Finite Group Databasebeta

← C11×#19852 #14597045

Subgroups — C11×#19852 #14597045

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3399C211yesmaximal, characteristic, complemented
2C11×#3361C211yesmaximal, characteristic, complemented
3C11×#3335C211yesmaximal, characteristic, complemented
4C11×#3284C211yesmaximal, characteristic, complemented
5C11×#1715C211yesmaximal, characteristic, complemented
6C11×#1692C211yesmaximal, characteristic, complemented
7C11×#1677C211yesmaximal, characteristic, complemented
8C11×#1667C211yesmaximal, characteristic, complemented
9C11×#1666C211yesmaximal, characteristic, complemented
10C11×#1640C211yesmaximal, characteristic, complemented
11C11×#1631C211yesmaximal, characteristic, complemented
12C11×#1625C211yesmaximal, characteristic, complemented
13C11×#1622C211yesmaximal, characteristic, complemented
14C11×#1582C211yesmaximal, characteristic, complemented
15C11×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17C11×#559C2211yescharacteristic
18C11×#554C2211yescharacteristic
19C11×#550C2211yescharacteristic
20C11×#547C2211yescharacteristic
21C11×#498C2211yescharacteristic
22C11×#496—21no—
23C11×#493C2211yescharacteristic
24C11×#492C2211yescharacteristic
25C11×#492C2211yescharacteristic
26C11×#488—21no—
27C11×#486C2211yescharacteristic
28C11×#486C2211yescharacteristic
29C11×#483—21no—
30C11×#481—21no—
31C11×#478—21no—
32C11×#477C2211yescharacteristic
33C11×#476C2211yescharacteristic
34C11×#475C2211yescharacteristic
35C11×#465—21no—
36C11×#465—21no—
37C11×#463—21no—
38C11×#463—21no—
39C11×#462C2211yescharacteristic
40C11×#460C2211yescharacteristic
41C11×#459—21no—
42C11×#459C2211yescharacteristic
43C11×#459C2211yescharacteristic
44C11×#459C2211yescharacteristic
45C11×#452—21no—
46C11×#449—21no—
47C11×#446C2211yescharacteristic
48C8×Q8×C11C2211yescharacteristic
49C11×#442—21no—
50C4×C11×SD16C2211yescharacteristic
51C4×C11×SD16C2211yescharacteristic
52C4×C11×D8—21no—
53C8×D4×C11C2211yescharacteristic
54C8×D4×C11C2211yescharacteristic
55C2×C11×#106—21no—
56C11×#335C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#333C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#331C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×Q8⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C11×#135—44no—
70C2×C11×Q16—21no—
71C2×C11×SD16—21no—
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—41no—
75C2×C11×SD16D411yescharacteristic
76C2×C11×SD16D411yescharacteristic
77C2×C11×D8—21no—
78C2×C11×D8—21no—
79C2×C11×D8—21no—
80C2×C11×D8—21no—
81C2×C11×D8—21no—
82C22×C8×C11—21no—
83C22×C8×C11—21no—
84C11×C4⋊Q8C2311yescharacteristic
85C11×C4⋊Q8C2311yescharacteristic
86C11×#127—21no—
87C11×#127C2311yescharacteristic
88C11×#127C2311yescharacteristic
89C11×#125—21no—
90C11×#124—21no—
91C11×#124—21no—
92C11×#123—41no—
93C11×#123—41no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8—41no—
97C11×#121—21no—
98C11×#121—21no—
99C11×#121—41no—
100C4×Q8×C11C2311yescharacteristic
101C4×Q8×C11C2311yescharacteristic
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11—21no—
106C4×D4×C11C2311yescharacteristic
107C4×D4×C11C2311yescharacteristic
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C11×#107—21no—
111C11×#106—21no—
112C11×#106—21no—
113C11×#106—21no—
114C11×#106—21no—
115C11×#106D411yescharacteristic
116C11×#106D411yescharacteristic
117C11×C4⋊C8—21no—
118C11×C4⋊C8—21no—
119C11×C4⋊C8C2311yescharacteristic
120C11×C4⋊C8C2311yescharacteristic
121C11×C4⋊C8C2311yescharacteristic
122C11×C4⋊C8C2311yescharacteristic
123C11×#103—21no—
124C11×#103—21no—
125C11×#103—21no—
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—41no—
136C11×#102D411yescharacteristic
137C11×#102D411yescharacteristic
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C11×#97—21no—
141C4×C8×C11—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144C4×C8×C11C2311yescharacteristic
145#19852C1111yesmaximal, characteristic, direct product factor, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C11×#41—81no—
149C11×#41—81no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11C2×D411yescharacteristic
153C2×Q8×C11C2×D411yescharacteristic
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×C11—41no—
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11C2×D411yescharacteristic
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C11×Q16—42no—
172C11×SD16—22no—
173C11×SD16—22no—
174C11×SD16—42no—
175C11×SD16—81no—
176C11×SD16—81no—
177C11×SD16—82no—
178C11×D8—42no—
179C11×D8—42no—
180C11×D8—42no—
181C11×D8—81no—
182C11×D8—81no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—42no—
189C2×C8×C11—42no—
190C2×C8×C11C2×D411yescharacteristic
191C2×C8×C11C2×D411yescharacteristic
192C2×C8×C11C2×D411yescharacteristic
193C2×C8×C11C2×D411yescharacteristic
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—41no—
201C11×C4⋊C4—41no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4C2×D411yescharacteristic
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—41no—
210C11×C22⋊C4—41no—
211C11×C22⋊C4—41no—
212C11×C22⋊C4—41no—
213C11×C22⋊C4—41no—
214C11×C22⋊C4—41no—
215C42×C11—21no—
216C42×C11—21no—
217C42×C11C2411yescharacteristic
218#3399C2×C1111yescharacteristic, complemented
219#3361C2×C1111yescharacteristic, complemented
220#3335C2×C1111yescharacteristic, complemented
221#3284C2×C1111yescharacteristic, complemented
222#1715C2×C1111yescharacteristic, complemented
223#1692C2×C1111yescharacteristic, complemented
224#1677C2×C1111yescharacteristic, complemented
225#1667C2×C1111yescharacteristic, complemented
226#1666C2×C1111yescharacteristic, complemented
227#1640C2×C1111yescharacteristic, complemented
228#1631C2×C1111yescharacteristic, complemented
229#1625C2×C1111yescharacteristic, complemented
230#1622C2×C1111yescharacteristic, complemented
231#1582C2×C1111yescharacteristic, complemented
232SD16⋊C8C2×C1111yescharacteristic, complemented
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—41no—
236C23×C11—41no—
237Q8×C11—21no—
238Q8×C11—21no—
239Q8×C11—21no—
240Q8×C11—21no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—81no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—21no—
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—82no—
258D4×C11—82no—
259D4×C11—161no—
260D4×C11AGL(1,ℤ/8)12yes—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—82no—
274C2×C4×C11—82no—
275C2×C4×C11—161no—
276C2×C4×C11—161no—
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—41no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11—41no—
287C8×C11—41no—
288C8×C11#13512yescomplemented
289C2×#135—21no—
290#559C22×C1111yescharacteristic
291#554C22×C1111yescharacteristic
292#550C22×C1111yescharacteristic
293#547C22×C1111yescharacteristic
294#498C22×C1111yescharacteristic
295#496—21no—
296#493C22×C1111yescharacteristic
297#492C22×C1111yescharacteristic
298#492C22×C1111yescharacteristic
299#488—21no—
300#486C22×C1111yescharacteristic
301#486C22×C1111yescharacteristic
302#483—21no—
303#481—21no—
304#478—21no—
305#477C22×C1111yescharacteristic
306#476C22×C1111yescharacteristic
307#475C22×C1111yescharacteristic
308#465—21no—
309#465—21no—
310#463—21no—
311#463—21no—
312#462C22×C1111yescharacteristic
313#460C22×C1111yescharacteristic
314#459—21no—
315#459C22×C1111yescharacteristic
316#459C22×C1111yescharacteristic
317#459C22×C1111yescharacteristic
318#452—21no—
319#449—21no—
320#446C22×C1111yescharacteristic
321C8×Q8C22×C1111yescharacteristic
322#442—21no—
323C4×SD16C22×C1111yescharacteristic
324C4×SD16C22×C1111yescharacteristic
325C4×D8—21no—
326C8×D4C22×C1111yescharacteristic
327C8×D4C22×C1111yescharacteristic
328C2×#106—21no—
329#335C22×C1111yescharacteristic
330#334C22×C1111yescharacteristic
331#333C22×C1111yescharacteristic
332#332C22×C1111yescharacteristic
333#331C22×C1111yescharacteristic
334#331C22×C1111yescharacteristic
335Q8⋊C8C22×C1111yescharacteristic
336Q8⋊C8C22×C1111yescharacteristic
337D4⋊C8C22×C1111yescharacteristic
338D4⋊C8C22×C1111yescharacteristic
339#322C22×C1111yescharacteristic
340C22×C11—22no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11D4211yescharacteristic
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11C2×#13511yescharacteristic
363C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
364C4×C11#57711yescharacteristic
365C4×C11#57711yescharacteristic
366C2×#41—21no—
367C2×#41—21no—
368#135—44no—
369C2×Q16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—41no—
374C2×SD16D4×C1111yescharacteristic
375C2×SD16D4×C1111yescharacteristic
376C2×D8—21no—
377C2×D8—21no—
378C2×D8—21no—
379C2×D8—21no—
380C2×D8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8C23×C1111yescharacteristic
384C4⋊Q8C23×C1111yescharacteristic
385#127—21no—
386#127C23×C1111yescharacteristic
387#127C23×C1111yescharacteristic
388#125—21no—
389#124—21no—
390#124—21no—
391#123—41no—
392#123—41no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—41no—
396#121—21no—
397#121—21no—
398#121—41no—
399C4×Q8C23×C1111yescharacteristic
400C4×Q8C23×C1111yescharacteristic
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C1111yescharacteristic
406C4×D4C23×C1111yescharacteristic
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409#107—21no—
410#106—21no—
411#106—21no—
412#106—21no—
413#106—21no—
414#106D4×C1111yescharacteristic
415#106D4×C1111yescharacteristic
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C23×C1111yescharacteristic
419C4⋊C8C23×C1111yescharacteristic
420C4⋊C8C23×C1111yescharacteristic
421C4⋊C8C23×C1111yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103D4×C1111yescharacteristic
426#103D4×C1111yescharacteristic
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—41no—
435#102D4×C1111yescharacteristic
436#102D4×C1111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440C4×C8—21no—
441C4×C8C23×C1111yescharacteristic
442C4×C8C23×C1111yescharacteristic
443C4×C8C23×C1111yescharacteristic
444C2×C11—42no—
445C2×C11—81no—
446C2×C11—161no—
447C2×C11—161no—
448C2×C11#326511yescharacteristic
449C2×C11#328411yescharacteristic
450C2×C11#328811yescharacteristic
451#41—42no—
452#41—42no—
453#41—81no—
454#41—81no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8C2×D4×C1111yescharacteristic
458C2×Q8C2×D4×C1111yescharacteristic
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4C2×D4×C1111yescharacteristic
469C2×D4C2×D4×C1111yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476Q16—42no—
477SD16—22no—
478SD16—22no—
479SD16—42no—
480SD16—81no—
481SD16—81no—
482SD16—82no—
483D8—42no—
484D8—42no—
485D8—42no—
486D8—81no—
487D8—81no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—42no—
495C2×C8C2×D4×C1111yescharacteristic
496C2×C8C2×D4×C1111yescharacteristic
497C2×C8C2×D4×C1111yescharacteristic
498C2×C8C2×D4×C1111yescharacteristic
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C1111yescharacteristic
509C4⋊C4C2×D4×C1111yescharacteristic
510C4⋊C4C2×D4×C1111yescharacteristic
511C4⋊C4C2×D4×C1111yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C42—21no—
521C42—21no—
522C42C24×C1111yescharacteristic
523C11#1985211yescharacteristic, direct product factor, Sylow
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—81no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—161no—
551D4C11×AGL(1,ℤ/8)12yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C1111yescharacteristic
569C2×C4C22×D4×C1111yescharacteristic
570C2×C4C11×H(5,𝔽2)11yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8C11×#13512yescomplemented
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C1111yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4C2×C11×#13511yescharacteristic
603C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
604C4C11×#57711yescharacteristic
605C4C11×#57711yescharacteristic
606C2—42no—
607C2—81no—
608C2—161no—
609C2—161no—
610C2C11×#326511yescharacteristic
611C2C11×#328411yescharacteristic
612C2C11×#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×#3399C2semidirect
2. C11×#3361C2semidirect
3. C11×#3335C2semidirect
4. C11×#3284C2semidirect
5. C11×#1715C2semidirect
6. C11×#1692C2semidirect
7. C11×#1677C2semidirect
8. C11×#1667C2semidirect
9. C11×#1666C2semidirect
10. C11×#1640C2semidirect
11. C11×#1631C2semidirect
12. C11×#1625C2semidirect
13. C11×#1622C2semidirect
14. C11×#1582C2semidirect
15. C11×SD16⋊C8C2semidirect
145. #19852C11direct (N × H)
218. #3399C2×C11semidirect
219. #3361C2×C11semidirect
220. #3335C2×C11semidirect
221. #3284C2×C11semidirect
222. #1715C2×C11semidirect
223. #1692C2×C11semidirect
224. #1677C2×C11semidirect
225. #1667C2×C11semidirect
226. #1666C2×C11semidirect
227. #1640C2×C11semidirect
228. #1631C2×C11semidirect
229. #1625C2×C11semidirect
230. #1622C2×C11semidirect
231. #1582C2×C11semidirect
232. SD16⋊C8C2×C11semidirect
288. C8×C11#135semidirect
523. C11#19852direct (N × H)
579. C8C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#33992
C11×#33612
C11×#33352
C11×#32842
C11×#17152
C11×#16922
C11×#16772
C11×#16672
C11×#16662
C11×#16402
C11×#16312
C11×#16252
C11×#16222
C11×#15822
C11×SD16⋊C82
#1985211