Finite Group Databasebeta

← C11×#19014 #14596207

Subgroups — C11×#19014 #14596207

Order 2816.

1140 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×#3558C211yesmaximal, characteristic, complemented
2C11×#3217C211yesmaximal, characteristic, complemented
3C11×#3151C211yesmaximal, characteristic, complemented
4C2×C11×#496C211yesmaximal, characteristic, complemented
5C11×#1656C214yesmaximal, complemented
6C11×#1655C214yesmaximal, complemented
7C11×#1530C211yesmaximal, characteristic, complemented
8C11×#1527C211yesmaximal, characteristic, complemented
9C11×#1524C211yesmaximal, characteristic, complemented
10C2×C11×AGL(1,ℤ/8)—22no—
11C22×C11×SD16—21no—
12C22×C11×D8—21no—
13C11×#562C2212yescomplemented
14C11×H(3,𝔽4)C2212yescomplemented
15C11×#559—21no—
16C11×#548—21no—
17C11×#546—22no—
18C11×#546—21no—
19D42×C11—21no—
20C11×#542—21no—
21C11×#538—22no—
22C11×#538—21no—
23C11×#535—21no—
24C11×#534—21no—
25C11×#532C2211yescharacteristic
26C2×C11×#127C2211yescharacteristic, complemented
27C11×#529C2211yescharacteristic
28C2×C11×#124C2211yescharacteristic
29C11×#496—22no—
30C11×#496C2214yescomplemented
31C11×#496C2214yescomplemented
32C11×#496C2212yescomplemented
33C11×#493—21no—
34C11×#492—21no—
35C11×#490C2212yescomplemented
36C11×#460—21no—
37C11×#459—21no—
38C11×#450—21no—
39C11×#447—21no—
40C11×#432C2211yescharacteristic, complemented
41C4×C11×M16C2211yescharacteristic, complemented
42C2×C11×#97C2211yescharacteristic, complemented
43C11×#330C2212yescomplemented
44C11×#329C2212yescomplemented
45C11×#329C2214yescomplemented
46C11×#329C2214yescomplemented
47C2×C11×#41—21no—
48C2×C11×#41D412yes—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11—22no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11D411yescharacteristic
56C11×AGL(1,ℤ/8)—48no—
57C2×C11×SD16—24no—
58C2×C11×SD16—24no—
59C2×C11×SD16—22no—
60C2×C11×SD16—44no—
61C2×C11×D8—24no—
62C2×C11×D8—24no—
63C2×C11×D8—22no—
64C2×C11×D8—44no—
65C2×C11×M16—21no—
66C22×C8×C11—21no—
67C11×C4⋊Q8D411yescharacteristic
68C11×#127—21no—
69C11×#127—21no—
70C11×#127—21no—
71C11×#127—21no—
72C11×#127D411yescharacteristic
73C11×#127C2312yes—
74C11×#126—22no—
75C11×#126—21no—
76C11×#125C2311yescharacteristic
77C11×#124—21no—
78C11×#124—22no—
79C11×#124—22no—
80C11×#124—22no—
81C11×#124—21no—
82C11×#124—21no—
83C11×#124D412yes—
84C11×#124C2312yes—
85C11×#124C2311yescharacteristic
86C11×#124C2312yes—
87C11×#123—22no—
88C11×#123—22no—
89C11×#123—21no—
90C11×#123—22no—
91C11×#123—22no—
92C11×C22⋊Q8—21no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—22no—
95C11×C22⋊Q8D411yescharacteristic
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—22no—
99C11×#121—21no—
100C11×#121—22no—
101C11×#121—22no—
102C11×#121—21no—
103C11×#121—21no—
104C11×#121D411yescharacteristic
105C11×#120—22no—
106C11×#120—22no—
107C11×#120—22no—
108C11×#120—22no—
109C11×#120—22no—
110C4×Q8×C11—21no—
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×C11D411yescharacteristic
119C11×#117—21no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C42×C11C2311yescharacteristic
124C11×C4⋊C8—21no—
125C11×#102—22no—
126C11×#102—22no—
127C11×C22⋊C8—21no—
128C11×#97—21no—
129C11×#97C2312yes—
130C11×#97C2312yes—
131C11×#97C2312yes—
132C4×C8×C11—21no—
133#19014C1111yesmaximal, characteristic, direct product factor, Sylow
134C24×C11—22no—
135C24×C11—21no—
136C24×C11—41no—
137C11×#41—44no—
138C11×#41—82no—
139C2×Q8×C11—21no—
140C2×Q8×C11—42no—
141C2×Q8×C11C2×D411yescharacteristic
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11C2×D412yes—
144C2×D4×C11—22no—
145C2×D4×C11—21no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11—44no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11—82no—
165C2×D4×C11—82no—
166C2×D4×C11—84no—
167C2×D4×C11C2×D411yescharacteristic
168C2×D4×C11C2×D412yes—
169C2×D4×C11C2×D412yes—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—22no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C11×SD16—48no—
179C11×SD16—48no—
180C11×SD16—82no—
181C11×D8—48no—
182C11×D8—48no—
183C11×D8—82no—
184C11×M16—24no—
185C2×C8×C11—24no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C22⋊C4—22no—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C42×C11—22no—
216C42×C11—21no—
217C42×C11C2×D411yescharacteristic
218C42×C11C2×D411yescharacteristic
219C42×C11C2×D411yescharacteristic
220C42×C11C2411yescharacteristic
221#3558C2×C1111yescharacteristic, complemented
222#3217C2×C1111yescharacteristic, complemented
223#3151C2×C1111yescharacteristic, complemented
224C2×#496C2×C1111yescharacteristic, complemented
225#1656C2×C1114yescomplemented
226#1655C2×C1114yescomplemented
227#1530C2×C1111yescharacteristic, complemented
228#1527C2×C1111yescharacteristic, complemented
229#1524C2×C1111yescharacteristic, complemented
230C23×C11—21no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—81no—
236C23×C11—81no—
237C23×C11—82no—
238C23×C11—82no—
239C23×C11—82no—
240C23×C11—82no—
241C23×C11—82no—
242C23×C11—82no—
243C23×C11#12011yescharacteristic
244Q8×C11—42no—
245Q8×C11—42no—
246Q8×C11—41no—
247Q8×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—41no—
251D4×C11—42no—
252D4×C11—44no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11—42no—
256D4×C11—42no—
257D4×C11—44no—
258D4×C11—42no—
259D4×C11—42no—
260D4×C11—81no—
261D4×C11—82no—
262D4×C11—82no—
263D4×C11—82no—
264D4×C11—82no—
265D4×C11—82no—
266D4×C11—82no—
267D4×C11—82no—
268D4×C11—82no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—41no—
277C2×C4×C11—42no—
278C2×C4×C11—82no—
279C2×C4×C11—81no—
280C2×C4×C11—82no—
281C2×C4×C11—82no—
282C2×C4×C11#12011yescharacteristic
283C2×C4×C11#12011yescharacteristic
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C8×C11—24no—
289C8×C11—24no—
290C8×C11—42no—
291C2×AGL(1,ℤ/8)—22no—
292C22×SD16—21no—
293C22×D8—21no—
294#562C22×C1112yescomplemented
295H(3,𝔽4)C22×C1112yescomplemented
296#559—21no—
297#548—21no—
298#546—22no—
299#546—21no—
300D42—21no—
301#542—21no—
302#538—22no—
303#538—21no—
304#535—21no—
305#534—21no—
306#532C22×C1111yescharacteristic
307C2×#127C22×C1111yescharacteristic, complemented
308#529C22×C1111yescharacteristic
309C2×#124C22×C1111yescharacteristic
310#496—22no—
311#496C22×C1114yescomplemented
312#496C22×C1114yescomplemented
313#496C22×C1112yescomplemented
314#493—21no—
315#492—21no—
316#490C22×C1112yescomplemented
317#460—21no—
318#459—21no—
319#450—21no—
320#447—21no—
321#432C22×C1111yescharacteristic, complemented
322C4×M16C22×C1111yescharacteristic, complemented
323C2×#97C22×C1111yescharacteristic, complemented
324#330C22×C1112yescomplemented
325#329C22×C1112yescomplemented
326#329C22×C1114yescomplemented
327#329C22×C1114yescomplemented
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—41no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—82no—
340C22×C11—82no—
341C22×C11—82no—
342C22×C11—162no—
343C22×C11—164no—
344C22×C11—164no—
345C22×C11#45312yes—
346C22×C11C2×#12011yescharacteristic
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11#45312yes—
358C2×#41—21no—
359C2×#41D4×C1112yes—
360C22×Q8D4×C1111yescharacteristic
361C22×D4—22no—
362C22×D4—21no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4D4×C1111yescharacteristic
367AGL(1,ℤ/8)—48no—
368C2×SD16—24no—
369C2×SD16—24no—
370C2×SD16—22no—
371C2×SD16—44no—
372C2×D8—24no—
373C2×D8—24no—
374C2×D8—22no—
375C2×D8—44no—
376C2×M16—21no—
377C22×C8—21no—
378C4⋊Q8D4×C1111yescharacteristic
379#127—21no—
380#127—21no—
381#127—21no—
382#127—21no—
383#127D4×C1111yescharacteristic
384#127C23×C1112yes—
385#126—22no—
386#126—21no—
387#125C23×C1111yescharacteristic
388#124—21no—
389#124—22no—
390#124—22no—
391#124—22no—
392#124—21no—
393#124—21no—
394#124D4×C1112yes—
395#124C23×C1112yes—
396#124C23×C1111yescharacteristic
397#124C23×C1112yes—
398#123—22no—
399#123—22no—
400#123—21no—
401#123—22no—
402#123—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8D4×C1111yescharacteristic
407#121—22no—
408#121—22no—
409#121—22no—
410#121—21no—
411#121—22no—
412#121—22no—
413#121—21no—
414#121—21no—
415#121D4×C1111yescharacteristic
416#120—22no—
417#120—22no—
418#120—22no—
419#120—22no—
420#120—22no—
421C4×Q8—21no—
422C4×Q8D4×C1111yescharacteristic
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4D4×C1111yescharacteristic
430#117—21no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C42C23×C1111yescharacteristic
435C4⋊C8—21no—
436#102—22no—
437#102—22no—
438C22⋊C8—21no—
439#97—21no—
440#97C23×C1112yes—
441#97C23×C1112yes—
442#97C23×C1112yes—
443C4×C8—21no—
444C2×C11—22no—
445C2×C11—82no—
446C2×C11—81no—
447C2×C11—82no—
448C2×C11—162no—
449C2×C11C2×#45311yescharacteristic
450C2×C11C2×#45311yescharacteristic
451C2×C11#302111yescharacteristic
452C24—22no—
453C24—21no—
454C24—41no—
455#41—44no—
456#41—82no—
457C2×Q8—21no—
458C2×Q8—42no—
459C2×Q8C2×D4×C1111yescharacteristic
460C2×Q8C2×D4×C1112yes—
461C2×Q8C2×D4×C1112yes—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—44no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—82no—
483C2×D4—82no—
484C2×D4—84no—
485C2×D4C2×D4×C1111yescharacteristic
486C2×D4C2×D4×C1112yes—
487C2×D4C2×D4×C1112yes—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4C2×D4×C1111yescharacteristic
494C22×C4C2×D4×C1111yescharacteristic
495C22×C4C2×D4×C1111yescharacteristic
496SD16—48no—
497SD16—48no—
498SD16—82no—
499D8—48no—
500D8—48no—
501D8—82no—
502M16—24no—
503C2×C8—24no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4C2×D4×C1111yescharacteristic
516C4⋊C4C2×D4×C1111yescharacteristic
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—22no—
524C22⋊C4—21no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C42—22no—
534C42—21no—
535C42C2×D4×C1111yescharacteristic
536C42C2×D4×C1111yescharacteristic
537C42C2×D4×C1111yescharacteristic
538C42C24×C1111yescharacteristic
539C11#1901411yescharacteristic, direct product factor, Sylow
540C23—21no—
541C23—22no—
542C23—22no—
543C23—42no—
544C23—42no—
545C23—81no—
546C23—81no—
547C23—82no—
548C23—82no—
549C23—82no—
550C23—82no—
551C23—82no—
552C23—82no—
553C23C11×#12011yescharacteristic
554Q8—42no—
555Q8—42no—
556Q8—41no—
557Q8—42no—
558D4—42no—
559D4—42no—
560D4—41no—
561D4—42no—
562D4—44no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—44no—
568D4—42no—
569D4—42no—
570D4—81no—
571D4—82no—
572D4—82no—
573D4—82no—
574D4—82no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—82no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—82no—
589C2×C4—81no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4C11×#12011yescharacteristic
593C2×C4C11×#12011yescharacteristic
594C2×C4C11×#12011yescharacteristic
595C2×C4C22×D4×C1111yescharacteristic
596C2×C4C22×D4×C1111yescharacteristic
597C2×C4C22×D4×C1111yescharacteristic
598C8—24no—
599C8—24no—
600C8—42no—
601C22—21no—
602C22—21no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—41no—
609C22—41no—
610C22—42no—
611C22—42no—
612C22—82no—
613C22—82no—
614C22—82no—
615C22—162no—
616C22—164no—
617C22—164no—
618C22C11×#45312yes—
619C22C2×C11×#12011yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—42no—
629C4—41no—
630C4C11×#45312yes—
631C2—22no—
632C2—81no—
633C2—82no—
634C2—82no—
635C2—162no—
636C2C2×C11×#45311yescharacteristic
637C2C2×C11×#45311yescharacteristic
638C2C11×#302111yescharacteristic
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×#3558C2semidirect
2. C11×#3217C2semidirect
3. C11×#3151C2semidirect
4. C2×C11×#496C2semidirect
5. C11×#1656C2semidirect
6. C11×#1655C2semidirect
7. C11×#1530C2semidirect
8. C11×#1527C2semidirect
9. C11×#1524C2semidirect
13. C11×#562C22semidirect
14. C11×H(3,𝔽4)C22semidirect
26. C2×C11×#127C22semidirect
30. C11×#496C22semidirect
31. C11×#496C22semidirect
32. C11×#496C22semidirect
35. C11×#490C22semidirect
40. C11×#432C22semidirect
41. C4×C11×M16C22semidirect
42. C2×C11×#97C22semidirect
43. C11×#330C22semidirect
44. C11×#329C22semidirect
45. C11×#329C22semidirect
46. C11×#329C22semidirect
133. #19014C11direct (N × H)
221. #3558C2×C11semidirect
222. #3217C2×C11semidirect
223. #3151C2×C11semidirect
224. C2×#496C2×C11semidirect
225. #1656C2×C11semidirect
226. #1655C2×C11semidirect
227. #1530C2×C11semidirect
228. #1527C2×C11semidirect
229. #1524C2×C11semidirect
294. #562C22×C11semidirect
295. H(3,𝔽4)C22×C11semidirect
307. C2×#127C22×C11semidirect
311. #496C22×C11semidirect
312. #496C22×C11semidirect
313. #496C22×C11semidirect
316. #490C22×C11semidirect
321. #432C22×C11semidirect
322. C4×M16C22×C11semidirect
323. C2×#97C22×C11semidirect
324. #330C22×C11semidirect
325. #329C22×C11semidirect
326. #329C22×C11semidirect
327. #329C22×C11semidirect
539. C11#19014direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35582
C11×#32172
C11×#31512
C2×C11×#4962
C11×#16562
C11×#16552
C11×#15302
C11×#15272
C11×#15242
#1901411