Finite Group Databasebeta

← C11×#19044 #14596237

Subgroups — C11×#19044 #14596237

Order 2816.

956 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3559C211yesmaximal, characteristic, complemented
2C11×#3234C211yesmaximal, characteristic, complemented
3C11×#3180C211yesmaximal, characteristic, complemented
4C11×#3150C211yesmaximal, characteristic, complemented
5C11×#1661C212yesmaximal, complemented
6C11×#1660C212yesmaximal, complemented
7C11×#1657C212yesmaximal, complemented
8C11×#1656C212yesmaximal, complemented
9C11×#1532C211yesmaximal, characteristic, complemented
10C11×#1530C211yesmaximal, characteristic, complemented
11C2×C11×#330C211yesmaximal, characteristic, complemented
12C2×C11×#135—22no—
13C11×#563C2212yes—
14C11×#562C2212yes—
15C11×#554—21no—
16C11×#553—21no—
17C11×#553—21no—
18C11×#547—22no—
19C11×#547—21no—
20C11×#544—21no—
21C11×#540—21no—
22C11×#539—22no—
23C11×#539—21no—
24C11×#537—21no—
25C11×#532C2211yescharacteristic
26C11×#532C2211yescharacteristic
27C11×#529C2211yescharacteristic
28C2×C11×#125C2211yescharacteristic
29C11×#501C2211yescharacteristic
30C11×#501C2212yes—
31C11×#497—21no—
32C11×#497C2212yes—
33C11×#496—21no—
34C11×#496C2212yes—
35C11×#496C2211yescharacteristic
36C11×#490C2211yescharacteristic
37C11×#490C2212yes—
38C11×#489C2211yescharacteristic
39C11×#481—21no—
40C11×#480—21no—
41C11×#478—22no—
42C11×#466—21no—
43C11×#465—21no—
44C11×#442—21no—
45C11×#440—21no—
46C11×#432C2211yescharacteristic
47C2×C11×#97C2211yescharacteristic
48C2×C11×#97C2211yescharacteristic
49C11×#330C2212yes—
50C11×#330C2212yes—
51C11×#330C2212yes—
52C11×#329C2212yes—
53C11×#329C2212yes—
54C11×#329C2212yes—
55C2×C11×#41—22no—
56C2×C11×#41—21no—
57C2×C11×#41D412yes—
58C11×#135—48no—
59C2×C11×Q16—22no—
60C2×C11×SD16—22no—
61C2×C11×SD16—21no—
62C2×C11×SD16—22no—
63C2×C11×D8—22no—
64C2×C11×D8—21no—
65C22×C8×C11—21no—
66C22×C8×C11—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8D411yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#127D411yescharacteristic
72C11×#127C2311yescharacteristic
73C11×#126—22no—
74C11×#126—22no—
75C11×#126—21no—
76C11×#125—22no—
77C11×#125—21no—
78C11×#125—21no—
79C11×#125—21no—
80C11×#125D412yes—
81C11×#125C2312yes—
82C11×#125C2311yescharacteristic
83C11×#124—21no—
84C11×#124C2311yescharacteristic
85C11×#124C2312yes—
86C11×#123—22no—
87C11×#123—22no—
88C11×#123—22no—
89C11×#123—22no—
90C11×#123—21no—
91C11×#123—22no—
92C11×#123—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8D411yescharacteristic
100C11×#121—22no—
101C11×#121—22no—
102C11×#121—21no—
103C11×#121—21no—
104C11×#121—22no—
105C11×#121—22no—
106C11×#121—21no—
107C11×#121—21no—
108C11×#121—21no—
109C11×#121—21no—
110C11×#121D411yescharacteristic
111C4×Q8×C11D411yescharacteristic
112C4×D4×C11—22no—
113C4×D4×C11—22no—
114C4×D4×C11—21no—
115C4×D4×C11—21no—
116C4×D4×C11—21no—
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11D411yescharacteristic
122C11×#117—21no—
123C11×#117—21no—
124C2×C11×C4⋊C4—22no—
125C2×C11×C4⋊C4—21no—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—21no—
128C2×C11×C4⋊C4D411yescharacteristic
129C2×C11×C4⋊C4D411yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C11×#107—21no—
132C11×#107—22no—
133C11×#106—21no—
134C11×#106—22no—
135C11×C4⋊C8—21no—
136C11×#103—21no—
137C11×#102—21no—
138C11×#102—21no—
139C11×#102—21no—
140C11×#102—22no—
141C11×#102—22no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C11×#97—21no—
145C11×#97C2311yescharacteristic
146C11×#97C2312yes—
147C11×#97C2311yescharacteristic
148C11×#97C2312yes—
149#19044C1111yesmaximal, characteristic, direct product factor, Sylow
150C11×#41—44no—
151C11×#41—44no—
152C11×#41—84no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×Q8×C11C2×D412yes—
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—41no—
167C2×D4×C11C2×D411yescharacteristic
168C2×D4×C11C2×D412yes—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11—41no—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C11×Q16—44no—
181C11×SD16—42no—
182C11×SD16—44no—
183C11×SD16—44no—
184C11×D8—42no—
185C11×D8—44no—
186C2×C8×C11—24no—
187C2×C8×C11—21no—
188C2×C8×C11—22no—
189C2×C8×C11—21no—
190C2×C8×C11—22no—
191C2×C8×C11—42no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4C2×D412yes—
211C11×C4⋊C4C2×D411yescharacteristic
212C11×C4⋊C4C2×D412yes—
213C11×C4⋊C4C2×D411yescharacteristic
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—21no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—21no—
226C11×C22⋊C4—41no—
227C11×C22⋊C4—41no—
228C42×C11—22no—
229C42×C11—21no—
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2×D411yescharacteristic
233C42×C11C2411yescharacteristic
234#3559C2×C1111yescharacteristic, complemented
235#3234C2×C1111yescharacteristic, complemented
236#3180C2×C1111yescharacteristic, complemented
237#3150C2×C1111yescharacteristic, complemented
238#1661C2×C1112yescomplemented
239#1660C2×C1112yescomplemented
240#1657C2×C1112yescomplemented
241#1656C2×C1112yescomplemented
242#1532C2×C1111yescharacteristic, complemented
243#1530C2×C1111yescharacteristic, complemented
244C2×#330C2×C1111yescharacteristic, complemented
245C23×C11—22no—
246C23×C11—21no—
247C23×C11—41no—
248C23×C11#12011yescharacteristic
249Q8×C11—42no—
250Q8×C11—41no—
251Q8×C11—42no—
252Q8×C11—82no—
253D4×C11—42no—
254D4×C11—41no—
255D4×C11—42no—
256D4×C11—42no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—42no—
260D4×C11—44no—
261D4×C11—42no—
262D4×C11—81no—
263D4×C11—82no—
264D4×C11—82no—
265D4×C11—82no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—41no—
278C2×C4×C11—82no—
279C2×C4×C11—82no—
280C2×C4×C11—81no—
281C2×C4×C11—82no—
282C2×C4×C11—82no—
283C2×C4×C11—82no—
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C8×C11—24no—
291C8×C11—22no—
292C8×C11—42no—
293C8×C11—41no—
294C2×#135—22no—
295#563C22×C1112yes—
296#562C22×C1112yes—
297#554—21no—
298#553—21no—
299#553—21no—
300#547—22no—
301#547—21no—
302#544—21no—
303#540—21no—
304#539—22no—
305#539—21no—
306#537—21no—
307#532C22×C1111yescharacteristic
308#532C22×C1111yescharacteristic
309#529C22×C1111yescharacteristic
310C2×#125C22×C1111yescharacteristic
311#501C22×C1111yescharacteristic
312#501C22×C1112yes—
313#497—21no—
314#497C22×C1112yes—
315#496—21no—
316#496C22×C1112yes—
317#496C22×C1111yescharacteristic
318#490C22×C1111yescharacteristic
319#490C22×C1112yes—
320#489C22×C1111yescharacteristic
321#481—21no—
322#480—21no—
323#478—22no—
324#466—21no—
325#465—21no—
326#442—21no—
327#440—21no—
328#432C22×C1111yescharacteristic
329C2×#97C22×C1111yescharacteristic
330C2×#97C22×C1111yescharacteristic
331#330C22×C1112yes—
332#330C22×C1112yes—
333#330C22×C1112yes—
334#329C22×C1112yes—
335#329C22×C1112yes—
336#329C22×C1112yes—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—42no—
340C22×C11—41no—
341C22×C11—42no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—42no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11#45312yes—
349C22×C11C2×#12011yescharacteristic
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—81no—
363C2×#41—22no—
364C2×#41—21no—
365C2×#41D4×C1112yes—
366#135—48no—
367C2×Q16—22no—
368C2×SD16—22no—
369C2×SD16—21no—
370C2×SD16—22no—
371C2×D8—22no—
372C2×D8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C4⋊Q8—21no—
376C4⋊Q8—22no—
377C4⋊Q8D4×C1111yescharacteristic
378C4⋊Q8C23×C1111yescharacteristic
379#127D4×C1111yescharacteristic
380#127C23×C1111yescharacteristic
381#126—22no—
382#126—22no—
383#126—21no—
384#125—22no—
385#125—21no—
386#125—21no—
387#125—21no—
388#125D4×C1112yes—
389#125C23×C1112yes—
390#125C23×C1111yescharacteristic
391#124—21no—
392#124C23×C1111yescharacteristic
393#124C23×C1112yes—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398#123—21no—
399#123—22no—
400#123—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8D4×C1111yescharacteristic
408#121—22no—
409#121—22no—
410#121—21no—
411#121—21no—
412#121—22no—
413#121—22no—
414#121—21no—
415#121—21no—
416#121—21no—
417#121—21no—
418#121D4×C1111yescharacteristic
419C4×Q8D4×C1111yescharacteristic
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4D4×C1111yescharacteristic
430#117—21no—
431#117—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4D4×C1111yescharacteristic
437C2×C4⋊C4D4×C1111yescharacteristic
438C2×C42C23×C1111yescharacteristic
439#107—21no—
440#107—22no—
441#106—21no—
442#106—22no—
443C4⋊C8—21no—
444#103—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—22no—
449#102—22no—
450C22⋊C8—21no—
451#97—21no—
452#97—21no—
453#97C23×C1112yes—
454#97C23×C1111yescharacteristic
455#97C23×C1111yescharacteristic
456#97C23×C1112yes—
457C2×C11—22no—
458C2×C11—82no—
459C2×C11—81no—
460C2×C11—161no—
461C2×C11C2×#45311yescharacteristic
462C2×C11#301811yescharacteristic
463C2×C11#302011yescharacteristic
464#41—44no—
465#41—44no—
466#41—84no—
467C2×Q8—22no—
468C2×Q8—21no—
469C2×Q8C2×D4×C1111yescharacteristic
470C2×Q8C2×D4×C1112yes—
471C2×D4—22no—
472C2×D4—21no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—41no—
481C2×D4C2×D4×C1111yescharacteristic
482C2×D4C2×D4×C1112yes—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—41no—
491C22×C4C2×D4×C1111yescharacteristic
492C22×C4C2×D4×C1111yescharacteristic
493C22×C4C2×D4×C1111yescharacteristic
494Q16—44no—
495SD16—44no—
496SD16—44no—
497SD16—42no—
498D8—44no—
499D8—42no—
500C2×C8—24no—
501C2×C8—21no—
502C2×C8—22no—
503C2×C8—21no—
504C2×C8—22no—
505C2×C8—42no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4C2×D4×C1112yes—
525C4⋊C4C2×D4×C1111yescharacteristic
526C4⋊C4C2×D4×C1112yes—
527C4⋊C4C2×D4×C1111yescharacteristic
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C42—22no—
543C42—21no—
544C42C2×D4×C1111yescharacteristic
545C42C2×D4×C1111yescharacteristic
546C42C2×D4×C1111yescharacteristic
547C42C24×C1111yescharacteristic
548C11#1904411yescharacteristic, direct product factor, Sylow
549C23—22no—
550C23—21no—
551C23—41no—
552C23C11×#12011yescharacteristic
553Q8—42no—
554Q8—41no—
555Q8—42no—
556Q8—82no—
557D4—42no—
558D4—41no—
559D4—42no—
560D4—42no—
561D4—41no—
562D4—41no—
563D4—42no—
564D4—44no—
565D4—42no—
566D4—81no—
567D4—82no—
568D4—82no—
569D4—82no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—81no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4C11×#12011yescharacteristic
589C2×C4C11×#12011yescharacteristic
590C2×C4C11×#12011yescharacteristic
591C2×C4C22×D4×C1111yescharacteristic
592C2×C4C22×D4×C1111yescharacteristic
593C2×C4C22×D4×C1111yescharacteristic
594C8—24no—
595C8—22no—
596C8—41no—
597C8—42no—
598C22—21no—
599C22—21no—
600C22—42no—
601C22—41no—
602C22—42no—
603C22—41no—
604C22—41no—
605C22—42no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22C11×#45312yes—
610C22C2×C11×#12011yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—42no—
618C4—42no—
619C4—41no—
620C4—42no—
621C4—41no—
622C4—41no—
623C4—81no—
624C2—22no—
625C2—82no—
626C2—81no—
627C2—161no—
628C2C2×C11×#45311yescharacteristic
629C2C11×#301811yescharacteristic
630C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
LCSG ▷ C42 ▷ 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×#3559C2semidirect
2. C11×#3234C2semidirect
3. C11×#3180C2semidirect
4. C11×#3150C2semidirect
5. C11×#1661C2semidirect
6. C11×#1660C2semidirect
7. C11×#1657C2semidirect
8. C11×#1656C2semidirect
9. C11×#1532C2semidirect
10. C11×#1530C2semidirect
11. C2×C11×#330C2semidirect
149. #19044C11direct (N × H)
234. #3559C2×C11semidirect
235. #3234C2×C11semidirect
236. #3180C2×C11semidirect
237. #3150C2×C11semidirect
238. #1661C2×C11semidirect
239. #1660C2×C11semidirect
240. #1657C2×C11semidirect
241. #1656C2×C11semidirect
242. #1532C2×C11semidirect
243. #1530C2×C11semidirect
244. C2×#330C2×C11semidirect
548. C11#19044direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35592
C11×#32342
C11×#31802
C11×#31502
C11×#16612
C11×#16602
C11×#16572
C11×#16562
C11×#15322
C11×#15302
C2×C11×#3302
#1904411