Finite Group Databasebeta

← C11×#18217 #14595410

Subgroups — C11×#18217 #14595410

Order 2816.

932 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×#3493C211yesmaximal, characteristic
2C11×#3108C212yesmaximal, complemented
3C11×#2599C211yesmaximal, characteristic, complemented
4C11×#1612C212yesmaximal, complemented
5C11×#1611C211yesmaximal, characteristic, complemented
6C11×#1610C211yesmaximal, characteristic, complemented
7C11×#1606C212yesmaximal, complemented
8C11×#1605C211yesmaximal, characteristic, complemented
9C11×#1604C211yesmaximal, characteristic, complemented
10C11×#1521C212yesmaximal, complemented
11C11×#1458C211yesmaximal, characteristic, complemented
12C11×#556—22no—
13C11×#555—22no—
14C11×#553—22no—
15C11×#552—22no—
16C11×#544C2211yescharacteristic
17C11×#538—21no—
18C11×#538C2212yes—
19C11×#537C2211yescharacteristic
20C11×#529—21no—
21C11×#529C2212yes—
22C11×#525—21no—
23C11×#520—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C11×#117C2211yescharacteristic
26C11×#483C2212yes—
27C11×#480C2212yes—
28C11×#479—22no—
29C11×#464—22no—
30C11×#451C2212yes—
31C11×#448C2212yes—
32C4×C11×Q16—22no—
33C4×C11×SD16—22no—
34C11×#431C2212yes—
35C11×#398C2211yescharacteristic
36C11×#397C2211yescharacteristic
37C11×#395C2211yescharacteristic
38C11×#393C2211yescharacteristic
39C11×#388—21no—
40C11×#387—21no—
41C11×#387—21no—
42C11×#385—21no—
43C11×#383C2211yescharacteristic
44C11×#328C2212yes—
45C11×#328C2212yes—
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2211yescharacteristic
49C11×#324C2211yescharacteristic
50C11×#323C2212yes—
51C2×C11×#41—21no—
52C22×Q8×C11C2311yescharacteristic
53C23×C4×C11D411yescharacteristic
54C2×C11×Q16—22no—
55C2×C11×SD16—22no—
56C11×C4⋊Q8—22no—
57C11×#126—22no—
58C11×#126—22no—
59C11×#126—22no—
60C11×#126—22no—
61C11×#125—21no—
62C11×#125—22no—
63C11×#125D412yes—
64C11×#124—21no—
65C11×#124—22no—
66C11×#124—22no—
67C11×#124D412yes—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8C2312yes—
76C11×#121—21no—
77C11×#121—21no—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121—22no—
81C11×#121—21no—
82C11×#121C2312yes—
83C11×#120—22no—
84C4×Q8×C11—22no—
85C4×Q8×C11—21no—
86C4×Q8×C11—22no—
87C4×Q8×C11—22no—
88C4×Q8×C11D412yes—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—21no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11D412yes—
96C11×#117—22no—
97C11×#117—22no—
98C11×#117—21no—
99C11×#117—22no—
100C11×#117—22no—
101C11×#117—22no—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4D411yescharacteristic
112C2×C11×C22⋊C4C2311yescharacteristic
113C2×C42×C11—21no—
114C2×C42×C11D411yescharacteristic
115C2×C42×C11C2311yescharacteristic
116C11×#107—22no—
117C11×#106—22no—
118C11×C4⋊C8—22no—
119C11×#103—22no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#102—22no—
123C11×C22⋊C8C2312yes—
124C11×C22⋊C8C2312yes—
125C4×C8×C11—22no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18217C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11C2×D411yescharacteristic
136C11×#41—42no—
137C11×#41—42no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—42no—
142C2×Q8×C11C2×D412yes—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—21no—
148C2×D4×C11C2×D412yes—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—41no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C11×Q16—44no—
167C11×SD16—44no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4C2×D412yes—
188C11×C4⋊C4C2×D412yes—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4—42no—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—22no—
207C42×C11—42no—
208C42×C11C2×D412yes—
209C42×C11C2×D412yes—
210#3493C2×C1111yescharacteristic
211#3108C2×C1112yescomplemented
212#2599C2×C1111yescharacteristic, complemented
213#1612C2×C1112yescomplemented
214#1611C2×C1111yescharacteristic, complemented
215#1610C2×C1111yescharacteristic, complemented
216#1606C2×C1112yescomplemented
217#1605C2×C1111yescharacteristic, complemented
218#1604C2×C1111yescharacteristic, complemented
219#1521C2×C1112yescomplemented
220#1458C2×C1111yescharacteristic, complemented
221C23×C11—21no—
222C23×C11—22no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C22×D411yescharacteristic
228Q8×C11—24no—
229Q8×C11—42no—
230Q8×C11—42no—
231Q8×C11—42no—
232Q8×C11—81no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—82no—
238D4×C11—81no—
239D4×C11—82no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—44no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
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—82no—
269C2×C4×C11—82no—
270C2×C4×C11#12012yes—
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11#12011yescharacteristic
273C2×C4×C11#13512yes—
274C2×C4×C11C22×D412yes—
275C8×C11—42no—
276C8×C11—42no—
277#556—22no—
278#555—22no—
279#553—22no—
280#552—22no—
281#544C22×C1111yescharacteristic
282#538—21no—
283#538C22×C1112yes—
284#537C22×C1111yescharacteristic
285#529—21no—
286#529C22×C1112yes—
287#525—21no—
288#520—21no—
289C2×C4×Q8C22×C1111yescharacteristic
290C2×#117C22×C1111yescharacteristic
291#483C22×C1112yes—
292#480C22×C1112yes—
293#479—22no—
294#464—22no—
295#451C22×C1112yes—
296#448C22×C1112yes—
297C4×Q16—22no—
298C4×SD16—22no—
299#431C22×C1112yes—
300#398C22×C1111yescharacteristic
301#397C22×C1111yescharacteristic
302#395C22×C1111yescharacteristic
303#393C22×C1111yescharacteristic
304#388—21no—
305#387—21no—
306#387—21no—
307#385—21no—
308#383C22×C1111yescharacteristic
309#328C22×C1112yes—
310#328C22×C1112yes—
311#327C22×C1112yes—
312#327C22×C1112yes—
313#324C22×C1111yescharacteristic
314#324C22×C1111yescharacteristic
315#323C22×C1112yes—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—42no—
319C22×C11—41no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—41no—
323C22×C11—42no—
324C22×C11—41no—
325C22×C11—81no—
326C22×C11C2×#12011yescharacteristic
327C22×C11C2×#13511yescharacteristic
328C22×C11#57511yescharacteristic
329C4×C11—22no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—42no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—42no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11—81no—
343C2×#41—21no—
344C22×Q8C23×C1111yescharacteristic
345C23×C4D4×C1111yescharacteristic
346C2×Q16—22no—
347C2×SD16—22no—
348C4⋊Q8—22no—
349#126—22no—
350#126—22no—
351#126—22no—
352#126—22no—
353#125—21no—
354#125—22no—
355#125D4×C1112yes—
356#124—21no—
357#124—22no—
358#124—22no—
359#124D4×C1112yes—
360#123—22no—
361#123—22no—
362#123—22no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—22no—
367C22⋊Q8C23×C1112yes—
368#121—21no—
369#121—21no—
370#121—22no—
371#121—22no—
372#121—22no—
373#121—21no—
374#121C23×C1112yes—
375#120—22no—
376C4×Q8—22no—
377C4×Q8—21no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8D4×C1112yes—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4D4×C1112yes—
388#117—22no—
389#117—22no—
390#117—21no—
391#117—22no—
392#117—22no—
393#117—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4D4×C1111yescharacteristic
399C2×C4⋊C4C23×C1111yescharacteristic
400C2×C4⋊C4C23×C1111yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4D4×C1111yescharacteristic
404C2×C22⋊C4C23×C1111yescharacteristic
405C2×C42—21no—
406C2×C42D4×C1111yescharacteristic
407C2×C42C23×C1111yescharacteristic
408#107—22no—
409#106—22no—
410C4⋊C8—22no—
411#103—22no—
412#103—22no—
413#103—22no—
414#102—22no—
415C22⋊C8C23×C1112yes—
416C22⋊C8C23×C1112yes—
417C4×C8—22no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95C23×C1111yescharacteristic
425#95C23×C1111yescharacteristic
426C2×C11—21no—
427C2×C11—21no—
428C2×C11—82no—
429C2×C11—81no—
430C2×C11#300211yescharacteristic
431C2×C11#302211yescharacteristic
432C2×C11#302511yescharacteristic
433C24C2×D4×C1111yescharacteristic
434#41—42no—
435#41—42no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—22no—
439C2×Q8—42no—
440C2×Q8C2×D4×C1112yes—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—21no—
446C2×D4C2×D4×C1112yes—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—41no—
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C2×D4×C1111yescharacteristic
461C22×C4C2×D4×C1111yescharacteristic
462C22×C4C2×D4×C1111yescharacteristic
463C22×C4C24×C1111yescharacteristic
464Q16—44no—
465SD16—44no—
466C2×C8—22no—
467C2×C8—22no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—42no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—42no—
485C4⋊C4C2×D4×C1112yes—
486C4⋊C4C2×D4×C1112yes—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C42—22no—
501C42—22no—
502C42—21no—
503C42—21no—
504C42—22no—
505C42—42no—
506C42C2×D4×C1112yes—
507C42C2×D4×C1112yes—
508C11#1821711yescharacteristic, direct product factor, Sylow
509C23—21no—
510C23—22no—
511C23—21no—
512C23—21no—
513C23—41no—
514C23—41no—
515C23C22×D4×C1111yescharacteristic
516Q8—24no—
517Q8—42no—
518Q8—42no—
519Q8—42no—
520Q8—81no—
521D4—42no—
522D4—42no—
523D4—42no—
524D4—42no—
525D4—82no—
526D4—81no—
527D4—82no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—44no—
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—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4C11×#12012yes—
559C2×C4C11×#12011yescharacteristic
560C2×C4C11×#12011yescharacteristic
561C2×C4C11×#13512yes—
562C2×C4C22×D4×C1112yes—
563C8—42no—
564C8—42no—
565C22—21no—
566C22—21no—
567C22—42no—
568C22—41no—
569C22—42no—
570C22—42no—
571C22—41no—
572C22—42no—
573C22—41no—
574C22—81no—
575C22C2×C11×#12011yescharacteristic
576C22C2×C11×#13511yescharacteristic
577C22C11×#57511yescharacteristic
578C4—22no—
579C4—21no—
580C4—21no—
581C4—22no—
582C4—22no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—42no—
589C4—81no—
590C4—81no—
591C4—81no—
592C2—21no—
593C2—21no—
594C2—81no—
595C2—82no—
596C2C11×#300211yescharacteristic
597C2C11×#302211yescharacteristic
598C2C11×#302511yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#3493C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C11×#3108C2semidirect
3. C11×#2599C2semidirect
4. C11×#1612C2semidirect
5. C11×#1611C2semidirect
6. C11×#1610C2semidirect
7. C11×#1606C2semidirect
8. C11×#1605C2semidirect
9. C11×#1604C2semidirect
10. C11×#1521C2semidirect
11. C11×#1458C2semidirect
134. #18217C11direct (N × H)
211. #3108C2×C11semidirect
212. #2599C2×C11semidirect
213. #1612C2×C11semidirect
214. #1611C2×C11semidirect
215. #1610C2×C11semidirect
216. #1606C2×C11semidirect
217. #1605C2×C11semidirect
218. #1604C2×C11semidirect
219. #1521C2×C11semidirect
220. #1458C2×C11semidirect
508. C11#18217direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34932
C11×#31082
C11×#25992
C11×#16122
C11×#16112
C11×#16102
C11×#16062
C11×#16052
C11×#16042
C11×#15212
C11×#14582
#1821711