Finite Group Databasebeta

← C11×#23932 #14601125

Subgroups — C11×#23932 #14601125

Order 2816.

1556 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#532C211yesmaximal, characteristic, complemented
2C2×C11×#449C212yesmaximal, complemented
3C11×#2297C211yesmaximal, characteristic, complemented
4C11×#2024C211yesmaximal, characteristic, complemented
5C11×#2023C211yesmaximal, characteristic, complemented
6C11×#2014C211yesmaximal, characteristic, complemented
7C11×#2011C211yesmaximal, characteristic, complemented
8C11×#1879C212yesmaximal, complemented
9C11×#1877C212yesmaximal, complemented
10C11×#1875C212yesmaximal, complemented
11C11×#1817C211yesmaximal, characteristic, complemented
12C22×C11×#41—21no—
13C22×C11×#41C2211yescharacteristic
14C22×C11×SD16C2212yes—
15C22×C11×D8C2212yes—
16C11×#532—28no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#127C2211yescharacteristic
19C2×C11×#124—21no—
20C2×C11×#121—21no—
21C2×C11×#121C2212yes—
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2212yes—
24C2×C11×#117C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C11×#449—28no—
27C2×C11×#103C2212yes—
28C2×C11×#102C2212yes—
29C2×C11×#102C2212yes—
30C2×C11×#102C2212yes—
31C2×C11×C22⋊C8C2212yes—
32C11×#391C2211yescharacteristic
33C11×#391C2211yescharacteristic
34C11×#390C2211yescharacteristic
35C11×#390C2211yescharacteristic
36C11×#386—21no—
37C11×#386—21no—
38C4×C11×C22⋊C4—21no—
39C4×C11×C22⋊C4—21no—
40C11×#340C2212yes—
41C11×#340C2212yes—
42C11×#336C2212yes—
43C11×#336C2211yescharacteristic
44C11×#336C2211yescharacteristic
45C2×C11×#41—28no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—24no—
49C2×C11×#41—42no—
50C2×C11×#41—44no—
51C2×C11×#41—44no—
52C22×Q8×C11—21no—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11C2312yes—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—22no—
62C23×C4×C11D411yescharacteristic
63C23×C4×C11D411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C2×C11×SD16—24no—
66C2×C11×SD16—24no—
67C2×C11×SD16—42no—
68C2×C11×D8—24no—
69C2×C11×D8—24no—
70C2×C11×D8—42no—
71C22×C8×C11C2312yes—
72C22×C8×C11C2312yes—
73C11×C4⋊Q8—24no—
74C11×#127—24no—
75C11×#124—28no—
76C11×#121—28no—
77C11×#121—24no—
78C11×#121D418yes—
79C4×D4×C11—28no—
80C4×D4×C11—24no—
81C4×D4×C11—24no—
82C11×#117—42no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C42×C11—24no—
95C2×C42×C11—21no—
96C2×C42×C11D411yescharacteristic
97C2×C42×C11D411yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C11×#103—24no—
101C11×#102—24no—
102C11×#102—42no—
103C11×#102—42no—
104C11×C22⋊C8—24no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109#23932C1111yesmaximal, characteristic, direct product factor, Sylow
110C24×C11—21no—
111C24×C11—22no—
112C24×C11C2×D411yescharacteristic
113C11×#41—48no—
114C11×#41—48no—
115C11×#41—432no—
116C2×Q8×C11—24no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11#4112yescomplemented
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—28no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11C2×D414yes—
144C2×D4×C11#4112yescomplemented
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—28no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—41no—
160C22×C4×C11—42no—
161C22×C4×C11—44no—
162C22×C4×C11—42no—
163C22×C4×C11—44no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D414yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C11×SD16—48no—
172C11×D8—48no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4C2×D414yes—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—22no—
194C42×C11—22no—
195C42×C11—42no—
196C2×#532C2×C1111yescharacteristic, complemented
197C2×#449C2×C1112yescomplemented
198#2297C2×C1111yescharacteristic, complemented
199#2024C2×C1111yescharacteristic, complemented
200#2023C2×C1111yescharacteristic, complemented
201#2014C2×C1111yescharacteristic, complemented
202#2011C2×C1111yescharacteristic, complemented
203#1879C2×C1112yescomplemented
204#1877C2×C1112yescomplemented
205#1875C2×C1112yescomplemented
206#1817C2×C1111yescharacteristic, complemented
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—42no—
217C23×C11—41no—
218C23×C11—42no—
219C23×C11—41no—
220C23×C11—42no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11#12012yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—24no—
230Q8×C11—48no—
231Q8×C11—42no—
232D4×C11—24no—
233D4×C11—24no—
234D4×C11—24no—
235D4×C11—48no—
236D4×C11—48no—
237D4×C11—48no—
238D4×C11—416no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—42no—
242C2×C4×C11—28no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—21no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—44no—
259C2×C4×C11—48no—
260C2×C4×C11—416no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11#12012yes—
272C2×C4×C11#13512yes—
273C2×C4×C11AGL(1,ℤ/8)12yes—
274C2×C4×C11AGL(1,ℤ/8)12yes—
275C2×C4×C11C22×D412yes—
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)12yes—
279C8×C11—42no—
280C8×C11—42no—
281C22×#41—21no—
282C22×#41C22×C1111yescharacteristic
283C22×SD16C22×C1112yes—
284C22×D8C22×C1112yes—
285#532—28no—
286C2×C4⋊Q8C22×C1111yescharacteristic
287C2×#127C22×C1111yescharacteristic
288C2×#124—21no—
289C2×#121—21no—
290C2×#121C22×C1112yes—
291C2×C4×D4—21no—
292C2×C4×D4C22×C1112yes—
293C2×#117C22×C1111yescharacteristic
294C22×C42C22×C1111yescharacteristic
295#449—28no—
296C2×#103C22×C1112yes—
297C2×#102C22×C1112yes—
298C2×#102C22×C1112yes—
299C2×#102C22×C1112yes—
300C2×C22⋊C8C22×C1112yes—
301#391C22×C1111yescharacteristic
302#391C22×C1111yescharacteristic
303#390C22×C1111yescharacteristic
304#390C22×C1111yescharacteristic
305#386—21no—
306#386—21no—
307C4×C22⋊C4—21no—
308C4×C22⋊C4—21no—
309#340C22×C1112yes—
310#340C22×C1112yes—
311#336C22×C1112yes—
312#336C22×C1111yescharacteristic
313#336C22×C1111yescharacteristic
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—82no—
328C22×C11—82no—
329C22×C11—81no—
330C22×C11—82no—
331C22×C11—81no—
332C22×C11—82no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11C2×#12011yescharacteristic
336C22×C11#52511yescharacteristic
337C22×C11#53511yescharacteristic
338C22×C11C2×#13511yescharacteristic
339C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C11#57511yescharacteristic
342C4×C11—22no—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—22no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—44no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11#54612yes—
352C4×C11#54612yes—
353C2×#41—28no—
354C2×#41—22no—
355C2×#41—22no—
356C2×#41—24no—
357C2×#41—42no—
358C2×#41—44no—
359C2×#41—44no—
360C22×Q8—21no—
361C22×Q8C23×C1111yescharacteristic
362C22×D4—22no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4C23×C1112yes—
367C22×D4C23×C1111yescharacteristic
368C23×C4—22no—
369C23×C4—21no—
370C23×C4D4×C1111yescharacteristic
371C23×C4D4×C1111yescharacteristic
372C23×C4C23×C1111yescharacteristic
373C2×SD16—24no—
374C2×SD16—24no—
375C2×SD16—42no—
376C2×D8—24no—
377C2×D8—24no—
378C2×D8—42no—
379C22×C8C23×C1112yes—
380C22×C8C23×C1112yes—
381C4⋊Q8—24no—
382#127—24no—
383#124—28no—
384#121—28no—
385#121—24no—
386#121D4×C1118yes—
387C4×D4—28no—
388C4×D4—24no—
389C4×D4—24no—
390#117—42no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1112yes—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C42—24no—
403C2×C42—21no—
404C2×C42D4×C1111yescharacteristic
405C2×C42D4×C1111yescharacteristic
406C2×C42C23×C1111yescharacteristic
407C2×C42C23×C1111yescharacteristic
408#103—24no—
409#102—24no—
410#102—42no—
411#102—42no—
412C22⋊C8—24no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417C2×C11—42no—
418C2×C11—82no—
419C2×C11—84no—
420C2×C11#240411yescharacteristic
421C2×C11#300211yescharacteristic
422C2×C11#300311yescharacteristic
423C2×C11#310611yescharacteristic
424C2×C11#311511yescharacteristic
425C2×C11#320711yescharacteristic
426C2×C11#321411yescharacteristic
427C24—21no—
428C24—22no—
429C24C2×D4×C1111yescharacteristic
430#41—48no—
431#41—48no—
432#41—432no—
433C2×Q8—24no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—42no—
438C2×Q8—42no—
439C2×Q8C11×#4112yescomplemented
440C2×D4—24no—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—28no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4C2×D4×C1114yes—
461C2×D4C11×#4112yescomplemented
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—28no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477C22×C4—42no—
478C22×C4—44no—
479C22×C4—42no—
480C22×C4—44no—
481C22×C4C2×D4×C1111yescharacteristic
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C2×D4×C1114yes—
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C24×C1111yescharacteristic
488SD16—48no—
489D8—48no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4C2×D4×C1114yes—
501C22⋊C4—28no—
502C22⋊C4—28no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—42no—
513C11#2393211yescharacteristic, direct product factor, Sylow
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—24no—
521C23—22no—
522C23—41no—
523C23—42no—
524C23—41no—
525C23—42no—
526C23—41no—
527C23—42no—
528C23—41no—
529C23—41no—
530C23—42no—
531C23—42no—
532C23—41no—
533C23—42no—
534C23C11×#12012yes—
535C23C22×D4×C1111yescharacteristic
536Q8—24no—
537Q8—48no—
538Q8—42no—
539D4—24no—
540D4—24no—
541D4—24no—
542D4—48no—
543D4—48no—
544D4—48no—
545D4—416no—
546D4—42no—
547D4—42no—
548D4—42no—
549C2×C4—28no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—21no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—416no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4C11×#12012yes—
579C2×C4C11×#13512yes—
580C2×C4C11×AGL(1,ℤ/8)12yes—
581C2×C4C11×AGL(1,ℤ/8)12yes—
582C2×C4C22×D4×C1112yes—
583C2×C4C2×C11×#4111yescharacteristic
584C2×C4C2×C11×#4111yescharacteristic
585C2×C4C11×H(5,𝔽2)12yes—
586C8—42no—
587C8—42no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—42no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—42no—
600C22—42no—
601C22—81no—
602C22—82no—
603C22—81no—
604C22—82no—
605C22—81no—
606C22—81no—
607C22—82no—
608C22—82no—
609C22C2×C11×#12011yescharacteristic
610C22C11×#52511yescharacteristic
611C22C11×#53511yescharacteristic
612C22C2×C11×#13511yescharacteristic
613C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
614C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
615C22C11×#57511yescharacteristic
616C4—22no—
617C4—22no—
618C4—22no—
619C4—22no—
620C4—42no—
621C4—41no—
622C4—44no—
623C4—81no—
624C4—81no—
625C4C11×#54612yes—
626C4C11×#54612yes—
627C2—42no—
628C2—82no—
629C2—84no—
630C2C11×#240411yescharacteristic
631C2C11×#300211yescharacteristic
632C2C11×#300311yescharacteristic
633C2C11×#310611yescharacteristic
634C2C11×#311511yescharacteristic
635C2C11×#320711yescharacteristic
636C2C11×#321411yescharacteristic
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C22×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#532C2semidirect
2. C2×C11×#449C2semidirect
3. C11×#2297C2semidirect
4. C11×#2024C2semidirect
5. C11×#2023C2semidirect
6. C11×#2014C2semidirect
7. C11×#2011C2semidirect
8. C11×#1879C2semidirect
9. C11×#1877C2semidirect
10. C11×#1875C2semidirect
11. C11×#1817C2semidirect
109. #23932C11direct (N × H)
122. C2×Q8×C11#41semidirect
144. C2×D4×C11#41semidirect
196. C2×#532C2×C11semidirect
197. C2×#449C2×C11semidirect
198. #2297C2×C11semidirect
199. #2024C2×C11semidirect
200. #2023C2×C11semidirect
201. #2014C2×C11semidirect
202. #2011C2×C11semidirect
203. #1879C2×C11semidirect
204. #1877C2×C11semidirect
205. #1875C2×C11semidirect
206. #1817C2×C11semidirect
439. C2×Q8C11×#41semidirect
461. C2×D4C11×#41semidirect
513. C11#23932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5322
C2×C11×#4492
C11×#22972
C11×#20242
C11×#20232
C11×#20142
C11×#20112
C11×#18792
C11×#18772
C11×#18752
C11×#18172
#2393211