Finite Group Databasebeta

← C11×#19851 #14597044

Subgroups — C11×#19851 #14597044

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3397C211yesmaximal, characteristic, complemented
2C11×#3334C211yesmaximal, characteristic, complemented
3C11×#3302C211yesmaximal, characteristic, complemented
4C11×#3284C211yesmaximal, characteristic, complemented
5C11×#1714C211yesmaximal, characteristic, complemented
6C11×#1694C211yesmaximal, characteristic, complemented
7C11×#1679C211yesmaximal, characteristic, complemented
8C11×#1665C211yesmaximal, characteristic, complemented
9C11×#1665C211yesmaximal, characteristic, complemented
10C11×#1654C211yesmaximal, characteristic, complemented
11C11×#1652C211yesmaximal, characteristic, complemented
12C11×#1641C211yesmaximal, characteristic, complemented
13C11×#1625C211yesmaximal, characteristic, complemented
14C11×#1582C211yesmaximal, characteristic, complemented
15C11×#1580C211yesmaximal, characteristic, complemented
16C2×C11×#135—21no—
17C11×#556C2211yescharacteristic
18C11×#550C2211yescharacteristic
19C11×#547C2211yescharacteristic
20C11×#547C2211yescharacteristic
21C11×#500C2211yescharacteristic
22C11×#498C2211yescharacteristic
23C11×#496—21no—
24C11×#492C2211yescharacteristic
25C11×#492C2211yescharacteristic
26C11×#487C2211yescharacteristic
27C11×#486C2211yescharacteristic
28C11×#485—21no—
29C11×#480—21no—
30C11×#480—21no—
31C11×#474C2211yescharacteristic
32C11×#474C2211yescharacteristic
33C11×#474C2211yescharacteristic
34C11×#467—21no—
35C11×#466—21no—
36C11×#465—21no—
37C11×#463—21no—
38C11×#462C2211yescharacteristic
39C11×#462C2211yescharacteristic
40C11×#461C2211yescharacteristic
41C11×#460—21no—
42C11×#459C2211yescharacteristic
43C11×#459C2211yescharacteristic
44C11×#452—21no—
45C11×#452—21no—
46C11×#449—21no—
47C11×#446C2211yescharacteristic
48C11×#440—21no—
49C4×C11×SD16C2211yescharacteristic
50C4×C11×D8C2211yescharacteristic
51C8×D4×C11C2211yescharacteristic
52C8×D4×C11C2211yescharacteristic
53C8×D4×C11C2211yescharacteristic
54C2×C11×#107—21no—
55C11×#416—21no—
56C11×#334C2211yescharacteristic
57C11×#334C2211yescharacteristic
58C11×#332C2211yescharacteristic
59C11×#332C2211yescharacteristic
60C11×#332C2211yescharacteristic
61C11×#331C2211yescharacteristic
62C11×Q8⋊C8C2211yescharacteristic
63C11×D4⋊C8C2211yescharacteristic
64C11×D4⋊C8C2211yescharacteristic
65C11×D4⋊C8C2211yescharacteristic
66C11×#322C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41—21no—
70C11×#135—44no—
71C2×C11×Q16—21no—
72C2×C11×Q16—21no—
73C2×C11×SD16—21no—
74C2×C11×SD16—21no—
75C2×C11×SD16—21no—
76C2×C11×SD16—21no—
77C2×C11×SD16—21no—
78C2×C11×SD16D411yescharacteristic
79C2×C11×D8—21no—
80C2×C11×D8—21no—
81C2×C11×D8D411yescharacteristic
82C22×C8×C11—21no—
83C22×C8×C11—21no—
84C22×C8×C11—21no—
85C11×C4⋊Q8C2311yescharacteristic
86C11×C4⋊Q8C2311yescharacteristic
87C11×C4⋊Q8C2311yescharacteristic
88C11×#127—21no—
89C11×#127C2311yescharacteristic
90C11×#126—41no—
91C11×#124—21no—
92C11×#123—41no—
93C11×#123—41no—
94C11×C22⋊Q8—21no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8—21no—
97C11×#121—21no—
98C11×#121—21no—
99C11×#121—21no—
100C11×#121—41no—
101C4×Q8×C11—21no—
102C4×Q8×C11C2311yescharacteristic
103C4×D4×C11—21no—
104C4×D4×C11C2311yescharacteristic
105C4×D4×C11C2311yescharacteristic
106C4×D4×C11C2311yescharacteristic
107C11×#117—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C11×#107—21no—
111C11×#107—21no—
112C11×#107—21no—
113C11×#107—21no—
114C11×#107—21no—
115C11×#107D411yescharacteristic
116C11×#106—41no—
117C11×#106D411yescharacteristic
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×#103—21no—
127C11×#103—21no—
128C11×#103D411yescharacteristic
129C11×#102—21no—
130C11×#102—21no—
131C11×#102—21no—
132C11×#102—21no—
133C11×#102—21no—
134C11×#102—41no—
135C11×#102D411yescharacteristic
136C11×#102D411yescharacteristic
137C11×#102D411yescharacteristic
138C11×C22⋊C8—21no—
139C11×C22⋊C8—21no—
140C11×C22⋊C8—21no—
141C11×#97—21no—
142C4×C8×C11C2311yescharacteristic
143C4×C8×C11C2311yescharacteristic
144C4×C8×C11C2311yescharacteristic
145#19851C1111yesmaximal, characteristic, direct product factor, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C11×#41—42no—
149C11×#41—81no—
150C11×#41—81no—
151C11×#41—81no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—41no—
160C2×D4×C11—41no—
161C2×D4×C11—41no—
162C2×D4×C11—41no—
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11C2×D411yescharacteristic
165C2×D4×C11C2×D411yescharacteristic
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C22×C4×C11—41no—
172C11×Q16—42no—
173C11×Q16—81no—
174C11×SD16—22no—
175C11×SD16—42no—
176C11×SD16—42no—
177C11×SD16—81no—
178C11×SD16—81no—
179C11×SD16—81no—
180C11×D8—22no—
181C11×D8—42no—
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×C11—81no—
191C2×C8×C11C2×D411yescharacteristic
192C2×C8×C11C2×D411yescharacteristic
193C2×C8×C11C2×D411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—41no—
203C11×C4⋊C4—41no—
204C11×C4⋊C4—41no—
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—41no—
213C11×C22⋊C4—41no—
214C11×C22⋊C4—41no—
215C11×C22⋊C4—41no—
216C11×C22⋊C4—41no—
217C42×C11—21no—
218C42×C11—41no—
219C42×C11C2411yescharacteristic
220#3397C2×C1111yescharacteristic, complemented
221#3334C2×C1111yescharacteristic, complemented
222#3302C2×C1111yescharacteristic, complemented
223#3284C2×C1111yescharacteristic, complemented
224#1714C2×C1111yescharacteristic, complemented
225#1694C2×C1111yescharacteristic, complemented
226#1679C2×C1111yescharacteristic, complemented
227#1665C2×C1111yescharacteristic, complemented
228#1665C2×C1111yescharacteristic, complemented
229#1654C2×C1111yescharacteristic, complemented
230#1652C2×C1111yescharacteristic, complemented
231#1641C2×C1111yescharacteristic, complemented
232#1625C2×C1111yescharacteristic, complemented
233#1582C2×C1111yescharacteristic, complemented
234#1580C2×C1111yescharacteristic, complemented
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—41no—
239Q8×C11—21no—
240Q8×C11—21no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247D4×C11—21no—
248D4×C11—21no—
249D4×C11—21no—
250D4×C11—21no—
251D4×C11—21no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—81no—
257D4×C11—82no—
258D4×C11—82no—
259D4×C11—82no—
260D4×C11—161no—
261D4×C11AGL(1,ℤ/8)12yes—
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—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—82no—
277C2×C4×C11—82no—
278C2×C4×C11—82no—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—21no—
285C8×C11—41no—
286C8×C11—41no—
287C8×C11—41no—
288C8×C11—41no—
289C8×C11—41no—
290C8×C11#13512yescomplemented
291C2×#135—21no—
292#556C22×C1111yescharacteristic
293#550C22×C1111yescharacteristic
294#547C22×C1111yescharacteristic
295#547C22×C1111yescharacteristic
296#500C22×C1111yescharacteristic
297#498C22×C1111yescharacteristic
298#496—21no—
299#492C22×C1111yescharacteristic
300#492C22×C1111yescharacteristic
301#487C22×C1111yescharacteristic
302#486C22×C1111yescharacteristic
303#485—21no—
304#480—21no—
305#480—21no—
306#474C22×C1111yescharacteristic
307#474C22×C1111yescharacteristic
308#474C22×C1111yescharacteristic
309#467—21no—
310#466—21no—
311#465—21no—
312#463—21no—
313#462C22×C1111yescharacteristic
314#462C22×C1111yescharacteristic
315#461C22×C1111yescharacteristic
316#460—21no—
317#459C22×C1111yescharacteristic
318#459C22×C1111yescharacteristic
319#452—21no—
320#452—21no—
321#449—21no—
322#446C22×C1111yescharacteristic
323#440—21no—
324C4×SD16C22×C1111yescharacteristic
325C4×D8C22×C1111yescharacteristic
326C8×D4C22×C1111yescharacteristic
327C8×D4C22×C1111yescharacteristic
328C8×D4C22×C1111yescharacteristic
329C2×#107—21no—
330#416—21no—
331#334C22×C1111yescharacteristic
332#334C22×C1111yescharacteristic
333#332C22×C1111yescharacteristic
334#332C22×C1111yescharacteristic
335#332C22×C1111yescharacteristic
336#331C22×C1111yescharacteristic
337Q8⋊C8C22×C1111yescharacteristic
338D4⋊C8C22×C1111yescharacteristic
339D4⋊C8C22×C1111yescharacteristic
340D4⋊C8C22×C1111yescharacteristic
341#322C22×C1111yescharacteristic
342C22×C11—22no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11D4211yescharacteristic
355C4×C11—21no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11—81no—
364C4×C11C2×#13511yescharacteristic
365C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
366C4×C11#57611yescharacteristic
367C4×C11#57711yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—21no—
371#135—44no—
372C2×Q16—21no—
373C2×Q16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16D4×C1111yescharacteristic
380C2×D8—21no—
381C2×D8—21no—
382C2×D8D4×C1111yescharacteristic
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—21no—
386C4⋊Q8C23×C1111yescharacteristic
387C4⋊Q8C23×C1111yescharacteristic
388C4⋊Q8C23×C1111yescharacteristic
389#127—21no—
390#127C23×C1111yescharacteristic
391#126—41no—
392#124—21no—
393#123—41no—
394#123—41no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—41no—
402C4×Q8—21no—
403C4×Q8C23×C1111yescharacteristic
404C4×D4—21no—
405C4×D4C23×C1111yescharacteristic
406C4×D4C23×C1111yescharacteristic
407C4×D4C23×C1111yescharacteristic
408#117—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411#107—21no—
412#107—21no—
413#107—21no—
414#107—21no—
415#107—21no—
416#107D4×C1111yescharacteristic
417#106—41no—
418#106D4×C1111yescharacteristic
419C4⋊C8—21no—
420C4⋊C8C23×C1111yescharacteristic
421C4⋊C8C23×C1111yescharacteristic
422C4⋊C8C23×C1111yescharacteristic
423C4⋊C8C23×C1111yescharacteristic
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103D4×C1111yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—41no—
436#102D4×C1111yescharacteristic
437#102D4×C1111yescharacteristic
438#102D4×C1111yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442#97—21no—
443C4×C8C23×C1111yescharacteristic
444C4×C8C23×C1111yescharacteristic
445C4×C8C23×C1111yescharacteristic
446C2×C11—42no—
447C2×C11—81no—
448C2×C11—81no—
449C2×C11—161no—
450C2×C11#326411yescharacteristic
451C2×C11#328411yescharacteristic
452C2×C11#328911yescharacteristic
453#41—42no—
454#41—42no—
455#41—42no—
456#41—81no—
457#41—81no—
458#41—81no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C1111yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4C2×D4×C1111yescharacteristic
471C2×D4C2×D4×C1111yescharacteristic
472C2×D4C2×D4×C1111yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479Q16—42no—
480Q16—81no—
481SD16—22no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487D8—22no—
488D8—42no—
489D8—81no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—42no—
496C2×C8—42no—
497C2×C8—81no—
498C2×C8C2×D4×C1111yescharacteristic
499C2×C8C2×D4×C1111yescharacteristic
500C2×C8C2×D4×C1111yescharacteristic
501C2×C8C2×D4×C1111yescharacteristic
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4C2×D4×C1111yescharacteristic
513C4⋊C4C2×D4×C1111yescharacteristic
514C4⋊C4C2×D4×C1111yescharacteristic
515C4⋊C4C2×D4×C1111yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C42—21no—
525C42—41no—
526C42C24×C1111yescharacteristic
527C11#1985111yescharacteristic, direct product factor, Sylow
528C23—21no—
529C23—21no—
530C23—21no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—81no—
550D4—82no—
551D4—82no—
552D4—82no—
553D4—161no—
554D4C11×AGL(1,ℤ/8)12yes—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4C22×D4×C1111yescharacteristic
573C2×C4C22×D4×C1111yescharacteristic
574C2×C4C11×H(5,𝔽2)11yescharacteristic
575C8—21no—
576C8—21no—
577C8—21no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8C11×#13512yescomplemented
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C1111yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4C2×C11×#13511yescharacteristic
607C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
608C4C11×#57611yescharacteristic
609C4C11×#57711yescharacteristic
610C2—42no—
611C2—81no—
612C2—81no—
613C2—161no—
614C2C11×#326411yescharacteristic
615C2C11×#328411yescharacteristic
616C2C11×#328911yescharacteristic
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×#3397C2semidirect
2. C11×#3334C2semidirect
3. C11×#3302C2semidirect
4. C11×#3284C2semidirect
5. C11×#1714C2semidirect
6. C11×#1694C2semidirect
7. C11×#1679C2semidirect
8. C11×#1665C2semidirect
9. C11×#1665C2semidirect
10. C11×#1654C2semidirect
11. C11×#1652C2semidirect
12. C11×#1641C2semidirect
13. C11×#1625C2semidirect
14. C11×#1582C2semidirect
15. C11×#1580C2semidirect
145. #19851C11direct (N × H)
220. #3397C2×C11semidirect
221. #3334C2×C11semidirect
222. #3302C2×C11semidirect
223. #3284C2×C11semidirect
224. #1714C2×C11semidirect
225. #1694C2×C11semidirect
226. #1679C2×C11semidirect
227. #1665C2×C11semidirect
228. #1665C2×C11semidirect
229. #1654C2×C11semidirect
230. #1652C2×C11semidirect
231. #1641C2×C11semidirect
232. #1625C2×C11semidirect
233. #1582C2×C11semidirect
234. #1580C2×C11semidirect
290. C8×C11#135semidirect
527. C11#19851direct (N × H)
583. C8C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#33972
C11×#33342
C11×#33022
C11×#32842
C11×#17142
C11×#16942
C11×#16792
C11×#16652
C11×#16542
C11×#16522
C11×#16412
C11×#16252
C11×#15822
C11×#15802
#1985111