Finite Group Databasebeta

← C11×#18193 #14595386

Subgroups — C11×#18193 #14595386

Order 2816.

1200 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3492C211yesmaximal, characteristic, complemented
2C11×#3002C212yesmaximal, complemented
3C11×#2406C211yesmaximal, characteristic, complemented
4C11×#1605C211yesmaximal, characteristic, complemented
5C11×#1604C211yesmaximal, characteristic, complemented
6C11×#1603C212yesmaximal, complemented
7C11×#1599C211yesmaximal, characteristic, complemented
8C11×#1598C211yesmaximal, characteristic, complemented
9C11×#1597C212yesmaximal, complemented
10C11×#1516C212yesmaximal, complemented
11C2×C11×#324C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×C11×#135—22no—
14C11×#554—22no—
15C11×#553—22no—
16C11×#552—22no—
17C11×#547—22no—
18C11×#544C2211yescharacteristic
19C11×#539—21no—
20C11×#539C2212yes—
21C11×#537C2211yescharacteristic
22C11×#525—21no—
23C11×#525—21no—
24C11×#525C2212yes—
25C2×C11×#123—21no—
26C11×#520—21no—
27C22×C11×C4⋊C4C2211yescharacteristic
28C11×#452—22no—
29C11×#451C2212yes—
30C11×#450C2212yes—
31C11×#449—22no—
32C11×#448C2212yes—
33C11×#447C2212yes—
34C11×#416—22no—
35C2×C11×C22⋊C8C2212yes—
36C11×#395C2211yescharacteristic
37C11×#395C2211yescharacteristic
38C11×#394C2211yescharacteristic
39C11×#394C2211yescharacteristic
40C11×#386—21no—
41C11×#385—21no—
42C11×#385—21no—
43C11×#381C2211yescharacteristic
44C11×#328C2212yes—
45C11×#328C2212yes—
46C11×#327C2212yes—
47C11×#327C2212yes—
48C11×#324C2212yes—
49C11×#324C2211yescharacteristic
50C11×#324C2211yescharacteristic
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41—44no—
56C2×C11×#41D412yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C11×#135—48no—
65C2×C11×Q16—22no—
66C2×C11×SD16—22no—
67C2×C11×SD16—22no—
68C2×C11×D8—22no—
69C22×C8×C11—22no—
70C11×C4⋊Q8—22no—
71C11×#126—22no—
72C11×#126—22no—
73C11×#125—22no—
74C11×#125—22no—
75C11×#125—22no—
76C11×#123—22no—
77C11×#123—22no—
78C11×#123—22no—
79C11×#123—22no—
80C11×#123—22no—
81C11×#123—44no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—22no—
89C11×C22⋊Q8D412yes—
90C11×C22⋊Q8C2312yes—
91C11×#121—21no—
92C11×#121—21no—
93C11×#121—21no—
94C11×#121—22no—
95C11×#121—21no—
96C11×#121D412yes—
97C11×#121C2312yes—
98C11×#120—22no—
99C4×Q8×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—22no—
102C4×D4×C11—22no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C11×#117—22no—
108C11×#117—21no—
109C11×#117—21no—
110C11×#117D412yes—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—21no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4D411yescharacteristic
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C11×C22⋊C4—21no—
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C11×#103—22no—
126C11×#103—22no—
127C11×#102—22no—
128C11×#102—22no—
129C11×C22⋊C8—22no—
130C11×C22⋊C8C2312yes—
131C11×C22⋊C8C2312yes—
132C11×#95—21no—
133C11×#95—21no—
134C11×#95—21no—
135C11×#95C2311yescharacteristic
136C11×#95C2311yescharacteristic
137#18193C1111yesmaximal, characteristic, direct product factor, Sylow
138C24×C11—21no—
139C24×C11C2×D411yescharacteristic
140C11×#41—28no—
141C11×#41—42no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C11×#41—44no—
146C11×#41—42no—
147C11×#41—82no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—22no—
151C2×Q8×C11—42no—
152C2×Q8×C11C2×D412yes—
153C2×D4×C11—21no—
154C2×D4×C11—24no—
155C2×D4×C11—22no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—41no—
163C2×D4×C11—41no—
164C2×D4×C11C2×D412yes—
165C22×C4×C11—22no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—41no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D412yes—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2411yescharacteristic
190C11×Q16—44no—
191C11×SD16—44no—
192C11×SD16—44no—
193C11×D8—44no—
194C2×C8×C11—22no—
195C2×C8×C11—22no—
196C2×C8×C11—44no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—22no—
208C11×C4⋊C4—22no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—22no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—42no—
213C11×C4⋊C4C2×D412yes—
214C11×C4⋊C4C2×D412yes—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—22no—
218C11×C22⋊C4—22no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—42no—
225C11×C22⋊C4—42no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C42×C11—22no—
230C42×C11—22no—
231C42×C11—22no—
232#3492C2×C1111yescharacteristic, complemented
233#3002C2×C1112yescomplemented
234#2406C2×C1111yescharacteristic, complemented
235#1605C2×C1111yescharacteristic, complemented
236#1604C2×C1111yescharacteristic, complemented
237#1603C2×C1112yescomplemented
238#1599C2×C1111yescharacteristic, complemented
239#1598C2×C1111yescharacteristic, complemented
240#1597C2×C1112yescomplemented
241#1516C2×C1112yescomplemented
242C2×#324C2×C1111yescharacteristic, complemented
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11#12011yescharacteristic
256C23×C11#12011yescharacteristic
257C23×C11C22×D411yescharacteristic
258Q8×C11—24no—
259Q8×C11—42no—
260Q8×C11—42no—
261Q8×C11—42no—
262Q8×C11—81no—
263D4×C11—24no—
264D4×C11—42no—
265D4×C11—42no—
266D4×C11—42no—
267D4×C11—44no—
268D4×C11—44no—
269D4×C11—42no—
270D4×C11—42no—
271D4×C11—44no—
272D4×C11—44no—
273D4×C11—81no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—24no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—41no—
287C2×C4×C11—42no—
288C2×C4×C11—41no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—44no—
292C2×C4×C11—48no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—42no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—82no—
305C2×C4×C11—81no—
306C2×C4×C11—82no—
307C2×C4×C11#12012yes—
308C2×C4×C11#13512yescomplemented
309C2×C4×C11C22×D412yes—
310C8×C11—42no—
311C8×C11—42no—
312C22×#41C22×C1111yescharacteristic
313C2×#135—22no—
314#554—22no—
315#553—22no—
316#552—22no—
317#547—22no—
318#544C22×C1111yescharacteristic
319#539—21no—
320#539C22×C1112yes—
321#537C22×C1111yescharacteristic
322#525—21no—
323#525—21no—
324#525C22×C1112yes—
325C2×#123—21no—
326#520—21no—
327C22×C4⋊C4C22×C1111yescharacteristic
328#452—22no—
329#451C22×C1112yes—
330#450C22×C1112yes—
331#449—22no—
332#448C22×C1112yes—
333#447C22×C1112yes—
334#416—22no—
335C2×C22⋊C8C22×C1112yes—
336#395C22×C1111yescharacteristic
337#395C22×C1111yescharacteristic
338#394C22×C1111yescharacteristic
339#394C22×C1111yescharacteristic
340#386—21no—
341#385—21no—
342#385—21no—
343#381C22×C1111yescharacteristic
344#328C22×C1112yes—
345#328C22×C1112yes—
346#327C22×C1112yes—
347#327C22×C1112yes—
348#324C22×C1112yes—
349#324C22×C1111yescharacteristic
350#324C22×C1111yescharacteristic
351C22×C11—21no—
352C22×C11—21no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—21no—
357C22×C11—21no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11B(4,𝔽2)12yes—
371C22×C11C2×#12011yescharacteristic
372C22×C11C2×#13511yescharacteristic
373C22×C11#57511yescharacteristic
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—22no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—42no—
380C4×C11—42no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—81no—
385C4×C11—81no—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41—22no—
389C2×#41—22no—
390C2×#41—44no—
391C2×#41D4×C1112yes—
392C22×Q8C23×C1111yescharacteristic
393C22×D4—21no—
394C22×D4C23×C1111yescharacteristic
395C23×C4—21no—
396C23×C4D4×C1111yescharacteristic
397C23×C4D4×C1111yescharacteristic
398C23×C4C23×C1111yescharacteristic
399#135—48no—
400C2×Q16—22no—
401C2×SD16—22no—
402C2×SD16—22no—
403C2×D8—22no—
404C22×C8—22no—
405C4⋊Q8—22no—
406#126—22no—
407#126—22no—
408#125—22no—
409#125—22no—
410#125—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414#123—22no—
415#123—22no—
416#123—44no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—22no—
421C22⋊Q8—22no—
422C22⋊Q8—21no—
423C22⋊Q8—22no—
424C22⋊Q8D4×C1112yes—
425C22⋊Q8C23×C1112yes—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—22no—
430#121—21no—
431#121D4×C1112yes—
432#121C23×C1112yes—
433#120—22no—
434C4×Q8—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442#117—22no—
443#117—21no—
444#117—21no—
445#117D4×C1112yes—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4D4×C1111yescharacteristic
452C2×C4⋊C4D4×C1111yescharacteristic
453C2×C4⋊C4C23×C1111yescharacteristic
454C2×C4⋊C4C23×C1111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460#103—22no—
461#103—22no—
462#102—22no—
463#102—22no—
464C22⋊C8—22no—
465C22⋊C8C23×C1112yes—
466C22⋊C8C23×C1112yes—
467#95—21no—
468#95—21no—
469#95—21no—
470#95C23×C1111yescharacteristic
471#95C23×C1111yescharacteristic
472C2×C11—21no—
473C2×C11—21no—
474C2×C11—22no—
475C2×C11—41no—
476C2×C11—82no—
477C2×C11—82no—
478C2×C11#300211yescharacteristic
479C2×C11#302011yescharacteristic
480C2×C11C2×B(4,𝔽2)11yescharacteristic
481C24—21no—
482C24C2×D4×C1111yescharacteristic
483#41—28no—
484#41—44no—
485#41—42no—
486#41—44no—
487#41—44no—
488#41—44no—
489#41—42no—
490#41—82no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—22no—
494C2×Q8—42no—
495C2×Q8C2×D4×C1112yes—
496C2×D4—21no—
497C2×D4—24no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—22no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4C2×D4×C1112yes—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—41no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4C2×D4×C1111yescharacteristic
526C22×C4C2×D4×C1112yes—
527C22×C4C2×D4×C1111yescharacteristic
528C22×C4C2×D4×C1111yescharacteristic
529C22×C4C2×D4×C1111yescharacteristic
530C22×C4C2×D4×C1111yescharacteristic
531C22×C4C2×D4×C1112yes—
532C22×C4C24×C1111yescharacteristic
533Q16—44no—
534SD16—44no—
535SD16—44no—
536D8—44no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—44no—
540C4⋊C4—21no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4C2×D4×C1112yes—
557C4⋊C4C2×D4×C1112yes—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C42—22no—
573C42—22no—
574C42—22no—
575C11#1819311yescharacteristic, direct product factor, Sylow
576C23—21no—
577C23—21no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23C11×#12011yescharacteristic
589C23C11×#12011yescharacteristic
590C23C22×D4×C1111yescharacteristic
591Q8—24no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—81no—
596D4—24no—
597D4—42no—
598D4—42no—
599D4—42no—
600D4—44no—
601D4—44no—
602D4—42no—
603D4—42no—
604D4—44no—
605D4—44no—
606D4—81no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—44no—
625C2×C4—48no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—82no—
638C2×C4—81no—
639C2×C4—82no—
640C2×C4C11×#12012yes—
641C2×C4C11×#13512yescomplemented
642C2×C4C22×D4×C1112yes—
643C8—42no—
644C8—42no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—21no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22C11×B(4,𝔽2)12yes—
665C22C2×C11×#12011yescharacteristic
666C22C2×C11×#13511yescharacteristic
667C22C11×#57511yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—41no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—41no—
676C4—41no—
677C4—42no—
678C4—81no—
679C4—81no—
680C2—21no—
681C2—21no—
682C2—22no—
683C2—41no—
684C2—82no—
685C2—82no—
686C2C11×#300211yescharacteristic
687C2C11×#302011yescharacteristic
688C2C2×C11×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3492C2semidirect
2. C11×#3002C2semidirect
3. C11×#2406C2semidirect
4. C11×#1605C2semidirect
5. C11×#1604C2semidirect
6. C11×#1603C2semidirect
7. C11×#1599C2semidirect
8. C11×#1598C2semidirect
9. C11×#1597C2semidirect
10. C11×#1516C2semidirect
11. C2×C11×#324C2semidirect
137. #18193C11direct (N × H)
232. #3492C2×C11semidirect
233. #3002C2×C11semidirect
234. #2406C2×C11semidirect
235. #1605C2×C11semidirect
236. #1604C2×C11semidirect
237. #1603C2×C11semidirect
238. #1599C2×C11semidirect
239. #1598C2×C11semidirect
240. #1597C2×C11semidirect
241. #1516C2×C11semidirect
242. C2×#324C2×C11semidirect
308. C2×C4×C11#135semidirect
575. C11#18193direct (N × H)
641. C2×C4C11×#135semidirect

Maximal subgroups

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

subgroupindex
C11×#34922
C11×#30022
C11×#24062
C11×#16052
C11×#16042
C11×#16032
C11×#15992
C11×#15982
C11×#15972
C11×#15162
C2×C11×#3242
#1819311