Finite Group Databasebeta

← C11×#24263 #14601456

Subgroups — C11×#24263 #14601456

Order 2816.

1502 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
1C11×#3496C211yesmaximal, characteristic
2C2×C11×#458C212yesmaximal, complemented
3C11×#2618C212yesmaximal, complemented
4C11×#2322C211yesmaximal, characteristic, complemented
5C11×#2044C212yesmaximal, complemented
6C11×#2022C212yesmaximal, complemented
7C11×#1964C212yesmaximal, complemented
8C11×#1799C211yesmaximal, characteristic, complemented
9C11×#1790C212yesmaximal, complemented
10C2×C11×H(5,𝔽2)C2212yes—
11C11×#547—22no—
12C11×#546—24no—
13D42×C11—22no—
14C11×#537—21no—
15C11×#534—21no—
16C11×#534C2212yes—
17C11×#532—21no—
18C2×C11×#123C2211yescharacteristic
19C2×C11×#123C2214yescomplemented
20C2×C11×#121—21no—
21C2×C11×#121C2212yes—
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C11×#458—28no—
25C2×C11×#99C2212yes—
26C2×C11×#99C2214yescomplemented
27C2×C11×#99C2214yescomplemented
28C11×#398—22no—
29C11×#396—24no—
30C11×#394—22no—
31C11×#389—21no—
32C11×#388—21no—
33C11×#387—21no—
34C11×#386C2211yescharacteristic
35C11×#386C2214yescomplemented
36C11×#385—21no—
37C11×#385C2211yescharacteristic, complemented
38C11×#381C2211yescharacteristic, complemented
39C11×#380C2212yescomplemented
40C4×C11×C22⋊C4C2211yescharacteristic, complemented
41C11×#342C2212yescomplemented
42C11×H(5,𝔽2)—24no—
43C11×H(5,𝔽2)—24no—
44C11×H(5,𝔽2)—44no—
45C2×C11×#41—22no—
46C2×C11×#41—24no—
47C22×D4×C11—22no—
48C22×D4×C11—24no—
49C22×D4×C11—21no—
50C22×D4×C11D412yes—
51C22×D4×C11C2314yes—
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C11×C4⋊Q8—21no—
58C11×#127—21no—
59C11×#124—22no—
60C11×#123—24no—
61C11×#123—22no—
62C11×#123—24no—
63C11×#123—28no—
64C11×#123—44no—
65C11×#123D414yescomplemented
66C11×C22⋊Q8—24no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—24no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—22no—
73C11×#121—22no—
74C11×#121—22no—
75C11×#121—22no—
76C11×#120—24no—
77C11×#120—24no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4D412yes—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—24no—
98C2×C11×C22⋊C4D411yescharacteristic
99C2×C11×C22⋊C4D414yes—
100C2×C11×C22⋊C4C2314yes—
101C2×C11×C22⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4C2311yescharacteristic
103C2×C11×C22⋊C4C2311yescharacteristic
104C2×C42×C11—21no—
105C2×C42×C11D411yescharacteristic
106C11×#99—24no—
107C11×#99—28no—
108C11×#99—44no—
109C11×#95—21no—
110C11×#95—22no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—24no—
116#24263C1111yesmaximal, characteristic, direct product factor, Sylow
117C24×C11—22no—
118C24×C11C2×D414yes—
119C24×C11C2×D411yescharacteristic
120C24×C11C2411yescharacteristic
121C11×#41—48no—
122C11×#41—48no—
123C11×#41—44no—
124C11×#41—44no—
125C2×Q8×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—48no—
141C2×D4×C11—48no—
142C2×D4×C11—44no—
143C2×D4×C11—44no—
144C2×D4×C11—82no—
145C2×D4×C11—82no—
146C2×D4×C11C2×D412yes—
147C2×D4×C11#4112yes—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—81no—
162C22×C4×C11—81no—
163C22×C4×C11—81no—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yescomplemented
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—48no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—82no—
184C11×C4⋊C4—81no—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—48no—
197C11×C22⋊C4—81no—
198C11×C22⋊C4—84no—
199C11×C22⋊C4C2×D412yescomplemented
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—81no—
203#3496C2×C1111yescharacteristic
204C2×#458C2×C1112yescomplemented
205#2618C2×C1112yescomplemented
206#2322C2×C1111yescharacteristic, complemented
207#2044C2×C1112yescomplemented
208#2022C2×C1112yescomplemented
209#1964C2×C1112yescomplemented
210#1799C2×C1111yescharacteristic, complemented
211#1790C2×C1112yescomplemented
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11—82no—
225C23×C11—82no—
226C23×C11#12112yes—
227C23×C11C22×D411yescharacteristic
228C23×C11C22×D412yes—
229C23×C11C22×D411yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11H(5,𝔽2)12yes—
232Q8×C11—44no—
233D4×C11—24no—
234D4×C11—24no—
235D4×C11—44no—
236D4×C11—44no—
237D4×C11—48no—
238D4×C11—44no—
239D4×C11—44no—
240D4×C11—44no—
241D4×C11—44no—
242D4×C11—82no—
243D4×C11—82no—
244D4×C11—82no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—48no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—44no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—44no—
271C2×C4×C11—41no—
272C2×C4×C11—44no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—44no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—44no—
279C2×C4×C11—81no—
280C2×C4×C11#12011yescharacteristic
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11#12012yes—
283C2×C4×C11#12112yes—
284C2×H(5,𝔽2)C22×C1112yes—
285#547—22no—
286#546—24no—
287D42—22no—
288#537—21no—
289#534—21no—
290#534C22×C1112yes—
291#532—21no—
292C2×#123C22×C1111yescharacteristic
293C2×#123C22×C1114yescomplemented
294C2×#121—21no—
295C2×#121C22×C1112yes—
296C2×C4×D4C22×C1111yescharacteristic
297C22×C4⋊C4C22×C1111yescharacteristic, complemented
298#458—28no—
299C2×#99C22×C1112yes—
300C2×#99C22×C1114yescomplemented
301C2×#99C22×C1114yescomplemented
302#398—22no—
303#396—24no—
304#394—22no—
305#389—21no—
306#388—21no—
307#387—21no—
308#386C22×C1111yescharacteristic
309#386C22×C1114yescomplemented
310#385—21no—
311#385C22×C1111yescharacteristic, complemented
312#381C22×C1111yescharacteristic, complemented
313#380C22×C1112yescomplemented
314C4×C22⋊C4C22×C1111yescharacteristic, complemented
315#342C22×C1112yescomplemented
316C22×C11—21no—
317C22×C11—22no—
318C22×C11—21no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—81no—
331C22×C11—84no—
332C22×C11—84no—
333C22×C11—164no—
334C22×C11C2×#12011yescharacteristic
335C22×C11C2×#12111yescharacteristic
336C22×C11#53511yescharacteristic
337C22×C11D4212yes—
338C22×C11#54612yes—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—22no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—44no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—84no—
349C4×C11—81no—
350C4×C11—81no—
351H(5,𝔽2)—24no—
352H(5,𝔽2)—24no—
353H(5,𝔽2)—44no—
354C2×#41—22no—
355C2×#41—24no—
356C22×D4—22no—
357C22×D4—24no—
358C22×D4—21no—
359C22×D4D4×C1112yes—
360C22×D4C23×C1114yes—
361C22×D4C23×C1111yescharacteristic
362C23×C4D4×C1111yescharacteristic
363C23×C4C23×C1111yescharacteristic
364C23×C4C23×C1111yescharacteristic
365C23×C4C23×C1111yescharacteristic
366C4⋊Q8—21no—
367#127—21no—
368#124—22no—
369#123—24no—
370#123—22no—
371#123—24no—
372#123—28no—
373#123—44no—
374#123D4×C1114yescomplemented
375C22⋊Q8—24no—
376#121—22no—
377#121—22no—
378#121—24no—
379#121—22no—
380#121—22no—
381#121—22no—
382#121—22no—
383#121—22no—
384#121—22no—
385#120—24no—
386#120—24no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4D4×C1111yescharacteristic
401C2×C4⋊C4D4×C1112yes—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4D4×C1111yescharacteristic
408C2×C22⋊C4D4×C1114yes—
409C2×C22⋊C4C23×C1114yes—
410C2×C22⋊C4C23×C1111yescharacteristic
411C2×C22⋊C4C23×C1111yescharacteristic
412C2×C22⋊C4C23×C1111yescharacteristic
413C2×C42—21no—
414C2×C42D4×C1111yescharacteristic
415#99—24no—
416#99—28no—
417#99—44no—
418#95—21no—
419#95—22no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—24no—
425C2×C11—21no—
426C2×C11—22no—
427C2×C11—21no—
428C2×C11—22no—
429C2×C11—42no—
430C2×C11—84no—
431C2×C11#240811yescharacteristic
432C2×C11#302611yescharacteristic
433C2×C11#302811yescharacteristic
434C24—22no—
435C24C2×D4×C1114yes—
436C24C2×D4×C1111yescharacteristic
437C24C24×C1111yescharacteristic
438#41—48no—
439#41—48no—
440#41—44no—
441#41—44no—
442C2×Q8—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—24no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—24no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—48no—
458C2×D4—48no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—82no—
462C2×D4—82no—
463C2×D4C2×D4×C1112yes—
464C2×D4C11×#4112yes—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4C2×D4×C1114yes—
482C22×C4C2×D4×C1111yescharacteristic
483C22×C4C2×D4×C1111yescharacteristic
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1112yes—
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1112yes—
489C22×C4C2×D4×C1112yescomplemented
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—24no—
496C4⋊C4—48no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—42no—
500C4⋊C4—82no—
501C4⋊C4—81no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—24no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—24no—
508C22⋊C4—22no—
509C22⋊C4—24no—
510C22⋊C4—24no—
511C22⋊C4—22no—
512C22⋊C4—24no—
513C22⋊C4—48no—
514C22⋊C4—81no—
515C22⋊C4—84no—
516C22⋊C4C2×D4×C1112yescomplemented
517C42—21no—
518C42—21no—
519C42—81no—
520C11#2426311yescharacteristic, direct product factor, Sylow
521C23—21no—
522C23—21no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—44no—
531C23—44no—
532C23—44no—
533C23—82no—
534C23—82no—
535C23C11×#12112yes—
536C23C22×D4×C1111yescharacteristic
537C23C22×D4×C1112yes—
538C23C22×D4×C1111yescharacteristic
539C23C2×C11×#4111yescharacteristic
540C23C11×H(5,𝔽2)12yes—
541Q8—44no—
542D4—24no—
543D4—24no—
544D4—44no—
545D4—44no—
546D4—48no—
547D4—44no—
548D4—44no—
549D4—44no—
550D4—44no—
551D4—82no—
552D4—82no—
553D4—82no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—48no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—44no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—44no—
580C2×C4—41no—
581C2×C4—44no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—44no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—44no—
588C2×C4—81no—
589C2×C4C11×#12011yescharacteristic
590C2×C4C11×#12011yescharacteristic
591C2×C4C11×#12012yes—
592C2×C4C11×#12112yes—
593C22—21no—
594C22—22no—
595C22—21no—
596C22—22no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22—42no—
601C22—42no—
602C22—41no—
603C22—41no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—81no—
608C22—84no—
609C22—84no—
610C22—164no—
611C22C2×C11×#12011yescharacteristic
612C22C2×C11×#12111yescharacteristic
613C22C11×#53511yescharacteristic
614C22D42×C1112yes—
615C22C11×#54612yes—
616C4—22no—
617C4—21no—
618C4—21no—
619C4—22no—
620C4—42no—
621C4—44no—
622C4—42no—
623C4—41no—
624C4—41no—
625C4—84no—
626C4—81no—
627C4—81no—
628C2—21no—
629C2—22no—
630C2—21no—
631C2—22no—
632C2—42no—
633C2—84no—
634C2C11×#240811yescharacteristic
635C2C11×#302611yescharacteristic
636C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC11×#3496C2
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
2. C2×C11×#458C2semidirect
3. C11×#2618C2semidirect
4. C11×#2322C2semidirect
5. C11×#2044C2semidirect
6. C11×#2022C2semidirect
7. C11×#1964C2semidirect
8. C11×#1799C2semidirect
9. C11×#1790C2semidirect
19. C2×C11×#123C22semidirect
23. C22×C11×C4⋊C4C22semidirect
26. C2×C11×#99C22semidirect
27. C2×C11×#99C22semidirect
35. C11×#386C22semidirect
37. C11×#385C22semidirect
38. C11×#381C22semidirect
39. C11×#380C22semidirect
40. C4×C11×C22⋊C4C22semidirect
41. C11×#342C22semidirect
65. C11×#123D4semidirect
116. #24263C11direct (N × H)
172. C22×C4×C11C2×D4semidirect
199. C11×C22⋊C4C2×D4semidirect
204. C2×#458C2×C11semidirect
205. #2618C2×C11semidirect
206. #2322C2×C11semidirect
207. #2044C2×C11semidirect
208. #2022C2×C11semidirect
209. #1964C2×C11semidirect
210. #1799C2×C11semidirect
211. #1790C2×C11semidirect
293. C2×#123C22×C11semidirect
297. C22×C4⋊C4C22×C11semidirect
300. C2×#99C22×C11semidirect
301. C2×#99C22×C11semidirect
309. #386C22×C11semidirect
311. #385C22×C11semidirect
312. #381C22×C11semidirect
313. #380C22×C11semidirect
314. C4×C22⋊C4C22×C11semidirect
315. #342C22×C11semidirect
374. #123D4×C11semidirect
489. C22×C4C2×D4×C11semidirect
516. C22⋊C4C2×D4×C11semidirect
520. C11#24263direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34962
C2×C11×#4582
C11×#26182
C11×#23222
C11×#20442
C11×#20222
C11×#19642
C11×#17992
C11×#17902
#2426311