Finite Group Databasebeta

← C11×#18888 #14596081

Subgroups — C11×#18888 #14596081

Order 2816.

964 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3511C211yesmaximal, characteristic, complemented
2C11×#3245C211yesmaximal, characteristic, complemented
3C11×#3227C211yesmaximal, characteristic, complemented
4C11×#3035C211yesmaximal, characteristic, complemented
5C11×#1654C212yesmaximal, complemented
6C11×#1652C212yesmaximal, complemented
7C11×#1628C212yesmaximal, complemented
8C11×#1625C212yesmaximal, complemented
9C2×C11×#332C211yesmaximal, characteristic, complemented
10C11×#1480C211yesmaximal, characteristic, complemented
11C11×#1477C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C11×#556C2212yes—
14C11×#555—21no—
15C11×#554—21no—
16C11×#553—22no—
17C11×#548—22no—
18C11×#547C2212yes—
19C11×#542—22no—
20C11×#537—21no—
21C11×#533—21no—
22C11×#532—21no—
23C11×#532C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic
26C11×#520—21no—
27C4×C11×#41C2211yescharacteristic
28C11×#498C2212yes—
29C11×#486C2212yes—
30C11×#481—22no—
31C11×#476—22no—
32C11×#474—21no—
33C11×#474C2212yes—
34C11×#466—22no—
35C11×#464—21no—
36C11×#463—21no—
37C11×#462C2211yescharacteristic
38C11×#461C2211yescharacteristic
39C11×#460C2211yescharacteristic
40C11×#459—21no—
41C11×#459C2211yescharacteristic
42C11×#459C2212yes—
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#416—21no—
47C11×#332C2212yes—
48C11×#332C2212yes—
49C11×Q8⋊C8C2212yes—
50C11×D4⋊C8C2212yes—
51C11×D4⋊C8C2212yes—
52C11×D4⋊C8C2212yes—
53C2×C11×#41—22no—
54C2×C11×#41—21no—
55C2×C11×#41—21no—
56C2×C11×#41D411yescharacteristic
57C22×Q8×C11—21no—
58C11×#135—44no—
59C2×C11×Q16—21no—
60C2×C11×SD16—21no—
61C2×C11×SD16—21no—
62C2×C11×D8—21no—
63C2×C11×D8—22no—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8D412yes—
69C11×C4⋊Q8D411yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2312yes—
72C11×#127D411yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#126—24no—
75C11×#125—22no—
76C11×#124—24no—
77C11×#124—22no—
78C11×#124—21no—
79C11×#124—21no—
80C11×#123—24no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—24no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×#121—22no—
86C11×#121—22no—
87C11×#121—24no—
88C11×#121—22no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121D412yes—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11D411yescharacteristic
96C4×Q8×C11C2311yescharacteristic
97C4×D4×C11—22no—
98C4×D4×C11—24no—
99C4×D4×C11—22no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11D411yescharacteristic
106C4×D4×C11C2311yescharacteristic
107C4×D4×C11C2312yes—
108C11×#117—22no—
109C11×#117—22no—
110C11×#117—21no—
111C11×#117D411yescharacteristic
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4D412yes—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C11×#107—22no—
118C11×#106—24no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8C2311yescharacteristic
123C11×C4⋊C8C2311yescharacteristic
124C11×C4⋊C8C2312yes—
125C11×#103—21no—
126C11×#103—21no—
127C11×#102—22no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—22no—
131C11×#102—24no—
132C11×C22⋊C8—21no—
133C4×C8×C11C2312yes—
134#18888C1111yesmaximal, characteristic, direct product factor, Sylow
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—42no—
138C11×#41—42no—
139C11×#41—42no—
140C11×#41—42no—
141C11×#41—82no—
142C11×#41—82no—
143C2×Q8×C11—21no—
144C2×Q8×C11—22no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—81no—
148C2×Q8×C11—81no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—22no—
152C2×D4×C11—24no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—41no—
159C2×D4×C11C2×D412yes—
160C2×D4×C11C2×D411yescharacteristic
161C22×C4×C11—24no—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—41no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C11×Q16—42no—
172C11×SD16—42no—
173C11×SD16—42no—
174C11×D8—42no—
175C11×D8—82no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—42no—
181C2×C8×C11—81no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C2×D411yescharacteristic
193C11×C4⋊C4C2×D411yescharacteristic
194C11×C4⋊C4C2×D414yes—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C42×C11—24no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11C2×D411yescharacteristic
211C42×C11C2×D411yescharacteristic
212C42×C11C2×D411yescharacteristic
213C42×C11C2411yescharacteristic
214#3511C2×C1111yescharacteristic, complemented
215#3245C2×C1111yescharacteristic, complemented
216#3227C2×C1111yescharacteristic, complemented
217#3035C2×C1111yescharacteristic, complemented
218#1654C2×C1112yescomplemented
219#1652C2×C1112yescomplemented
220#1628C2×C1112yescomplemented
221#1625C2×C1112yescomplemented
222C2×#332C2×C1111yescharacteristic, complemented
223#1480C2×C1111yescharacteristic, complemented
224#1477C2×C1111yescharacteristic, complemented
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11#12011yescharacteristic
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—42no—
232Q8×C11—42no—
233Q8×C11—42no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—82no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—44no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—42no—
250D4×C11—84no—
251D4×C11—82no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—24no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—41no—
267C2×C4×C11—82no—
268C2×C4×C11—84no—
269C2×C4×C11—82no—
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11#12011yescharacteristic
273C2×C4×C11#13512yes—
274C2×C4×C11AGL(1,ℤ/8)12yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C8×C11—42no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—42no—
282C2×#135—21no—
283#556C22×C1112yes—
284#555—21no—
285#554—21no—
286#553—22no—
287#548—22no—
288#547C22×C1112yes—
289#542—22no—
290#537—21no—
291#533—21no—
292#532—21no—
293#532C22×C1111yescharacteristic
294#532C22×C1111yescharacteristic
295C2×C4⋊Q8C22×C1111yescharacteristic
296#520—21no—
297C4×#41C22×C1111yescharacteristic
298#498C22×C1112yes—
299#486C22×C1112yes—
300#481—22no—
301#476—22no—
302#474—21no—
303#474C22×C1112yes—
304#466—22no—
305#464—21no—
306#463—21no—
307#462C22×C1111yescharacteristic
308#461C22×C1111yescharacteristic
309#460C22×C1111yescharacteristic
310#459—21no—
311#459C22×C1111yescharacteristic
312#459C22×C1112yes—
313#431C22×C1111yescharacteristic
314C2×C4⋊C8C22×C1111yescharacteristic
315C2×C4⋊C8C22×C1111yescharacteristic
316#416—21no—
317#332C22×C1112yes—
318#332C22×C1112yes—
319Q8⋊C8C22×C1112yes—
320D4⋊C8C22×C1112yes—
321D4⋊C8C22×C1112yes—
322D4⋊C8C22×C1112yes—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—41no—
326C22×C11—42no—
327C22×C11—41no—
328C22×C11—42no—
329C22×C11—41no—
330C22×C11—42no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11#44912yes—
335C22×C11C2×#12011yescharacteristic
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—41no—
342C4×C11—44no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11#44912yes—
346C4×C11C2×#13511yescharacteristic
347C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
348C4×C11#57611yescharacteristic
349C4×C11#57711yescharacteristic
350C2×#41—22no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41D4×C1111yescharacteristic
354C22×Q8—21no—
355#135—44no—
356C2×Q16—21no—
357C2×SD16—21no—
358C2×SD16—21no—
359C2×D8—21no—
360C2×D8—22no—
361C22×C8—21no—
362C22×C8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8D4×C1112yes—
366C4⋊Q8D4×C1111yescharacteristic
367C4⋊Q8C23×C1111yescharacteristic
368C4⋊Q8C23×C1112yes—
369#127D4×C1111yescharacteristic
370#127C23×C1111yescharacteristic
371#126—24no—
372#125—22no—
373#124—24no—
374#124—22no—
375#124—21no—
376#124—21no—
377#123—24no—
378C22⋊Q8—22no—
379C22⋊Q8—24no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382#121—22no—
383#121—22no—
384#121—24no—
385#121—22no—
386#121—21no—
387#121—21no—
388#121—21no—
389#121D4×C1112yes—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8D4×C1111yescharacteristic
393C4×Q8C23×C1111yescharacteristic
394C4×D4—22no—
395C4×D4—24no—
396C4×D4—22no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4D4×C1111yescharacteristic
403C4×D4C23×C1111yescharacteristic
404C4×D4C23×C1112yes—
405#117—22no—
406#117—22no—
407#117—21no—
408#117D4×C1111yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4D4×C1112yes—
412C2×C42—21no—
413C2×C42C23×C1111yescharacteristic
414#107—22no—
415#106—24no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C1111yescharacteristic
420C4⋊C8C23×C1111yescharacteristic
421C4⋊C8C23×C1112yes—
422#103—21no—
423#103—21no—
424#102—22no—
425#102—21no—
426#102—21no—
427#102—22no—
428#102—24no—
429C22⋊C8—21no—
430C4×C8C23×C1112yes—
431C2×C11—22no—
432C2×C11—81no—
433C2×C11—82no—
434C2×C11—161no—
435C2×C11C2×#44911yescharacteristic
436C2×C11#301211yescharacteristic
437C2×C11#302011yescharacteristic
438#41—22no—
439#41—22no—
440#41—42no—
441#41—42no—
442#41—42no—
443#41—42no—
444#41—82no—
445#41—82no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—21no—
450C2×Q8—81no—
451C2×Q8—81no—
452C2×Q8C2×D4×C1111yescharacteristic
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—24no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4C2×D4×C1112yes—
463C2×D4C2×D4×C1111yescharacteristic
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—41no—
471C22×C4C2×D4×C1111yescharacteristic
472C22×C4C2×D4×C1111yescharacteristic
473C22×C4C2×D4×C1111yescharacteristic
474Q16—42no—
475SD16—42no—
476SD16—42no—
477D8—42no—
478D8—82no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—42no—
484C2×C8—81no—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4C2×D4×C1111yescharacteristic
496C4⋊C4C2×D4×C1111yescharacteristic
497C4⋊C4C2×D4×C1114yes—
498C4⋊C4C2×D4×C1112yes—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—22no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—24no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42C2×D4×C1111yescharacteristic
514C42C2×D4×C1111yescharacteristic
515C42C2×D4×C1111yescharacteristic
516C42C24×C1111yescharacteristic
517C11#1888811yescharacteristic, direct product factor, Sylow
518C23—21no—
519C23—22no—
520C23—41no—
521C23C11×#12011yescharacteristic
522Q8—21no—
523Q8—21no—
524Q8—42no—
525Q8—42no—
526Q8—42no—
527Q8—41no—
528Q8—41no—
529Q8—82no—
530D4—21no—
531D4—21no—
532D4—22no—
533D4—22no—
534D4—42no—
535D4—42no—
536D4—42no—
537D4—44no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—42no—
543D4—84no—
544D4—82no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—24no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—84no—
562C2×C4—82no—
563C2×C4C11×#12011yescharacteristic
564C2×C4C11×#12011yescharacteristic
565C2×C4C11×#12011yescharacteristic
566C2×C4C11×#13512yes—
567C2×C4C11×AGL(1,ℤ/8)12yes—
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C22×D4×C1111yescharacteristic
570C2×C4C22×D4×C1111yescharacteristic
571C8—42no—
572C8—41no—
573C8—41no—
574C8—42no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—42no—
579C22—41no—
580C22—42no—
581C22—41no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22C11×#44912yes—
587C22C2×C11×#12011yescharacteristic
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—44no—
595C4—41no—
596C4—81no—
597C4C11×#44912yes—
598C4C2×C11×#13511yescharacteristic
599C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
600C4C11×#57611yescharacteristic
601C4C11×#57711yescharacteristic
602C2—22no—
603C2—81no—
604C2—82no—
605C2—161no—
606C2C2×C11×#44911yescharacteristic
607C2C11×#301211yescharacteristic
608C2C11×#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×#3511C2semidirect
2. C11×#3245C2semidirect
3. C11×#3227C2semidirect
4. C11×#3035C2semidirect
5. C11×#1654C2semidirect
6. C11×#1652C2semidirect
7. C11×#1628C2semidirect
8. C11×#1625C2semidirect
9. C2×C11×#332C2semidirect
10. C11×#1480C2semidirect
11. C11×#1477C2semidirect
134. #18888C11direct (N × H)
214. #3511C2×C11semidirect
215. #3245C2×C11semidirect
216. #3227C2×C11semidirect
217. #3035C2×C11semidirect
218. #1654C2×C11semidirect
219. #1652C2×C11semidirect
220. #1628C2×C11semidirect
221. #1625C2×C11semidirect
222. C2×#332C2×C11semidirect
223. #1480C2×C11semidirect
224. #1477C2×C11semidirect
517. C11#18888direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35112
C11×#32452
C11×#32272
C11×#30352
C11×#16542
C11×#16522
C11×#16282
C11×#16252
C2×C11×#3322
C11×#14802
C11×#14772
#1888811