Finite Group Databasebeta

← C11×#18393 #14595586

Subgroups — C11×#18393 #14595586

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3491C211yesmaximal, characteristic
2C11×#3232C212yesmaximal, complemented
3C11×#2611C211yesmaximal, characteristic, complemented
4C11×#1615C212yesmaximal, complemented
5C11×#1614C211yesmaximal, characteristic, complemented
6C11×#1613C211yesmaximal, characteristic
7C11×#1609C212yesmaximal, complemented
8C11×#1608C211yesmaximal, characteristic, complemented
9C11×#1607C211yesmaximal, characteristic
10C11×#1500C212yesmaximal, complemented
11C11×#1458C211yesmaximal, characteristic, complemented
12C11×#552—22no—
13C11×#552—22no—
14C11×#551—22no—
15C11×#551—22no—
16C11×#543C2211yescharacteristic
17C11×#539—21no—
18C11×#539C2212yes—
19C11×#534C2211yescharacteristic
20C11×#529—21no—
21C11×#529C2212yes—
22C2×C11×#125C2211yescharacteristic, complemented
23C2×C11×#123—21no—
24C11×#518—21no—
25C2×C11×#117C2211yescharacteristic
26C11×#499—22no—
27C11×#488—22no—
28C11×#484C2212yescomplemented
29C11×#483C2212yescomplemented
30C11×#481C2212yes—
31C11×#480C2212yes—
32C11×#479—22no—
33C11×#478—22no—
34C11×#431C2212yescomplemented
35C11×#400C2211yescharacteristic, complemented
36C11×#399C2211yescharacteristic
37C11×#398C2211yescharacteristic, complemented
38C11×#397C2211yescharacteristic
39C11×#389—21no—
40C11×#388—21no—
41C11×#387—21no—
42C11×#385—21no—
43C11×#376C2211yescharacteristic, complemented
44C11×#328C2212yescomplemented
45C11×#328C2212yescomplemented
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2212yescomplemented
49C11×#323C2211yescharacteristic
50C11×#323C2211yescharacteristic
51C22×D4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C11×#126—22no—
54C11×#126—22no—
55C11×#126—22no—
56C11×#126—22no—
57C11×#125—21no—
58C11×#125—22no—
59C11×#125—22no—
60C11×#125—22no—
61C11×#125—22no—
62C11×#125D412yes—
63C11×#124—21no—
64C11×#124D412yes—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×#123—22no—
70C11×#123—22no—
71C11×#123—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8C2312yes—
78C11×#121—21no—
79C11×#121C2312yes—
80C11×#120—22no—
81C4×Q8×C11—21no—
82C4×Q8×C11D412yes—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—21no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11D412yes—
89C11×#117—22no—
90C11×#117—22no—
91C11×#117—22no—
92C11×#117—22no—
93C11×#117—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C11×C22⋊C4—21no—
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4D411yescharacteristic
111C2×C11×C22⋊C4C2311yescharacteristic
112C2×C42×C11—21no—
113C2×C42×C11D411yescharacteristic
114C2×C42×C11C2311yescharacteristic
115C11×#107—22no—
116C11×#107—22no—
117C11×#106—22no—
118C11×#106—22no—
119C11×C4⋊C8—22no—
120C11×#103—22no—
121C11×#103—22no—
122C11×#102—22no—
123C11×#102—22no—
124C11×C22⋊C8C2312yes—
125C11×C22⋊C8C2312yes—
126C4×C8×C11—22no—
127C11×#95—21no—
128C11×#95—21no—
129C11×#95—21no—
130C11×#95—21no—
131C11×#95—21no—
132C11×#95C2311yescharacteristic
133C11×#95C2311yescharacteristic
134#18393C1111yesmaximal, characteristic, direct product factor, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C2×Q8×C11—21no—
138C2×Q8×C11C2×D412yes—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—21no—
142C2×D4×C11—42no—
143C2×D4×C11—42no—
144C2×D4×C11C2×D412yes—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
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
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—41no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4C2×D412yes—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
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—42no—
200C11×C22⋊C4—42no—
201C42×C11—22no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—22no—
205C42×C11—42no—
206C42×C11C2×D412yes—
207C42×C11C2×D412yes—
208#3491C2×C1111yescharacteristic
209#3232C2×C1112yescomplemented
210#2611C2×C1111yescharacteristic, complemented
211#1615C2×C1112yescomplemented
212#1614C2×C1111yescharacteristic, complemented
213#1613C2×C1111yescharacteristic
214#1609C2×C1112yescomplemented
215#1608C2×C1111yescharacteristic, complemented
216#1607C2×C1111yescharacteristic
217#1500C2×C1112yescomplemented
218#1458C2×C1111yescharacteristic, complemented
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—22no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—42no—
225C23×C11—81no—
226C23×C11—81no—
227C23×C11#13512yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—42no—
230Q8×C11—81no—
231D4×C11—42no—
232D4×C11—44no—
233D4×C11—42no—
234D4×C11—42no—
235D4×C11—81no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—41no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
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—82no—
266C2×C4×C11—81no—
267C2×C4×C11—82no—
268C2×C4×C11—81no—
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11#12012yes—
272C2×C4×C11C22×D412yes—
273C8×C11—42no—
274C8×C11—42no—
275#552—22no—
276#552—22no—
277#551—22no—
278#551—22no—
279#543C22×C1111yescharacteristic
280#539—21no—
281#539C22×C1112yes—
282#534C22×C1111yescharacteristic
283#529—21no—
284#529C22×C1112yes—
285C2×#125C22×C1111yescharacteristic, complemented
286C2×#123—21no—
287#518—21no—
288C2×#117C22×C1111yescharacteristic
289#499—22no—
290#488—22no—
291#484C22×C1112yescomplemented
292#483C22×C1112yescomplemented
293#481C22×C1112yes—
294#480C22×C1112yes—
295#479—22no—
296#478—22no—
297#431C22×C1112yescomplemented
298#400C22×C1111yescharacteristic, complemented
299#399C22×C1111yescharacteristic
300#398C22×C1111yescharacteristic, complemented
301#397C22×C1111yescharacteristic
302#389—21no—
303#388—21no—
304#387—21no—
305#385—21no—
306#376C22×C1111yescharacteristic, complemented
307#328C22×C1112yescomplemented
308#328C22×C1112yescomplemented
309#327C22×C1112yes—
310#327C22×C1112yes—
311#324C22×C1112yescomplemented
312#323C22×C1111yescharacteristic
313#323C22×C1111yescharacteristic
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—22no—
317C22×C11—42no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—81no—
324C22×C11—162no—
325C22×C11C2×#12011yescharacteristic
326C22×C11C2×#13511yescharacteristic
327C22×C11#57511yescharacteristic
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—22no—
331C4×C11—22no—
332C4×C11—42no—
333C4×C11—41no—
334C4×C11—42no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C22×D4—21no—
343C23×C4D4×C1111yescharacteristic
344#126—22no—
345#126—22no—
346#126—22no—
347#126—22no—
348#125—21no—
349#125—22no—
350#125—22no—
351#125—22no—
352#125—22no—
353#125D4×C1112yes—
354#124—21no—
355#124D4×C1112yes—
356#123—22no—
357#123—22no—
358#123—22no—
359#123—22no—
360#123—22no—
361#123—22no—
362#123—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—22no—
366C22⋊Q8—21no—
367C22⋊Q8—22no—
368C22⋊Q8C23×C1112yes—
369#121—21no—
370#121C23×C1112yes—
371#120—22no—
372C4×Q8—21no—
373C4×Q8D4×C1112yes—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4D4×C1112yes—
380#117—22no—
381#117—22no—
382#117—22no—
383#117—22no—
384#117—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4D4×C1111yescharacteristic
392C2×C4⋊C4C23×C1111yescharacteristic
393C2×C4⋊C4C23×C1111yescharacteristic
394C2×C4⋊C4C23×C1111yescharacteristic
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4D4×C1111yescharacteristic
402C2×C22⋊C4C23×C1111yescharacteristic
403C2×C42—21no—
404C2×C42D4×C1111yescharacteristic
405C2×C42C23×C1111yescharacteristic
406#107—22no—
407#107—22no—
408#106—22no—
409#106—22no—
410C4⋊C8—22no—
411#103—22no—
412#103—22no—
413#102—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#95C23×C1111yescharacteristic
424#95C23×C1111yescharacteristic
425C2×C11—21no—
426C2×C11—21no—
427C2×C11—42no—
428C2×C11—82no—
429C2×C11#300211yescharacteristic
430C2×C11#301811yescharacteristic
431C2×C11#302811yescharacteristic
432C24—21no—
433C24C2×D4×C1111yescharacteristic
434C2×Q8—21no—
435C2×Q8C2×D4×C1112yes—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4C2×D4×C1112yes—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4C2×D4×C1111yescharacteristic
456C22×C4C2×D4×C1111yescharacteristic
457C22×C4C2×D4×C1111yescharacteristic
458C22×C4C2×D4×C1111yescharacteristic
459C22×C4C2×D4×C1111yescharacteristic
460C22×C4C24×C1111yescharacteristic
461C2×C8—22no—
462C2×C8—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—42no—
482C4⋊C4C2×D4×C1112yes—
483C4⋊C4C2×D4×C1112yes—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
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—42no—
497C22⋊C4—42no—
498C42—22no—
499C42—21no—
500C42—21no—
501C42—22no—
502C42—42no—
503C42C2×D4×C1112yes—
504C42C2×D4×C1112yes—
505C11#1839311yescharacteristic, direct product factor, Sylow
506C23—21no—
507C23—21no—
508C23—22no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—81no—
513C23—81no—
514C23C11×#13512yes—
515C23C22×D4×C1111yescharacteristic
516Q8—42no—
517Q8—81no—
518D4—42no—
519D4—44no—
520D4—42no—
521D4—42no—
522D4—81no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
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—82no—
553C2×C4—81no—
554C2×C4—82no—
555C2×C4—81no—
556C2×C4C11×#12011yescharacteristic
557C2×C4C11×#12011yescharacteristic
558C2×C4C11×#12012yes—
559C2×C4C22×D4×C1112yes—
560C8—42no—
561C8—42no—
562C22—21no—
563C22—21no—
564C22—22no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—162no—
573C22C2×C11×#12011yescharacteristic
574C22C2×C11×#13511yescharacteristic
575C22C11×#57511yescharacteristic
576C4—21no—
577C4—21no—
578C4—22no—
579C4—22no—
580C4—42no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—42no—
585C4—41no—
586C4—42no—
587C4—81no—
588C4—81no—
589C4—81no—
590C2—21no—
591C2—21no—
592C2—42no—
593C2—82no—
594C2C11×#300211yescharacteristic
595C2C11×#301811yescharacteristic
596C2C11×#302811yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
prime radicalC11×#534C22
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×#3232C2semidirect
3. C11×#2611C2semidirect
4. C11×#1615C2semidirect
5. C11×#1614C2semidirect
7. C11×#1609C2semidirect
8. C11×#1608C2semidirect
10. C11×#1500C2semidirect
11. C11×#1458C2semidirect
22. C2×C11×#125C22semidirect
28. C11×#484C22semidirect
29. C11×#483C22semidirect
34. C11×#431C22semidirect
35. C11×#400C22semidirect
37. C11×#398C22semidirect
43. C11×#376C22semidirect
44. C11×#328C22semidirect
45. C11×#328C22semidirect
48. C11×#324C22semidirect
134. #18393C11direct (N × H)
209. #3232C2×C11semidirect
210. #2611C2×C11semidirect
211. #1615C2×C11semidirect
212. #1614C2×C11semidirect
214. #1609C2×C11semidirect
215. #1608C2×C11semidirect
217. #1500C2×C11semidirect
218. #1458C2×C11semidirect
285. C2×#125C22×C11semidirect
291. #484C22×C11semidirect
292. #483C22×C11semidirect
297. #431C22×C11semidirect
298. #400C22×C11semidirect
300. #398C22×C11semidirect
306. #376C22×C11semidirect
307. #328C22×C11semidirect
308. #328C22×C11semidirect
311. #324C22×C11semidirect
505. C11#18393direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34912
C11×#32322
C11×#26112
C11×#16152
C11×#16142
C11×#16132
C11×#16092
C11×#16082
C11×#16072
C11×#15002
C11×#14582
#1839311