Finite Group Databasebeta

← C11×#19412 #14596605

Subgroups — C11×#19412 #14596605

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3207C211yesmaximal, characteristic, complemented
2C11×#3115C211yesmaximal, characteristic, complemented
3C11×#3106C211yesmaximal, characteristic, complemented
4C11×#2988C211yesmaximal, characteristic, complemented
5C11×#1684C211yesmaximal, characteristic, complemented
6C11×#1683C211yesmaximal, characteristic, complemented
7C11×#1678C211yesmaximal, characteristic, complemented
8C11×#1677C211yesmaximal, characteristic, complemented
9C11×#1668C211yesmaximal, characteristic, complemented
10C11×#1667C211yesmaximal, characteristic, complemented
11C11×#1666C211yesmaximal, characteristic, complemented
12C11×#1665C211yesmaximal, characteristic, complemented
13C11×#1572C211yesmaximal, characteristic, complemented
14C11×#1551C211yesmaximal, characteristic, complemented
15C11×#1540C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19C11×#493C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#482—21no—
24C11×#482—21no—
25C11×#477C2211yescharacteristic
26C11×#476C2211yescharacteristic
27C11×#475C2211yescharacteristic
28C11×#474C2211yescharacteristic
29C11×#463—21no—
30C11×#463—21no—
31C11×#460C2211yescharacteristic
32C11×#460C2211yescharacteristic
33C11×#459C2211yescharacteristic
34C11×#459C2211yescharacteristic
35C11×#449—21no—
36C11×#449—21no—
37C11×#449—21no—
38C11×#449—21no—
39C8×Q8×C11C2211yescharacteristic
40C8×Q8×C11C2211yescharacteristic
41C11×#442—21no—
42C11×#440—21no—
43C4×C11×SD16—21no—
44C4×C11×D8—21no—
45C8×D4×C11—21no—
46C8×D4×C11—21no—
47C8×D4×C11C2211yescharacteristic
48C8×D4×C11C2211yescharacteristic
49C11×#432C2211yescharacteristic
50C11×#431—21no—
51C11×#431C2211yescharacteristic
52C11×#431C2211yescharacteristic
53C2×C11×C4⋊C8—21no—
54C2×C11×C4⋊C8C2211yescharacteristic
55C11×#335C2211yescharacteristic
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#334C2211yescharacteristic
59C11×#333C2211yescharacteristic
60C11×#333C2211yescharacteristic
61C11×#332C2211yescharacteristic
62C11×#332C2211yescharacteristic
63C11×#331C2211yescharacteristic
64C11×#331C2211yescharacteristic
65C11×#331C2211yescharacteristic
66C11×#331C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41D411yescharacteristic
70C2×C11×SD16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×D8—21no—
75C2×C11×D8—21no—
76C2×C11×D8—21no—
77C2×C11×D8—21no—
78C22×C8×C11—21no—
79C22×C8×C11—21no—
80C22×C8×C11—21no—
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×#127C2311yescharacteristic
84C11×#127C2311yescharacteristic
85C11×#124—21no—
86C11×#124—21no—
87C11×#121—21no—
88C11×#121—21no—
89C11×#121—21no—
90C11×#121—21no—
91C4×Q8×C11D411yescharacteristic
92C4×Q8×C11C2311yescharacteristic
93C4×D4×C11—21no—
94C4×D4×C11—21no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—21no—
99C4×D4×C11D411yescharacteristic
100C4×D4×C11C2311yescharacteristic
101C11×#117—21no—
102C11×#117D411yescharacteristic
103C2×C42×C11—21no—
104C2×C42×C11C2311yescharacteristic
105C11×#107—21no—
106C11×#107—21no—
107C11×#106—21no—
108C11×#106—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8D411yescharacteristic
113C11×C4⋊C8D411yescharacteristic
114C11×C4⋊C8C2311yescharacteristic
115C11×C4⋊C8C2311yescharacteristic
116C11×C4⋊C8C2311yescharacteristic
117C11×C4⋊C8C2311yescharacteristic
118C11×C4⋊C8C2311yescharacteristic
119C11×C4⋊C8C2311yescharacteristic
120C11×#103—21no—
121C11×#103—21no—
122C11×#103—21no—
123C11×#103—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×C22⋊C8—21no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8—21no—
135C11×C22⋊C8—21no—
136C11×C22⋊C8D411yescharacteristic
137C11×C22⋊C8D411yescharacteristic
138C11×#97—21no—
139C4×C8×C11—21no—
140C4×C8×C11—21no—
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144#19412C1111yesmaximal, characteristic, direct product factor, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—81no—
148C11×#41—81no—
149C11×#41—82no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11C2×D411yescharacteristic
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11#4111yescharacteristic
171C11×SD16—42no—
172C11×SD16—42no—
173C11×SD16—81no—
174C11×SD16—81no—
175C11×D8—42no—
176C11×D8—42no—
177C11×D8—81no—
178C11×D8—81no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—81no—
186C2×C8×C11—81no—
187C2×C8×C11—81no—
188C2×C8×C11C2×D411yescharacteristic
189C2×C8×C11C2×D411yescharacteristic
190C2×C8×C11C2×D411yescharacteristic
191C2×C8×C11C2×D411yescharacteristic
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C11×C22⋊C4—21no—
203C11×C22⋊C4—41no—
204C11×C22⋊C4—41no—
205C11×C22⋊C4—41no—
206C11×C22⋊C4—41no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11C2×D411yescharacteristic
211C42×C11C2×D411yescharacteristic
212C42×C11#4111yescharacteristic
213C42×C11C2411yescharacteristic
214#3207C2×C1111yescharacteristic, complemented
215#3115C2×C1111yescharacteristic, complemented
216#3106C2×C1111yescharacteristic, complemented
217#2988C2×C1111yescharacteristic, complemented
218#1684C2×C1111yescharacteristic, complemented
219#1683C2×C1111yescharacteristic, complemented
220#1678C2×C1111yescharacteristic, complemented
221#1677C2×C1111yescharacteristic, complemented
222#1668C2×C1111yescharacteristic, complemented
223#1667C2×C1111yescharacteristic, complemented
224#1666C2×C1111yescharacteristic, complemented
225#1665C2×C1111yescharacteristic, complemented
226#1572C2×C1111yescharacteristic, complemented
227#1551C2×C1111yescharacteristic, complemented
228#1540C2×C1111yescharacteristic, complemented
229C23×C11—21no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11#12111yescharacteristic
233Q8×C11—21no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—81no—
237Q8×C11#13512yes—
238D4×C11—24no—
239D4×C11—21no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—81no—
249D4×C11—81no—
250D4×C11—82no—
251D4×C11—82no—
252D4×C11#13512yes—
253C2×C4×C11—24no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—81no—
267C2×C4×C11—82no—
268C2×C4×C11—82no—
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11#12111yescharacteristic
271C2×C4×C11#12111yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—41no—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C8×C11—41no—
285#532C22×C1111yescharacteristic
286#532C22×C1111yescharacteristic
287C4×#41C22×C1111yescharacteristic
288#493C22×C1111yescharacteristic
289#492C22×C1111yescharacteristic
290#487C22×C1111yescharacteristic
291#486C22×C1111yescharacteristic
292#482—21no—
293#482—21no—
294#477C22×C1111yescharacteristic
295#476C22×C1111yescharacteristic
296#475C22×C1111yescharacteristic
297#474C22×C1111yescharacteristic
298#463—21no—
299#463—21no—
300#460C22×C1111yescharacteristic
301#460C22×C1111yescharacteristic
302#459C22×C1111yescharacteristic
303#459C22×C1111yescharacteristic
304#449—21no—
305#449—21no—
306#449—21no—
307#449—21no—
308C8×Q8C22×C1111yescharacteristic
309C8×Q8C22×C1111yescharacteristic
310#442—21no—
311#440—21no—
312C4×SD16—21no—
313C4×D8—21no—
314C8×D4—21no—
315C8×D4—21no—
316C8×D4C22×C1111yescharacteristic
317C8×D4C22×C1111yescharacteristic
318#432C22×C1111yescharacteristic
319#431—21no—
320#431C22×C1111yescharacteristic
321#431C22×C1111yescharacteristic
322C2×C4⋊C8—21no—
323C2×C4⋊C8C22×C1111yescharacteristic
324#335C22×C1111yescharacteristic
325#335C22×C1111yescharacteristic
326#334C22×C1111yescharacteristic
327#334C22×C1111yescharacteristic
328#333C22×C1111yescharacteristic
329#333C22×C1111yescharacteristic
330#332C22×C1111yescharacteristic
331#332C22×C1111yescharacteristic
332#331C22×C1111yescharacteristic
333#331C22×C1111yescharacteristic
334#331C22×C1111yescharacteristic
335#331C22×C1111yescharacteristic
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—21no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11C2×#12111yescharacteristic
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—22no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11C2×#13511yescharacteristic
359C4×C11C2×#13511yescharacteristic
360C4×C11#57611yescharacteristic
361C4×C11#57711yescharacteristic
362C2×#41—21no—
363C2×#41—21no—
364C2×#41D4×C1111yescharacteristic
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×D8—21no—
370C2×D8—21no—
371C2×D8—21no—
372C2×D8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C4⋊Q8C23×C1111yescharacteristic
377C4⋊Q8C23×C1111yescharacteristic
378#127C23×C1111yescharacteristic
379#127C23×C1111yescharacteristic
380#124—21no—
381#124—21no—
382#121—21no—
383#121—21no—
384#121—21no—
385#121—21no—
386C4×Q8D4×C1111yescharacteristic
387C4×Q8C23×C1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4D4×C1111yescharacteristic
395C4×D4C23×C1111yescharacteristic
396#117—21no—
397#117D4×C1111yescharacteristic
398C2×C42—21no—
399C2×C42C23×C1111yescharacteristic
400#107—21no—
401#107—21no—
402#106—21no—
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8D4×C1111yescharacteristic
408C4⋊C8D4×C1111yescharacteristic
409C4⋊C8C23×C1111yescharacteristic
410C4⋊C8C23×C1111yescharacteristic
411C4⋊C8C23×C1111yescharacteristic
412C4⋊C8C23×C1111yescharacteristic
413C4⋊C8C23×C1111yescharacteristic
414C4⋊C8C23×C1111yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8D4×C1111yescharacteristic
432C22⋊C8D4×C1111yescharacteristic
433#97—21no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C23×C1111yescharacteristic
438C4×C8C23×C1111yescharacteristic
439C2×C11—41no—
440C2×C11—42no—
441C2×C11—161no—
442C2×C11—161no—
443C2×C11#304511yescharacteristic
444C2×C11#305011yescharacteristic
445C2×C11#306811yescharacteristic
446#41—22no—
447#41—22no—
448#41—81no—
449#41—81no—
450#41—82no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8C2×D4×C1111yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C2×D4×C1111yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4C2×D4×C1111yescharacteristic
470C22×C4C2×D4×C1111yescharacteristic
471C22×C4C11×#4111yescharacteristic
472SD16—42no—
473SD16—42no—
474SD16—81no—
475SD16—81no—
476D8—42no—
477D8—42no—
478D8—81no—
479D8—81no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—81no—
487C2×C8—81no—
488C2×C8—81no—
489C2×C8C2×D4×C1111yescharacteristic
490C2×C8C2×D4×C1111yescharacteristic
491C2×C8C2×D4×C1111yescharacteristic
492C2×C8C2×D4×C1111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4C2×D4×C1111yescharacteristic
500C4⋊C4C2×D4×C1111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42C2×D4×C1111yescharacteristic
512C42C2×D4×C1111yescharacteristic
513C42C11×#4111yescharacteristic
514C42C24×C1111yescharacteristic
515C11#1941211yescharacteristic, direct product factor, Sylow
516C23—21no—
517C23—41no—
518C23—41no—
519C23C11×#12111yescharacteristic
520Q8—21no—
521Q8—41no—
522Q8—41no—
523Q8—81no—
524Q8C11×#13512yes—
525D4—24no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—81no—
536D4—81no—
537D4—82no—
538D4—82no—
539D4C11×#13512yes—
540C2×C4—24no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—81no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4C11×#12111yescharacteristic
557C2×C4C11×#12111yescharacteristic
558C2×C4C11×#12111yescharacteristic
559C2×C4C22×D4×C1111yescharacteristic
560C2×C4C22×D4×C1111yescharacteristic
561C2×C4C2×C11×#4111yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22C2×C11×#12111yescharacteristic
585C4—21no—
586C4—21no—
587C4—22no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4C2×C11×#13511yescharacteristic
595C4C2×C11×#13511yescharacteristic
596C4C11×#57611yescharacteristic
597C4C11×#57711yescharacteristic
598C2—41no—
599C2—42no—
600C2—161no—
601C2—161no—
602C2C11×#304511yescharacteristic
603C2C11×#305011yescharacteristic
604C2C11×#306811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#121
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×#3207C2semidirect
2. C11×#3115C2semidirect
3. C11×#3106C2semidirect
4. C11×#2988C2semidirect
5. C11×#1684C2semidirect
6. C11×#1683C2semidirect
7. C11×#1678C2semidirect
8. C11×#1677C2semidirect
9. C11×#1668C2semidirect
10. C11×#1667C2semidirect
11. C11×#1666C2semidirect
12. C11×#1665C2semidirect
13. C11×#1572C2semidirect
14. C11×#1551C2semidirect
15. C11×#1540C2semidirect
144. #19412C11direct (N × H)
214. #3207C2×C11semidirect
215. #3115C2×C11semidirect
216. #3106C2×C11semidirect
217. #2988C2×C11semidirect
218. #1684C2×C11semidirect
219. #1683C2×C11semidirect
220. #1678C2×C11semidirect
221. #1677C2×C11semidirect
222. #1668C2×C11semidirect
223. #1667C2×C11semidirect
224. #1666C2×C11semidirect
225. #1665C2×C11semidirect
226. #1572C2×C11semidirect
227. #1551C2×C11semidirect
228. #1540C2×C11semidirect
515. C11#19412direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#32072
C11×#31152
C11×#31062
C11×#29882
C11×#16842
C11×#16832
C11×#16782
C11×#16772
C11×#16682
C11×#16672
C11×#16662
C11×#16652
C11×#15722
C11×#15512
C11×#15402
#1941211