Finite Group Databasebeta

← C11×#23904 #14601097

Subgroups — C11×#23904 #14601097

Order 2816.

2032 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3485C211yesmaximal, characteristic, complemented
2C2×C11×#535C211yesmaximal, characteristic, complemented
3C2×C11×B(4,𝔽2)C212yesmaximal, complemented
4C11×#2613C212yesmaximal, complemented
5C11×#2021C214yesmaximal, complemented
6C11×#1899C212yesmaximal, complemented
7C11×#1889C212yesmaximal, complemented
8C11×#1782C211yesmaximal, characteristic, complemented
9C2×C11×H(5,𝔽2)C2211yescharacteristic
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic, complemented
12C11×#547—24no—
13C11×#546—24no—
14C11×#536—21no—
15C11×#535—28no—
16C11×#534—21no—
17C11×#534C2212yes—
18C2×C11×#127—21no—
19C2×C11×#124—21no—
20C11×#525—21no—
21C2×C11×#123—21no—
22C2×C11×#123C2212yes—
23C2×C11×#121—21no—
24C2×C11×#121—21no—
25C2×C11×#120C2214yes—
26C2×C11×#120C2212yes—
27C2×C11×#120C2212yescomplemented
28C11×#518C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic, complemented
30C11×B(4,𝔽2)—28no—
31C2×C11×#99C2212yes—
32C2×C11×#99C2214yes—
33C2×C11×#99C2212yescomplemented
34C11×#394—24no—
35C11×#392—24no—
36C11×#381C2212yescomplemented
37C11×#379C2214yescomplemented
38C11×#342C2214yescomplemented
39C25×C11C2312yes—
40C11×H(5,𝔽2)—24no—
41C11×H(5,𝔽2)—42no—
42C2×C11×#41—24no—
43C2×C11×#41—21no—
44C2×C11×#41—24no—
45C2×C11×#41—22no—
46C2×C11×#41—42no—
47C22×Q8×C11D411yescharacteristic, complemented
48C22×D4×C11—21no—
49C22×D4×C11—24no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—24no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—24no—
57C22×D4×C11—42no—
58C22×D4×C11D411yescharacteristic, complemented
59C22×D4×C11C2312yes—
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11D411yescharacteristic, complemented
63C23×C4×C11D411yescharacteristic, complemented
64C23×C4×C11C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×#127—28no—
67C11×#124—28no—
68C11×#124—22no—
69C11×#123—24no—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×#123—24no—
75C11×#123—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—24no—
78C11×#121—28no—
79C11×#121—28no—
80C11×#121—22no—
81C11×#121—24no—
82C11×#121—24no—
83C11×#120—22no—
84C11×#120—24no—
85C11×#120—22no—
86C11×#120—22no—
87C11×#120—24no—
88C11×#120—24no—
89C11×#120—28no—
90C11×#120—44no—
91C11×#120D418yescomplemented
92C4×D4×C11—24no—
93C4×D4×C11—24no—
94C11×#117—21no—
95C11×#117—24no—
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4D414yescomplemented
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—24no—
104C2×C11×C22⋊C4—28no—
105C2×C11×C22⋊C4D414yescomplemented
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C42×C11—21no—
110C11×#99—24no—
111C11×#99—28no—
112C11×#99—42no—
113C11×#95—24no—
114#23904C1111yesmaximal, characteristic, direct product factor, Sylow
115C24×C11—21no—
116C24×C11—24no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—24no—
120C24×C11—84no—
121C24×C11C2×D412yes—
122C24×C11C2×D411yescharacteristic
123C24×C11C2×D414yes—
124C24×C11C2×D411yescharacteristic
125C24×C11C2411yescharacteristic
126C11×#41—416no—
127C11×#41—48no—
128C11×#41—42no—
129C11×#41—42no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—41no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—24no—
140C2×D4×C11—22no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—28no—
150C2×D4×C11—28no—
151C2×D4×C11—22no—
152C2×D4×C11—41no—
153C2×D4×C11—416no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11—48no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—48no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—84no—
163C2×D4×C11—84no—
164C2×D4×C11—88no—
165C2×D4×C11C2×D414yes—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—21no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—24no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D414yes—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D414yes—
186C11×C4⋊C4—24no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—24no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—28no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—28no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—48no—
204C11×C22⋊C4—88no—
205C11×C22⋊C4C2×D414yes—
206C42×C11—24no—
207C42×C11—22no—
208#3485C2×C1111yescharacteristic, complemented
209C2×#535C2×C1111yescharacteristic, complemented
210C2×B(4,𝔽2)C2×C1112yescomplemented
211#2613C2×C1112yescomplemented
212#2021C2×C1114yescomplemented
213#1899C2×C1112yescomplemented
214#1889C2×C1112yescomplemented
215#1782C2×C1111yescharacteristic, complemented
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—24no—
219C23×C11—21no—
220C23×C11—22no—
221C23×C11—21no—
222C23×C11—28no—
223C23×C11—21no—
224C23×C11—24no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11—44no—
231C23×C11—44no—
232C23×C11—42no—
233C23×C11—44no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—44no—
237C23×C11—84no—
238C23×C11—84no—
239C23×C11—88no—
240C23×C11—82no—
241C23×C11#12012yes—
242C23×C11C22×D411yescharacteristic
243C23×C11C22×D412yes—
244C23×C11C22×D412yes—
245C23×C11H(5,𝔽2)12yes—
246Q8×C11—44no—
247Q8×C11—42no—
248D4×C11—28no—
249D4×C11—44no—
250D4×C11—48no—
251D4×C11—48no—
252D4×C11—42no—
253D4×C11—44no—
254D4×C11—42no—
255D4×C11—42no—
256D4×C11—44no—
257D4×C11—44no—
258D4×C11—84no—
259D4×C11—88no—
260D4×C11—88no—
261D4×C11—816no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—28no—
269C2×C4×C11—24no—
270C2×C4×C11—21no—
271C2×C4×C11—24no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—24no—
276C2×C4×C11—44no—
277C2×C4×C11—44no—
278C2×C4×C11—44no—
279C2×C4×C11—42no—
280C2×C4×C11—44no—
281C2×C4×C11—44no—
282C2×C4×C11—48no—
283C2×C4×C11—44no—
284C2×C4×C11—82no—
285C2×C4×C11#12012yes—
286C2×C4×C11#12012yes—
287C2×C4×C11#12012yes—
288C2×H(5,𝔽2)C22×C1111yescharacteristic
289C22×#41C22×C1111yescharacteristic
290C23×D4C22×C1111yescharacteristic, complemented
291#547—24no—
292#546—24no—
293#536—21no—
294#535—28no—
295#534—21no—
296#534C22×C1112yes—
297C2×#127—21no—
298C2×#124—21no—
299#525—21no—
300C2×#123—21no—
301C2×#123C22×C1112yes—
302C2×#121—21no—
303C2×#121—21no—
304C2×#120C22×C1114yes—
305C2×#120C22×C1112yes—
306C2×#120C22×C1112yescomplemented
307#518C22×C1111yescharacteristic
308C2×#117C22×C1111yescharacteristic, complemented
309B(4,𝔽2)—28no—
310C2×#99C22×C1112yes—
311C2×#99C22×C1114yes—
312C2×#99C22×C1112yescomplemented
313#394—24no—
314#392—24no—
315#381C22×C1112yescomplemented
316#379C22×C1114yescomplemented
317#342C22×C1114yescomplemented
318C22×C11—24no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—48no—
328C22×C11—48no—
329C22×C11—42no—
330C22×C11—41no—
331C22×C11—42no—
332C22×C11—44no—
333C22×C11—42no—
334C22×C11—44no—
335C22×C11—81no—
336C22×C11—84no—
337C22×C11—81no—
338C22×C11—88no—
339C22×C11—84no—
340C22×C11—84no—
341C22×C11—162no—
342C22×C11C2×#12011yescharacteristic
343C22×C11C2×#12011yescharacteristic
344C22×C11#53411yescharacteristic
345C22×C11D4214yes—
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—44no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—44no—
353C4×C11—84no—
354C25C23×C1112yes—
355H(5,𝔽2)—24no—
356H(5,𝔽2)—42no—
357C2×#41—24no—
358C2×#41—21no—
359C2×#41—24no—
360C2×#41—22no—
361C2×#41—42no—
362C22×Q8D4×C1111yescharacteristic, complemented
363C22×D4—21no—
364C22×D4—24no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—24no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—24no—
372C22×D4—42no—
373C22×D4D4×C1111yescharacteristic, complemented
374C22×D4C23×C1112yes—
375C22×D4C23×C1111yescharacteristic
376C22×D4C23×C1111yescharacteristic
377C23×C4D4×C1111yescharacteristic, complemented
378C23×C4D4×C1111yescharacteristic, complemented
379C23×C4C23×C1111yescharacteristic
380C4⋊Q8—22no—
381#127—28no—
382#124—28no—
383#124—22no—
384#123—24no—
385#123—22no—
386#123—22no—
387#123—22no—
388#123—22no—
389#123—24no—
390#123—22no—
391C22⋊Q8—22no—
392C22⋊Q8—24no—
393#121—28no—
394#121—28no—
395#121—22no—
396#121—24no—
397#121—24no—
398#120—22no—
399#120—24no—
400#120—22no—
401#120—22no—
402#120—24no—
403#120—24no—
404#120—28no—
405#120—44no—
406#120D4×C1118yescomplemented
407C4×D4—24no—
408C4×D4—24no—
409#117—21no—
410#117—24no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4D4×C1114yescomplemented
414C2×C22⋊C4—22no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4D4×C1114yescomplemented
421C2×C22⋊C4C23×C1114yes—
422C2×C22⋊C4C23×C1112yes—
423C2×C22⋊C4C23×C1112yes—
424C2×C42—21no—
425#99—24no—
426#99—28no—
427#99—42no—
428#95—24no—
429C2×C11—21no—
430C2×C11—24no—
431C2×C11—21no—
432C2×C11—42no—
433C2×C11—84no—
434C2×C11—81no—
435C2×C11—82no—
436C2×C11#240311yescharacteristic
437C2×C11#302712yes—
438C24—21no—
439C24—24no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—84no—
444C24C2×D4×C1112yes—
445C24C2×D4×C1111yescharacteristic
446C24C2×D4×C1114yes—
447C24C2×D4×C1111yescharacteristic
448C24C24×C1111yescharacteristic
449#41—416no—
450#41—48no—
451#41—42no—
452#41—42no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—41no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—24no—
460C2×D4—22no—
461C2×D4—21no—
462C2×D4—24no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—22no—
475C2×D4—41no—
476C2×D4—416no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—48no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—48no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—84no—
486C2×D4—84no—
487C2×D4—88no—
488C2×D4C2×D4×C1114yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4C2×D4×C1112yes—
503C22×C4C2×D4×C1111yescharacteristic
504C22×C4C2×D4×C1114yes—
505C22×C4C2×D4×C1111yescharacteristic
506C22×C4C2×D4×C1111yescharacteristic
507C22×C4C2×D4×C1111yescharacteristic
508C22×C4C2×D4×C1114yes—
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—22no—
512C4⋊C4—24no—
513C4⋊C4—24no—
514C22⋊C4—22no—
515C22⋊C4—28no—
516C22⋊C4—24no—
517C22⋊C4—24no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—24no—
522C22⋊C4—28no—
523C22⋊C4—24no—
524C22⋊C4—24no—
525C22⋊C4—24no—
526C22⋊C4—48no—
527C22⋊C4—88no—
528C22⋊C4C2×D4×C1114yes—
529C42—24no—
530C42—22no—
531C11#2390411yescharacteristic, direct product factor, Sylow
532C23—21no—
533C23—21no—
534C23—22no—
535C23—21no—
536C23—24no—
537C23—21no—
538C23—28no—
539C23—21no—
540C23—24no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—48no—
545C23—48no—
546C23—44no—
547C23—44no—
548C23—42no—
549C23—44no—
550C23—42no—
551C23—42no—
552C23—44no—
553C23—84no—
554C23—84no—
555C23—88no—
556C23—82no—
557C23C11×#12012yes—
558C23C22×D4×C1111yescharacteristic
559C23C22×D4×C1112yes—
560C23C22×D4×C1112yes—
561C23C11×H(5,𝔽2)12yes—
562Q8—44no—
563Q8—42no—
564D4—28no—
565D4—44no—
566D4—48no—
567D4—48no—
568D4—42no—
569D4—44no—
570D4—42no—
571D4—42no—
572D4—44no—
573D4—44no—
574D4—84no—
575D4—88no—
576D4—88no—
577D4—816no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—28no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—44no—
595C2×C4—42no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—48no—
599C2×C4—44no—
600C2×C4—82no—
601C2×C4C11×#12012yes—
602C2×C4C11×#12012yes—
603C2×C4C11×#12012yes—
604C22—24no—
605C22—22no—
606C22—22no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—44no—
612C22—44no—
613C22—48no—
614C22—48no—
615C22—42no—
616C22—41no—
617C22—42no—
618C22—44no—
619C22—42no—
620C22—44no—
621C22—81no—
622C22—84no—
623C22—81no—
624C22—88no—
625C22—84no—
626C22—84no—
627C22—162no—
628C22C2×C11×#12011yescharacteristic
629C22C2×C11×#12011yescharacteristic
630C22C11×#53411yescharacteristic
631C22D42×C1114yes—
632C4—22no—
633C4—22no—
634C4—22no—
635C4—44no—
636C4—42no—
637C4—41no—
638C4—44no—
639C4—84no—
640C2—21no—
641C2—24no—
642C2—21no—
643C2—42no—
644C2—84no—
645C2—81no—
646C2—82no—
647C2C11×#240311yescharacteristic
648C2C11×#302712yes—
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3485C2semidirect
2. C2×C11×#535C2semidirect
3. C2×C11×B(4,𝔽2)C2semidirect
4. C11×#2613C2semidirect
5. C11×#2021C2semidirect
6. C11×#1899C2semidirect
7. C11×#1889C2semidirect
8. C11×#1782C2semidirect
11. C23×D4×C11C22semidirect
27. C2×C11×#120C22semidirect
29. C2×C11×#117C22semidirect
33. C2×C11×#99C22semidirect
36. C11×#381C22semidirect
37. C11×#379C22semidirect
38. C11×#342C22semidirect
47. C22×Q8×C11D4semidirect
58. C22×D4×C11D4semidirect
62. C23×C4×C11D4semidirect
63. C23×C4×C11D4semidirect
91. C11×#120D4semidirect
98. C2×C11×C4⋊C4D4semidirect
105. C2×C11×C22⋊C4D4semidirect
114. #23904C11direct (N × H)
208. #3485C2×C11semidirect
209. C2×#535C2×C11semidirect
210. C2×B(4,𝔽2)C2×C11semidirect
211. #2613C2×C11semidirect
212. #2021C2×C11semidirect
213. #1899C2×C11semidirect
214. #1889C2×C11semidirect
215. #1782C2×C11semidirect
290. C23×D4C22×C11semidirect
306. C2×#120C22×C11semidirect
308. C2×#117C22×C11semidirect
312. C2×#99C22×C11semidirect
315. #381C22×C11semidirect
316. #379C22×C11semidirect
317. #342C22×C11semidirect
362. C22×Q8D4×C11semidirect
373. C22×D4D4×C11semidirect
377. C23×C4D4×C11semidirect
378. C23×C4D4×C11semidirect
406. #120D4×C11semidirect
413. C2×C4⋊C4D4×C11semidirect
420. C2×C22⋊C4D4×C11semidirect
531. C11#23904direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34852
C2×C11×#5352
C2×C11×B(4,𝔽2)2
C11×#26132
C11×#20212
C11×#18992
C11×#18892
C11×#17822
#2390411