—48no—
119C11×#41—48no—
120C11×#41—48no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11C2×D412yes—
130C2×Q8×C11C2×D412yes—
131C2×Q8×C11C2×D412yes—
132C2×Q8×C11#4112yes—
133C2×D4×C11—28no—
134C2×D4×C11—28no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—81no—
150C2×D4×C11—81no—
151C2×D4×C11—82no—
152C2×D4×C11—82no—
153C2×D4×C11C2×D414yes—
154C22×C4×C11—21no—
155C22×C4×C11—28no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—22no—
166C22×C4×C11—44no—
167C22×C4×C11—44no—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C11×Q16—28no—
173C11×SD16—48no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—22no—
181C2×C8×C11—21no—
182C2×C8×C11C2×D412yes—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—44no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—81no—
194C11×C4⋊C4C2×D412yes—
195C11×C22⋊C4—28no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—44no—
198C11×C22⋊C4—82no—
199C42×C11—24no—
200C42×C11—42no—
201C42×C11C2×D412yes—
202C42×C11C2×D412yes—
203C2×#550C2×C1111yescharacteristic
204C2×#460C2×C1111yescharacteristic, complemented
205C2×#452C2×C1112yescomplemented
206C2×C4×Q16C2×C1111yescharacteristic, complemented
207#2538C2×C1111yescharacteristic, complemented
208#2033C2×C1112yescomplemented
209#2000C2×C1112yescomplemented
210#1957C2×C1111yescharacteristic, complemented
211#1954C2×C1111yescharacteristic, complemented
212#1803C2×C1111yescharacteristic, complemented
213#1788C2×C1112yescomplemented
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—22no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11#12114yes—
237D4×C11—24no—
238D4×C11—24no—
239D4×C11—416no—
240D4×C11—42no—
241D4×C11—42no—
242D4×C11—44no—
243D4×C11—48no—
244D4×C11—84no—
245D4×C11—88no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—416no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—41no—
271C2×C4×C11#12012yes—
272C2×C4×C11#12012yes—
273C2×C4×C11#13512yes—
274C2×C4×C11#13712yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C8×C11—22no—
282C8×C11—41no—
283C8×C11—42no—
284C22×#41C22×C1112yes—
285C22×Q16C22×C1111yescharacteristic
286C22×SD16C22×C1112yes—
287#550—24no—
288#550—24no—
289C2×#127—21no—
290C2×#127C22×C1111yescharacteristic
291C2×C22⋊Q8C22×C1112yes—
292C2×#121—22no—
293C2×#121C22×C1112yes—
294C2×C4×Q8C22×C1111yescharacteristic
295C2×C4×Q8C22×C1111yescharacteristic
296C2×C4×D4—21no—
297C2×C4×D4C22×C1111yescharacteristic
298#460—24no—
299#452—28no—
300C4×Q16—24no—
301C2×#107C22×C1111yescharacteristic
302C2×C4⋊C8C22×C1111yescharacteristic
303C2×#103C22×C1112yes—
304C2×#103C22×C1111yescharacteristic
305C2×#103C22×C1111yescharacteristic
306C2×#102C22×C1112yes—
307C2×#102C22×C1112yes—
308C2×#102C22×C1112yes—
309C2×C22⋊C8C22×C1112yes—
310C2×C22⋊C8C22×C1112yes—
311C2×C4×C8C22×C1111yescharacteristic
312#396—22no—
313#390—21no—
314#389—21no—
315#384C22×C1111yescharacteristic
316#380C22×C1112yes—
317#340C22×C1112yes—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—82no—
329C22×C11—82no—
330C22×C11—82no—
331C22×C11—82no—
332C22×C11C2×#12011yescharacteristic
333C22×C11D4211yescharacteristic
334C22×C11#54611yescharacteristic
335C22×C11C2×#13511yescharacteristic
336C22×C11C2×#13711yescharacteristic
337C22×C11#57611yescharacteristic
338C22×C11#57711yescharacteristic
339C4×C11—24no—
340C4×C11—22no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—81no—
345C4×C11—82no—
346C4×C11#45214yescomplemented
347C4×C11C2×#12111yescharacteristic
348C4×C11#53511yescharacteristic
349C4×C11D4211yescharacteristic
350C4×C11#54611yescharacteristic
351C2×#41—24no—
352C2×#41—24no—
353C2×#41—24no—
354C2×#41—24no—
355C2×#41—42no—
356C2×#41—42no—
357C22×Q8C23×C1111yescharacteristic
358C22×Q8C23×C1111yescharacteristic
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—21no—
362C22×D4—21no—
363C22×D4D4×C1111yescharacteristic
364C22×D4C23×C1112yes—
365C23×C4—22no—
366C23×C4C23×C1112yes—
367C2×Q16—22no—
368C2×Q16—22no—
369C2×Q16D4×C1114yescomplemented
370C2×SD16—24no—
371C2×SD16—24no—
372C2×SD16—42no—
373C22×C8C23×C1112yes—
374C22×C8C23×C1111yescharacteristic
375C22×C8C23×C1111yescharacteristic
376#127—28no—
377#127—22no—
378#127D4×C1114yes—
379C22⋊Q8—24no—
380C22⋊Q8—42no—
381#121—216no—
382#121—24no—
383#121—24no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—22no—
387C4×Q8D4×C1114yes—
388C4×D4—28no—
389C4×D4—22no—
390C4×D4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4D4×C1111yescharacteristic
397C2×C4⋊C4C23×C1111yescharacteristic
398C2×C4⋊C4C23×C1112yes—
399C2×C4⋊C4C23×C1111yescharacteristic
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4D4×C1112yes—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42C23×C1111yescharacteristic
407#107—22no—
408C4⋊C8—22no—
409#103—22no—
410#103—24no—
411#103—22no—
412#102—24no—
413#102—24no—
414#102—42no—
415C22⋊C8—24no—
416C22⋊C8—42no—
417C4×C8—22no—
418#95—22no—
419C2×C11—82no—
420C2×C11—84no—
421C2×C11#240811yescharacteristic
422C2×C11C2×#45211yescharacteristic
423C2×C11#301211yescharacteristic
424C2×C11#327811yescharacteristic
425C2×C11#328711yescharacteristic
426C2×C11#330411yescharacteristic
427C2×C11#333311yescharacteristic
428C24—22no—
429C24C2×D4×C1112yes—
430#41—48no—
431#41—48no—
432#41—48no—
433#41—48no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C1112yes—
443C2×Q8C2×D4×C1112yes—
444C2×Q8C2×D4×C1112yes—
445C2×Q8C11×#4112yes—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—22no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4—82no—
465C2×D4—82no—
466C2×D4C2×D4×C1114yes—
467C22×C4—21no—
468C22×C4—28no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4C2×D4×C1112yes—
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C24×C1111yescharacteristic
485Q16—28no—
486SD16—48no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—21no—
493C2×C8—22no—
494C2×C8—21no—
495C2×C8C2×D4×C1112yes—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—44no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—81no—
507C4⋊C4C2×D4×C1112yes—
508C22⋊C4—28no—
509C22⋊C4—24no—
510C22⋊C4—44no—
511C22⋊C4—82no—
512C42—24no—
513C42—42no—
514C42C2×D4×C1112yes—
515C42C2×D4×C1112yes—
516C11#2424211yescharacteristic, direct product factor, Sylow
517C23—22no—
518C23—24no—
519C23—22no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23C22×D4×C1111yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—22no—
537Q8—41no—
538Q8—41no—
539Q8C11×#12114yes—
540D4—24no—
541D4—24no—
542D4—416no—
543D4—42no—
544D4—42no—
545D4—44no—
546D4—48no—
547D4—84no—
548D4—88no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—416no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4C11×#12012yes—
575C2×C4C11×#12012yes—
576C2×C4C11×#13512yes—
577C2×C4C11×#13712yes—
578C2×C4C22×D4×C1111yescharacteristic
579C2×C4C22×D4×C1111yescharacteristic
580C2×C4C22×D4×C1111yescharacteristic
581C2×C4C2×C11×#4111yescharacteristic
582C2×C4C11×H(5,𝔽2)11yescharacteristic
583C2×C4C11×H(5,𝔽2)11yescharacteristic
584C8—22no—
585C8—41no—
586C8—42no—
587C22—44no—
588C22—42no—
589C22—42no—
590C22—44no—
591C22—42no—
592C22—44no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—82no—
598C22—82no—
599C22—82no—
600C22—82no—
601C22C2×C11×#12011yescharacteristic
602C22D42×C1111yescharacteristic
603C22C11×#54611yescharacteristic
604C22C2×C11×#13511yescharacteristic
605C22C2×C11×#13711yescharacteristic
606C22C11×#57611yescharacteristic
607C22C11×#57711yescharacteristic
608C4—24no—
609C4—22no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—81no—
614C4—82no—
615C4C11×#45214yescomplemented
616C4C2×C11×#12111yescharacteristic
617C4C11×#53511yescharacteristic
618C4D42×C1111yescharacteristic
619C4C11×#54611yescharacteristic
620C2—82no—
621C2—84no—
622C2C11×#240811yescharacteristic
623C2C2×C11×#45211yescharacteristic
624C2C11×#301211yescharacteristic
625C2C11×#327811yescharacteristic
626C2C11×#328711yescharacteristic
627C2C11×#330411yescharacteristic
628C2C11×#333311yescharacteristic
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×#460C2semidirect
3. C2×C11×#452C2semidirect
4. C2×C4×C11×Q16C2semidirect
5. C11×#2538C2semidirect
6. C11×#2033C2semidirect
7. C11×#2000C2semidirect
8. C11×#1957C2semidirect
9. C11×#1954C2semidirect
10. C11×#1803C2semidirect
11. C11×#1788C2semidirect
64. C2×C11×Q16D4semidirect
114. #24242C11direct (N × H)
204. C2×#460C2×C11semidirect
205. C2×#452C2×C11semidirect
206. C2×C4×Q16C2×C11semidirect
207. #2538C2×C11semidirect
208. #2033C2×C11semidirect
209. #2000C2×C11semidirect
210. #1957C2×C11semidirect
211. #1954C2×C11semidirect
212. #1803C2×C11semidirect
213. #1788C2×C11semidirect
346. C4×C11#452semidirect
369. C2×Q16D4×C11semidirect
516. C11#24242direct (N × H)
615. C4C11×#452semidirect

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×#4602
C2×C11×#4522
C2×C4×C11×Q162
C11×#25382
C11×#20332
C11×#20002
C11×#19572
C11×#19542
C11×#18032
C11×#17882
#2424211