Finite Group Databasebeta

← C11×#23422 #14600615

Subgroups — C11×#23422 #14600615

Order 2816.

2290 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C23×C11×D8C211yesmaximal, characteristic, complemented
3C2×C11×#535C211yesmaximal, characteristic, complemented
4C2×C11×#418C211yesmaximal, characteristic, complemented
5C2×C11×#416C211yesmaximal, characteristic, complemented
6C11×#2309C211yesmaximal, characteristic, complemented
7C11×#2012C214yesmaximal, complemented
8C11×#2011C214yesmaximal, complemented
9C11×#1729C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C23×D4×C11C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)—24no—
14C2×C11×AGL(1,ℤ/8)—24no—
15C2×C11×AGL(1,ℤ/8)—24no—
16C22×C11×SD16C2212yescomplemented
17C22×C11×D8—24no—
18C22×C11×D8—24no—
19C22×C11×D8—24no—
20C22×C11×D8C2214yes—
21C22×C11×D8C2212yescomplemented
22C22×C11×M16C2211yescharacteristic
23C23×C8×C11C2211yescharacteristic
24C11×#535—24no—
25C11×#535—24no—
26C2×C11×#127C2212yescomplemented
27C2×C11×#124C2212yescomplemented
28C2×C11×#121—22no—
29C2×C11×#120—22no—
30C2×C11×#117C2211yescharacteristic
31C2×C11×#117C2211yescharacteristic
32C11×#418—24no—
33C11×#416—24no—
34C2×C11×#103C2212yescomplemented
35C2×C11×#102C2212yescomplemented
36C2×C11×#102C2214yescomplemented
37C11×#390—22no—
38C11×#390C2214yescomplemented
39C11×#379—22no—
40C11×#336C2214yescomplemented
41C25×C11—21no—
42C25×C11—21no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41D414yes—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—22no—
61C22×D4×C11—24no—
62C22×D4×C11—22no—
63C22×D4×C11—22no—
64C22×D4×C11D414yes—
65C22×D4×C11D414yescomplemented
66C22×D4×C11C2312yes—
67C22×D4×C11C2312yes—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C11×AGL(1,ℤ/8)—232no—
72C2×C11×SD16—24no—
73C2×C11×SD16—24no—
74C2×C11×SD16—24no—
75C2×C11×D8—232no—
76C2×C11×D8—28no—
77C2×C11×D8—28no—
78C2×C11×D8—24no—
79C2×C11×D8—24no—
80C2×C11×D8—28no—
81C2×C11×D8—24no—
82C2×C11×M16—22no—
83C2×C11×M16—22no—
84C2×C11×M16D414yescomplemented
85C22×C8×C11—22no—
86C22×C8×C11—22no—
87C22×C8×C11D414yescomplemented
88C22×C8×C11C2312yes—
89C22×C8×C11C2312yes—
90C11×#127—24no—
91C11×#127—24no—
92C11×#124—24no—
93C11×#124—24no—
94C11×#121—216no—
95C11×#120—216no—
96C11×#117—22no—
97C11×#117—22no—
98C11×#117—22no—
99C11×#117—22no—
100C2×C11×C4⋊C4D412yes—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C22⋊C4—24no—
103C2×C11×C22⋊C4—21no—
104C2×C11×C22⋊C4—28no—
105C2×C11×C22⋊C4D412yes—
106C2×C42×C11—21no—
107C2×C42×C11C2312yes—
108C11×#103—24no—
109C11×#102—24no—
110C11×#102—28no—
111#23422C1111yesmaximal, characteristic, direct product factor, Sylow
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—21no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—42no—
118C24×C11—42no—
119C24×C11—42no—
120C24×C11—42no—
121C24×C11—84no—
122C24×C11—84no—
123C24×C11C2×D411yescharacteristic
124C11×#41—28no—
125C11×#41—28no—
126C11×#41—44no—
127C11×#41—44no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—24no—
135C2×D4×C11—216no—
136C2×D4×C11—28no—
137C2×D4×C11—28no—
138C2×D4×C11—28no—
139C2×D4×C11—24no—
140C2×D4×C11—28no—
141C2×D4×C11—24no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11—21no—
154C2×D4×C11—22no—
155C2×D4×C11—21no—
156C2×D4×C11—22no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11—44no—
160C2×D4×C11—42no—
161C2×D4×C11—44no—
162C2×D4×C11—44no—
163C2×D4×C11—44no—
164C2×D4×C11—42no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—88no—
168C2×D4×C11C2×D414yes—
169C2×D4×C11C2×D412yes—
170C2×D4×C11C2×D414yes—
171C22×C4×C11—21no—
172C22×C4×C11—24no—
173C22×C4×C11—22no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11C2×D414yes—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11#4112yes—
184C22×C4×C11C2411yescharacteristic
185C11×SD16—216no—
186C11×D8—232no—
187C11×D8—216no—
188C11×M16—28no—
189C2×C8×C11—28no—
190C2×C8×C11—22no—
191C2×C8×C11—22no—
192C2×C8×C11—22no—
193C2×C8×C11—22no—
194C2×C8×C11C2×D414yes—
195C2×C8×C11C2×D414yes—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C22⋊C4—216no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—42no—
202C11×C22⋊C4—88no—
203C42×C11—22no—
204C42×C11—22no—
205C42×C11—42no—
206C22×AGL(1,ℤ/8)C2×C1111yescharacteristic, complemented
207C23×D8C2×C1111yescharacteristic, complemented
208C2×#535C2×C1111yescharacteristic, complemented
209C2×#418C2×C1111yescharacteristic, complemented
210C2×#416C2×C1111yescharacteristic, complemented
211#2309C2×C1111yescharacteristic, complemented
212#2012C2×C1114yescomplemented
213#2011C2×C1114yescomplemented
214#1729C2×C1111yescharacteristic, complemented
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—41no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—48no—
226C23×C11—44no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11—88no—
231C23×C11—88no—
232C23×C11—88no—
233C23×C11—88no—
234C23×C11—88no—
235C23×C11—88no—
236C23×C11#12012yes—
237C23×C11#12112yes—
238C23×C11#12712yes—
239C23×C11C22×D411yescharacteristic
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—41no—
243Q8×C11—41no—
244D4×C11—24no—
245D4×C11—24no—
246D4×C11—22no—
247D4×C11—24no—
248D4×C11—24no—
249D4×C11—22no—
250D4×C11—48no—
251D4×C11—42no—
252D4×C11—41no—
253D4×C11—42no—
254D4×C11—42no—
255D4×C11—42no—
256D4×C11—41no—
257D4×C11—48no—
258D4×C11—48no—
259D4×C11—816no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—28no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—48no—
266C2×C4×C11—42no—
267C2×C4×C11—44no—
268C2×C4×C11#12014yes—
269C2×C4×C11#12014yes—
270C2×C4×C11#12012yes—
271C2×C4×C11#12114yes—
272C2×C4×C11#12114yes—
273C2×C4×C11#12112yes—
274C2×C4×C11#12712yes—
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C8×C11—24no—
282C8×C11—24no—
283C22×#41C22×C1111yescharacteristic
284C23×D4C22×C1111yescharacteristic
285C23×D4C22×C1111yescharacteristic
286C2×AGL(1,ℤ/8)—24no—
287C2×AGL(1,ℤ/8)—24no—
288C2×AGL(1,ℤ/8)—24no—
289C22×SD16C22×C1112yescomplemented
290C22×D8—24no—
291C22×D8—24no—
292C22×D8—24no—
293C22×D8C22×C1114yes—
294C22×D8C22×C1112yescomplemented
295C22×M16C22×C1111yescharacteristic
296C23×C8C22×C1111yescharacteristic
297#535—24no—
298#535—24no—
299C2×#127C22×C1112yescomplemented
300C2×#124C22×C1112yescomplemented
301C2×#121—22no—
302C2×#120—22no—
303C2×#117C22×C1111yescharacteristic
304C2×#117C22×C1111yescharacteristic
305#418—24no—
306#416—24no—
307C2×#103C22×C1112yescomplemented
308C2×#102C22×C1112yescomplemented
309C2×#102C22×C1114yescomplemented
310#390—22no—
311#390C22×C1114yescomplemented
312#379—22no—
313#336C22×C1114yescomplemented
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—24no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—48no—
322C22×C11—48no—
323C22×C11—816no—
324C22×C11—816no—
325C22×C11—82no—
326C22×C11—84no—
327C22×C11—84no—
328C22×C11—84no—
329C22×C11—82no—
330C22×C11—84no—
331C22×C11#39214yes—
332C22×C11C2×#12011yescharacteristic
333C22×C11C2×#12111yescharacteristic
334C22×C11C2×#12711yescharacteristic
335C22×C11#57614yes—
336C4×C11—42no—
337C4×C11—44no—
338C4×C11—82no—
339C4×C11#39214yes—
340C4×C11C2×#12011yescharacteristic
341C4×C11C2×#12011yescharacteristic
342C4×C11C2×#12111yescharacteristic
343C4×C11C2×#12111yescharacteristic
344C25—21no—
345C25—21no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41D4×C1114yes—
352C22×Q8C23×C1111yescharacteristic
353C22×D4—21no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—21no—
362C22×D4—22no—
363C22×D4—21no—
364C22×D4—24no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4D4×C1114yes—
368C22×D4D4×C1114yescomplemented
369C22×D4C23×C1112yes—
370C22×D4C23×C1111yescharacteristic
371C22×D4C23×C1112yes—
372C23×C4—21no—
373C23×C4C23×C1111yescharacteristic
374AGL(1,ℤ/8)—232no—
375C2×SD16—24no—
376C2×SD16—24no—
377C2×SD16—24no—
378C2×D8—232no—
379C2×D8—28no—
380C2×D8—28no—
381C2×D8—24no—
382C2×D8—24no—
383C2×D8—28no—
384C2×D8—24no—
385C2×M16—22no—
386C2×M16—22no—
387C2×M16D4×C1114yescomplemented
388C22×C8—22no—
389C22×C8—22no—
390C22×C8D4×C1114yescomplemented
391C22×C8C23×C1112yes—
392C22×C8C23×C1112yes—
393#127—24no—
394#127—24no—
395#124—24no—
396#124—24no—
397#121—216no—
398#120—216no—
399#117—22no—
400#117—22no—
401#117—22no—
402#117—22no—
403C2×C4⋊C4D4×C1112yes—
404C2×C4⋊C4C23×C1112yes—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4D4×C1112yes—
409C2×C42—21no—
410C2×C42C23×C1112yes—
411#103—24no—
412#102—24no—
413#102—28no—
414C2×C11—24no—
415C2×C11—82no—
416C2×C11—84no—
417C2×C11—84no—
418C2×C11C2×#39211yescharacteristic
419C2×C11#300812yes—
420C2×C11#304112yes—
421C2×C11#315512yes—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—24no—
426C24—24no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—84no—
432C24—84no—
433C24C2×D4×C1111yescharacteristic
434#41—28no—
435#41—28no—
436#41—44no—
437#41—44no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8C2×D4×C1112yes—
444C2×D4—24no—
445C2×D4—216no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—24no—
450C2×D4—28no—
451C2×D4—24no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—44no—
470C2×D4—42no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—88no—
478C2×D4C2×D4×C1114yes—
479C2×D4C2×D4×C1112yes—
480C2×D4C2×D4×C1114yes—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4C2×D4×C1114yes—
487C22×C4C2×D4×C1112yes—
488C22×C4C2×D4×C1112yes—
489C22×C4C2×D4×C1112yes—
490C22×C4C2×D4×C1111yescharacteristic
491C22×C4C2×D4×C1112yes—
492C22×C4C2×D4×C1112yes—
493C22×C4C11×#4112yes—
494C22×C4C24×C1111yescharacteristic
495SD16—216no—
496D8—232no—
497D8—216no—
498M16—28no—
499C2×C8—28no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8C2×D4×C1114yes—
505C2×C8C2×D4×C1114yes—
506C4⋊C4—24no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C22⋊C4—216no—
510C22⋊C4—24no—
511C22⋊C4—42no—
512C22⋊C4—88no—
513C42—22no—
514C42—22no—
515C42—42no—
516C11#2342211yescharacteristic, direct product factor, Sylow
517C23—24no—
518C23—24no—
519C23—22no—
520C23—24no—
521C23—42no—
522C23—41no—
523C23—42no—
524C23—48no—
525C23—48no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—48no—
530C23—44no—
531C23—48no—
532C23—88no—
533C23—88no—
534C23—88no—
535C23—88no—
536C23—88no—
537C23—88no—
538C23C11×#12012yes—
539C23C11×#12112yes—
540C23C11×#12712yes—
541C23C22×D4×C1111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546D4—24no—
547D4—24no—
548D4—22no—
549D4—24no—
550D4—24no—
551D4—22no—
552D4—48no—
553D4—42no—
554D4—41no—
555D4—42no—
556D4—42no—
557D4—42no—
558D4—41no—
559D4—48no—
560D4—48no—
561D4—816no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—28no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—48no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4C11×#12014yes—
571C2×C4C11×#12014yes—
572C2×C4C11×#12012yes—
573C2×C4C11×#12114yes—
574C2×C4C11×#12114yes—
575C2×C4C11×#12112yes—
576C2×C4C11×#12712yes—
577C2×C4C22×D4×C1111yescharacteristic
578C2×C4C22×D4×C1111yescharacteristic
579C2×C4C22×D4×C1111yescharacteristic
580C2×C4C22×D4×C1111yescharacteristic
581C2×C4C22×D4×C1111yescharacteristic
582C2×C4C2×C11×#4111yescharacteristic
583C8—24no—
584C8—24no—
585C22—24no—
586C22—24no—
587C22—24no—
588C22—42no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—48no—
593C22—48no—
594C22—816no—
595C22—816no—
596C22—84no—
597C22—84no—
598C22—82no—
599C22—84no—
600C22—84no—
601C22—82no—
602C22C11×#39214yes—
603C22C2×C11×#12011yescharacteristic
604C22C2×C11×#12111yescharacteristic
605C22C2×C11×#12711yescharacteristic
606C22C11×#57614yes—
607C4—42no—
608C4—44no—
609C4—82no—
610C4C11×#39214yes—
611C4C2×C11×#12011yescharacteristic
612C4C2×C11×#12011yescharacteristic
613C4C2×C11×#12111yescharacteristic
614C4C2×C11×#12111yescharacteristic
615C2—24no—
616C2—84no—
617C2—84no—
618C2—82no—
619C2C2×C11×#39211yescharacteristic
620C2C11×#300812yes—
621C2C11×#304112yes—
622C2C11×#315512yes—
subgroupG/H
center, socleC23×C11C22×D4
commutator, Frattini, cosocleC22×C4C24×C11
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×AGL(1,ℤ/8)C2semidirect
2. C23×C11×D8C2semidirect
3. C2×C11×#535C2semidirect
4. C2×C11×#418C2semidirect
5. C2×C11×#416C2semidirect
6. C11×#2309C2semidirect
7. C11×#2012C2semidirect
8. C11×#2011C2semidirect
9. C11×#1729C2semidirect
16. C22×C11×SD16C22semidirect
21. C22×C11×D8C22semidirect
26. C2×C11×#127C22semidirect
27. C2×C11×#124C22semidirect
34. C2×C11×#103C22semidirect
35. C2×C11×#102C22semidirect
36. C2×C11×#102C22semidirect
38. C11×#390C22semidirect
40. C11×#336C22semidirect
65. C22×D4×C11D4semidirect
84. C2×C11×M16D4semidirect
87. C22×C8×C11D4semidirect
111. #23422C11direct (N × H)
206. C22×AGL(1,ℤ/8)C2×C11semidirect
207. C23×D8C2×C11semidirect
208. C2×#535C2×C11semidirect
209. C2×#418C2×C11semidirect
210. C2×#416C2×C11semidirect
211. #2309C2×C11semidirect
212. #2012C2×C11semidirect
213. #2011C2×C11semidirect
214. #1729C2×C11semidirect
289. C22×SD16C22×C11semidirect
294. C22×D8C22×C11semidirect
299. C2×#127C22×C11semidirect
300. C2×#124C22×C11semidirect
307. C2×#103C22×C11semidirect
308. C2×#102C22×C11semidirect
309. C2×#102C22×C11semidirect
311. #390C22×C11semidirect
313. #336C22×C11semidirect
368. C22×D4D4×C11semidirect
387. C2×M16D4×C11semidirect
390. C22×C8D4×C11semidirect
516. C11#23422direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×AGL(1,ℤ/8)2
C23×C11×D82
C2×C11×#5352
C2×C11×#4182
C2×C11×#4162
C11×#23092
C11×#20122
C11×#20112
C11×#17292
#2342211