Finite Group Databasebeta

← C127×#19307 #44582980

Subgroups — C127×#19307 #44582980

Order 32512.

656 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3185C211yesmaximal, characteristic, complemented
2C127×#3110C211yesmaximal, characteristic
3C127×#3077C211yesmaximal, characteristic
4D4×M16×C127C211yesmaximal, characteristic
5C127×#1703C211yesmaximal, characteristic, complemented
6C127×#1699C211yesmaximal, characteristic, complemented
7C127×#1691C211yesmaximal, characteristic, complemented
8C127×#1689C211yesmaximal, characteristic, complemented
9C127×#1683C211yesmaximal, characteristic, complemented
10C127×#1679C211yesmaximal, characteristic, complemented
11C127×#1671C211yesmaximal, characteristic, complemented
12C127×#1669C211yesmaximal, characteristic, complemented
13C127×#1569C211yesmaximal, characteristic, complemented
14C127×#1561C211yesmaximal, characteristic, complemented
15C127×#1559C211yesmaximal, characteristic, complemented
16C22×M16×C127—21no—
17#533×C127C2211yescharacteristic
18#533×C127C2211yescharacteristic
19C2×C4×D4×C127C2211yescharacteristic
20#498×C127C2211yescharacteristic, complemented
21#494×C127C2211yescharacteristic, complemented
22#487×C127C2211yescharacteristic, complemented
23#487×C127C2211yescharacteristic, complemented
24#484×C127—21no—
25#478×C127—21no—
26#478×C127—21no—
27#476×C127C2211yescharacteristic
28#476×C127C2211yescharacteristic
29#474×C127C2211yescharacteristic
30#474×C127C2211yescharacteristic
31#474×C127C2211yescharacteristic
32#474×C127C2211yescharacteristic
33#470×C127—21no—
34#470×C127—21no—
35#461×C127C2211yescharacteristic
36#461×C127C2211yescharacteristic
37#450×C127—21no—
38#441×C127—21no—
39#441×C127—21no—
40#440×C127—21no—
41#440×C127—21no—
42#436×C127C2211yescharacteristic
43#436×C127C2211yescharacteristic
44#435×C127—21no—
45#435×C127—21no—
46C8×D4×C127C2211yescharacteristic
47C8×D4×C127C2211yescharacteristic
48#432×C127C2211yescharacteristic
49#428×C127—21no—
50#423×C127C2211yescharacteristic
51#423×C127C2211yescharacteristic
52#418×C127—21no—
53#407×C127—21no—
54C4×M16×C127C2211yescharacteristic
55#335×C127C2211yescharacteristic, complemented
56#335×C127C2211yescharacteristic, complemented
57#334×C127C2211yescharacteristic, complemented
58#334×C127C2211yescharacteristic, complemented
59#333×C127C2211yescharacteristic, complemented
60#333×C127C2211yescharacteristic, complemented
61#332×C127C2211yescharacteristic, complemented
62#332×C127C2211yescharacteristic, complemented
63#332×C127C2211yescharacteristic, complemented
64#332×C127C2211yescharacteristic, complemented
65#332×C127C2211yescharacteristic, complemented
66#332×C127C2211yescharacteristic, complemented
67C22×D4×C127D411yescharacteristic
68C23×C4×C127—21no—
69C2×Q16×C127—21no—
70C2×Q16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×M16×C127—21no—
74C2×M16×C127—21no—
75C2×M16×C127—21no—
76C2×M16×C127—21no—
77C2×M16×C127—44no—
78C2×M16×C127D411yescharacteristic
79C2×M16×C127D411yescharacteristic
80C22×C8×C127—21no—
81C22×C8×C127—21no—
82C4⋊Q8×C127C2311yescharacteristic
83C4⋊Q8×C127C2311yescharacteristic
84C4⋊Q8×C127C2311yescharacteristic
85C4⋊Q8×C127C2311yescharacteristic
86#125×C127—21no—
87#125×C127—21no—
88C22⋊Q8×C127—21no—
89C22⋊Q8×C127—21no—
90C22⋊Q8×C127—21no—
91C22⋊Q8×C127—21no—
92C4×Q8×C127—21no—
93C4×Q8×C127—21no—
94C4×Q8×C127—21no—
95C4×Q8×C127—21no—
96C4×D4×C127—21no—
97C4×D4×C127—21no—
98C4×D4×C127D411yescharacteristic
99C4×D4×C127D411yescharacteristic
100C4×D4×C127C2311yescharacteristic
101C4×D4×C127C2311yescharacteristic
102#117×C127—21no—
103#117×C127—21no—
104C2×C4⋊C4×C127D411yescharacteristic
105C2×C22⋊C4×C127—21no—
106C2×C42×C127C2311yescharacteristic
107#107×C127—21no—
108#107×C127—21no—
109#107×C127—21no—
110#107×C127—21no—
111#106×C127—21no—
112#106×C127—21no—
113#106×C127—21no—
114#106×C127—21no—
115C4⋊C8×C127—21no—
116C4⋊C8×C127—21no—
117C4⋊C8×C127C2311yescharacteristic
118C4⋊C8×C127C2311yescharacteristic
119C4⋊C8×C127C2311yescharacteristic
120C4⋊C8×C127C2311yescharacteristic
121C4⋊C8×C127C2311yescharacteristic
122C4⋊C8×C127C2311yescharacteristic
123#103×C127—21no—
124#103×C127—21no—
125#103×C127—21no—
126#103×C127—21no—
127#103×C127—21no—
128#103×C127—21no—
129#102×C127—21no—
130#102×C127—21no—
131#102×C127—21no—
132#102×C127—21no—
133#102×C127—21no—
134#102×C127—21no—
135C22⋊C8×C127—21no—
136C22⋊C8×C127—21no—
137C22⋊C8×C127—21no—
138C22⋊C8×C127—21no—
139C22⋊C8×C127—21no—
140#97×C127—21no—
141#97×C127D411yescharacteristic
142#97×C127D411yescharacteristic
143C4×C8×C127C2311yescharacteristic
144C4×C8×C127C2311yescharacteristic
145C24×C127—21no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127—21no—
149C2×Q8×C127—21no—
150C2×D4×C127—22no—
151C2×D4×C127—21no—
152C2×D4×C127—41no—
153C2×D4×C127C2×D411yescharacteristic
154C2×D4×C127C2×D411yescharacteristic
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—42no—
161C22×C4×C127—42no—
162C22×C4×C127C2×D411yescharacteristic
163C22×C4×C127C2×D411yescharacteristic
164C22×C4×C127#4111yescharacteristic
165Q16×C127—42no—
166Q16×C127—42no—
167SD16×C127—42no—
168SD16×C127—42no—
169M16×C127—22no—
170M16×C127—41no—
171M16×C127—42no—
172M16×C127—42no—
173M16×C127—42no—
174M16×C127—42no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—21no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—42no—
182C2×C8×C127—42no—
183C2×C8×C127C2×D411yescharacteristic
184C2×C8×C127C2×D411yescharacteristic
185C2×C8×C127C2×D411yescharacteristic
186C2×C8×C127C2×D411yescharacteristic
187C4⋊C4×C127—21no—
188C4⋊C4×C127—21no—
189C4⋊C4×C127—21no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—21no—
192C4⋊C4×C127—21no—
193C4⋊C4×C127—21no—
194C4⋊C4×C127—21no—
195C4⋊C4×C127—21no—
196C4⋊C4×C127—41no—
197C4⋊C4×C127—41no—
198C4⋊C4×C127—41no—
199C4⋊C4×C127—41no—
200C4⋊C4×C127C2×D411yescharacteristic
201C4⋊C4×C127C2×D411yescharacteristic
202C22⋊C4×C127—21no—
203C22⋊C4×C127—21no—
204C22⋊C4×C127—21no—
205C22⋊C4×C127—21no—
206C22⋊C4×C127—41no—
207C22⋊C4×C127—41no—
208C42×C127—41no—
209C42×C127—41no—
210C42×C127C2×D411yescharacteristic
211C42×C127C2×D411yescharacteristic
212C42×C127#4111yescharacteristic
213C42×C127C2411yescharacteristic
214C23×C127—21no—
215C23×C127—21no—
216C23×C127—42no—
217C23×C127—42no—
218C23×C127—81no—
219C23×C127#12111yescharacteristic
220Q8×C127—41no—
221Q8×C127—41no—
222Q8×C127—41no—
223Q8×C127—41no—
224Q8×C127—41no—
225Q8×C127—41no—
226Q8×C127—81no—
227D4×C127—21no—
228D4×C127—21no—
229D4×C127—21no—
230D4×C127—42no—
231D4×C127#13712yes—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—21no—
235C2×C4×C127—21no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—41no—
239C2×C4×C127—42no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127—41no—
243C2×C4×C127—41no—
244C2×C4×C127—41no—
245C2×C4×C127—41no—
246C2×C4×C127—41no—
247C2×C4×C127—41no—
248C2×C4×C127—41no—
249C2×C4×C127—41no—
250C2×C4×C127#12111yescharacteristic
251C2×C4×C127#12111yescharacteristic
252C2×C4×C127#12111yescharacteristic
253C2×C4×C127C22×D411yescharacteristic
254C2×C4×C127C22×D411yescharacteristic
255C2×C4×C127C2×#4111yescharacteristic
256C8×C127—21no—
257C8×C127—21no—
258C8×C127—21no—
259C8×C127—41no—
260C8×C127—41no—
261C8×C127—41no—
262C8×C127—41no—
263C8×C127—41no—
264C8×C127—41no—
265C8×C127AGL(1,ℤ/8)12yes—
266C22×C127—21no—
267C22×C127—21no—
268C22×C127—22no—
269C22×C127—21no—
270C22×C127—41no—
271C22×C127—41no—
272C22×C127—41no—
273C22×C127—41no—
274C22×C127—41no—
275C22×C127—84no—
276C22×C127C2×#12111yescharacteristic
277C4×C127—21no—
278C4×C127—21no—
279C4×C127—21no—
280C4×C127—21no—
281C4×C127—41no—
282C4×C127—41no—
283C4×C127—81no—
284C4×C127—81no—
285C4×C127—81no—
286C4×C127—81no—
287C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
288C4×C127C2×#13711yescharacteristic
289C4×C127#57511yescharacteristic
290C4×C127#57511yescharacteristic
291#19307C12711yesmaximal, characteristic, direct product factor, Sylow
292C2×C127—41no—
293C2×C127—42no—
294C2×C127—81no—
295C2×C127#303611yescharacteristic
296C2×C127#305611yescharacteristic
297C2×C127#306911yescharacteristic
298#3185C2×C12711yescharacteristic, complemented
299#3110C2×C12711yescharacteristic
300#3077C2×C12711yescharacteristic
301D4×M16C2×C12711yescharacteristic
302#1703C2×C12711yescharacteristic, complemented
303#1699C2×C12711yescharacteristic, complemented
304#1691C2×C12711yescharacteristic, complemented
305#1689C2×C12711yescharacteristic, complemented
306#1683C2×C12711yescharacteristic, complemented
307#1679C2×C12711yescharacteristic, complemented
308#1671C2×C12711yescharacteristic, complemented
309#1669C2×C12711yescharacteristic, complemented
310#1569C2×C12711yescharacteristic, complemented
311#1561C2×C12711yescharacteristic, complemented
312#1559C2×C12711yescharacteristic, complemented
313C127#1930711yescharacteristic, direct product factor, Sylow
314C22×M16—21no—
315#533C22×C12711yescharacteristic
316#533C22×C12711yescharacteristic
317C2×C4×D4C22×C12711yescharacteristic
318#498C22×C12711yescharacteristic, complemented
319#494C22×C12711yescharacteristic, complemented
320#487C22×C12711yescharacteristic, complemented
321#487C22×C12711yescharacteristic, complemented
322#484—21no—
323#478—21no—
324#478—21no—
325#476C22×C12711yescharacteristic
326#476C22×C12711yescharacteristic
327#474C22×C12711yescharacteristic
328#474C22×C12711yescharacteristic
329#474C22×C12711yescharacteristic
330#474C22×C12711yescharacteristic
331#470—21no—
332#470—21no—
333#461C22×C12711yescharacteristic
334#461C22×C12711yescharacteristic
335#450—21no—
336#441—21no—
337#441—21no—
338#440—21no—
339#440—21no—
340#436C22×C12711yescharacteristic
341#436C22×C12711yescharacteristic
342#435—21no—
343#435—21no—
344C8×D4C22×C12711yescharacteristic
345C8×D4C22×C12711yescharacteristic
346#432C22×C12711yescharacteristic
347#428—21no—
348#423C22×C12711yescharacteristic
349#423C22×C12711yescharacteristic
350#418—21no—
351#407—21no—
352C4×M16C22×C12711yescharacteristic
353#335C22×C12711yescharacteristic, complemented
354#335C22×C12711yescharacteristic, complemented
355#334C22×C12711yescharacteristic, complemented
356#334C22×C12711yescharacteristic, complemented
357#333C22×C12711yescharacteristic, complemented
358#333C22×C12711yescharacteristic, complemented
359#332C22×C12711yescharacteristic, complemented
360#332C22×C12711yescharacteristic, complemented
361#332C22×C12711yescharacteristic, complemented
362#332C22×C12711yescharacteristic, complemented
363#332C22×C12711yescharacteristic, complemented
364#332C22×C12711yescharacteristic, complemented
365C22×D4D4×C12711yescharacteristic
366C23×C4—21no—
367C2×Q16—21no—
368C2×Q16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—44no—
376C2×M16D4×C12711yescharacteristic
377C2×M16D4×C12711yescharacteristic
378C22×C8—21no—
379C22×C8—21no—
380C4⋊Q8C23×C12711yescharacteristic
381C4⋊Q8C23×C12711yescharacteristic
382C4⋊Q8C23×C12711yescharacteristic
383C4⋊Q8C23×C12711yescharacteristic
384#125—21no—
385#125—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4D4×C12711yescharacteristic
397C4×D4D4×C12711yescharacteristic
398C4×D4C23×C12711yescharacteristic
399C4×D4C23×C12711yescharacteristic
400#117—21no—
401#117—21no—
402C2×C4⋊C4D4×C12711yescharacteristic
403C2×C22⋊C4—21no—
404C2×C42C23×C12711yescharacteristic
405#107—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412#106—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C12711yescharacteristic
416C4⋊C8C23×C12711yescharacteristic
417C4⋊C8C23×C12711yescharacteristic
418C4⋊C8C23×C12711yescharacteristic
419C4⋊C8C23×C12711yescharacteristic
420C4⋊C8C23×C12711yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438#97—21no—
439#97D4×C12711yescharacteristic
440#97D4×C12711yescharacteristic
441C4×C8C23×C12711yescharacteristic
442C4×C8C23×C12711yescharacteristic
443C24—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×D4—22no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4C2×D4×C12711yescharacteristic
452C2×D4C2×D4×C12711yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4C2×D4×C12711yescharacteristic
461C22×C4C2×D4×C12711yescharacteristic
462C22×C4#41×C12711yescharacteristic
463Q16—42no—
464Q16—42no—
465SD16—42no—
466SD16—42no—
467M16—22no—
468M16—41no—
469M16—42no—
470M16—42no—
471M16—42no—
472M16—42no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—42no—
481C2×C8C2×D4×C12711yescharacteristic
482C2×C8C2×D4×C12711yescharacteristic
483C2×C8C2×D4×C12711yescharacteristic
484C2×C8C2×D4×C12711yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4C2×D4×C12711yescharacteristic
499C4⋊C4C2×D4×C12711yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C42—41no—
507C42—41no—
508C42C2×D4×C12711yescharacteristic
509C42C2×D4×C12711yescharacteristic
510C42#41×C12711yescharacteristic
511C42C24×C12711yescharacteristic
512C23—21no—
513C23—21no—
514C23—42no—
515C23—42no—
516C23—81no—
517C23#121×C12711yescharacteristic
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—81no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4#137×C12712yes—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
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#121×C12711yescharacteristic
549C2×C4#121×C12711yescharacteristic
550C2×C4#121×C12711yescharacteristic
551C2×C4C22×D4×C12711yescharacteristic
552C2×C4C22×D4×C12711yescharacteristic
553C2×C4C2×#41×C12711yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8AGL(1,ℤ/8)×C12712yes—
564C22—21no—
565C22—21no—
566C22—22no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—84no—
574C22C2×#121×C12711yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
586C4C2×#137×C12711yescharacteristic
587C4#575×C12711yescharacteristic
588C4#575×C12711yescharacteristic
589C2—41no—
590C2—42no—
591C2—81no—
592C2C127×#303611yescharacteristic
593C2C127×#305611yescharacteristic
594C2C127×#306911yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ 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×#3185C2semidirect
5. C127×#1703C2semidirect
6. C127×#1699C2semidirect
7. C127×#1691C2semidirect
8. C127×#1689C2semidirect
9. C127×#1683C2semidirect
10. C127×#1679C2semidirect
11. C127×#1671C2semidirect
12. C127×#1669C2semidirect
13. C127×#1569C2semidirect
14. C127×#1561C2semidirect
15. C127×#1559C2semidirect
20. #498×C127C22semidirect
21. #494×C127C22semidirect
22. #487×C127C22semidirect
23. #487×C127C22semidirect
55. #335×C127C22semidirect
56. #335×C127C22semidirect
57. #334×C127C22semidirect
58. #334×C127C22semidirect
59. #333×C127C22semidirect
60. #333×C127C22semidirect
61. #332×C127C22semidirect
62. #332×C127C22semidirect
63. #332×C127C22semidirect
64. #332×C127C22semidirect
65. #332×C127C22semidirect
66. #332×C127C22semidirect
291. #19307C127direct (N × H)
298. #3185C2×C127semidirect
302. #1703C2×C127semidirect
303. #1699C2×C127semidirect
304. #1691C2×C127semidirect
305. #1689C2×C127semidirect
306. #1683C2×C127semidirect
307. #1679C2×C127semidirect
308. #1671C2×C127semidirect
309. #1669C2×C127semidirect
310. #1569C2×C127semidirect
311. #1561C2×C127semidirect
312. #1559C2×C127semidirect
313. C127#19307direct (N × H)
318. #498C22×C127semidirect
319. #494C22×C127semidirect
320. #487C22×C127semidirect
321. #487C22×C127semidirect
353. #335C22×C127semidirect
354. #335C22×C127semidirect
355. #334C22×C127semidirect
356. #334C22×C127semidirect
357. #333C22×C127semidirect
358. #333C22×C127semidirect
359. #332C22×C127semidirect
360. #332C22×C127semidirect
361. #332C22×C127semidirect
362. #332C22×C127semidirect
363. #332C22×C127semidirect
364. #332C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31852
C127×#31102
C127×#30772
D4×M16×C1272
C127×#17032
C127×#16992
C127×#16912
C127×#16892
C127×#16832
C127×#16792
C127×#16712
C127×#16692
C127×#15692
C127×#15612
C127×#15592
#19307127