Finite Group Databasebeta

← C11×#18958 #14596151

Subgroups — C11×#18958 #14596151

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#3554C211yesmaximal, characteristic, complemented
2C11×#3217C211yesmaximal, characteristic, complemented
3C11×#3208C211yesmaximal, characteristic, complemented
4C11×#3205C211yesmaximal, characteristic, complemented
5C11×#1627C212yesmaximal, complemented
6C11×#1626C212yesmaximal, complemented
7C11×#1621C212yesmaximal, complemented
8C11×#1620C212yesmaximal, complemented
9C11×#1553C211yesmaximal, characteristic, complemented
10C11×#1497C211yesmaximal, characteristic, complemented
11C11×#1482C211yesmaximal, characteristic, complemented
12C11×#562—22no—
13C11×#559—21no—
14C11×#559C2211yescharacteristic, complemented
15C11×#557C2211yescharacteristic, complemented
16C11×#554—21no—
17C11×#550C2211yescharacteristic, complemented
18D4×Q8×C11C2211yescharacteristic, complemented
19C11×#548—21no—
20C11×#547—21no—
21C11×#542—21no—
22C11×#542—21no—
23C11×#540—21no—
24C11×#539—22no—
25C11×#536—21no—
26C11×#533C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C2×C11×#127C2211yescharacteristic
29C11×#529C2211yescharacteristic
30C11×#496—21no—
31C11×#493C2212yes—
32C11×#492—21no—
33C11×#490—21no—
34C11×#486—21no—
35C11×#486C2212yes—
36C11×#460C2212yes—
37C11×#460C2212yes—
38C11×#460C2212yes—
39C11×#459—22no—
40C11×#459C2212yes—
41C11×#450—21no—
42C11×#450—21no—
43C11×#450—21no—
44C11×#447—22no—
45C11×#447—21no—
46C11×#432C2211yescharacteristic
47C11×#431C2211yescharacteristic
48C11×#431C2211yescharacteristic
49C11×#332C2212yescomplemented
50C11×#331C2212yescomplemented
51C11×Q8⋊C8C2212yescomplemented
52C11×Q8⋊C8C2212yescomplemented
53C11×Q8⋊C8C2212yescomplemented
54C11×D4⋊C8C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×Q8×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C2×C11×SD16—22no—
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×D8—24no—
65C2×C11×D8—22no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8—21no—
68C11×C4⋊Q8D411yescharacteristic
69C11×C4⋊Q8D411yescharacteristic
70C11×C4⋊Q8C2311yescharacteristic
71C11×#127—21no—
72C11×#127—21no—
73C11×#127—21no—
74C11×#127—21no—
75C11×#127C2312yes—
76C11×#127C2311yescharacteristic
77C11×#126—22no—
78C11×#126—21no—
79C11×#125—22no—
80C11×#125—21no—
81C11×#125—21no—
82C11×#125D411yescharacteristic
83C11×#124—22no—
84C11×#124—22no—
85C11×#124—21no—
86C11×#124—21no—
87C11×#124—21no—
88C11×#124D411yescharacteristic
89C11×#123—22no—
90C11×#123—22no—
91C11×#123—22no—
92C11×#123—22no—
93C11×#123—22no—
94C11×#123—22no—
95C11×#123—21no—
96C11×C22⋊Q8—22no—
97C11×C22⋊Q8—22no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8—21no—
101C11×C22⋊Q8—22no—
102C11×C22⋊Q8—21no—
103C11×C22⋊Q8D411yescharacteristic
104C11×C22⋊Q8D411yescharacteristic
105C11×C22⋊Q8D411yescharacteristic
106C11×#121—22no—
107C11×#121—22no—
108C11×#121—22no—
109C11×#121—21no—
110C11×#121—21no—
111C11×#121D411yescharacteristic
112C11×#121D412yes—
113C4×Q8×C11—21no—
114C4×Q8×C11—21no—
115C4×Q8×C11—21no—
116C4×Q8×C11C2311yescharacteristic
117C4×Q8×C11C2311yescharacteristic
118C4×Q8×C11C2311yescharacteristic
119C4×D4×C11—22no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C4×D4×C11—21no—
126C4×D4×C11D412yes—
127C4×D4×C11C2311yescharacteristic
128C11×#117—21no—
129C11×#117—21no—
130C2×C11×C4⋊C4—22no—
131C2×C42×C11C2311yescharacteristic
132C11×C4⋊C8—21no—
133C11×C4⋊C8C2312yes—
134C11×C4⋊C8C2312yes—
135C11×#102—22no—
136C11×#102—22no—
137C11×#102—24no—
138C11×#102—22no—
139C11×#102—22no—
140C11×C22⋊C8—21no—
141C11×C22⋊C8—21no—
142C11×C22⋊C8—21no—
143C11×#97—21no—
144C4×C8×C11—21no—
145C4×C8×C11C2312yes—
146#18958C1111yesmaximal, characteristic, direct product factor, Sylow
147C24×C11—41no—
148C11×#41—82no—
149C11×#41—82no—
150C2×Q8×C11—22no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—82no—
154C2×Q8×C11C2×D411yescharacteristic
155C2×Q8×C11C2×D411yescharacteristic
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—21no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—41no—
167C2×D4×C11—41no—
168C2×D4×C11—41no—
169C2×D4×C11—82no—
170C2×D4×C11—82no—
171C2×D4×C11—82no—
172C2×D4×C11C2×D411yescharacteristic
173C2×D4×C11C2×D412yes—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C11×SD16—82no—
183C11×SD16—82no—
184C11×SD16—82no—
185C11×D8—82no—
186C11×D8—84no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
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—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D411yescharacteristic
209C11×C4⋊C4C2×D412yes—
210C11×C4⋊C4C2×D411yescharacteristic
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—22no—
215C11×C22⋊C4—22no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C11×C22⋊C4—21no—
225C42×C11—22no—
226C42×C11—21no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11C2×D411yescharacteristic
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2411yescharacteristic
233#3554C2×C1111yescharacteristic, complemented
234#3217C2×C1111yescharacteristic, complemented
235#3208C2×C1111yescharacteristic, complemented
236#3205C2×C1111yescharacteristic, complemented
237#1627C2×C1112yescomplemented
238#1626C2×C1112yescomplemented
239#1621C2×C1112yescomplemented
240#1620C2×C1112yescomplemented
241#1553C2×C1111yescharacteristic, complemented
242#1497C2×C1111yescharacteristic, complemented
243#1482C2×C1111yescharacteristic, complemented
244C23×C11—21no—
245C23×C11—22no—
246C23×C11—42no—
247C23×C11—82no—
248C23×C11—82no—
249C23×C11—82no—
250C23×C11#12011yescharacteristic
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—42no—
255Q8×C11—81no—
256Q8×C11—82no—
257D4×C11—22no—
258D4×C11—42no—
259D4×C11—44no—
260D4×C11—42no—
261D4×C11—42no—
262D4×C11—42no—
263D4×C11—42no—
264D4×C11—42no—
265D4×C11—42no—
266D4×C11—82no—
267D4×C11—82no—
268D4×C11—82no—
269D4×C11—81no—
270D4×C11—82no—
271D4×C11—82no—
272D4×C11—82no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—41no—
284C2×C4×C11—42no—
285C2×C4×C11—82no—
286C2×C4×C11—82no—
287C2×C4×C11—82no—
288C2×C4×C11—82no—
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C8×C11—42no—
296C8×C11—42no—
297C8×C11—42no—
298#562—22no—
299#559—21no—
300#559C22×C1111yescharacteristic, complemented
301#557C22×C1111yescharacteristic, complemented
302#554—21no—
303#550C22×C1111yescharacteristic, complemented
304D4×Q8C22×C1111yescharacteristic, complemented
305#548—21no—
306#547—21no—
307#542—21no—
308#542—21no—
309#540—21no—
310#539—22no—
311#536—21no—
312#533C22×C1111yescharacteristic
313#532C22×C1111yescharacteristic
314C2×#127C22×C1111yescharacteristic
315#529C22×C1111yescharacteristic
316#496—21no—
317#493C22×C1112yes—
318#492—21no—
319#490—21no—
320#486—21no—
321#486C22×C1112yes—
322#460C22×C1112yes—
323#460C22×C1112yes—
324#460C22×C1112yes—
325#459—22no—
326#459C22×C1112yes—
327#450—21no—
328#450—21no—
329#450—21no—
330#447—22no—
331#447—21no—
332#432C22×C1111yescharacteristic
333#431C22×C1111yescharacteristic
334#431C22×C1111yescharacteristic
335#332C22×C1112yescomplemented
336#331C22×C1112yescomplemented
337Q8⋊C8C22×C1112yescomplemented
338Q8⋊C8C22×C1112yescomplemented
339Q8⋊C8C22×C1112yescomplemented
340D4⋊C8C22×C1112yescomplemented
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—41no—
345C22×C11—42no—
346C22×C11—41no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—41no—
350C22×C11—82no—
351C22×C11—82no—
352C22×C11—82no—
353C22×C11—164no—
354C22×C11C2×#12011yescharacteristic
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11#57612yes—
368C4×C11#57712yes—
369C2×#41—21no—
370C2×#41—21no—
371C22×Q8—21no—
372C22×D4—21no—
373C22×D4—21no—
374C22×D4—21no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—22no—
378C2×D8—24no—
379C2×D8—22no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8D4×C1111yescharacteristic
383C4⋊Q8D4×C1111yescharacteristic
384C4⋊Q8C23×C1111yescharacteristic
385#127—21no—
386#127—21no—
387#127—21no—
388#127—21no—
389#127C23×C1112yes—
390#127C23×C1111yescharacteristic
391#126—22no—
392#126—21no—
393#125—22no—
394#125—21no—
395#125—21no—
396#125D4×C1111yescharacteristic
397#124—22no—
398#124—22no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124D4×C1111yescharacteristic
403#123—22no—
404#123—22no—
405#123—22no—
406#123—22no—
407#123—22no—
408#123—22no—
409#123—21no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—22no—
416C22⋊Q8—21no—
417C22⋊Q8D4×C1111yescharacteristic
418C22⋊Q8D4×C1111yescharacteristic
419C22⋊Q8D4×C1111yescharacteristic
420#121—22no—
421#121—22no—
422#121—22no—
423#121—21no—
424#121—21no—
425#121D4×C1111yescharacteristic
426#121D4×C1112yes—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8C23×C1111yescharacteristic
431C4×Q8C23×C1111yescharacteristic
432C4×Q8C23×C1111yescharacteristic
433C4×D4—22no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4D4×C1112yes—
441C4×D4C23×C1111yescharacteristic
442#117—21no—
443#117—21no—
444C2×C4⋊C4—22no—
445C2×C42C23×C1111yescharacteristic
446C4⋊C8—21no—
447C4⋊C8C23×C1112yes—
448C4⋊C8C23×C1112yes—
449#102—24no—
450#102—22no—
451#102—22no—
452#102—22no—
453#102—22no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457#97—21no—
458C4×C8—21no—
459C4×C8C23×C1112yes—
460C2×C11—41no—
461C2×C11—81no—
462C2×C11—82no—
463C2×C11—162no—
464C2×C11#300811yescharacteristic
465C2×C11#301011yescharacteristic
466C2×C11#302111yescharacteristic
467C24—41no—
468#41—82no—
469#41—82no—
470C2×Q8—22no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—82no—
474C2×Q8C2×D4×C1111yescharacteristic
475C2×Q8C2×D4×C1111yescharacteristic
476C2×Q8C2×D4×C1111yescharacteristic
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—82no—
490C2×D4—82no—
491C2×D4—82no—
492C2×D4C2×D4×C1111yescharacteristic
493C2×D4C2×D4×C1112yes—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4C2×D4×C1111yescharacteristic
500C22×C4C2×D4×C1111yescharacteristic
501C22×C4C2×D4×C1111yescharacteristic
502SD16—82no—
503SD16—82no—
504SD16—82no—
505D8—82no—
506D8—84no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4C2×D4×C1111yescharacteristic
527C4⋊C4C2×D4×C1111yescharacteristic
528C4⋊C4C2×D4×C1111yescharacteristic
529C4⋊C4C2×D4×C1112yes—
530C4⋊C4C2×D4×C1111yescharacteristic
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C42—22no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42C2×D4×C1111yescharacteristic
550C42C2×D4×C1111yescharacteristic
551C42C2×D4×C1111yescharacteristic
552C42C24×C1111yescharacteristic
553C11#1895811yescharacteristic, direct product factor, Sylow
554C23—21no—
555C23—22no—
556C23—42no—
557C23—82no—
558C23—82no—
559C23—82no—
560C23C11×#12011yescharacteristic
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—42no—
565Q8—81no—
566Q8—82no—
567D4—22no—
568D4—42no—
569D4—44no—
570D4—42no—
571D4—42no—
572D4—42no—
573D4—42no—
574D4—42no—
575D4—42no—
576D4—82no—
577D4—82no—
578D4—82no—
579D4—81no—
580D4—82no—
581D4—82no—
582D4—82no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—82no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4C11×#12011yescharacteristic
600C2×C4C11×#12011yescharacteristic
601C2×C4C11×#12011yescharacteristic
602C2×C4C22×D4×C1111yescharacteristic
603C2×C4C22×D4×C1111yescharacteristic
604C2×C4C22×D4×C1111yescharacteristic
605C8—42no—
606C8—42no—
607C8—42no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—41no—
612C22—42no—
613C22—41no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22—82no—
618C22—82no—
619C22—82no—
620C22—164no—
621C22C2×C11×#12011yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4C11×#57612yes—
635C4C11×#57712yes—
636C2—41no—
637C2—81no—
638C2—82no—
639C2—162no—
640C2C11×#300811yescharacteristic
641C2C11×#301011yescharacteristic
642C2C11×#302111yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC42C24×C11
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×#3554C2semidirect
2. C11×#3217C2semidirect
3. C11×#3208C2semidirect
4. C11×#3205C2semidirect
5. C11×#1627C2semidirect
6. C11×#1626C2semidirect
7. C11×#1621C2semidirect
8. C11×#1620C2semidirect
9. C11×#1553C2semidirect
10. C11×#1497C2semidirect
11. C11×#1482C2semidirect
14. C11×#559C22semidirect
15. C11×#557C22semidirect
17. C11×#550C22semidirect
18. D4×Q8×C11C22semidirect
49. C11×#332C22semidirect
50. C11×#331C22semidirect
51. C11×Q8⋊C8C22semidirect
52. C11×Q8⋊C8C22semidirect
53. C11×Q8⋊C8C22semidirect
54. C11×D4⋊C8C22semidirect
146. #18958C11direct (N × H)
233. #3554C2×C11semidirect
234. #3217C2×C11semidirect
235. #3208C2×C11semidirect
236. #3205C2×C11semidirect
237. #1627C2×C11semidirect
238. #1626C2×C11semidirect
239. #1621C2×C11semidirect
240. #1620C2×C11semidirect
241. #1553C2×C11semidirect
242. #1497C2×C11semidirect
243. #1482C2×C11semidirect
300. #559C22×C11semidirect
301. #557C22×C11semidirect
303. #550C22×C11semidirect
304. D4×Q8C22×C11semidirect
335. #332C22×C11semidirect
336. #331C22×C11semidirect
337. Q8⋊C8C22×C11semidirect
338. Q8⋊C8C22×C11semidirect
339. Q8⋊C8C22×C11semidirect
340. D4⋊C8C22×C11semidirect
553. C11#18958direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#35542
C11×#32172
C11×#32082
C11×#32052
C11×#16272
C11×#16262
C11×#16212
C11×#16202
C11×#15532
C11×#14972
C11×#14822
#1895811