Finite Group Databasebeta

← C11×#19784 #14596977

Subgroups — C11×#19784 #14596977

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3358C211yesmaximal, characteristic, complemented
2C11×#3341C211yesmaximal, characteristic, complemented
3C11×#3329C211yesmaximal, characteristic, complemented
4C11×#3305C211yesmaximal, characteristic, complemented
5C11×#1719C211yesmaximal, characteristic, complemented
6C11×#1697C211yesmaximal, characteristic, complemented
7C11×#1683C211yesmaximal, characteristic, complemented
8C11×#1681C211yesmaximal, characteristic, complemented
9C11×#1676C211yesmaximal, characteristic, complemented
10C11×#1646C211yesmaximal, characteristic, complemented
11C11×#1637C211yesmaximal, characteristic, complemented
12C11×#1631C211yesmaximal, characteristic, complemented
13C11×#1624C211yesmaximal, characteristic, complemented
14C11×#1581C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C11×#555C2211yescharacteristic
17C11×#555C2211yescharacteristic
18C11×#550C2211yescharacteristic
19D4×Q8×C11C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#492C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#487C2211yescharacteristic
24C11×#486—21no—
25C11×#486C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#485—21no—
28C11×#482—21no—
29C11×#482—21no—
30C11×#482—21no—
31C11×#477C2211yescharacteristic
32C11×#477C2211yescharacteristic
33C11×#476C2211yescharacteristic
34C11×#476C2211yescharacteristic
35C11×#474—21no—
36C11×#474C2211yescharacteristic
37C11×#468—21no—
38C11×#466—21no—
39C11×#466—21no—
40C11×#461C2211yescharacteristic
41C11×#459—21no—
42C11×#459C2211yescharacteristic
43C11×#459C2211yescharacteristic
44C11×#449—21no—
45C11×#448—21no—
46C8×Q8×C11C2211yescharacteristic
47C4×C11×SD16C2211yescharacteristic
48C4×C11×D8—21no—
49C4×C11×D8C2211yescharacteristic
50C11×#436C2211yescharacteristic
51C8×D4×C11C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C11×#427—21no—
54C11×#419—21no—
55C11×#416—21no—
56C11×#335C2211yescharacteristic
57C11×#335C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×D4⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C22×Q8×C11—21no—
69C2×C11×SD16—21no—
70C2×C11×SD16—41no—
71C2×C11×SD16D411yescharacteristic
72C2×C11×D8—21no—
73C2×C11×D8—21no—
74C2×C11×D8D411yescharacteristic
75C2×C11×M16—21no—
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C11×C4⋊Q8—21no—
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×C4⋊Q8C2311yescharacteristic
82C11×#127—21no—
83C11×#127C2311yescharacteristic
84C11×#124—41no—
85C11×#124—41no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—41no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—41no—
94C4×Q8×C11C2311yescharacteristic
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11C2311yescharacteristic
98C4×D4×C11C2311yescharacteristic
99C4×D4×C11C2311yescharacteristic
100C11×#117—21no—
101C11×#117—21no—
102C11×#117—21no—
103C11×#117—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#107—21no—
109C11×#107D411yescharacteristic
110C11×#106—21no—
111C11×#106—21no—
112C11×#106D411yescharacteristic
113C11×C4⋊C8—21no—
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×#103—21no—
119C11×#103—21no—
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—41no—
124C11×#103D411yescharacteristic
125C11×#102—21no—
126C11×#102—21no—
127C11×#102—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102D411yescharacteristic
135C11×#102D411yescharacteristic
136C11×#102D411yescharacteristic
137C11×C22⋊C8—21no—
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C4×C8×C11—21no—
141C4×C8×C11C2311yescharacteristic
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19784C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—42no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—42no—
152C2×Q8×C11—81no—
153C2×Q8×C11C2×D411yescharacteristic
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—41no—
158C2×D4×C11—41no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11C2×D411yescharacteristic
162C2×D4×C11C2×D411yescharacteristic
163C2×D4×C11C2×D411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C11×SD16—22no—
170C11×SD16—81no—
171C11×SD16—82no—
172C11×D8—41no—
173C11×D8—42no—
174C11×D8—81no—
175C11×M16—81no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—42no—
182C2×C8×C11—81no—
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—21no—
194C11×C4⋊C4—41no—
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C22⋊C4—21no—
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—41no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C11×C22⋊C4—41no—
208C42×C11—21no—
209C42×C11—41no—
210C42×C11—41no—
211C42×C11C2411yescharacteristic
212#3358C2×C1111yescharacteristic, complemented
213#3341C2×C1111yescharacteristic, complemented
214#3329C2×C1111yescharacteristic, complemented
215#3305C2×C1111yescharacteristic, complemented
216#1719C2×C1111yescharacteristic, complemented
217#1697C2×C1111yescharacteristic, complemented
218#1683C2×C1111yescharacteristic, complemented
219#1681C2×C1111yescharacteristic, complemented
220#1676C2×C1111yescharacteristic, complemented
221#1646C2×C1111yescharacteristic, complemented
222#1637C2×C1111yescharacteristic, complemented
223#1631C2×C1111yescharacteristic, complemented
224#1624C2×C1111yescharacteristic, complemented
225#1581C2×C1111yescharacteristic, complemented
226SD16⋊C8C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—41no—
231Q8×C11—21no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—82no—
235Q8×C11—81no—
236Q8×C11—81no—
237Q8×C11#13512yes—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—82no—
249D4×C11—81no—
250D4×C11—161no—
251D4×C11—161no—
252D4×C11—161no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—82no—
268C2×C4×C11—82no—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C8×C11—41no—
281#555C22×C1111yescharacteristic
282#555C22×C1111yescharacteristic
283#550C22×C1111yescharacteristic
284D4×Q8C22×C1111yescharacteristic
285#500C22×C1111yescharacteristic
286#492C22×C1111yescharacteristic
287#487C22×C1111yescharacteristic
288#487C22×C1111yescharacteristic
289#486—21no—
290#486C22×C1111yescharacteristic
291#486C22×C1111yescharacteristic
292#485—21no—
293#482—21no—
294#482—21no—
295#482—21no—
296#477C22×C1111yescharacteristic
297#477C22×C1111yescharacteristic
298#476C22×C1111yescharacteristic
299#476C22×C1111yescharacteristic
300#474—21no—
301#474C22×C1111yescharacteristic
302#468—21no—
303#466—21no—
304#466—21no—
305#461C22×C1111yescharacteristic
306#459—21no—
307#459C22×C1111yescharacteristic
308#459C22×C1111yescharacteristic
309#449—21no—
310#448—21no—
311C8×Q8C22×C1111yescharacteristic
312C4×SD16C22×C1111yescharacteristic
313C4×D8—21no—
314C4×D8C22×C1111yescharacteristic
315#436C22×C1111yescharacteristic
316C8×D4C22×C1111yescharacteristic
317C8×D4C22×C1111yescharacteristic
318#427—21no—
319#419—21no—
320#416—21no—
321#335C22×C1111yescharacteristic
322#335C22×C1111yescharacteristic
323#333C22×C1111yescharacteristic
324#333C22×C1111yescharacteristic
325#332C22×C1111yescharacteristic
326#331C22×C1111yescharacteristic
327Q8⋊C8C22×C1111yescharacteristic
328D4⋊C8C22×C1111yescharacteristic
329D4⋊C8C22×C1111yescharacteristic
330D4⋊C8C22×C1111yescharacteristic
331#322C22×C1111yescharacteristic
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11D4211yescharacteristic
345C4×C11—22no—
346C4×C11—21no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11C2×#13511yescharacteristic
355C4×C11#57511yescharacteristic
356C4×C11#57611yescharacteristic
357C4×C11#57811yescharacteristic
358C2×#41—21no—
359C22×Q8—21no—
360C2×SD16—21no—
361C2×SD16—41no—
362C2×SD16D4×C1111yescharacteristic
363C2×D8—21no—
364C2×D8—21no—
365C2×D8D4×C1111yescharacteristic
366C2×M16—21no—
367C22×C8—21no—
368C22×C8—21no—
369C4⋊Q8—21no—
370C4⋊Q8C23×C1111yescharacteristic
371C4⋊Q8C23×C1111yescharacteristic
372C4⋊Q8C23×C1111yescharacteristic
373#127—21no—
374#127C23×C1111yescharacteristic
375#124—41no—
376#124—41no—
377C22⋊Q8—21no—
378C22⋊Q8—41no—
379#121—21no—
380#121—21no—
381#121—21no—
382#121—21no—
383#121—21no—
384#121—41no—
385C4×Q8C23×C1111yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4C23×C1111yescharacteristic
389C4×D4C23×C1111yescharacteristic
390C4×D4C23×C1111yescharacteristic
391#117—21no—
392#117—21no—
393#117—21no—
394#117—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107—21no—
399#107—21no—
400#107D4×C1111yescharacteristic
401#106—21no—
402#106—21no—
403#106D4×C1111yescharacteristic
404C4⋊C8—21no—
405C4⋊C8C23×C1111yescharacteristic
406C4⋊C8C23×C1111yescharacteristic
407C4⋊C8C23×C1111yescharacteristic
408C4⋊C8C23×C1111yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—41no—
415#103D4×C1111yescharacteristic
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102D4×C1111yescharacteristic
426#102D4×C1111yescharacteristic
427#102D4×C1111yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C4×C8—21no—
432C4×C8C23×C1111yescharacteristic
433C4×C8C23×C1111yescharacteristic
434C4×C8C23×C1111yescharacteristic
435C2×C11—81no—
436C2×C11—81no—
437C2×C11—81no—
438C2×C11—161no—
439C2×C11#326911yescharacteristic
440C2×C11#328011yescharacteristic
441C2×C11#328811yescharacteristic
442#41—42no—
443#41—81no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—41no—
448C2×Q8—42no—
449C2×Q8—81no—
450C2×Q8C2×D4×C1111yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4C2×D4×C1111yescharacteristic
459C2×D4C2×D4×C1111yescharacteristic
460C2×D4C2×D4×C1111yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—41no—
466SD16—22no—
467SD16—81no—
468SD16—82no—
469D8—41no—
470D8—42no—
471D8—81no—
472M16—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—81no—
480C2×C8C2×D4×C1111yescharacteristic
481C2×C8C2×D4×C1111yescharacteristic
482C2×C8C2×D4×C1111yescharacteristic
483C2×C8C2×D4×C1111yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C1111yescharacteristic
493C4⋊C4C2×D4×C1111yescharacteristic
494C4⋊C4C2×D4×C1111yescharacteristic
495C4⋊C4C2×D4×C1111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42C24×C1111yescharacteristic
509C11#1978411yescharacteristic, direct product factor, Sylow
510C23—21no—
511C23—21no—
512C23—21no—
513C23—41no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—82no—
518Q8—81no—
519Q8—81no—
520Q8C11×#13512yes—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—81no—
533D4—161no—
534D4—161no—
535D4—161no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4C22×D4×C1111yescharacteristic
553C2×C4C22×D4×C1111yescharacteristic
554C2×C4C11×H(5,𝔽2)11yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C1111yescharacteristic
577C4—22no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4C2×C11×#13511yescharacteristic
587C4C11×#57511yescharacteristic
588C4C11×#57611yescharacteristic
589C4C11×#57811yescharacteristic
590C2—81no—
591C2—81no—
592C2—81no—
593C2—161no—
594C2C11×#326911yescharacteristic
595C2C11×#328011yescharacteristic
596C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
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×#3358C2semidirect
2. C11×#3341C2semidirect
3. C11×#3329C2semidirect
4. C11×#3305C2semidirect
5. C11×#1719C2semidirect
6. C11×#1697C2semidirect
7. C11×#1683C2semidirect
8. C11×#1681C2semidirect
9. C11×#1676C2semidirect
10. C11×#1646C2semidirect
11. C11×#1637C2semidirect
12. C11×#1631C2semidirect
13. C11×#1624C2semidirect
14. C11×#1581C2semidirect
15. C11×SD16⋊C8C2semidirect
144. #19784C11direct (N × H)
212. #3358C2×C11semidirect
213. #3341C2×C11semidirect
214. #3329C2×C11semidirect
215. #3305C2×C11semidirect
216. #1719C2×C11semidirect
217. #1697C2×C11semidirect
218. #1683C2×C11semidirect
219. #1681C2×C11semidirect
220. #1676C2×C11semidirect
221. #1646C2×C11semidirect
222. #1637C2×C11semidirect
223. #1631C2×C11semidirect
224. #1624C2×C11semidirect
225. #1581C2×C11semidirect
226. SD16⋊C8C2×C11semidirect
509. C11#19784direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33582
C11×#33412
C11×#33292
C11×#33052
C11×#17192
C11×#16972
C11×#16832
C11×#16812
C11×#16762
C11×#16462
C11×#16372
C11×#16312
C11×#16242
C11×#15812
C11×SD16⋊C82
#1978411