Finite Group Databasebeta

← C11×#18886 #14596079

Subgroups — C11×#18886 #14596079

Order 2816.

908 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3509C211yesmaximal, characteristic, complemented
2C11×#3246C211yesmaximal, characteristic, complemented
3C11×#3226C211yesmaximal, characteristic, complemented
4C11×#3035C211yesmaximal, characteristic
5C11×#1650C212yesmaximal, complemented
6C11×#1648C212yesmaximal, complemented
7C11×#1628C212yesmaximal, complemented
8C11×#1626C212yesmaximal, complemented
9C2×C11×#332C211yesmaximal, characteristic, complemented
10C11×#1481C211yesmaximal, characteristic, complemented
11C11×#1477C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C11×#557—21no—
14C11×#557C2212yes—
15C11×#556—21no—
16C11×#556C2212yes—
17C11×#552—22no—
18C11×#552—22no—
19C11×#541—22no—
20C11×#536—21no—
21C11×#533—21no—
22C11×#533—21no—
23C11×#533C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic
26C11×#519—21no—
27C4×C11×#41C2211yescharacteristic
28C11×#500C2212yes—
29C11×#486C2212yes—
30C11×#480—22no—
31C11×#476—21no—
32C11×#475C2212yes—
33C11×#474—22no—
34C11×#465—22no—
35C11×#464—21no—
36C11×#463—21no—
37C11×#462C2211yescharacteristic
38C11×#461—21no—
39C11×#461C2211yescharacteristic
40C11×#460C2211yescharacteristic
41C11×#460C2212yes—
42C11×#459C2211yescharacteristic
43C11×#431C2211yescharacteristic
44C2×C11×C4⋊C8C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C11×#416—21no—
47C11×#332C2212yes—
48C11×#332C2212yes—
49C11×Q8⋊C8C2212yes—
50C11×Q8⋊C8C2212yes—
51C11×Q8⋊C8C2212yes—
52C11×D4⋊C8C2212yes—
53C2×C11×#41—21no—
54C2×C11×#41D411yescharacteristic
55C22×Q8×C11—21no—
56C11×#135—44no—
57C2×C11×Q16—21no—
58C2×C11×SD16—21no—
59C2×C11×SD16—21no—
60C2×C11×SD16—22no—
61C2×C11×D8—21no—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8D411yescharacteristic
68C11×C4⋊Q8D412yes—
69C11×C4⋊Q8D411yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2312yes—
72C11×#127C2311yescharacteristic
73C11×#126—24no—
74C11×#126—24no—
75C11×#125—22no—
76C11×#125—24no—
77C11×#125—22no—
78C11×#125—24no—
79C11×#125—21no—
80C11×#124—22no—
81C11×#124—21no—
82C11×#123—24no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8D412yes—
89C11×#121—21no—
90C11×#121—21no—
91C4×Q8×C11—22no—
92C4×Q8×C11—22no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11—21no—
98C4×Q8×C11D411yescharacteristic
99C4×Q8×C11C2311yescharacteristic
100C4×Q8×C11C2312yes—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11D411yescharacteristic
106C4×D4×C11C2311yescharacteristic
107C11×#117—24no—
108C11×#117—22no—
109C11×#117—21no—
110C11×#117—22no—
111C11×#117—21no—
112C11×#117D411yescharacteristic
113C2×C11×C4⋊C4—21no—
114C2×C11×C4⋊C4D412yes—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C11×#107—24no—
118C11×#106—22no—
119C11×C4⋊C8—21no—
120C11×C4⋊C8—21no—
121C11×C4⋊C8—21no—
122C11×C4⋊C8C2312yes—
123C11×C4⋊C8C2311yescharacteristic
124C11×C4⋊C8C2311yescharacteristic
125C11×#103—22no—
126C11×#103—21no—
127C11×#103—21no—
128C11×#102—21no—
129C11×#102—21no—
130C11×#102—22no—
131C11×#102—24no—
132C11×C22⋊C8—21no—
133C4×C8×C11C2312yes—
134#18886C1111yesmaximal, characteristic, direct product factor, Sylow
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—42no—
138C11×#41—42no—
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—21no—
143C2×Q8×C11—42no—
144C2×Q8×C11—42no—
145C2×Q8×C11C2×D412yes—
146C2×Q8×C11C2×D411yescharacteristic
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—41no—
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—41no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C11×Q16—42no—
162C11×SD16—42no—
163C11×SD16—42no—
164C11×SD16—82no—
165C11×D8—42no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—42no—
171C2×C8×C11—81no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C4⋊C4C2×D411yescharacteristic
190C11×C4⋊C4C2×D412yes—
191C11×C4⋊C4C2×D414yes—
192C11×C22⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—41no—
199C11×C22⋊C4—41no—
200C42×C11—24no—
201C42×C11—24no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—22no—
206C42×C11C2×D411yescharacteristic
207C42×C11C2×D411yescharacteristic
208C42×C11C2×D411yescharacteristic
209C42×C11C2411yescharacteristic
210#3509C2×C1111yescharacteristic, complemented
211#3246C2×C1111yescharacteristic, complemented
212#3226C2×C1111yescharacteristic, complemented
213#3035C2×C1111yescharacteristic
214#1650C2×C1112yescomplemented
215#1648C2×C1112yescomplemented
216#1628C2×C1112yescomplemented
217#1626C2×C1112yescomplemented
218C2×#332C2×C1111yescharacteristic, complemented
219#1481C2×C1111yescharacteristic, complemented
220#1477C2×C1111yescharacteristic, complemented
221C23×C11—21no—
222C23×C11—41no—
223C23×C11#12011yescharacteristic
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—42no—
229Q8×C11—42no—
230Q8×C11—42no—
231Q8×C11—44no—
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—82no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—44no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—82no—
259C2×C4×C11#12011yescharacteristic
260C2×C4×C11#12011yescharacteristic
261C2×C4×C11#12011yescharacteristic
262C2×C4×C11#13512yes—
263C2×C4×C11AGL(1,ℤ/8)12yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C8×C11—42no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—42no—
271C2×#135—21no—
272#557—21no—
273#557C22×C1112yes—
274#556—21no—
275#556C22×C1112yes—
276#552—22no—
277#552—22no—
278#541—22no—
279#536—21no—
280#533—21no—
281#533—21no—
282#533C22×C1111yescharacteristic
283#532C22×C1111yescharacteristic
284C2×C4⋊Q8C22×C1111yescharacteristic
285#519—21no—
286C4×#41C22×C1111yescharacteristic
287#500C22×C1112yes—
288#486C22×C1112yes—
289#480—22no—
290#476—21no—
291#475C22×C1112yes—
292#474—22no—
293#465—22no—
294#464—21no—
295#463—21no—
296#462C22×C1111yescharacteristic
297#461—21no—
298#461C22×C1111yescharacteristic
299#460C22×C1111yescharacteristic
300#460C22×C1112yes—
301#459C22×C1111yescharacteristic
302#431C22×C1111yescharacteristic
303C2×C4⋊C8C22×C1111yescharacteristic
304C2×C4⋊C8C22×C1111yescharacteristic
305#416—21no—
306#332C22×C1112yes—
307#332C22×C1112yes—
308Q8⋊C8C22×C1112yes—
309Q8⋊C8C22×C1112yes—
310Q8⋊C8C22×C1112yes—
311D4⋊C8C22×C1112yes—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11#44912yes—
321C22×C11C2×#12011yescharacteristic
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—41no—
326C4×C11—44no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11—41no—
330C4×C11—42no—
331C4×C11—81no—
332C4×C11#44912yes—
333C4×C11C2×#13511yescharacteristic
334C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
335C4×C11#57711yescharacteristic
336C4×C11#57811yescharacteristic
337C2×#41—21no—
338C2×#41D4×C1111yescharacteristic
339C22×Q8—21no—
340#135—44no—
341C2×Q16—21no—
342C2×SD16—21no—
343C2×SD16—21no—
344C2×SD16—22no—
345C2×D8—21no—
346C22×C8—21no—
347C22×C8—21no—
348C4⋊Q8—22no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8D4×C1111yescharacteristic
352C4⋊Q8D4×C1112yes—
353C4⋊Q8D4×C1111yescharacteristic
354C4⋊Q8C23×C1111yescharacteristic
355C4⋊Q8C23×C1112yes—
356#127C23×C1111yescharacteristic
357#126—24no—
358#126—24no—
359#125—22no—
360#125—24no—
361#125—22no—
362#125—24no—
363#125—21no—
364#124—22no—
365#124—21no—
366#123—24no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8D4×C1112yes—
373#121—21no—
374#121—21no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—21no—
382C4×Q8D4×C1111yescharacteristic
383C4×Q8C23×C1111yescharacteristic
384C4×Q8C23×C1112yes—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4D4×C1111yescharacteristic
390C4×D4C23×C1111yescharacteristic
391#117—24no—
392#117—22no—
393#117—21no—
394#117—22no—
395#117—21no—
396#117D4×C1111yescharacteristic
397C2×C4⋊C4—21no—
398C2×C4⋊C4D4×C1112yes—
399C2×C42—21no—
400C2×C42C23×C1111yescharacteristic
401#107—24no—
402#106—22no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C1112yes—
407C4⋊C8C23×C1111yescharacteristic
408C4⋊C8C23×C1111yescharacteristic
409#103—22no—
410#103—21no—
411#103—21no—
412#102—21no—
413#102—21no—
414#102—22no—
415#102—24no—
416C22⋊C8—21no—
417C4×C8C23×C1112yes—
418C2×C11—22no—
419C2×C11—81no—
420C2×C11—161no—
421C2×C11C2×#44911yescharacteristic
422C2×C11#301311yescharacteristic
423C2×C11#302011yescharacteristic
424#41—22no—
425#41—22no—
426#41—42no—
427#41—42no—
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8—42no—
433C2×Q8—42no—
434C2×Q8C2×D4×C1112yes—
435C2×Q8C2×D4×C1111yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4C2×D4×C1111yescharacteristic
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4C2×D4×C1111yescharacteristic
448C22×C4C2×D4×C1111yescharacteristic
449C22×C4C2×D4×C1111yescharacteristic
450Q16—42no—
451SD16—42no—
452SD16—42no—
453SD16—82no—
454D8—42no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8—81no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4C2×D4×C1111yescharacteristic
478C4⋊C4C2×D4×C1111yescharacteristic
479C4⋊C4C2×D4×C1112yes—
480C4⋊C4C2×D4×C1114yes—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—21no—
484C22⋊C4—22no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C42—24no—
490C42—24no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—22no—
495C42C2×D4×C1111yescharacteristic
496C42C2×D4×C1111yescharacteristic
497C42C2×D4×C1111yescharacteristic
498C42C24×C1111yescharacteristic
499C11#1888611yescharacteristic, direct product factor, Sylow
500C23—21no—
501C23—41no—
502C23C11×#12011yescharacteristic
503Q8—21no—
504Q8—21no—
505Q8—22no—
506Q8—22no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—44no—
511Q8—41no—
512Q8—41no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—42no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—82no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4C11×#12011yescharacteristic
539C2×C4C11×#12011yescharacteristic
540C2×C4C11×#12011yescharacteristic
541C2×C4C11×#13512yes—
542C2×C4C11×AGL(1,ℤ/8)12yes—
543C2×C4C22×D4×C1111yescharacteristic
544C2×C4C22×D4×C1111yescharacteristic
545C2×C4C22×D4×C1111yescharacteristic
546C8—42no—
547C8—41no—
548C8—41no—
549C8—42no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22C11×#44912yes—
559C22C2×C11×#12011yescharacteristic
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—44no—
565C4—41no—
566C4—42no—
567C4—41no—
568C4—42no—
569C4—81no—
570C4C11×#44912yes—
571C4C2×C11×#13511yescharacteristic
572C4C2×C11×AGL(1,ℤ/8)11yescharacteristic
573C4C11×#57711yescharacteristic
574C4C11×#57811yescharacteristic
575C2—22no—
576C2—81no—
577C2—161no—
578C2C2×C11×#44911yescharacteristic
579C2C11×#301311yescharacteristic
580C2C11×#302011yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
prime radicalC11×#3035C2
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×#3509C2semidirect
2. C11×#3246C2semidirect
3. C11×#3226C2semidirect
5. C11×#1650C2semidirect
6. C11×#1648C2semidirect
7. C11×#1628C2semidirect
8. C11×#1626C2semidirect
9. C2×C11×#332C2semidirect
10. C11×#1481C2semidirect
11. C11×#1477C2semidirect
134. #18886C11direct (N × H)
210. #3509C2×C11semidirect
211. #3246C2×C11semidirect
212. #3226C2×C11semidirect
214. #1650C2×C11semidirect
215. #1648C2×C11semidirect
216. #1628C2×C11semidirect
217. #1626C2×C11semidirect
218. C2×#332C2×C11semidirect
219. #1481C2×C11semidirect
220. #1477C2×C11semidirect
499. C11#18886direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35092
C11×#32462
C11×#32262
C11×#30352
C11×#16502
C11×#16482
C11×#16282
C11×#16262
C2×C11×#3322
C11×#14812
C11×#14772
#1888611