Finite Group Databasebeta

← C127×#18459 #44582132

Subgroups — C127×#18459 #44582132

Order 32512.

972 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3561C211yesmaximal, characteristic, complemented
2C127×#3215C211yesmaximal, characteristic, complemented
3C127×#3211C211yesmaximal, characteristic, complemented
4C127×#2819C211yesmaximal, characteristic, complemented
5C127×#1606C212yesmaximal, complemented
6C127×#1602C212yesmaximal, complemented
7C127×#1600C212yesmaximal, complemented
8C127×#1596C212yesmaximal, complemented
9C127×#1518C211yesmaximal, characteristic, complemented
10C127×#1512C211yesmaximal, characteristic, complemented
11C127×#1469C211yesmaximal, characteristic, complemented
12#563×C127—21no—
13#562×C127—21no—
14#556×C127—21no—
15#551×C127—22no—
16D4×Q8×C127—21no—
17#548×C127—21no—
18#546×C127—21no—
19#543×C127C2212yes—
20#542×C127—21no—
21#542×C127—22no—
22#538×C127C2212yes—
23#536×C127—21no—
24#533×C127C2211yescharacteristic
25#529×C127C2211yescharacteristic
26C2×#124×C127C2211yescharacteristic
27C2×#124×C127C2211yescharacteristic
28#497×C127—21no—
29#495×C127—21no—
30#489×C127—21no—
31#488×C127—21no—
32#464×C127—21no—
33#464×C127—22no—
34#463×C127—21no—
35#451×C127C2211yescharacteristic
36#451×C127C2212yes—
37#450×C127C2211yescharacteristic
38#450×C127C2212yes—
39#448×C127C2211yescharacteristic
40#447×C127C2211yescharacteristic
41#432×C127C2211yescharacteristic
42#431×C127C2211yescharacteristic
43#394×C127—22no—
44#393×C127—21no—
45#393×C127C2212yes—
46#392×C127—21no—
47#392×C127C2212yes—
48#382×C127C2211yescharacteristic
49#328×C127C2212yes—
50#328×C127C2212yes—
51#328×C127C2212yes—
52#327×C127C2212yes—
53#323×C127C2212yes—
54#323×C127C2212yes—
55C2×#41×C127—21no—
56C22×Q8×C127—21no—
57C22×Q8×C127D411yescharacteristic
58C22×Q8×C127C2311yescharacteristic
59C22×D4×C127—22no—
60C22×D4×C127D411yescharacteristic
61C22×D4×C127C2311yescharacteristic
62C2×Q16×C127—22no—
63C2×Q16×C127—21no—
64C2×SD16×C127—22no—
65C2×SD16×C127—21no—
66C2×SD16×C127—21no—
67C2×D8×C127—21no—
68C4⋊Q8×C127—21no—
69C4⋊Q8×C127—22no—
70C4⋊Q8×C127D411yescharacteristic, complemented
71C4⋊Q8×C127D411yescharacteristic, complemented
72#126×C127—22no—
73#126×C127—22no—
74#126×C127—22no—
75#126×C127—21no—
76#125×C127—21no—
77#125×C127D411yescharacteristic, complemented
78#124×C127—21no—
79#124×C127—22no—
80#124×C127—22no—
81#124×C127—21no—
82#124×C127—21no—
83#124×C127—21no—
84#124×C127—21no—
85#124×C127—21no—
86#124×C127—21no—
87#124×C127—21no—
88#124×C127—21no—
89#124×C127D411yescharacteristic, complemented
90#123×C127—22no—
91#123×C127—22no—
92#123×C127—22no—
93#123×C127—21no—
94#123×C127—22no—
95C22⋊Q8×C127—22no—
96C22⋊Q8×C127—21no—
97C22⋊Q8×C127—22no—
98C22⋊Q8×C127—22no—
99C22⋊Q8×C127—22no—
100C22⋊Q8×C127—21no—
101C22⋊Q8×C127—22no—
102C22⋊Q8×C127—22no—
103C22⋊Q8×C127—22no—
104C22⋊Q8×C127C2311yescharacteristic
105C22⋊Q8×C127C2312yes—
106#121×C127—21no—
107#121×C127—22no—
108#121×C127—22no—
109#121×C127C2311yescharacteristic
110#120×C127—22no—
111C4×Q8×C127—21no—
112C4×Q8×C127—21no—
113C4×Q8×C127D411yescharacteristic, complemented
114C4×Q8×C127D412yescomplemented
115C4×D4×C127—21no—
116C4×D4×C127—22no—
117C4×D4×C127—21no—
118C4×D4×C127—22no—
119C4×D4×C127D411yescharacteristic, complemented
120#117×C127—22no—
121#117×C127—21no—
122#117×C127—21no—
123C2×C4⋊C4×C127—21no—
124C2×C22⋊C4×C127—22no—
125C2×C22⋊C4×C127—21no—
126C2×C22⋊C4×C127—21no—
127C2×C22⋊C4×C127—22no—
128C2×C22⋊C4×C127—22no—
129C2×C22⋊C4×C127D412yes—
130C2×C22⋊C4×C127C2312yes—
131C2×C42×C127C2311yescharacteristic
132C4⋊C8×C127—21no—
133C4⋊C8×C127—21no—
134#103×C127—21no—
135#103×C127—21no—
136#103×C127—22no—
137#102×C127—21no—
138#102×C127—21no—
139#102×C127—22no—
140C22⋊C8×C127C2312yes—
141C22⋊C8×C127C2311yescharacteristic
142C22⋊C8×C127C2311yescharacteristic
143#97×C127—21no—
144C4×C8×C127—21no—
145#95×C127—21no—
146#95×C127—22no—
147#95×C127C2312yes—
148C24×C127—21no—
149C24×C127C2×D412yes—
150#41×C127—82no—
151C2×Q8×C127—22no—
152C2×Q8×C127—21no—
153C2×Q8×C127—21no—
154C2×Q8×C127—21no—
155C2×Q8×C127—21no—
156C2×Q8×C127—21no—
157C2×Q8×C127—81no—
158C2×Q8×C127—81no—
159C2×Q8×C127—82no—
160C2×Q8×C127C2×D411yescharacteristic
161C2×Q8×C127C2×D412yes—
162C2×D4×C127—21no—
163C2×D4×C127—22no—
164C2×D4×C127—22no—
165C2×D4×C127—21no—
166C2×D4×C127—21no—
167C2×D4×C127—21no—
168C2×D4×C127—21no—
169C2×D4×C127—81no—
170C2×D4×C127—81no—
171C2×D4×C127—82no—
172C2×D4×C127—82no—
173C2×D4×C127—82no—
174C2×D4×C127C2×D411yescharacteristic
175C22×C4×C127—22no—
176C22×C4×C127—22no—
177C22×C4×C127—22no—
178C22×C4×C127—21no—
179C22×C4×C127—22no—
180C22×C4×C127—21no—
181C22×C4×C127C2×D411yescharacteristic
182C22×C4×C127C2×D412yes—
183C22×C4×C127C2×D411yescharacteristic
184C22×C4×C127C2411yescharacteristic
185Q16×C127—81no—
186Q16×C127—82no—
187SD16×C127—81no—
188SD16×C127—81no—
189SD16×C127—82no—
190D8×C127—81no—
191C2×C8×C127—21no—
192C2×C8×C127—21no—
193C2×C8×C127—22no—
194C4⋊C4×C127—22no—
195C4⋊C4×C127—22no—
196C4⋊C4×C127—22no—
197C4⋊C4×C127—22no—
198C4⋊C4×C127—21no—
199C4⋊C4×C127—21no—
200C4⋊C4×C127—21no—
201C4⋊C4×C127—21no—
202C4⋊C4×C127—21no—
203C4⋊C4×C127—21no—
204C4⋊C4×C127—22no—
205C4⋊C4×C127—21no—
206C4⋊C4×C127—22no—
207C4⋊C4×C127—81no—
208C4⋊C4×C127C2×D411yescharacteristic
209C4⋊C4×C127C2×D411yescharacteristic
210C4⋊C4×C127C2×D412yes—
211C22⋊C4×C127—22no—
212C22⋊C4×C127—22no—
213C22⋊C4×C127—22no—
214C22⋊C4×C127—22no—
215C22⋊C4×C127—22no—
216C22⋊C4×C127—21no—
217C22⋊C4×C127—22no—
218C22⋊C4×C127—22no—
219C22⋊C4×C127—22no—
220C22⋊C4×C127—21no—
221C22⋊C4×C127—21no—
222C22⋊C4×C127—21no—
223C22⋊C4×C127—22no—
224C22⋊C4×C127—22no—
225C22⋊C4×C127—21no—
226C22⋊C4×C127—41no—
227C22⋊C4×C127—41no—
228C22⋊C4×C127—41no—
229C22⋊C4×C127—41no—
230C22⋊C4×C127—82no—
231C22⋊C4×C127—82no—
232C42×C127—22no—
233C42×C127—22no—
234C42×C127—21no—
235C42×C127C2×D411yescharacteristic
236C42×C127C2×D411yescharacteristic
237C42×C127C2×D411yescharacteristic
238C42×C127C2×D411yescharacteristic
239C23×C127—22no—
240C23×C127—21no—
241C23×C127—22no—
242C23×C127—22no—
243C23×C127—42no—
244C23×C127—42no—
245C23×C127—42no—
246C23×C127—42no—
247C23×C127—41no—
248C23×C127—41no—
249C23×C127—41no—
250C23×C127C22×D411yescharacteristic
251Q8×C127—41no—
252Q8×C127—42no—
253Q8×C127—42no—
254Q8×C127—42no—
255Q8×C127—41no—
256Q8×C127—41no—
257Q8×C127—42no—
258Q8×C127—81no—
259Q8×C127—82no—
260D4×C127—41no—
261D4×C127—42no—
262D4×C127—41no—
263D4×C127—41no—
264D4×C127—42no—
265D4×C127—41no—
266D4×C127—41no—
267D4×C127—81no—
268D4×C127—82no—
269D4×C127—82no—
270D4×C127—88no—
271C2×C4×C127—21no—
272C2×C4×C127—21no—
273C2×C4×C127—21no—
274C2×C4×C127—22no—
275C2×C4×C127—21no—
276C2×C4×C127—22no—
277C2×C4×C127—22no—
278C2×C4×C127—21no—
279C2×C4×C127—41no—
280C2×C4×C127—41no—
281C2×C4×C127—42no—
282C2×C4×C127—42no—
283C2×C4×C127—42no—
284C2×C4×C127—42no—
285C2×C4×C127—42no—
286C2×C4×C127—41no—
287C2×C4×C127—42no—
288C2×C4×C127—82no—
289C2×C4×C127—82no—
290C2×C4×C127—82no—
291C2×C4×C127#12011yescharacteristic
292C2×C4×C127#12011yescharacteristic
293C2×C4×C127#12011yescharacteristic
294C2×C4×C127#12011yescharacteristic
295C2×C4×C127C22×D411yescharacteristic
296C2×C4×C127C22×D411yescharacteristic
297C8×C127—41no—
298C8×C127—41no—
299C8×C127—42no—
300C22×C127—21no—
301C22×C127—21no—
302C22×C127—41no—
303C22×C127—42no—
304C22×C127—41no—
305C22×C127—42no—
306C22×C127—42no—
307C22×C127—41no—
308C22×C127—82no—
309C22×C127—82no—
310C22×C127—82no—
311C22×C127—82no—
312C22×C127—81no—
313C22×C127—81no—
314C22×C127—81no—
315C22×C127C2×#12011yescharacteristic
316C22×C127#57711yescharacteristic
317C22×C127#57811yescharacteristic
318C4×C127—21no—
319C4×C127—21no—
320C4×C127—21no—
321C4×C127—21no—
322C4×C127—21no—
323C4×C127—21no—
324C4×C127—41no—
325C4×C127—41no—
326C4×C127—42no—
327C4×C127—42no—
328C4×C127—41no—
329C4×C127—42no—
330C4×C127—82no—
331C4×C127—81no—
332#18459C12711yesmaximal, characteristic, direct product factor, Sylow
333C2×C127—21no—
334C2×C127—21no—
335C2×C127—81no—
336C2×C127—82no—
337C2×C127—161no—
338C2×C127#301311yescharacteristic
339C2×C127#301911yescharacteristic
340C2×C127#302711yescharacteristic
341#3561C2×C12711yescharacteristic, complemented
342#3215C2×C12711yescharacteristic, complemented
343#3211C2×C12711yescharacteristic, complemented
344#2819C2×C12711yescharacteristic, complemented
345#1606C2×C12712yescomplemented
346#1602C2×C12712yescomplemented
347#1600C2×C12712yescomplemented
348#1596C2×C12712yescomplemented
349#1518C2×C12711yescharacteristic, complemented
350#1512C2×C12711yescharacteristic, complemented
351#1469C2×C12711yescharacteristic, complemented
352C127#1845911yescharacteristic, direct product factor, Sylow
353#563—21no—
354#562—21no—
355#556—21no—
356#551—22no—
357D4×Q8—21no—
358#548—21no—
359#546—21no—
360#543C22×C12712yes—
361#542—21no—
362#542—22no—
363#538C22×C12712yes—
364#536—21no—
365#533C22×C12711yescharacteristic
366#529C22×C12711yescharacteristic
367C2×#124C22×C12711yescharacteristic
368C2×#124C22×C12711yescharacteristic
369#497—21no—
370#495—21no—
371#489—21no—
372#488—21no—
373#464—21no—
374#464—22no—
375#463—21no—
376#451C22×C12711yescharacteristic
377#451C22×C12712yes—
378#450C22×C12711yescharacteristic
379#450C22×C12712yes—
380#448C22×C12711yescharacteristic
381#447C22×C12711yescharacteristic
382#432C22×C12711yescharacteristic
383#431C22×C12711yescharacteristic
384#394—22no—
385#393—21no—
386#393C22×C12712yes—
387#392—21no—
388#392C22×C12712yes—
389#382C22×C12711yescharacteristic
390#328C22×C12712yes—
391#328C22×C12712yes—
392#328C22×C12712yes—
393#327C22×C12712yes—
394#323C22×C12712yes—
395#323C22×C12712yes—
396C2×#41—21no—
397C22×Q8—21no—
398C22×Q8D4×C12711yescharacteristic
399C22×Q8C23×C12711yescharacteristic
400C22×D4—22no—
401C22×D4D4×C12711yescharacteristic
402C22×D4C23×C12711yescharacteristic
403C2×Q16—21no—
404C2×Q16—22no—
405C2×SD16—21no—
406C2×SD16—22no—
407C2×SD16—21no—
408C2×D8—21no—
409C4⋊Q8—21no—
410C4⋊Q8—22no—
411C4⋊Q8D4×C12711yescharacteristic, complemented
412C4⋊Q8D4×C12711yescharacteristic, complemented
413#126—22no—
414#126—22no—
415#126—22no—
416#126—21no—
417#125—21no—
418#125D4×C12711yescharacteristic, complemented
419#124—21no—
420#124—22no—
421#124—22no—
422#124—21no—
423#124—21no—
424#124—21no—
425#124—21no—
426#124—21no—
427#124—21no—
428#124—21no—
429#124—21no—
430#124D4×C12711yescharacteristic, complemented
431#123—22no—
432#123—22no—
433#123—22no—
434#123—21no—
435#123—22no—
436C22⋊Q8—22no—
437C22⋊Q8—21no—
438C22⋊Q8—22no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—21no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—22no—
445C22⋊Q8C23×C12711yescharacteristic
446C22⋊Q8C23×C12712yes—
447#121—21no—
448#121—22no—
449#121—22no—
450#121C23×C12711yescharacteristic
451#120—22no—
452C4×Q8—21no—
453C4×Q8—21no—
454C4×Q8D4×C12711yescharacteristic, complemented
455C4×Q8D4×C12712yescomplemented
456C4×D4—21no—
457C4×D4—22no—
458C4×D4—21no—
459C4×D4—22no—
460C4×D4D4×C12711yescharacteristic, complemented
461#117—22no—
462#117—21no—
463#117—21no—
464C2×C4⋊C4—21no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4D4×C12712yes—
471C2×C22⋊C4C23×C12712yes—
472C2×C42C23×C12711yescharacteristic
473C4⋊C8—21no—
474C4⋊C8—21no—
475#103—21no—
476#103—21no—
477#103—22no—
478#102—21no—
479#102—21no—
480#102—22no—
481C22⋊C8C23×C12712yes—
482C22⋊C8C23×C12711yescharacteristic
483C22⋊C8C23×C12711yescharacteristic
484#97—21no—
485C4×C8—21no—
486#95—21no—
487#95—22no—
488#95C23×C12712yes—
489C24—21no—
490C24C2×D4×C12712yes—
491#41—82no—
492C2×Q8—22no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—81no—
499C2×Q8—81no—
500C2×Q8—82no—
501C2×Q8C2×D4×C12711yescharacteristic
502C2×Q8C2×D4×C12712yes—
503C2×D4—21no—
504C2×D4—22no—
505C2×D4—22no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—81no—
511C2×D4—81no—
512C2×D4—82no—
513C2×D4—82no—
514C2×D4—82no—
515C2×D4C2×D4×C12711yescharacteristic
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4C2×D4×C12711yescharacteristic
523C22×C4C2×D4×C12712yes—
524C22×C4C2×D4×C12711yescharacteristic
525C22×C4C24×C12711yescharacteristic
526Q16—81no—
527Q16—82no—
528SD16—81no—
529SD16—81no—
530SD16—82no—
531D8—81no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—22no—
546C4⋊C4—21no—
547C4⋊C4—22no—
548C4⋊C4—81no—
549C4⋊C4C2×D4×C12711yescharacteristic
550C4⋊C4C2×D4×C12711yescharacteristic
551C4⋊C4C2×D4×C12712yes—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—21no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—21no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—82no—
572C22⋊C4—82no—
573C42—22no—
574C42—22no—
575C42—21no—
576C42C2×D4×C12711yescharacteristic
577C42C2×D4×C12711yescharacteristic
578C42C2×D4×C12711yescharacteristic
579C42C2×D4×C12711yescharacteristic
580C23—22no—
581C23—21no—
582C23—22no—
583C23—22no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23C22×D4×C12711yescharacteristic
592Q8—41no—
593Q8—42no—
594Q8—42no—
595Q8—42no—
596Q8—41no—
597Q8—41no—
598Q8—42no—
599Q8—81no—
600Q8—82no—
601D4—41no—
602D4—42no—
603D4—41no—
604D4—41no—
605D4—42no—
606D4—41no—
607D4—41no—
608D4—81no—
609D4—82no—
610D4—82no—
611D4—88no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—82no—
630C2×C4—82no—
631C2×C4—82no—
632C2×C4#120×C12711yescharacteristic
633C2×C4#120×C12711yescharacteristic
634C2×C4#120×C12711yescharacteristic
635C2×C4#120×C12711yescharacteristic
636C2×C4C22×D4×C12711yescharacteristic
637C2×C4C22×D4×C12711yescharacteristic
638C8—41no—
639C8—41no—
640C8—42no—
641C22—21no—
642C22—21no—
643C22—41no—
644C22—42no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—41no—
649C22—82no—
650C22—82no—
651C22—82no—
652C22—82no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22C2×#120×C12711yescharacteristic
657C22#577×C12711yescharacteristic
658C22#578×C12711yescharacteristic
659C4—21no—
660C4—21no—
661C4—21no—
662C4—21no—
663C4—21no—
664C4—21no—
665C4—41no—
666C4—41no—
667C4—42no—
668C4—42no—
669C4—41no—
670C4—42no—
671C4—82no—
672C4—81no—
673C2—21no—
674C2—21no—
675C2—82no—
676C2—81no—
677C2—161no—
678C2C127×#301311yescharacteristic
679C2C127×#301911yescharacteristic
680C2C127×#302711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3561C2semidirect
2. C127×#3215C2semidirect
3. C127×#3211C2semidirect
4. C127×#2819C2semidirect
5. C127×#1606C2semidirect
6. C127×#1602C2semidirect
7. C127×#1600C2semidirect
8. C127×#1596C2semidirect
9. C127×#1518C2semidirect
10. C127×#1512C2semidirect
11. C127×#1469C2semidirect
70. C4⋊Q8×C127D4semidirect
71. C4⋊Q8×C127D4semidirect
77. #125×C127D4semidirect
89. #124×C127D4semidirect
113. C4×Q8×C127D4semidirect
114. C4×Q8×C127D4semidirect
119. C4×D4×C127D4semidirect
332. #18459C127direct (N × H)
341. #3561C2×C127semidirect
342. #3215C2×C127semidirect
343. #3211C2×C127semidirect
344. #2819C2×C127semidirect
345. #1606C2×C127semidirect
346. #1602C2×C127semidirect
347. #1600C2×C127semidirect
348. #1596C2×C127semidirect
349. #1518C2×C127semidirect
350. #1512C2×C127semidirect
351. #1469C2×C127semidirect
352. C127#18459direct (N × H)
411. C4⋊Q8D4×C127semidirect
412. C4⋊Q8D4×C127semidirect
418. #125D4×C127semidirect
430. #124D4×C127semidirect
454. C4×Q8D4×C127semidirect
455. C4×Q8D4×C127semidirect
460. C4×D4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35612
C127×#32152
C127×#32112
C127×#28192
C127×#16062
C127×#16022
C127×#16002
C127×#15962
C127×#15182
C127×#15122
C127×#14692
#18459127