Finite Group Databasebeta

← C11×#18159 #14595352

Subgroups — C11×#18159 #14595352

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3459C211yesmaximal, characteristic
2C11×#3117C212yesmaximal, complemented
3C11×#2580C211yesmaximal, characteristic, complemented
4C11×#1618C212yesmaximal, complemented
5C11×#1614C211yesmaximal, characteristic, complemented
6C11×#1613C211yesmaximal, characteristic, complemented
7C11×#1606C212yesmaximal, complemented
8C11×#1602C211yesmaximal, characteristic, complemented
9C11×#1601C211yesmaximal, characteristic, complemented
10C11×#1512C212yesmaximal, complemented
11C11×#1466C211yesmaximal, characteristic, complemented
12C11×#543C2211yescharacteristic
13C11×#539—22no—
14C11×#539—21no—
15C11×#538—22no—
16C11×#538C2212yes—
17C11×#534—21no—
18C11×#534C2211yescharacteristic
19C11×#529—22no—
20C11×#529C2212yes—
21C11×#525—21no—
22C11×#525—22no—
23C2×C4×Q8×C11C2211yescharacteristic, complemented
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C11×#484C2212yescomplemented
27C11×#481C2212yes—
28C11×#479—22no—
29C11×#464—22no—
30C11×#451C2212yescomplemented
31C11×#448C2212yes—
32C11×#441—22no—
33C11×#440—22no—
34C11×#432C2212yescomplemented
35C11×#399C2211yescharacteristic
36C11×#399C2211yescharacteristic, complemented
37C11×#393C2211yescharacteristic
38C11×#393C2211yescharacteristic, complemented
39C11×#390—21no—
40C11×#389—21no—
41C11×#385—21no—
42C11×#385—21no—
43C11×#382C2211yescharacteristic, complemented
44C11×#328C2212yescomplemented
45C11×#328C2212yescomplemented
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#323C2211yescharacteristic
49C11×#323C2211yescharacteristic
50C11×#323C2212yescomplemented
51C2×C11×#41—21no—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11D411yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11D411yescharacteristic
57C23×C4×C11D411yescharacteristic
58C2×C11×Q16—22no—
59C2×C11×SD16—22no—
60C11×#126—22no—
61C11×#126—22no—
62C11×#126—22no—
63C11×#125—22no—
64C11×#125D412yes—
65C11×#124—22no—
66C11×#124D412yes—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8C2312yes—
79C11×#121—22no—
80C11×#121—21no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—21no—
84C11×#121C2312yes—
85C11×#120—22no—
86C11×#120—22no—
87C11×#120—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—22no—
90C4×Q8×C11D412yes—
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11D412yes—
99C11×#117—21no—
100C11×#117—22no—
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⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4C2311yescharacteristic
116C2×C42×C11—21no—
117C2×C42×C11—21no—
118C2×C42×C11C2311yescharacteristic
119C11×#107—22no—
120C11×#106—22no—
121C11×C4⋊C8—22no—
122C11×#103—22no—
123C11×#103—22no—
124C11×#103—22no—
125C11×#102—22no—
126C11×C22⋊C8C2312yes—
127C11×C22⋊C8C2312yes—
128C11×#97—22no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18159C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C24×C11C2×D411yescharacteristic
138C11×#41—82no—
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—42no—
142C2×Q8×C11C2×D412yes—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—41no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11C2×D412yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—81no—
168C22×C4×C11—81no—
169C22×C4×C11—82no—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C11×Q16—44no—
176C11×SD16—44no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4—41no—
191C11×C4⋊C4—41no—
192C11×C4⋊C4—81no—
193C11×C4⋊C4—81no—
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—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—42no—
209C11×C22⋊C4—42no—
210C11×C22⋊C4—81no—
211C11×C22⋊C4—81no—
212C42×C11—22no—
213C42×C11—22no—
214C42×C11—42no—
215C42×C11C2×D412yes—
216C42×C11C2×D412yes—
217#3459C2×C1111yescharacteristic
218#3117C2×C1112yescomplemented
219#2580C2×C1111yescharacteristic, complemented
220#1618C2×C1112yescomplemented
221#1614C2×C1111yescharacteristic, complemented
222#1613C2×C1111yescharacteristic, complemented
223#1606C2×C1112yescomplemented
224#1602C2×C1111yescharacteristic, complemented
225#1601C2×C1111yescharacteristic, complemented
226#1512C2×C1112yescomplemented
227#1466C2×C1111yescharacteristic, complemented
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—22no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—42no—
239C23×C11—81no—
240C23×C11—81no—
241C23×C11#13712yes—
242C23×C11C22×D411yescharacteristic
243Q8×C11—24no—
244Q8×C11—42no—
245Q8×C11—42no—
246Q8×C11—81no—
247D4×C11—44no—
248D4×C11—42no—
249D4×C11—44no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—82no—
253D4×C11—81no—
254D4×C11—82no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—44no—
268C2×C4×C11—42no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—81no—
283C2×C4×C11—81no—
284C2×C4×C11—81no—
285C2×C4×C11—82no—
286C2×C4×C11—81no—
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11#12012yes—
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11C22×D412yes—
291C8×C11—42no—
292C8×C11—42no—
293#543C22×C1111yescharacteristic
294#539—22no—
295#539—21no—
296#538—22no—
297#538C22×C1112yes—
298#534—21no—
299#534C22×C1111yescharacteristic
300#529—22no—
301#529C22×C1112yes—
302#525—21no—
303#525—22no—
304C2×C4×Q8C22×C1111yescharacteristic, complemented
305C2×C4×D4—21no—
306C2×C4×D4C22×C1111yescharacteristic
307#484C22×C1112yescomplemented
308#481C22×C1112yes—
309#479—22no—
310#464—22no—
311#451C22×C1112yescomplemented
312#448C22×C1112yes—
313#441—22no—
314#440—22no—
315#432C22×C1112yescomplemented
316#399C22×C1111yescharacteristic
317#399C22×C1111yescharacteristic, complemented
318#393C22×C1111yescharacteristic
319#393C22×C1111yescharacteristic, complemented
320#390—21no—
321#389—21no—
322#385—21no—
323#385—21no—
324#382C22×C1111yescharacteristic, complemented
325#328C22×C1112yescomplemented
326#328C22×C1112yescomplemented
327#327C22×C1112yes—
328#327C22×C1112yes—
329#323C22×C1111yescharacteristic
330#323C22×C1111yescharacteristic
331#323C22×C1112yescomplemented
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—22no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—42no—
341C22×C11—41no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—41no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—84no—
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×#13711yescharacteristic
350C22×C11#57511yescharacteristic
351C4×C11—22no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—22no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11—81no—
364C2×#41—21no—
365C22×Q8C23×C1111yescharacteristic
366C22×D4—21no—
367C22×D4D4×C1111yescharacteristic
368C23×C4—21no—
369C23×C4D4×C1111yescharacteristic
370C23×C4D4×C1111yescharacteristic
371C2×Q16—22no—
372C2×SD16—22no—
373#126—22no—
374#126—22no—
375#126—22no—
376#125—22no—
377#125D4×C1112yes—
378#124—22no—
379#124D4×C1112yes—
380#123—22no—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386C22⋊Q8—21no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—21no—
390C22⋊Q8—22no—
391C22⋊Q8C23×C1112yes—
392#121—22no—
393#121—21no—
394#121—22no—
395#121—22no—
396#121—21no—
397#121C23×C1112yes—
398#120—22no—
399#120—22no—
400#120—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8D4×C1112yes—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4D4×C1112yes—
412#117—21no—
413#117—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4D4×C1111yescharacteristic
420C2×C4⋊C4C23×C1111yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4C23×C1111yescharacteristic
428C2×C22⋊C4C23×C1111yescharacteristic
429C2×C42—21no—
430C2×C42—21no—
431C2×C42C23×C1111yescharacteristic
432#107—22no—
433#106—22no—
434C4⋊C8—22no—
435#103—22no—
436#103—22no—
437#103—22no—
438#102—22no—
439C22⋊C8C23×C1112yes—
440C22⋊C8C23×C1112yes—
441#97—22no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95C23×C1111yescharacteristic
446#95C23×C1111yescharacteristic
447C2×C11—21no—
448C2×C11—21no—
449C2×C11—42no—
450C2×C11—81no—
451C2×C11—82no—
452C2×C11#300711yescharacteristic
453C2×C11#301911yescharacteristic
454C2×C11#302511yescharacteristic
455C24—21no—
456C24C2×D4×C1111yescharacteristic
457C24C2×D4×C1111yescharacteristic
458#41—82no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—42no—
462C2×Q8C2×D4×C1112yes—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4C2×D4×C1112yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—82no—
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C24×C1111yescharacteristic
495Q16—44no—
496SD16—44no—
497C2×C8—22no—
498C2×C8—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—42no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—81no—
513C4⋊C4—81no—
514C4⋊C4C2×D4×C1112yes—
515C4⋊C4C2×D4×C1112yes—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—81no—
532C42—22no—
533C42—22no—
534C42—42no—
535C42C2×D4×C1112yes—
536C42C2×D4×C1112yes—
537C11#1815911yescharacteristic, direct product factor, Sylow
538C23—21no—
539C23—21no—
540C23—21no—
541C23—22no—
542C23—21no—
543C23—21no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—42no—
549C23—81no—
550C23—81no—
551C23C11×#13712yes—
552C23C22×D4×C1111yescharacteristic
553Q8—24no—
554Q8—42no—
555Q8—42no—
556Q8—81no—
557D4—44no—
558D4—42no—
559D4—44no—
560D4—42no—
561D4—42no—
562D4—82no—
563D4—81no—
564D4—82no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—82no—
596C2×C4—81no—
597C2×C4C11×#12011yescharacteristic
598C2×C4C11×#12012yes—
599C2×C4C11×#12011yescharacteristic
600C2×C4C22×D4×C1112yes—
601C8—42no—
602C8—42no—
603C22—21no—
604C22—21no—
605C22—22no—
606C22—42no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—42no—
612C22—41no—
613C22—42no—
614C22—42no—
615C22—41no—
616C22—81no—
617C22—81no—
618C22—84no—
619C22C2×C11×#12011yescharacteristic
620C22C2×C11×#13711yescharacteristic
621C22C11×#57511yescharacteristic
622C4—22no—
623C4—21no—
624C4—21no—
625C4—22no—
626C4—42no—
627C4—41no—
628C4—41no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—81no—
633C4—81no—
634C4—81no—
635C2—21no—
636C2—21no—
637C2—42no—
638C2—81no—
639C2—82no—
640C2C11×#300711yescharacteristic
641C2C11×#301911yescharacteristic
642C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3459C2
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
2. C11×#3117C2semidirect
3. C11×#2580C2semidirect
4. C11×#1618C2semidirect
5. C11×#1614C2semidirect
6. C11×#1613C2semidirect
7. C11×#1606C2semidirect
8. C11×#1602C2semidirect
9. C11×#1601C2semidirect
10. C11×#1512C2semidirect
11. C11×#1466C2semidirect
23. C2×C4×Q8×C11C22semidirect
26. C11×#484C22semidirect
30. C11×#451C22semidirect
34. C11×#432C22semidirect
36. C11×#399C22semidirect
38. C11×#393C22semidirect
43. C11×#382C22semidirect
44. C11×#328C22semidirect
45. C11×#328C22semidirect
50. C11×#323C22semidirect
134. #18159C11direct (N × H)
218. #3117C2×C11semidirect
219. #2580C2×C11semidirect
220. #1618C2×C11semidirect
221. #1614C2×C11semidirect
222. #1613C2×C11semidirect
223. #1606C2×C11semidirect
224. #1602C2×C11semidirect
225. #1601C2×C11semidirect
226. #1512C2×C11semidirect
227. #1466C2×C11semidirect
304. C2×C4×Q8C22×C11semidirect
307. #484C22×C11semidirect
311. #451C22×C11semidirect
315. #432C22×C11semidirect
317. #399C22×C11semidirect
319. #393C22×C11semidirect
324. #382C22×C11semidirect
325. #328C22×C11semidirect
326. #328C22×C11semidirect
331. #323C22×C11semidirect
537. C11#18159direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34592
C11×#31172
C11×#25802
C11×#16182
C11×#16142
C11×#16132
C11×#16062
C11×#16022
C11×#16012
C11×#15122
C11×#14662
#1815911