Finite Group Databasebeta

← C11×#18304 #14595497

Subgroups — C11×#18304 #14595497

Order 2816.

1054 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3455C211yesmaximal, characteristic, complemented
2C11×#3208C211yesmaximal, characteristic, complemented
3C11×#3205C211yesmaximal, characteristic, complemented
4C11×#2619C211yesmaximal, characteristic, complemented
5C11×#1600C214yesmaximal, complemented
6C11×#1597C214yesmaximal, complemented
7C11×#1518C211yesmaximal, characteristic, complemented
8C11×#1517C211yesmaximal, characteristic, complemented
9C11×#1458C211yesmaximal, characteristic, complemented
10C11×#542—21no—
11C11×#542—21no—
12C11×#541—21no—
13C11×#540—21no—
14C11×#539—21no—
15C11×#539C2212yes—
16C11×#538—21no—
17C11×#538C2212yes—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C2×C11×#127C2211yescharacteristic
21C11×#529—22no—
22C11×#529—22no—
23C11×#525—21no—
24C2×C11×#121—21no—
25C4×C11×#41—21no—
26C2×C11×#117C2211yescharacteristic
27C11×#493—21no—
28C11×#492—21no—
29C11×#486—21no—
30C11×#486—21no—
31C11×#460—22no—
32C11×#459—22no—
33C11×#450C2214yes—
34C11×#447C2214yes—
35C11×#431C2211yescharacteristic
36C11×#431C2211yescharacteristic
37C11×#394—21no—
38C11×#394C2212yes—
39C11×#392—21no—
40C11×#392C2212yes—
41C11×#390—21no—
42C11×#382C2211yescharacteristic
43C11×#328C2214yes—
44C11×#327C2214yes—
45C11×#324C2212yes—
46C11×#323C2212yes—
47C2×C11×#41—21no—
48C22×D4×C11—22no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11C2312yes—
52C23×C4×C11D411yescharacteristic
53C2×C11×SD16—24no—
54C2×C11×D8—24no—
55C11×C4⋊Q8D411yescharacteristic, complemented
56C11×C4⋊Q8D411yescharacteristic, complemented
57C11×C4⋊Q8D411yescharacteristic, complemented
58C11×#127—21no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127—21no—
62C11×#127D411yescharacteristic, complemented
63C11×#126—22no—
64C11×#126—22no—
65C11×#126—22no—
66C11×#126—22no—
67C11×#125—22no—
68C11×#125—22no—
69C11×#125—21no—
70C11×#124—22no—
71C11×#124—22no—
72C11×#124—21no—
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—22no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8C2312yes—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—22no—
87C11×#121—22no—
88C11×#121—21no—
89C11×#121—44no—
90C11×#121C2312yes—
91C11×#120—22no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11D412yescomplemented
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—21no—
103C4×D4×C11D412yescomplemented
104C11×#117—22no—
105C11×#117—21no—
106C11×#117—21no—
107C11×#117—21no—
108C11×#117—21no—
109C11×#117—21no—
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C11×C22⋊C4C2311yescharacteristic
118C2×C42×C11—22no—
119C2×C42×C11D411yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C11×C4⋊C8—21no—
122C11×C4⋊C8—21no—
123C11×#102—24no—
124C11×#102—24no—
125C11×C22⋊C8C2312yes—
126C11×C22⋊C8C2312yes—
127C4×C8×C11—21no—
128C4×C8×C11—21no—
129C11×#95—21no—
130C11×#95C2312yes—
131#18304C1111yesmaximal, characteristic, direct product factor, Sylow
132C24×C11—22no—
133C24×C11C2×D411yescharacteristic
134C11×#41—42no—
135C11×#41—42no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—44no—
147C2×D4×C11—41no—
148C2×D4×C11—41no—
149C2×D4×C11—41no—
150C2×D4×C11—41no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11—82no—
154C2×D4×C11—82no—
155C2×D4×C11—82no—
156C2×D4×C11—82no—
157C2×D4×C11C2×D412yes—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C11×SD16—84no—
173C11×D8—84no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4C2×D412yes—
192C11×C4⋊C4C2×D412yes—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—21no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—44no—
207C11×C22⋊C4—82no—
208C11×C22⋊C4—82no—
209C42×C11—22no—
210C42×C11—22no—
211C42×C11—21no—
212C42×C11—22no—
213C42×C11—21no—
214C42×C11C2×D411yescharacteristic
215C42×C11C2×D411yescharacteristic
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218#3455C2×C1111yescharacteristic, complemented
219#3208C2×C1111yescharacteristic, complemented
220#3205C2×C1111yescharacteristic, complemented
221#2619C2×C1111yescharacteristic, complemented
222#1600C2×C1114yescomplemented
223#1597C2×C1114yescomplemented
224#1518C2×C1111yescharacteristic, complemented
225#1517C2×C1111yescharacteristic, complemented
226#1458C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—22no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11C22×D411yescharacteristic
241Q8×C11—42no—
242Q8×C11—42no—
243Q8×C11—81no—
244D4×C11—42no—
245D4×C11—44no—
246D4×C11—44no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—81no—
251D4×C11—82no—
252D4×C11—82no—
253D4×C11—82no—
254D4×C11—82no—
255D4×C11—88no—
256D4×C11—82no—
257D4×C11—82no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—44no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—82no—
277C2×C4×C11—82no—
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12011yescharacteristic
280C2×C4×C11#12011yescharacteristic
281C2×C4×C11#12011yescharacteristic
282C2×C4×C11#13512yes—
283C2×C4×C11AGL(1,ℤ/8)12yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C8×C11—42no—
287C8×C11—42no—
288#542—21no—
289#542—21no—
290#541—21no—
291#540—21no—
292#539—21no—
293#539C22×C1112yes—
294#538—21no—
295#538C22×C1112yes—
296#533C22×C1111yescharacteristic
297#532C22×C1111yescharacteristic
298C2×#127C22×C1111yescharacteristic
299#529—22no—
300#529—22no—
301#525—21no—
302C2×#121—21no—
303C4×#41—21no—
304C2×#117C22×C1111yescharacteristic
305#493—21no—
306#492—21no—
307#486—21no—
308#486—21no—
309#460—22no—
310#459—22no—
311#450C22×C1114yes—
312#447C22×C1114yes—
313#431C22×C1111yescharacteristic
314#431C22×C1111yescharacteristic
315#394—21no—
316#394C22×C1112yes—
317#392—21no—
318#392C22×C1112yes—
319#390—21no—
320#382C22×C1111yescharacteristic
321#328C22×C1114yes—
322#327C22×C1114yes—
323#324C22×C1112yes—
324#323C22×C1112yes—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—42no—
328C22×C11—41no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—41no—
332C22×C11—42no—
333C22×C11—41no—
334C22×C11—81no—
335C22×C11—82no—
336C22×C11—82no—
337C22×C11—82no—
338C22×C11—82no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11C2×#12011yescharacteristic
343C22×C11C2×#13511yescharacteristic
344C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—82no—
356C4×C11#44912yes—
357C4×C11#44912yes—
358C2×#41—21no—
359C22×D4—22no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4C23×C1112yes—
363C23×C4D4×C1111yescharacteristic
364C2×SD16—24no—
365C2×D8—24no—
366C4⋊Q8D4×C1111yescharacteristic, complemented
367C4⋊Q8D4×C1111yescharacteristic, complemented
368C4⋊Q8D4×C1111yescharacteristic, complemented
369#127—21no—
370#127—21no—
371#127—21no—
372#127—21no—
373#127D4×C1111yescharacteristic, complemented
374#126—22no—
375#126—22no—
376#126—22no—
377#126—22no—
378#125—22no—
379#125—22no—
380#125—21no—
381#124—22no—
382#124—22no—
383#124—21no—
384#123—22no—
385#123—22no—
386#123—22no—
387#123—22no—
388#123—22no—
389C22⋊Q8—21no—
390C22⋊Q8—21no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8C23×C1112yes—
395#121—21no—
396#121—21no—
397#121—22no—
398#121—22no—
399#121—21no—
400#121—44no—
401#121C23×C1112yes—
402#120—22no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8D4×C1112yescomplemented
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—21no—
414C4×D4D4×C1112yescomplemented
415#117—22no—
416#117—21no—
417#117—21no—
418#117—21no—
419#117—21no—
420#117—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4D4×C1111yescharacteristic
423C2×C4⋊C4C23×C1111yescharacteristic
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4D4×C1111yescharacteristic
428C2×C22⋊C4C23×C1111yescharacteristic
429C2×C42—22no—
430C2×C42D4×C1111yescharacteristic
431C2×C42C23×C1111yescharacteristic
432C4⋊C8—21no—
433C4⋊C8—21no—
434#102—24no—
435#102—24no—
436C22⋊C8C23×C1112yes—
437C22⋊C8C23×C1112yes—
438C4×C8—21no—
439C4×C8—21no—
440#95—21no—
441#95C23×C1112yes—
442C2×C11—21no—
443C2×C11—21no—
444C2×C11—82no—
445C2×C11—81no—
446C2×C11—162no—
447C2×C11C2×#44911yescharacteristic
448C2×C11#302111yescharacteristic
449C2×C11#302711yescharacteristic
450C24—22no—
451C24C2×D4×C1111yescharacteristic
452#41—42no—
453#41—42no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8C2×D4×C1112yes—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—44no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—82no—
472C2×D4—82no—
473C2×D4—82no—
474C2×D4—82no—
475C2×D4C2×D4×C1112yes—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4C2×D4×C1111yescharacteristic
485C22×C4C2×D4×C1111yescharacteristic
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C24×C1111yescharacteristic
490SD16—84no—
491D8—84no—
492C2×C8—22no—
493C2×C8—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—42no—
509C4⋊C4C2×D4×C1112yes—
510C4⋊C4C2×D4×C1112yes—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—22no—
524C22⋊C4—44no—
525C22⋊C4—82no—
526C22⋊C4—82no—
527C42—22no—
528C42—22no—
529C42—21no—
530C42—22no—
531C42—21no—
532C42C2×D4×C1111yescharacteristic
533C42C2×D4×C1111yescharacteristic
534C42C2×D4×C1111yescharacteristic
535C42C2×D4×C1111yescharacteristic
536C11#1830411yescharacteristic, direct product factor, Sylow
537C23—21no—
538C23—22no—
539C23—21no—
540C23—21no—
541C23—41no—
542C23—41no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23C22×D4×C1111yescharacteristic
551Q8—42no—
552Q8—42no—
553Q8—81no—
554D4—42no—
555D4—44no—
556D4—44no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—81no—
561D4—82no—
562D4—82no—
563D4—82no—
564D4—82no—
565D4—88no—
566D4—82no—
567D4—82no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—44no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4C11×#12011yescharacteristic
589C2×C4C11×#12011yescharacteristic
590C2×C4C11×#12011yescharacteristic
591C2×C4C11×#12011yescharacteristic
592C2×C4C11×#13512yes—
593C2×C4C11×AGL(1,ℤ/8)12yes—
594C2×C4C22×D4×C1111yescharacteristic
595C2×C4C22×D4×C1111yescharacteristic
596C8—42no—
597C8—42no—
598C22—21no—
599C22—21no—
600C22—42no—
601C22—41no—
602C22—42no—
603C22—42no—
604C22—41no—
605C22—42no—
606C22—41no—
607C22—81no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22C2×C11×#12011yescharacteristic
616C22C2×C11×#13511yescharacteristic
617C22C2×C11×AGL(1,ℤ/8)11yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—42no—
626C4—41no—
627C4—42no—
628C4—82no—
629C4C11×#44912yes—
630C4C11×#44912yes—
631C2—21no—
632C2—21no—
633C2—81no—
634C2—82no—
635C2—162no—
636C2C2×C11×#44911yescharacteristic
637C2C11×#302111yescharacteristic
638C2C11×#302711yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3455C2semidirect
2. C11×#3208C2semidirect
3. C11×#3205C2semidirect
4. C11×#2619C2semidirect
5. C11×#1600C2semidirect
6. C11×#1597C2semidirect
7. C11×#1518C2semidirect
8. C11×#1517C2semidirect
9. C11×#1458C2semidirect
55. C11×C4⋊Q8D4semidirect
56. C11×C4⋊Q8D4semidirect
57. C11×C4⋊Q8D4semidirect
62. C11×#127D4semidirect
95. C4×Q8×C11D4semidirect
103. C4×D4×C11D4semidirect
131. #18304C11direct (N × H)
218. #3455C2×C11semidirect
219. #3208C2×C11semidirect
220. #3205C2×C11semidirect
221. #2619C2×C11semidirect
222. #1600C2×C11semidirect
223. #1597C2×C11semidirect
224. #1518C2×C11semidirect
225. #1517C2×C11semidirect
226. #1458C2×C11semidirect
366. C4⋊Q8D4×C11semidirect
367. C4⋊Q8D4×C11semidirect
368. C4⋊Q8D4×C11semidirect
373. #127D4×C11semidirect
406. C4×Q8D4×C11semidirect
414. C4×D4D4×C11semidirect
536. C11#18304direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34552
C11×#32082
C11×#32052
C11×#26192
C11×#16002
C11×#15972
C11×#15182
C11×#15172
C11×#14582
#1830411