Finite Group Databasebeta

← C11×#18207 #14595400

Subgroups — C11×#18207 #14595400

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3505C211yesmaximal, characteristic
2C2×C11×#484C211yesmaximal, characteristic, complemented
3C2×C11×#481C211yesmaximal, characteristic, complemented
4C11×#2487C211yesmaximal, characteristic, complemented
5C11×#1618C214yesmaximal, complemented
6C11×#1615C214yesmaximal, complemented
7C11×#1520C211yesmaximal, characteristic, complemented
8C11×#1519C211yesmaximal, characteristic, complemented
9C11×#1459C211yesmaximal, characteristic, complemented
10C11×#553—22no—
11C11×#553—21no—
12C11×#552—21no—
13C11×#551—22no—
14C11×#548—21no—
15C11×#546—21no—
16C11×#539C2212yes—
17C11×#538C2212yes—
18C11×#534—21no—
19C11×#529—21no—
20C11×#525—21no—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C11×#518—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C11×#484—22no—
27C11×#484C2214yescomplemented
28C11×#481—22no—
29C11×#481C2214yes—
30C2×C11×#107—21no—
31C2×C11×#106—21no—
32C2×C11×#103—21no—
33C2×C11×#102—21no—
34C2×C11×C22⋊C8C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#400C2212yescomplemented
37C11×#399C2212yescomplemented
38C11×#389—21no—
39C11×#386—21no—
40C11×#385—21no—
41C11×#380—21no—
42C11×#380C2211yescharacteristic
43C11×#328C2214yescomplemented
44C11×#327C2214yes—
45C11×#324C2212yescomplemented
46C11×#323C2212yescomplemented
47C2×C11×#41—21no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C22×D4×C11D411yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11D411yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C22×C8×C11—21no—
56C22×C8×C11—21no—
57C11×#126—22no—
58C11×#126—22no—
59C11×#126—22no—
60C11×#125—21no—
61C11×#125—22no—
62C11×#124—21no—
63C11×#124—22no—
64C11×#123—22no—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8D412yes—
74C11×C22⋊Q8C2312yes—
75C11×#121—21no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—21no—
80C11×#121—21no—
81C11×#121D412yes—
82C11×#121C2312yes—
83C11×#120—22no—
84C11×#120—22no—
85C4×Q8×C11—21no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11—21no—
93C4×D4×C11—21no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C11×#117—22no—
97C11×#117—21no—
98C11×#117—22no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4—21no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4D411yescharacteristic
117C2×C11×C22⋊C4C2311yescharacteristic
118C2×C42×C11D411yescharacteristic
119C11×#107—24no—
120C11×#106—24no—
121C11×#103—24no—
122C11×#102—24no—
123C11×C22⋊C8—21no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8C2312yes—
126C11×C22⋊C8C2312yes—
127C11×#95—22no—
128C11×#95—22no—
129C11×#95C2312yes—
130#18207C1111yesmaximal, characteristic, direct product factor, Sylow
131C24×C11—21no—
132C24×C11C2×D411yescharacteristic
133C24×C11C2×D411yescharacteristic
134C11×#41—82no—
135C2×Q8×C11—21no—
136C2×Q8×C11—42no—
137C2×Q8×C11C2×D412yes—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—21no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11C2×D412yes—
151C22×C4×C11—21no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C22×C4×C11—82no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—42no—
177C2×C8×C11—42no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—82no—
194C11×C4⋊C4C2×D412yes—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—42no—
211C11×C22⋊C4—82no—
212C42×C11—22no—
213C42×C11—22no—
214C42×C11—21no—
215C42×C11—21no—
216#3505C2×C1111yescharacteristic
217C2×#484C2×C1111yescharacteristic, complemented
218C2×#481C2×C1111yescharacteristic, complemented
219#2487C2×C1111yescharacteristic, complemented
220#1618C2×C1114yescomplemented
221#1615C2×C1114yescomplemented
222#1520C2×C1111yescharacteristic, complemented
223#1519C2×C1111yescharacteristic, complemented
224#1459C2×C1111yescharacteristic, complemented
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—42no—
234C23×C11—81no—
235C23×C11—81no—
236C23×C11#12011yescharacteristic
237C23×C11#12011yescharacteristic
238C23×C11#13512yes—
239C23×C11#13712yes—
240C23×C11C22×D411yescharacteristic
241Q8×C11—42no—
242Q8×C11—42no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—42no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—44no—
249D4×C11—42no—
250D4×C11—82no—
251D4×C11—82no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—81no—
277C2×C4×C11—81no—
278C2×C4×C11—81no—
279C2×C4×C11—82no—
280C2×C4×C11—82no—
281C2×C4×C11—82no—
282C2×C4×C11—82no—
283C2×C4×C11#12011yescharacteristic
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C8×C11—42no—
288C8×C11—42no—
289#553—22no—
290#553—21no—
291#552—21no—
292#551—22no—
293#548—21no—
294#546—21no—
295#539C22×C1112yes—
296#538C22×C1112yes—
297#534—21no—
298#529—21no—
299#525—21no—
300C2×C22⋊Q8C22×C1111yescharacteristic
301C2×#121C22×C1111yescharacteristic
302#518—21no—
303C2×C4×D4C22×C1111yescharacteristic
304C22×C4⋊C4C22×C1111yescharacteristic
305#484—22no—
306#484C22×C1114yescomplemented
307#481—22no—
308#481C22×C1114yes—
309C2×#107—21no—
310C2×#106—21no—
311C2×#103—21no—
312C2×#102—21no—
313C2×C22⋊C8C22×C1111yescharacteristic
314C2×C22⋊C8C22×C1111yescharacteristic
315#400C22×C1112yescomplemented
316#399C22×C1112yescomplemented
317#389—21no—
318#386—21no—
319#385—21no—
320#380—21no—
321#380C22×C1111yescharacteristic
322#328C22×C1114yescomplemented
323#327C22×C1114yes—
324#324C22×C1112yescomplemented
325#323C22×C1112yescomplemented
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—41no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—42no—
341C22×C11—81no—
342C22×C11—162no—
343C22×C11#45212yes—
344C22×C11#45212yes—
345C22×C11C2×#12011yescharacteristic
346C22×C11C2×#13511yescharacteristic
347C22×C11C2×#13711yescharacteristic
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—82no—
358C4×C11—82no—
359C4×C11#45812yes—
360C2×#41—21no—
361C22×Q8D4×C1111yescharacteristic
362C22×D4—21no—
363C22×D4D4×C1111yescharacteristic
364C22×D4D4×C1111yescharacteristic
365C23×C4—21no—
366C23×C4D4×C1111yescharacteristic
367C23×C4C23×C1111yescharacteristic
368C22×C8—21no—
369C22×C8—21no—
370#126—22no—
371#126—22no—
372#126—22no—
373#125—21no—
374#125—22no—
375#124—21no—
376#124—22no—
377#123—22no—
378#123—22no—
379#123—22no—
380#123—22no—
381#123—22no—
382C22⋊Q8—21no—
383C22⋊Q8—22no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8D4×C1112yes—
387C22⋊Q8C23×C1112yes—
388#121—21no—
389#121—22no—
390#121—22no—
391#121—22no—
392#121—21no—
393#121—21no—
394#121D4×C1112yes—
395#121C23×C1112yes—
396#120—22no—
397#120—22no—
398C4×Q8—21no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—22no—
408C4×D4—22no—
409#117—22no—
410#117—21no—
411#117—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4D4×C1111yescharacteristic
421C2×C4⋊C4D4×C1111yescharacteristic
422C2×C4⋊C4C23×C1112yes—
423C2×C4⋊C4C23×C1111yescharacteristic
424C2×C22⋊C4—22no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4D4×C1111yescharacteristic
430C2×C22⋊C4C23×C1111yescharacteristic
431C2×C42D4×C1111yescharacteristic
432#107—24no—
433#106—24no—
434#103—24no—
435#102—24no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8C23×C1112yes—
439C22⋊C8C23×C1112yes—
440#95—22no—
441#95—22no—
442#95C23×C1112yes—
443C2×C11—21no—
444C2×C11—21no—
445C2×C11—22no—
446C2×C11—22no—
447C2×C11—81no—
448C2×C11—82no—
449C2×C11C2×#45211yescharacteristic
450C2×C11#302111yescharacteristic
451C2×C11C2×#45811yescharacteristic
452C24—21no—
453C24C2×D4×C1111yescharacteristic
454C24C2×D4×C1111yescharacteristic
455#41—82no—
456C2×Q8—21no—
457C2×Q8—42no—
458C2×Q8C2×D4×C1112yes—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4C2×D4×C1112yes—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—82no—
486C22×C4C2×D4×C1111yescharacteristic
487C22×C4C2×D4×C1111yescharacteristic
488C22×C4C2×D4×C1111yescharacteristic
489C22×C4C2×D4×C1111yescharacteristic
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C24×C1111yescharacteristic
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—42no—
498C2×C8—42no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—42no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—82no—
515C4⋊C4C2×D4×C1112yes—
516C4⋊C4C2×D4×C1112yes—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C22⋊C4—21no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—42no—
532C22⋊C4—82no—
533C42—22no—
534C42—22no—
535C42—21no—
536C42—21no—
537C11#1820711yescharacteristic, direct product factor, Sylow
538C23—21no—
539C23—22no—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—42no—
547C23—81no—
548C23—81no—
549C23C11×#12011yescharacteristic
550C23C11×#12011yescharacteristic
551C23C11×#13512yes—
552C23C11×#13712yes—
553C23C22×D4×C1111yescharacteristic
554Q8—42no—
555Q8—42no—
556D4—42no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—44no—
562D4—42no—
563D4—82no—
564D4—82no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4C11×#12011yescharacteristic
597C2×C4C11×#12011yescharacteristic
598C2×C4C22×D4×C1111yescharacteristic
599C2×C4C22×D4×C1111yescharacteristic
600C8—42no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—41no—
612C22—42no—
613C22—42no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—81no—
618C22—162no—
619C22C11×#45212yes—
620C22C11×#45212yes—
621C22C2×C11×#12011yescharacteristic
622C22C2×C11×#13511yescharacteristic
623C22C2×C11×#13711yescharacteristic
624C4—21no—
625C4—21no—
626C4—21no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—42no—
633C4—82no—
634C4—82no—
635C4C11×#45812yes—
636C2—21no—
637C2—21no—
638C2—22no—
639C2—22no—
640C2—81no—
641C2—82no—
642C2C2×C11×#45211yescharacteristic
643C2C11×#302111yescharacteristic
644C2C2×C11×#45811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3505C2
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
2. C2×C11×#484C2semidirect
3. C2×C11×#481C2semidirect
4. C11×#2487C2semidirect
5. C11×#1618C2semidirect
6. C11×#1615C2semidirect
7. C11×#1520C2semidirect
8. C11×#1519C2semidirect
9. C11×#1459C2semidirect
27. C11×#484C22semidirect
36. C11×#400C22semidirect
37. C11×#399C22semidirect
43. C11×#328C22semidirect
45. C11×#324C22semidirect
46. C11×#323C22semidirect
130. #18207C11direct (N × H)
217. C2×#484C2×C11semidirect
218. C2×#481C2×C11semidirect
219. #2487C2×C11semidirect
220. #1618C2×C11semidirect
221. #1615C2×C11semidirect
222. #1520C2×C11semidirect
223. #1519C2×C11semidirect
224. #1459C2×C11semidirect
306. #484C22×C11semidirect
315. #400C22×C11semidirect
316. #399C22×C11semidirect
322. #328C22×C11semidirect
324. #324C22×C11semidirect
325. #323C22×C11semidirect
537. C11#18207direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35052
C2×C11×#4842
C2×C11×#4812
C11×#24872
C11×#16182
C11×#16152
C11×#15202
C11×#15192
C11×#14592
#1820711