Finite Group Databasebeta

← C11×#18378 #14595571

Subgroups — C11×#18378 #14595571

Order 2816.

1006 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3492C211yesmaximal, characteristic, complemented
2C11×#3188C212yesmaximal, complemented
3C11×#2591C211yesmaximal, characteristic, complemented
4C11×#1617C211yesmaximal, characteristic, complemented
5C11×#1616C211yesmaximal, characteristic, complemented
6C11×#1615C212yesmaximal, complemented
7C11×#1599C211yesmaximal, characteristic, complemented
8C11×#1598C211yesmaximal, characteristic, complemented
9C11×#1597C212yesmaximal, complemented
10C11×#1501C212yesmaximal, complemented
11C2×C11×#324C211yesmaximal, characteristic, complemented
12C11×#554—22no—
13C11×#553—22no—
14C11×#552—22no—
15C11×#547—22no—
16C11×#544C2211yescharacteristic
17C11×#539—21no—
18C11×#539C2212yes—
19C11×#537C2211yescharacteristic
20C11×#525—21no—
21C11×#525—21no—
22C11×#525C2212yes—
23C2×C11×#121C2211yescharacteristic
24C11×#520—21no—
25C22×C11×C4⋊C4C2211yescharacteristic
26C11×#484C2212yes—
27C11×#482—22no—
28C11×#481C2212yes—
29C11×#466—22no—
30C11×#465—22no—
31C11×#450C2212yes—
32C11×#449—22no—
33C11×#447C2212yes—
34C2×C11×C22⋊C8C2212yes—
35C11×#400C2211yescharacteristic
36C11×#400C2211yescharacteristic
37C11×#394C2211yescharacteristic
38C11×#394C2211yescharacteristic
39C11×#388—21no—
40C11×#388—21no—
41C11×#386—21no—
42C11×#386—21no—
43C4×C11×C22⋊C4C2211yescharacteristic
44C11×#328C2212yes—
45C11×#328C2212yes—
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2212yes—
49C11×#324C2211yescharacteristic
50C11×#324C2211yescharacteristic
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41D412yes—
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D411yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C2×C11×SD16—22no—
60C2×C11×D8—22no—
61C22×C8×C11—22no—
62C11×C4⋊Q8—22no—
63C11×#126—22no—
64C11×#126—22no—
65C11×#125—22no—
66C11×#125—22no—
67C11×#125—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8D412yes—
81C11×C22⋊Q8C2312yes—
82C11×#121—21no—
83C11×#121—21no—
84C11×#121—21no—
85C11×#121—22no—
86C11×#121—21no—
87C11×#121—22no—
88C11×#121—22no—
89C11×#121D412yes—
90C11×#121C2312yes—
91C11×#120—22no—
92C4×Q8×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C11×#117—22no—
101C11×#117—21no—
102C11×#117—21no—
103C11×#117D412yes—
104C2×C11×C4⋊C4—22no—
105C2×C11×C4⋊C4—22no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C42×C11—21no—
119C11×#107—22no—
120C11×#106—22no—
121C11×#103—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×#102—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8C2312yes—
127C11×C22⋊C8C2312yes—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18378C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C11×#41—42no—
138C11×#41—42no—
139C11×#41—82no—
140C11×#41—82no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11C2×D412yes—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—22no—
150C2×D4×C11—42no—
151C2×D4×C11—42no—
152C2×D4×C11—41no—
153C2×D4×C11—41no—
154C2×D4×C11—81no—
155C2×D4×C11C2×D412yes—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—41no—
168C22×C4×C11—81no—
169C22×C4×C11—81no—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2411yescharacteristic
178C11×SD16—82no—
179C11×D8—82no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—82no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4C2×D412yes—
199C11×C4⋊C4C2×D412yes—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—42no—
213C11×C22⋊C4—81no—
214C11×C22⋊C4—81no—
215C42×C11—22no—
216C42×C11—22no—
217C42×C11—22no—
218C42×C11—81no—
219#3492C2×C1111yescharacteristic, complemented
220#3188C2×C1112yescomplemented
221#2591C2×C1111yescharacteristic, complemented
222#1617C2×C1111yescharacteristic, complemented
223#1616C2×C1111yescharacteristic, complemented
224#1615C2×C1112yescomplemented
225#1599C2×C1111yescharacteristic, complemented
226#1598C2×C1111yescharacteristic, complemented
227#1597C2×C1112yescomplemented
228#1501C2×C1112yescomplemented
229C2×#324C2×C1111yescharacteristic, complemented
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11#12011yescharacteristic
243C23×C11#12011yescharacteristic
244C23×C11C22×D411yescharacteristic
245Q8×C11—42no—
246Q8×C11—42no—
247Q8×C11—81no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—44no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11—44no—
256D4×C11—81no—
257D4×C11—82no—
258D4×C11—82no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—41no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—41no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—44no—
276C2×C4×C11—42no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—82no—
289C2×C4×C11—81no—
290C2×C4×C11—82no—
291C2×C4×C11#12012yes—
292C2×C4×C11#13512yes—
293C2×C4×C11C22×D412yes—
294C8×C11—42no—
295C8×C11—42no—
296#554—22no—
297#553—22no—
298#552—22no—
299#547—22no—
300#544C22×C1111yescharacteristic
301#539—21no—
302#539C22×C1112yes—
303#537C22×C1111yescharacteristic
304#525—21no—
305#525—21no—
306#525C22×C1112yes—
307C2×#121C22×C1111yescharacteristic
308#520—21no—
309C22×C4⋊C4C22×C1111yescharacteristic
310#484C22×C1112yes—
311#482—22no—
312#481C22×C1112yes—
313#466—22no—
314#465—22no—
315#450C22×C1112yes—
316#449—22no—
317#447C22×C1112yes—
318C2×C22⋊C8C22×C1112yes—
319#400C22×C1111yescharacteristic
320#400C22×C1111yescharacteristic
321#394C22×C1111yescharacteristic
322#394C22×C1111yescharacteristic
323#388—21no—
324#388—21no—
325#386—21no—
326#386—21no—
327C4×C22⋊C4C22×C1111yescharacteristic
328#328C22×C1112yes—
329#328C22×C1112yes—
330#327C22×C1112yes—
331#327C22×C1112yes—
332#324C22×C1112yes—
333#324C22×C1111yescharacteristic
334#324C22×C1111yescharacteristic
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11#45412yes—
355C22×C11C2×#12011yescharacteristic
356C22×C11C2×#13511yescharacteristic
357C22×C11#57511yescharacteristic
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—41no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11—81no—
370C2×#41—21no—
371C2×#41—21no—
372C2×#41D4×C1112yes—
373C22×D4—21no—
374C22×D4C23×C1111yescharacteristic
375C23×C4D4×C1111yescharacteristic
376C23×C4D4×C1111yescharacteristic
377C23×C4C23×C1111yescharacteristic
378C2×SD16—22no—
379C2×D8—22no—
380C22×C8—22no—
381C4⋊Q8—22no—
382#126—22no—
383#126—22no—
384#125—22no—
385#125—22no—
386#125—22no—
387#123—22no—
388#123—22no—
389#123—22no—
390#123—22no—
391#123—22no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8D4×C1112yes—
400C22⋊Q8C23×C1112yes—
401#121—21no—
402#121—21no—
403#121—21no—
404#121—22no—
405#121—21no—
406#121—22no—
407#121—22no—
408#121D4×C1112yes—
409#121C23×C1112yes—
410#120—22no—
411C4×Q8—22no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419#117—22no—
420#117—21no—
421#117—21no—
422#117D4×C1112yes—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4D4×C1111yescharacteristic
427C2×C4⋊C4D4×C1111yescharacteristic
428C2×C4⋊C4C23×C1111yescharacteristic
429C2×C4⋊C4C23×C1111yescharacteristic
430C2×C4⋊C4C23×C1111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C42—21no—
438#107—22no—
439#106—22no—
440#103—22no—
441#102—22no—
442#102—22no—
443#102—22no—
444C22⋊C8—22no—
445C22⋊C8C23×C1112yes—
446C22⋊C8C23×C1112yes—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95C23×C1111yescharacteristic
452#95C23×C1111yescharacteristic
453C2×C11—21no—
454C2×C11—21no—
455C2×C11—22no—
456C2×C11—41no—
457C2×C11—82no—
458C2×C11—161no—
459C2×C11#300211yescharacteristic
460C2×C11C2×#45411yescharacteristic
461C2×C11#302611yescharacteristic
462C24—21no—
463C24C2×D4×C1111yescharacteristic
464#41—42no—
465#41—42no—
466#41—82no—
467#41—82no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8C2×D4×C1112yes—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—81no—
482C2×D4C2×D4×C1112yes—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4C2×D4×C1111yescharacteristic
498C22×C4C2×D4×C1111yescharacteristic
499C22×C4C2×D4×C1111yescharacteristic
500C22×C4C2×D4×C1111yescharacteristic
501C22×C4C2×D4×C1111yescharacteristic
502C22×C4C2×D4×C1112yes—
503C22×C4C2×D4×C1112yes—
504C22×C4C24×C1111yescharacteristic
505SD16—82no—
506D8—82no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—82no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4C2×D4×C1112yes—
526C4⋊C4C2×D4×C1112yes—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—81no—
541C22⋊C4—81no—
542C42—22no—
543C42—22no—
544C42—22no—
545C42—81no—
546C11#1837811yescharacteristic, direct product factor, Sylow
547C23—21no—
548C23—21no—
549C23—22no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C11×#12011yescharacteristic
560C23C11×#12011yescharacteristic
561C23C22×D4×C1111yescharacteristic
562Q8—42no—
563Q8—42no—
564Q8—81no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—42no—
569D4—44no—
570D4—42no—
571D4—42no—
572D4—44no—
573D4—81no—
574D4—82no—
575D4—82no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—82no—
606C2×C4—81no—
607C2×C4—82no—
608C2×C4C11×#12012yes—
609C2×C4C11×#13512yes—
610C2×C4C22×D4×C1112yes—
611C8—42no—
612C8—42no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22C11×#45412yes—
633C22C2×C11×#12011yescharacteristic
634C22C2×C11×#13511yescharacteristic
635C22C11×#57511yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—41no—
640C4—42no—
641C4—42no—
642C4—41no—
643C4—41no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—81no—
648C2—21no—
649C2—21no—
650C2—22no—
651C2—41no—
652C2—82no—
653C2—161no—
654C2C11×#300211yescharacteristic
655C2C2×C11×#45411yescharacteristic
656C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3492C2semidirect
2. C11×#3188C2semidirect
3. C11×#2591C2semidirect
4. C11×#1617C2semidirect
5. C11×#1616C2semidirect
6. C11×#1615C2semidirect
7. C11×#1599C2semidirect
8. C11×#1598C2semidirect
9. C11×#1597C2semidirect
10. C11×#1501C2semidirect
11. C2×C11×#324C2semidirect
134. #18378C11direct (N × H)
219. #3492C2×C11semidirect
220. #3188C2×C11semidirect
221. #2591C2×C11semidirect
222. #1617C2×C11semidirect
223. #1616C2×C11semidirect
224. #1615C2×C11semidirect
225. #1599C2×C11semidirect
226. #1598C2×C11semidirect
227. #1597C2×C11semidirect
228. #1501C2×C11semidirect
229. C2×#324C2×C11semidirect
546. C11#18378direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34922
C11×#31882
C11×#25912
C11×#16172
C11×#16162
C11×#16152
C11×#15992
C11×#15982
C11×#15972
C11×#15012
C2×C11×#3242
#1837811