Finite Group Databasebeta

← C11×#19823 #14597016

Subgroups — C11×#19823 #14597016

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3360C211yesmaximal, characteristic, complemented
2C11×#3340C211yesmaximal, characteristic, complemented
3C11×#3325C211yesmaximal, characteristic
4C11×#3295C211yesmaximal, characteristic, complemented
5C11×#1720C211yesmaximal, characteristic, complemented
6C11×#1703C211yesmaximal, characteristic, complemented
7C11×#1678C211yesmaximal, characteristic, complemented
8C11×#1677C211yesmaximal, characteristic, complemented
9C11×#1671C211yesmaximal, characteristic, complemented
10C11×#1639C211yesmaximal, characteristic, complemented
11C11×#1634C211yesmaximal, characteristic, complemented
12C11×#1632C211yesmaximal, characteristic, complemented
13C11×#1628C211yesmaximal, characteristic, complemented
14C11×#1583C211yesmaximal, characteristic, complemented
15C11×#1580C211yesmaximal, characteristic, complemented
16C11×#556C2211yescharacteristic, complemented
17C11×#555C2211yescharacteristic
18C11×#554C2211yescharacteristic
19D42×C11C2211yescharacteristic
20C11×#498C2211yescharacteristic, complemented
21C11×#494C2211yescharacteristic, complemented
22C11×#488—21no—
23C11×#487C2211yescharacteristic, complemented
24C11×#486C2211yescharacteristic
25C11×#486C2211yescharacteristic
26C11×#486C2211yescharacteristic
27C11×#485—21no—
28C11×#482—21no—
29C11×#482—21no—
30C11×#481—21no—
31C11×#479—21no—
32C11×#477C2211yescharacteristic, complemented
33C11×#476C2211yescharacteristic
34C11×#476C2211yescharacteristic
35C11×#476C2211yescharacteristic, complemented
36C11×#474C2211yescharacteristic
37C11×#469—21no—
38C11×#465—21no—
39C11×#465—21no—
40C11×#463—21no—
41C11×#461C2211yescharacteristic
42C11×#460C2211yescharacteristic
43C11×#459C2211yescharacteristic
44C11×#450—21no—
45C11×#447—21no—
46C8×Q8×C11C2211yescharacteristic, complemented
47C4×C11×SD16—21no—
48C4×C11×SD16C2211yescharacteristic
49C4×C11×D8C2211yescharacteristic
50C11×#436C2211yescharacteristic
51C8×D4×C11C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic, complemented
53C11×#427—21no—
54C11×#418—21no—
55C2×C11×#102—21no—
56C11×#334C2211yescharacteristic, complemented
57C11×#334C2211yescharacteristic, complemented
58C11×#333C2211yescharacteristic, complemented
59C11×#333C2211yescharacteristic, complemented
60C11×#332C2211yescharacteristic, complemented
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic, complemented
63C11×D4⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic, complemented
66C11×#322C2211yescharacteristic, complemented
67C22×D4×C11—21no—
68C22×D4×C11—21no—
69C2×C11×Q16—41no—
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16D411yescharacteristic
73C2×C11×D8—21no—
74C2×C11×D8D411yescharacteristic
75C2×C11×M16—21no—
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C11×C4⋊Q8C2311yescharacteristic
79C11×C4⋊Q8C2311yescharacteristic
80C11×C4⋊Q8C2311yescharacteristic
81C11×#127C2311yescharacteristic
82C11×#126—41no—
83C11×#125—21no—
84C11×#124—21no—
85C11×#124—41no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—41no—
89C11×#121—21no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121—21no—
93C11×#120—41no—
94C4×Q8×C11—21no—
95C4×Q8×C11C2311yescharacteristic
96C4×D4×C11—21no—
97C4×D4×C11C2311yescharacteristic
98C4×D4×C11C2311yescharacteristic
99C4×D4×C11C2311yescharacteristic
100C11×#117—21no—
101C11×#117—21no—
102C11×#117—21no—
103C2×C11×C4⋊C4—21no—
104C11×#107—21no—
105C11×#107—21no—
106C11×#107D411yescharacteristic
107C11×#106—21no—
108C11×#106—21no—
109C11×#106—21no—
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×#103D411yescharacteristic
123C11×#102—21no—
124C11×#102—21no—
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—41no—
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#19823C1111yesmaximal, characteristic, direct product factor, Sylow
145C24×C11—41no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11—41no—
158C2×D4×C11—81no—
159C2×D4×C11—81no—
160C2×D4×C11C2×D411yescharacteristic
161C2×D4×C11C2×D411yescharacteristic
162C2×D4×C11C2×D411yescharacteristic
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—41no—
167C11×Q16—82no—
168C11×SD16—41no—
169C11×SD16—42no—
170C11×SD16—81no—
171C11×D8—22no—
172C11×D8—81no—
173C11×M16—81no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—42no—
180C2×C8×C11—81no—
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—41no—
193C11×C4⋊C4—41no—
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#3360C2×C1111yescharacteristic, complemented
213#3340C2×C1111yescharacteristic, complemented
214#3325C2×C1111yescharacteristic
215#3295C2×C1111yescharacteristic, complemented
216#1720C2×C1111yescharacteristic, complemented
217#1703C2×C1111yescharacteristic, complemented
218#1678C2×C1111yescharacteristic, complemented
219#1677C2×C1111yescharacteristic, complemented
220#1671C2×C1111yescharacteristic, complemented
221#1639C2×C1111yescharacteristic, complemented
222#1634C2×C1111yescharacteristic, complemented
223#1632C2×C1111yescharacteristic, complemented
224#1628C2×C1111yescharacteristic, complemented
225#1583C2×C1111yescharacteristic, complemented
226#1580C2×C1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—41no—
231C23×C11—82no—
232C23×C11—82no—
233C23×C11—161no—
234Q8×C11—21no—
235Q8×C11—21no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—81no—
239Q8×C11—81no—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—21no—
243D4×C11—21no—
244D4×C11—21no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—81no—
250D4×C11—82no—
251D4×C11—82no—
252D4×C11—161no—
253D4×C11#13512yes—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
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—41no—
268C2×C4×C11—161no—
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#556C22×C1111yescharacteristic, complemented
282#555C22×C1111yescharacteristic
283#554C22×C1111yescharacteristic
284D42C22×C1111yescharacteristic
285#498C22×C1111yescharacteristic, complemented
286#494C22×C1111yescharacteristic, complemented
287#488—21no—
288#487C22×C1111yescharacteristic, complemented
289#486C22×C1111yescharacteristic
290#486C22×C1111yescharacteristic
291#486C22×C1111yescharacteristic
292#485—21no—
293#482—21no—
294#482—21no—
295#481—21no—
296#479—21no—
297#477C22×C1111yescharacteristic, complemented
298#476C22×C1111yescharacteristic
299#476C22×C1111yescharacteristic
300#476C22×C1111yescharacteristic, complemented
301#474C22×C1111yescharacteristic
302#469—21no—
303#465—21no—
304#465—21no—
305#463—21no—
306#461C22×C1111yescharacteristic
307#460C22×C1111yescharacteristic
308#459C22×C1111yescharacteristic
309#450—21no—
310#447—21no—
311C8×Q8C22×C1111yescharacteristic, complemented
312C4×SD16—21no—
313C4×SD16C22×C1111yescharacteristic
314C4×D8C22×C1111yescharacteristic
315#436C22×C1111yescharacteristic
316C8×D4C22×C1111yescharacteristic
317C8×D4C22×C1111yescharacteristic, complemented
318#427—21no—
319#418—21no—
320C2×#102—21no—
321#334C22×C1111yescharacteristic, complemented
322#334C22×C1111yescharacteristic, complemented
323#333C22×C1111yescharacteristic, complemented
324#333C22×C1111yescharacteristic, complemented
325#332C22×C1111yescharacteristic, complemented
326#331C22×C1111yescharacteristic
327Q8⋊C8C22×C1111yescharacteristic, complemented
328D4⋊C8C22×C1111yescharacteristic
329D4⋊C8C22×C1111yescharacteristic
330D4⋊C8C22×C1111yescharacteristic, complemented
331#322C22×C1111yescharacteristic, complemented
332C22×C11—22no—
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×C11—164no—
345C22×C11D4211yescharacteristic
346C4×C11—21no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11C2×#13511yescharacteristic
356C4×C11#57511yescharacteristic
357C4×C11#57711yescharacteristic
358C4×C11#57711yescharacteristic
359C22×D4—21no—
360C22×D4—21no—
361C2×Q16—41no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16D4×C1111yescharacteristic
365C2×D8—21no—
366C2×D8D4×C1111yescharacteristic
367C2×M16—21no—
368C22×C8—21no—
369C22×C8—21no—
370C4⋊Q8C23×C1111yescharacteristic
371C4⋊Q8C23×C1111yescharacteristic
372C4⋊Q8C23×C1111yescharacteristic
373#127C23×C1111yescharacteristic
374#126—41no—
375#125—21no—
376#124—21no—
377#124—41no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—41no—
381#121—21no—
382#121—21no—
383#121—21no—
384#121—21no—
385#120—41no—
386C4×Q8—21no—
387C4×Q8C23×C1111yescharacteristic
388C4×D4—21no—
389C4×D4C23×C1111yescharacteristic
390C4×D4C23×C1111yescharacteristic
391C4×D4C23×C1111yescharacteristic
392#117—21no—
393#117—21no—
394#117—21no—
395C2×C4⋊C4—21no—
396#107—21no—
397#107—21no—
398#107D4×C1111yescharacteristic
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106—21no—
404#106D4×C1111yescharacteristic
405C4⋊C8—21no—
406C4⋊C8C23×C1111yescharacteristic
407C4⋊C8C23×C1111yescharacteristic
408C4⋊C8C23×C1111yescharacteristic
409C4⋊C8C23×C1111yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103D4×C1111yescharacteristic
415#102—21no—
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#102—41no—
426#102D4×C1111yescharacteristic
427#102D4×C1111yescharacteristic
428#102D4×C1111yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C4×C8—21no—
433C4×C8C23×C1111yescharacteristic
434C4×C8C23×C1111yescharacteristic
435C4×C8C23×C1111yescharacteristic
436C2×C11—42no—
437C2×C11—81no—
438C2×C11—81no—
439C2×C11—161no—
440C2×C11#326711yescharacteristic
441C2×C11#328211yescharacteristic
442C2×C11#328811yescharacteristic
443C24—41no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C2×D4×C1111yescharacteristic
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—41no—
456C2×D4—81no—
457C2×D4—81no—
458C2×D4C2×D4×C1111yescharacteristic
459C2×D4C2×D4×C1111yescharacteristic
460C2×D4C2×D4×C1111yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465Q16—82no—
466SD16—41no—
467SD16—42no—
468SD16—81no—
469D8—22no—
470D8—81no—
471M16—81no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—81no—
479C2×C8C2×D4×C1111yescharacteristic
480C2×C8C2×D4×C1111yescharacteristic
481C2×C8C2×D4×C1111yescharacteristic
482C2×C8C2×D4×C1111yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4C2×D4×C1111yescharacteristic
494C4⋊C4C2×D4×C1111yescharacteristic
495C4⋊C4C2×D4×C1111yescharacteristic
496C4⋊C4C2×D4×C1111yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42C24×C1111yescharacteristic
510C11#1982311yescharacteristic, direct product factor, Sylow
511C23—21no—
512C23—21no—
513C23—21no—
514C23—41no—
515C23—82no—
516C23—82no—
517C23—161no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523Q8—81no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—81no—
534D4—82no—
535D4—82no—
536D4—161no—
537D4C11×#13512yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—161no—
553C2×C4C22×D4×C1111yescharacteristic
554C2×C4C22×D4×C1111yescharacteristic
555C2×C4C11×H(5,𝔽2)11yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—164no—
578C22D42×C1111yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4C2×C11×#13511yescharacteristic
589C4C11×#57511yescharacteristic
590C4C11×#57711yescharacteristic
591C4C11×#57711yescharacteristic
592C2—42no—
593C2—81no—
594C2—81no—
595C2—161no—
596C2C11×#326711yescharacteristic
597C2C11×#328211yescharacteristic
598C2C11×#328811yescharacteristic
subgroupG/H
center, socleC22×C11D42
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3325C2
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×#3360C2semidirect
2. C11×#3340C2semidirect
4. C11×#3295C2semidirect
5. C11×#1720C2semidirect
6. C11×#1703C2semidirect
7. C11×#1678C2semidirect
8. C11×#1677C2semidirect
9. C11×#1671C2semidirect
10. C11×#1639C2semidirect
11. C11×#1634C2semidirect
12. C11×#1632C2semidirect
13. C11×#1628C2semidirect
14. C11×#1583C2semidirect
15. C11×#1580C2semidirect
16. C11×#556C22semidirect
20. C11×#498C22semidirect
21. C11×#494C22semidirect
23. C11×#487C22semidirect
32. C11×#477C22semidirect
35. C11×#476C22semidirect
46. C8×Q8×C11C22semidirect
52. C8×D4×C11C22semidirect
56. C11×#334C22semidirect
57. C11×#334C22semidirect
58. C11×#333C22semidirect
59. C11×#333C22semidirect
60. C11×#332C22semidirect
62. C11×Q8⋊C8C22semidirect
65. C11×D4⋊C8C22semidirect
66. C11×#322C22semidirect
144. #19823C11direct (N × H)
212. #3360C2×C11semidirect
213. #3340C2×C11semidirect
215. #3295C2×C11semidirect
216. #1720C2×C11semidirect
217. #1703C2×C11semidirect
218. #1678C2×C11semidirect
219. #1677C2×C11semidirect
220. #1671C2×C11semidirect
221. #1639C2×C11semidirect
222. #1634C2×C11semidirect
223. #1632C2×C11semidirect
224. #1628C2×C11semidirect
225. #1583C2×C11semidirect
226. #1580C2×C11semidirect
281. #556C22×C11semidirect
285. #498C22×C11semidirect
286. #494C22×C11semidirect
288. #487C22×C11semidirect
297. #477C22×C11semidirect
300. #476C22×C11semidirect
311. C8×Q8C22×C11semidirect
317. C8×D4C22×C11semidirect
321. #334C22×C11semidirect
322. #334C22×C11semidirect
323. #333C22×C11semidirect
324. #333C22×C11semidirect
325. #332C22×C11semidirect
327. Q8⋊C8C22×C11semidirect
330. D4⋊C8C22×C11semidirect
331. #322C22×C11semidirect
510. C11#19823direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#33602
C11×#33402
C11×#33252
C11×#32952
C11×#17202
C11×#17032
C11×#16782
C11×#16772
C11×#16712
C11×#16392
C11×#16342
C11×#16322
C11×#16282
C11×#15832
C11×#15802
#1982311