Finite Group Databasebeta

← C127×#19589 #44583262

Subgroups — C127×#19589 #44583262

Order 32512.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3247C211yesmaximal, characteristic
2C127×#3227C211yesmaximal, characteristic, complemented
3C127×#3218C211yesmaximal, characteristic, complemented
4C127×#2994C211yesmaximal, characteristic, complemented
5C127×#1702C211yesmaximal, characteristic, complemented
6C127×#1701C211yesmaximal, characteristic, complemented
7C127×#1692C211yesmaximal, characteristic, complemented
8C127×#1691C211yesmaximal, characteristic, complemented
9C127×#1682C211yesmaximal, characteristic, complemented
10C127×#1681C211yesmaximal, characteristic, complemented
11C127×#1672C211yesmaximal, characteristic, complemented
12C127×#1671C211yesmaximal, characteristic, complemented
13C127×#1573C211yesmaximal, characteristic, complemented
14C127×#1551C211yesmaximal, characteristic, complemented
15C2×#332×C127C211yesmaximal, characteristic, complemented
16#532×C127C2211yescharacteristic
17C2×C4⋊Q8×C127C2211yescharacteristic
18#529×C127C2211yescharacteristic
19#498×C127C2211yescharacteristic
20#498×C127C2211yescharacteristic
21#497×C127—21no—
22#491×C127—21no—
23#486×C127C2211yescharacteristic
24#486×C127C2211yescharacteristic
25#481×C127—21no—
26#481×C127—21no—
27#478×C127—21no—
28#477×C127C2211yescharacteristic
29#476×C127—21no—
30#476×C127—21no—
31#476×C127C2211yescharacteristic
32#466×C127—21no—
33#465×C127—21no—
34#463×C127—21no—
35#462×C127C2211yescharacteristic
36#462×C127C2211yescharacteristic
37#461×C127C2211yescharacteristic
38#461×C127C2211yescharacteristic
39#460×C127C2211yescharacteristic
40#459×C127C2211yescharacteristic
41#451×C127—21no—
42#448×C127—21no—
43#446×C127C2211yescharacteristic
44C8×Q8×C127C2211yescharacteristic
45#436×C127C2211yescharacteristic
46#435×C127—21no—
47C8×D4×C127—21no—
48C8×D4×C127C2211yescharacteristic
49#433×C127—21no—
50#432×C127C2211yescharacteristic
51#431×C127C2211yescharacteristic
52#424×C127—21no—
53C2×C4⋊C8×C127C2211yescharacteristic
54C2×C4⋊C8×C127C2211yescharacteristic
55#335×C127C2211yescharacteristic
56#335×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#334×C127C2211yescharacteristic
59#333×C127C2211yescharacteristic
60#333×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62#332×C127C2211yescharacteristic
63#332×C127C2211yescharacteristic
64#332×C127C2211yescharacteristic
65#331×C127C2211yescharacteristic
66#331×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C22×Q8×C127—21no—
69C2×Q16×C127—21no—
70C2×Q16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×SD16×C127—21no—
74C2×D8×C127—21no—
75C2×M16×C127—21no—
76C22×C8×C127—21no—
77C22×C8×C127—21no—
78C22×C8×C127—21no—
79C4⋊Q8×C127—21no—
80C4⋊Q8×C127—21no—
81C4⋊Q8×C127—21no—
82C4⋊Q8×C127C2311yescharacteristic
83C4⋊Q8×C127C2311yescharacteristic
84C4⋊Q8×C127C2311yescharacteristic
85#127×C127C2311yescharacteristic
86#126×C127—21no—
87#125×C127D411yescharacteristic
88#124×C127—21no—
89#124×C127D411yescharacteristic
90#123×C127—21no—
91C22⋊Q8×C127D411yescharacteristic
92#121×C127—21no—
93#121×C127—21no—
94#121×C127D411yescharacteristic
95C4×Q8×C127C2311yescharacteristic
96C4×D4×C127—21no—
97C4×D4×C127—21no—
98C4×D4×C127—21no—
99C4×D4×C127C2311yescharacteristic
100#117×C127—21no—
101C2×C4⋊C4×C127—21no—
102C2×C4⋊C4×C127—21no—
103C2×C42×C127C2311yescharacteristic
104#107×C127—21no—
105#106×C127—21no—
106#106×C127—21no—
107#106×C127—21no—
108#106×C127—21no—
109#106×C127—21no—
110C4⋊C8×C127—21no—
111C4⋊C8×C127—21no—
112C4⋊C8×C127—21no—
113C4⋊C8×C127—21no—
114C4⋊C8×C127D411yescharacteristic
115C4⋊C8×C127D411yescharacteristic
116C4⋊C8×C127C2311yescharacteristic
117C4⋊C8×C127C2311yescharacteristic
118C4⋊C8×C127C2311yescharacteristic
119C4⋊C8×C127C2311yescharacteristic
120C4⋊C8×C127C2311yescharacteristic
121C4⋊C8×C127C2311yescharacteristic
122#103×C127—21no—
123#103×C127—21no—
124#103×C127—21no—
125#103×C127—21no—
126#103×C127—21no—
127#102×C127—21no—
128#102×C127—21no—
129#102×C127—21no—
130#102×C127—21no—
131#102×C127—21no—
132#102×C127—21no—
133#102×C127—21no—
134C22⋊C8×C127—21no—
135C22⋊C8×C127—21no—
136C22⋊C8×C127—21no—
137C22⋊C8×C127D411yescharacteristic
138C22⋊C8×C127D411yescharacteristic
139#97×C127—21no—
140#97×C127—21no—
141C4×C8×C127—21no—
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144#41×C127—82no—
145C2×Q8×C127—21no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127—41no—
149C2×Q8×C127—81no—
150C2×Q8×C127—81no—
151C2×Q8×C127C2×D411yescharacteristic
152C2×D4×C127—21no—
153C2×D4×C127—21no—
154C2×D4×C127—21no—
155C2×D4×C127—21no—
156C2×D4×C127—41no—
157C2×D4×C127C2×D411yescharacteristic
158C22×C4×C127—21no—
159C22×C4×C127—41no—
160C22×C4×C127—41no—
161C22×C4×C127C2×D411yescharacteristic
162C22×C4×C127C2×D411yescharacteristic
163C22×C4×C127#4111yescharacteristic
164Q16×C127—81no—
165Q16×C127—81no—
166SD16×C127—81no—
167SD16×C127—81no—
168SD16×C127—81no—
169D8×C127—81no—
170M16×C127—81no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—21no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—81no—
178C2×C8×C127—81no—
179C2×C8×C127—81no—
180C2×C8×C127C2×D411yescharacteristic
181C2×C8×C127C2×D411yescharacteristic
182C2×C8×C127C2×D411yescharacteristic
183C2×C8×C127C2×D411yescharacteristic
184C4⋊C4×C127—21no—
185C4⋊C4×C127—21no—
186C4⋊C4×C127—21no—
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—41no—
195C4⋊C4×C127—41no—
196C4⋊C4×C127C2×D411yescharacteristic
197C4⋊C4×C127C2×D411yescharacteristic
198C22⋊C4×C127—21no—
199C22⋊C4×C127—21no—
200C22⋊C4×C127—21no—
201C22⋊C4×C127—21no—
202C22⋊C4×C127—21no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C42×C127—21no—
206C42×C127C2×D411yescharacteristic
207C42×C127C2×D411yescharacteristic
208C42×C127#4111yescharacteristic
209C42×C127C2411yescharacteristic
210C23×C127—21no—
211C23×C127—41no—
212C23×C127#12111yescharacteristic
213Q8×C127—21no—
214Q8×C127—21no—
215Q8×C127—41no—
216Q8×C127—41no—
217Q8×C127—41no—
218Q8×C127—41no—
219Q8×C127—81no—
220Q8×C127—82no—
221D4×C127—21no—
222D4×C127—21no—
223D4×C127—42no—
224D4×C127—41no—
225D4×C127—41no—
226D4×C127—41no—
227D4×C127—41no—
228D4×C127—81no—
229D4×C127—82no—
230C2×C4×C127—22no—
231C2×C4×C127—21no—
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—41no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—41no—
243C2×C4×C127—82no—
244C2×C4×C127—82no—
245C2×C4×C127#12111yescharacteristic
246C2×C4×C127#12111yescharacteristic
247C2×C4×C127#12111yescharacteristic
248C2×C4×C127C22×D411yescharacteristic
249C2×C4×C127C22×D411yescharacteristic
250C2×C4×C127C2×#4111yescharacteristic
251C8×C127—21no—
252C8×C127—21no—
253C8×C127—21no—
254C8×C127—21no—
255C8×C127—41no—
256C8×C127—41no—
257C8×C127—41no—
258C8×C127—41no—
259C8×C127—41no—
260C8×C127—41no—
261C22×C127—21no—
262C22×C127—21no—
263C22×C127—41no—
264C22×C127—41no—
265C22×C127—41no—
266C22×C127—81no—
267C22×C127—81no—
268C22×C127—81no—
269C22×C127#47112yes—
270C22×C127C2×#12111yescharacteristic
271C4×C127—21no—
272C4×C127—21no—
273C4×C127—21no—
274C4×C127—21no—
275C4×C127—41no—
276C4×C127—41no—
277C4×C127—41no—
278C4×C127—81no—
279C4×C127—81no—
280C4×C127—81no—
281C4×C127#57611yescharacteristic
282C4×C127#57711yescharacteristic
283C4×C127#57711yescharacteristic
284C4×C127#57811yescharacteristic
285#19589C12711yesmaximal, characteristic, direct product factor, Sylow
286C2×C127—22no—
287C2×C127—81no—
288C2×C127—161no—
289C2×C127#304611yescharacteristic
290C2×C127#306211yescharacteristic
291C2×C127C2×#47111yescharacteristic
292#3247C2×C12711yescharacteristic
293#3227C2×C12711yescharacteristic, complemented
294#3218C2×C12711yescharacteristic, complemented
295#2994C2×C12711yescharacteristic, complemented
296#1702C2×C12711yescharacteristic, complemented
297#1701C2×C12711yescharacteristic, complemented
298#1692C2×C12711yescharacteristic, complemented
299#1691C2×C12711yescharacteristic, complemented
300#1682C2×C12711yescharacteristic, complemented
301#1681C2×C12711yescharacteristic, complemented
302#1672C2×C12711yescharacteristic, complemented
303#1671C2×C12711yescharacteristic, complemented
304#1573C2×C12711yescharacteristic, complemented
305#1551C2×C12711yescharacteristic, complemented
306C2×#332C2×C12711yescharacteristic, complemented
307C127#1958911yescharacteristic, direct product factor, Sylow
308#532C22×C12711yescharacteristic
309C2×C4⋊Q8C22×C12711yescharacteristic
310#529C22×C12711yescharacteristic
311#498C22×C12711yescharacteristic
312#498C22×C12711yescharacteristic
313#497—21no—
314#491—21no—
315#486C22×C12711yescharacteristic
316#486C22×C12711yescharacteristic
317#481—21no—
318#481—21no—
319#478—21no—
320#477C22×C12711yescharacteristic
321#476—21no—
322#476—21no—
323#476C22×C12711yescharacteristic
324#466—21no—
325#465—21no—
326#463—21no—
327#462C22×C12711yescharacteristic
328#462C22×C12711yescharacteristic
329#461C22×C12711yescharacteristic
330#461C22×C12711yescharacteristic
331#460C22×C12711yescharacteristic
332#459C22×C12711yescharacteristic
333#451—21no—
334#448—21no—
335#446C22×C12711yescharacteristic
336C8×Q8C22×C12711yescharacteristic
337#436C22×C12711yescharacteristic
338#435—21no—
339C8×D4—21no—
340C8×D4C22×C12711yescharacteristic
341#433—21no—
342#432C22×C12711yescharacteristic
343#431C22×C12711yescharacteristic
344#424—21no—
345C2×C4⋊C8C22×C12711yescharacteristic
346C2×C4⋊C8C22×C12711yescharacteristic
347#335C22×C12711yescharacteristic
348#335C22×C12711yescharacteristic
349#334C22×C12711yescharacteristic
350#334C22×C12711yescharacteristic
351#333C22×C12711yescharacteristic
352#333C22×C12711yescharacteristic
353#332C22×C12711yescharacteristic
354#332C22×C12711yescharacteristic
355#332C22×C12711yescharacteristic
356#332C22×C12711yescharacteristic
357#331C22×C12711yescharacteristic
358#331C22×C12711yescharacteristic
359C2×#41—21no—
360C22×Q8—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×D8—21no—
367C2×M16—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8C23×C12711yescharacteristic
375C4⋊Q8C23×C12711yescharacteristic
376C4⋊Q8C23×C12711yescharacteristic
377#127C23×C12711yescharacteristic
378#126—21no—
379#125D4×C12711yescharacteristic
380#124—21no—
381#124D4×C12711yescharacteristic
382#123—21no—
383C22⋊Q8D4×C12711yescharacteristic
384#121—21no—
385#121—21no—
386#121D4×C12711yescharacteristic
387C4×Q8C23×C12711yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4C23×C12711yescharacteristic
392#117—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C42C23×C12711yescharacteristic
396#107—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8D4×C12711yescharacteristic
407C4⋊C8D4×C12711yescharacteristic
408C4⋊C8C23×C12711yescharacteristic
409C4⋊C8C23×C12711yescharacteristic
410C4⋊C8C23×C12711yescharacteristic
411C4⋊C8C23×C12711yescharacteristic
412C4⋊C8C23×C12711yescharacteristic
413C4⋊C8C23×C12711yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8D4×C12711yescharacteristic
430C22⋊C8D4×C12711yescharacteristic
431#97—21no—
432#97—21no—
433C4×C8—21no—
434C4×C8C23×C12711yescharacteristic
435C4×C8C23×C12711yescharacteristic
436#41—82no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—41no—
441C2×Q8—81no—
442C2×Q8—81no—
443C2×Q8C2×D4×C12711yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—41no—
449C2×D4C2×D4×C12711yescharacteristic
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C12711yescharacteristic
454C22×C4C2×D4×C12711yescharacteristic
455C22×C4#41×C12711yescharacteristic
456Q16—81no—
457Q16—81no—
458SD16—81no—
459SD16—81no—
460SD16—81no—
461D8—81no—
462M16—81no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—81no—
470C2×C8—81no—
471C2×C8—81no—
472C2×C8C2×D4×C12711yescharacteristic
473C2×C8C2×D4×C12711yescharacteristic
474C2×C8C2×D4×C12711yescharacteristic
475C2×C8C2×D4×C12711yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C12711yescharacteristic
489C4⋊C4C2×D4×C12711yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42C2×D4×C12711yescharacteristic
499C42C2×D4×C12711yescharacteristic
500C42#41×C12711yescharacteristic
501C42C24×C12711yescharacteristic
502C23—21no—
503C23—41no—
504C23#121×C12711yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—81no—
512Q8—82no—
513D4—21no—
514D4—21no—
515D4—42no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—81no—
521D4—82no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4#121×C12711yescharacteristic
538C2×C4#121×C12711yescharacteristic
539C2×C4#121×C12711yescharacteristic
540C2×C4C22×D4×C12711yescharacteristic
541C2×C4C22×D4×C12711yescharacteristic
542C2×C4C2×#41×C12711yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C22—21no—
554C22—21no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22#471×C12712yes—
562C22C2×#121×C12711yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4#576×C12711yescharacteristic
574C4#577×C12711yescharacteristic
575C4#577×C12711yescharacteristic
576C4#578×C12711yescharacteristic
577C2—22no—
578C2—81no—
579C2—161no—
580C2C127×#304611yescharacteristic
581C2C127×#306211yescharacteristic
582C2C2×#471×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3247C2
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
2. C127×#3227C2semidirect
3. C127×#3218C2semidirect
4. C127×#2994C2semidirect
5. C127×#1702C2semidirect
6. C127×#1701C2semidirect
7. C127×#1692C2semidirect
8. C127×#1691C2semidirect
9. C127×#1682C2semidirect
10. C127×#1681C2semidirect
11. C127×#1672C2semidirect
12. C127×#1671C2semidirect
13. C127×#1573C2semidirect
14. C127×#1551C2semidirect
15. C2×#332×C127C2semidirect
285. #19589C127direct (N × H)
293. #3227C2×C127semidirect
294. #3218C2×C127semidirect
295. #2994C2×C127semidirect
296. #1702C2×C127semidirect
297. #1701C2×C127semidirect
298. #1692C2×C127semidirect
299. #1691C2×C127semidirect
300. #1682C2×C127semidirect
301. #1681C2×C127semidirect
302. #1672C2×C127semidirect
303. #1671C2×C127semidirect
304. #1573C2×C127semidirect
305. #1551C2×C127semidirect
306. C2×#332C2×C127semidirect
307. C127#19589direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32472
C127×#32272
C127×#32182
C127×#29942
C127×#17022
C127×#17012
C127×#16922
C127×#16912
C127×#16822
C127×#16812
C127×#16722
C127×#16712
C127×#15732
C127×#15512
C2×#332×C1272
#19589127