Finite Group Databasebeta

← C11×#19874 #14597067

Subgroups — C11×#19874 #14597067

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3400C211yesmaximal, characteristic, complemented
2C11×#3396C211yesmaximal, characteristic, complemented
3C11×#3396C211yesmaximal, characteristic, complemented
4C11×#3365C211yesmaximal, characteristic, complemented
5C11×#1721C211yesmaximal, characteristic
6C11×#1688C211yesmaximal, characteristic, complemented
7C11×#1682C211yesmaximal, characteristic, complemented
8C11×#1668C211yesmaximal, characteristic, complemented
9C11×#1666C211yesmaximal, characteristic, complemented
10C11×#1640C211yesmaximal, characteristic, complemented
11C11×#1626C211yesmaximal, characteristic, complemented
12C11×#1620C211yesmaximal, characteristic, complemented
13C11×#1620C211yesmaximal, characteristic, complemented
14C11×#1584C211yesmaximal, characteristic, complemented
15C11×#1579C211yesmaximal, characteristic, complemented
16C11×#559C2211yescharacteristic
17C11×#559C2211yescharacteristic
18C11×#559C2211yescharacteristic
19C11×#557C2211yescharacteristic
20C11×#497—21no—
21C11×#495—21no—
22C11×#495—21no—
23C11×#493C2211yescharacteristic
24C11×#493C2211yescharacteristic
25C11×#493C2211yescharacteristic
26C11×#492C2211yescharacteristic
27C11×#488—21no—
28C11×#486C2211yescharacteristic
29C11×#486C2211yescharacteristic
30C11×#478—21no—
31C11×#475C2211yescharacteristic
32C11×#464—21no—
33C11×#464—21no—
34C11×#463—21no—
35C11×#463—21no—
36C11×#463—21no—
37C11×#463—21no—
38C11×#462C2211yescharacteristic
39C11×#461—21no—
40C11×#460C2211yescharacteristic
41C11×#460C2211yescharacteristic
42C11×#460C2211yescharacteristic
43C11×#460C2211yescharacteristic
44C11×#460C2211yescharacteristic
45C11×#460C2211yescharacteristic
46C11×#446C2211yescharacteristic
47C8×Q8×C11C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C8×Q8×C11C2211yescharacteristic
50C11×#440—21no—
51C4×C11×Q16C2211yescharacteristic
52C4×C11×Q16C2211yescharacteristic
53C4×C11×SD16—21no—
54C4×C11×D8—21no—
55C4×C11×D8—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#332C2211yescharacteristic
59C11×#331C2211yescharacteristic
60C11×#331C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×Q8⋊C8C2211yescharacteristic
65C11×Q8⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×Q16—21no—
68C2×C11×Q16D411yescharacteristic
69C2×C11×Q16D411yescharacteristic
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×SD16—21no—
78C2×C11×D8—21no—
79C2×C11×D8—21no—
80C2×C11×D8—21no—
81C2×C11×D8—21no—
82C2×C11×D8—41no—
83C11×C4⋊Q8—21no—
84C11×C4⋊Q8C2311yescharacteristic
85C11×#127C2311yescharacteristic
86C11×#127C2311yescharacteristic
87C11×#127C2311yescharacteristic
88C11×#125—21no—
89C11×#125—41no—
90C11×#124—21no—
91C11×#124—21no—
92C11×#124—21no—
93C11×#124—21no—
94C11×#124—21no—
95C11×#124—21no—
96C11×#123—41no—
97C11×#123—41no—
98C11×#123—41no—
99C4×Q8×C11—21no—
100C4×Q8×C11—21no—
101C4×Q8×C11C2311yescharacteristic
102C4×Q8×C11C2311yescharacteristic
103C4×Q8×C11C2311yescharacteristic
104C4×Q8×C11C2311yescharacteristic
105C4×D4×C11—21no—
106C4×D4×C11—21no—
107C4×D4×C11—21no—
108C4×D4×C11—21no—
109C4×D4×C11—21no—
110C4×D4×C11—21no—
111C11×#107D411yescharacteristic
112C11×#107D411yescharacteristic
113C11×#106—21no—
114C11×C4⋊C8—21no—
115C11×C4⋊C8—21no—
116C11×C4⋊C8—21no—
117C11×C4⋊C8—21no—
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×C4⋊C8C2311yescharacteristic
122C11×#103—21no—
123C11×#103—21no—
124C11×#103D411yescharacteristic
125C11×#103D411yescharacteristic
126C11×#103D411yescharacteristic
127C11×#103D411yescharacteristic
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—21no—
135C11×#102—21no—
136C11×#102—41no—
137C11×#97—21no—
138C4×C8×C11—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19874C1111yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C2×D411yescharacteristic
147C2×Q8×C11C2×D411yescharacteristic
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C22×C4×C11—41no—
160C22×C4×C11—41no—
161C22×C4×C11—41no—
162C11×Q16—22no—
163C11×Q16—41no—
164C11×Q16—81no—
165C11×SD16—42no—
166C11×SD16—42no—
167C11×SD16—81no—
168C11×SD16—81no—
169C11×SD16—81no—
170C11×SD16—81no—
171C11×SD16—81no—
172C11×SD16—81no—
173C11×D8—42no—
174C11×D8—42no—
175C11×D8—81no—
176C11×D8—81no—
177C11×D8—82no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C2×C8×C11C2×D411yescharacteristic
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—41no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4—41no—
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C22⋊C4—41no—
201C11×C22⋊C4—41no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C11×C22⋊C4—41no—
209C42×C11—21no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—21no—
213C42×C11—41no—
214C42×C11C2411yescharacteristic
215#3400C2×C1111yescharacteristic, complemented
216#3396C2×C1111yescharacteristic, complemented
217#3396C2×C1111yescharacteristic, complemented
218#3365C2×C1111yescharacteristic, complemented
219#1721C2×C1111yescharacteristic
220#1688C2×C1111yescharacteristic, complemented
221#1682C2×C1111yescharacteristic, complemented
222#1668C2×C1111yescharacteristic, complemented
223#1666C2×C1111yescharacteristic, complemented
224#1640C2×C1111yescharacteristic, complemented
225#1626C2×C1111yescharacteristic, complemented
226#1620C2×C1111yescharacteristic, complemented
227#1620C2×C1111yescharacteristic, complemented
228#1584C2×C1111yescharacteristic, complemented
229#1579C2×C1111yescharacteristic, complemented
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—21no—
237Q8×C11—21no—
238Q8×C11—21no—
239Q8×C11—21no—
240Q8×C11—21no—
241Q8×C11—41no—
242Q8×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—81no—
256D4×C11—81no—
257D4×C11—81no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—161no—
268C2×C4×C11—161no—
269C2×C4×C11—161no—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11#13512yes—
282#559C22×C1111yescharacteristic
283#559C22×C1111yescharacteristic
284#559C22×C1111yescharacteristic
285#557C22×C1111yescharacteristic
286#497—21no—
287#495—21no—
288#495—21no—
289#493C22×C1111yescharacteristic
290#493C22×C1111yescharacteristic
291#493C22×C1111yescharacteristic
292#492C22×C1111yescharacteristic
293#488—21no—
294#486C22×C1111yescharacteristic
295#486C22×C1111yescharacteristic
296#478—21no—
297#475C22×C1111yescharacteristic
298#464—21no—
299#464—21no—
300#463—21no—
301#463—21no—
302#463—21no—
303#463—21no—
304#462C22×C1111yescharacteristic
305#461—21no—
306#460C22×C1111yescharacteristic
307#460C22×C1111yescharacteristic
308#460C22×C1111yescharacteristic
309#460C22×C1111yescharacteristic
310#460C22×C1111yescharacteristic
311#460C22×C1111yescharacteristic
312#446C22×C1111yescharacteristic
313C8×Q8C22×C1111yescharacteristic
314C8×Q8C22×C1111yescharacteristic
315C8×Q8C22×C1111yescharacteristic
316#440—21no—
317C4×Q16C22×C1111yescharacteristic
318C4×Q16C22×C1111yescharacteristic
319C4×SD16—21no—
320C4×D8—21no—
321C4×D8—21no—
322#335C22×C1111yescharacteristic
323#334C22×C1111yescharacteristic
324#332C22×C1111yescharacteristic
325#331C22×C1111yescharacteristic
326#331C22×C1111yescharacteristic
327#331C22×C1111yescharacteristic
328Q8⋊C8C22×C1111yescharacteristic
329Q8⋊C8C22×C1111yescharacteristic
330Q8⋊C8C22×C1111yescharacteristic
331Q8⋊C8C22×C1111yescharacteristic
332#322C22×C1111yescharacteristic
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11D4211yescharacteristic
343C4×C11—21no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—81no—
353C4×C11C2×#13511yescharacteristic
354C4×C11#57511yescharacteristic
355C4×C11#57611yescharacteristic
356C4×C11#57711yescharacteristic
357C2×Q16—21no—
358C2×Q16D4×C1111yescharacteristic
359C2×Q16D4×C1111yescharacteristic
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×D8—21no—
369C2×D8—21no—
370C2×D8—21no—
371C2×D8—21no—
372C2×D8—41no—
373C4⋊Q8—21no—
374C4⋊Q8C23×C1111yescharacteristic
375#127C23×C1111yescharacteristic
376#127C23×C1111yescharacteristic
377#127C23×C1111yescharacteristic
378#125—21no—
379#125—41no—
380#124—21no—
381#124—21no—
382#124—21no—
383#124—21no—
384#124—21no—
385#124—21no—
386#123—41no—
387#123—41no—
388#123—41no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8C23×C1111yescharacteristic
392C4×Q8C23×C1111yescharacteristic
393C4×Q8C23×C1111yescharacteristic
394C4×Q8C23×C1111yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401#107D4×C1111yescharacteristic
402#107D4×C1111yescharacteristic
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8C23×C1111yescharacteristic
409C4⋊C8C23×C1111yescharacteristic
410C4⋊C8C23×C1111yescharacteristic
411C4⋊C8C23×C1111yescharacteristic
412#103—21no—
413#103—21no—
414#103D4×C1111yescharacteristic
415#103D4×C1111yescharacteristic
416#103D4×C1111yescharacteristic
417#103D4×C1111yescharacteristic
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—41no—
427#97—21no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8C23×C1111yescharacteristic
432C4×C8C23×C1111yescharacteristic
433C4×C8C23×C1111yescharacteristic
434C2×C11—161no—
435C2×C11—161no—
436C2×C11—161no—
437C2×C11#327111yescharacteristic
438C2×C11#328711yescharacteristic
439C2×C11#328811yescharacteristic
440C2×Q8—21no—
441C2×Q8C2×D4×C1111yescharacteristic
442C2×Q8C2×D4×C1111yescharacteristic
443C2×Q8C2×D4×C1111yescharacteristic
444C2×Q8C2×D4×C1111yescharacteristic
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457Q16—22no—
458Q16—41no—
459Q16—81no—
460SD16—42no—
461SD16—42no—
462SD16—81no—
463SD16—81no—
464SD16—81no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468D8—42no—
469D8—42no—
470D8—81no—
471D8—81no—
472D8—82no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8C2×D4×C1111yescharacteristic
479C2×C8C2×D4×C1111yescharacteristic
480C2×C8C2×D4×C1111yescharacteristic
481C2×C8C2×D4×C1111yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C1111yescharacteristic
492C4⋊C4C2×D4×C1111yescharacteristic
493C4⋊C4C2×D4×C1111yescharacteristic
494C4⋊C4C2×D4×C1111yescharacteristic
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—41no—
509C42C24×C1111yescharacteristic
510C11#1987411yescharacteristic, direct product factor, Sylow
511C23—41no—
512C23—41no—
513C23—41no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—21no—
521Q8—21no—
522Q8—41no—
523Q8—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—81no—
537D4—81no—
538D4—81no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—161no—
549C2×C4—161no—
550C2×C4—161no—
551C2×C4C22×D4×C1111yescharacteristic
552C2×C4C22×D4×C1111yescharacteristic
553C2×C4C11×H(5,𝔽2)11yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8C11×#13512yes—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22D42×C1111yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4C2×C11×#13511yescharacteristic
584C4C11×#57511yescharacteristic
585C4C11×#57611yescharacteristic
586C4C11×#57711yescharacteristic
587C2—161no—
588C2—161no—
589C2—161no—
590C2C11×#327111yescharacteristic
591C2C11×#328711yescharacteristic
592C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#1721C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C11×#3400C2semidirect
2. C11×#3396C2semidirect
3. C11×#3396C2semidirect
4. C11×#3365C2semidirect
6. C11×#1688C2semidirect
7. C11×#1682C2semidirect
8. C11×#1668C2semidirect
9. C11×#1666C2semidirect
10. C11×#1640C2semidirect
11. C11×#1626C2semidirect
12. C11×#1620C2semidirect
13. C11×#1620C2semidirect
14. C11×#1584C2semidirect
15. C11×#1579C2semidirect
144. #19874C11direct (N × H)
215. #3400C2×C11semidirect
216. #3396C2×C11semidirect
217. #3396C2×C11semidirect
218. #3365C2×C11semidirect
220. #1688C2×C11semidirect
221. #1682C2×C11semidirect
222. #1668C2×C11semidirect
223. #1666C2×C11semidirect
224. #1640C2×C11semidirect
225. #1626C2×C11semidirect
226. #1620C2×C11semidirect
227. #1620C2×C11semidirect
228. #1584C2×C11semidirect
229. #1579C2×C11semidirect
510. C11#19874direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34002
C11×#33962
C11×#33652
C11×#17212
C11×#16882
C11×#16822
C11×#16682
C11×#16662
C11×#16402
C11×#16262
C11×#16202
C11×#15842
C11×#15792
#1987411