Finite Group Databasebeta

← C127×#19588 #44583261

Subgroups — C127×#19588 #44583261

Order 32512.

568 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3248C211yesmaximal, characteristic
2C127×#3238C211yesmaximal, characteristic
3C127×#3229C211yesmaximal, characteristic, complemented
4C127×#2994C211yesmaximal, characteristic
5C127×#1704C211yesmaximal, characteristic, complemented
6C127×#1703C211yesmaximal, characteristic, complemented
7C127×#1692C211yesmaximal, characteristic, complemented
8C127×#1691C211yesmaximal, characteristic, complemented
9C127×#1684C211yesmaximal, characteristic, complemented
10C127×#1683C211yesmaximal, characteristic, complemented
11C127×#1672C211yesmaximal, characteristic, complemented
12C127×#1671C211yesmaximal, characteristic, complemented
13C127×#1573C211yesmaximal, characteristic, complemented
14C127×#1552C211yesmaximal, characteristic, complemented
15C2×#333×C127C211yesmaximal, characteristic, complemented
16#533×C127C2211yescharacteristic
17C2×C4⋊Q8×C127C2211yescharacteristic
18#529×C127C2211yescharacteristic
19#501×C127—21no—
20#498×C127C2211yescharacteristic
21#498×C127C2211yescharacteristic
22#489×C127—21no—
23#487×C127C2211yescharacteristic
24#487×C127C2211yescharacteristic
25#483×C127—21no—
26#483×C127—21no—
27#483×C127—21no—
28#480×C127—21no—
29#479×C127—21no—
30#477×C127C2211yescharacteristic
31#477×C127C2211yescharacteristic
32#476×C127C2211yescharacteristic
33#476×C127C2211yescharacteristic
34#475×C127—21no—
35#475×C127—21no—
36#475×C127C2211yescharacteristic
37#474×C127C2211yescharacteristic
38#467×C127—21no—
39#465×C127—21no—
40#464×C127—21no—
41#462×C127C2211yescharacteristic
42#461×C127C2211yescharacteristic
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#333×C127C2211yescharacteristic
62#333×C127C2211yescharacteristic
63#332×C127C2211yescharacteristic
64#332×C127C2211yescharacteristic
65#332×C127C2211yescharacteristic
66#332×C127C2211yescharacteristic
67C22×Q8×C127—21no—
68C2×Q16×C127—21no—
69C2×SD16×C127—21no—
70C2×M16×C127—21no—
71C22×C8×C127—21no—
72C22×C8×C127—21no—
73C22×C8×C127—21no—
74C4⋊Q8×C127—21no—
75C4⋊Q8×C127—21no—
76C4⋊Q8×C127—21no—
77C4⋊Q8×C127C2311yescharacteristic
78C4⋊Q8×C127C2311yescharacteristic
79C4⋊Q8×C127C2311yescharacteristic
80C4⋊Q8×C127C2311yescharacteristic
81#126×C127—21no—
82#125×C127—21no—
83#125×C127D411yescharacteristic
84#124×C127D411yescharacteristic
85#123×C127—21no—
86C22⋊Q8×C127—21no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127D411yescharacteristic
89#121×C127D411yescharacteristic
90C4×Q8×C127—21no—
91C4×Q8×C127—21no—
92C4×Q8×C127C2311yescharacteristic
93C4×D4×C127—21no—
94C4×D4×C127C2311yescharacteristic
95#117×C127—21no—
96#117×C127—21no—
97C2×C4⋊C4×C127—21no—
98C2×C4⋊C4×C127—21no—
99C2×C42×C127C2311yescharacteristic
100#107×C127—21no—
101#107×C127—21no—
102#107×C127—21no—
103#106×C127—21no—
104#106×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#103×C127—21no—
128#103×C127—21no—
129#103×C127—21no—
130#103×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
144C2×Q8×C127—21no—
145C2×Q8×C127—21no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127—41no—
149C2×Q8×C127—82no—
150C2×Q8×C127C2×D411yescharacteristic
151C2×D4×C127—21no—
152C2×D4×C127C2×D411yescharacteristic
153C22×C4×C127—21no—
154C22×C4×C127—41no—
155C22×C4×C127C2×D411yescharacteristic
156C22×C4×C127C2×D411yescharacteristic
157C22×C4×C127#4111yescharacteristic
158Q16×C127—81no—
159SD16×C127—81no—
160M16×C127—81no—
161C2×C8×C127—21no—
162C2×C8×C127—21no—
163C2×C8×C127—21no—
164C2×C8×C127—21no—
165C2×C8×C127—21no—
166C2×C8×C127—21no—
167C2×C8×C127—81no—
168C2×C8×C127—81no—
169C2×C8×C127—81no—
170C2×C8×C127C2×D411yescharacteristic
171C2×C8×C127C2×D411yescharacteristic
172C2×C8×C127C2×D411yescharacteristic
173C2×C8×C127C2×D411yescharacteristic
174C4⋊C4×C127—21no—
175C4⋊C4×C127—21no—
176C4⋊C4×C127—21no—
177C4⋊C4×C127—21no—
178C4⋊C4×C127—21no—
179C4⋊C4×C127—21no—
180C4⋊C4×C127—21no—
181C4⋊C4×C127—21no—
182C4⋊C4×C127—21no—
183C4⋊C4×C127—21no—
184C4⋊C4×C127—21no—
185C4⋊C4×C127—21no—
186C4⋊C4×C127—41no—
187C4⋊C4×C127—41no—
188C4⋊C4×C127—41no—
189C4⋊C4×C127—41no—
190C4⋊C4×C127C2×D411yescharacteristic
191C4⋊C4×C127C2×D411yescharacteristic
192C22⋊C4×C127—21no—
193C22⋊C4×C127—21no—
194C22⋊C4×C127—21no—
195C22⋊C4×C127—21no—
196C22⋊C4×C127—21no—
197C22⋊C4×C127—41no—
198C42×C127—21no—
199C42×C127—41no—
200C42×C127C2×D411yescharacteristic
201C42×C127C2×D411yescharacteristic
202C42×C127#4111yescharacteristic
203C42×C127C2411yescharacteristic
204C23×C127—21no—
205C23×C127#12111yescharacteristic
206Q8×C127—21no—
207Q8×C127—21no—
208Q8×C127—41no—
209Q8×C127—41no—
210Q8×C127—41no—
211Q8×C127—41no—
212Q8×C127—81no—
213Q8×C127—81no—
214Q8×C127—82no—
215D4×C127—21no—
216D4×C127—21no—
217D4×C127—42no—
218C2×C4×C127—22no—
219C2×C4×C127—21no—
220C2×C4×C127—21no—
221C2×C4×C127—21no—
222C2×C4×C127—21no—
223C2×C4×C127—21no—
224C2×C4×C127—21no—
225C2×C4×C127—21no—
226C2×C4×C127—41no—
227C2×C4×C127—41no—
228C2×C4×C127—41no—
229C2×C4×C127—41no—
230C2×C4×C127—41no—
231C2×C4×C127—41no—
232C2×C4×C127—82no—
233C2×C4×C127#12111yescharacteristic
234C2×C4×C127#12111yescharacteristic
235C2×C4×C127#12111yescharacteristic
236C2×C4×C127C22×D411yescharacteristic
237C2×C4×C127C22×D411yescharacteristic
238C2×C4×C127C2×#4111yescharacteristic
239C8×C127—21no—
240C8×C127—21no—
241C8×C127—21no—
242C8×C127—21no—
243C8×C127—41no—
244C8×C127—41no—
245C8×C127—41no—
246C8×C127—41no—
247C8×C127—41no—
248C8×C127—41no—
249C22×C127—21no—
250C22×C127—21no—
251C22×C127—41no—
252C22×C127—41no—
253C22×C127—41no—
254C22×C127#47112yes—
255C22×C127C2×#12111yescharacteristic
256C4×C127—21no—
257C4×C127—21no—
258C4×C127—21no—
259C4×C127—21no—
260C4×C127—41no—
261C4×C127—41no—
262C4×C127—41no—
263C4×C127—81no—
264C4×C127—81no—
265C4×C127—81no—
266C4×C127—81no—
267C4×C127#57711yescharacteristic
268C4×C127#57711yescharacteristic
269C4×C127#57811yescharacteristic
270C4×C127#57811yescharacteristic
271#19588C12711yesmaximal, characteristic, direct product factor, Sylow
272C2×C127—22no—
273C2×C127—81no—
274C2×C127#304611yescharacteristic
275C2×C127#306311yescharacteristic
276C2×C127C2×#47111yescharacteristic
277#3248C2×C12711yescharacteristic
278#3238C2×C12711yescharacteristic
279#3229C2×C12711yescharacteristic, complemented
280#2994C2×C12711yescharacteristic
281#1704C2×C12711yescharacteristic, complemented
282#1703C2×C12711yescharacteristic, complemented
283#1692C2×C12711yescharacteristic, complemented
284#1691C2×C12711yescharacteristic, complemented
285#1684C2×C12711yescharacteristic, complemented
286#1683C2×C12711yescharacteristic, complemented
287#1672C2×C12711yescharacteristic, complemented
288#1671C2×C12711yescharacteristic, complemented
289#1573C2×C12711yescharacteristic, complemented
290#1552C2×C12711yescharacteristic, complemented
291C2×#333C2×C12711yescharacteristic, complemented
292C127#1958811yescharacteristic, direct product factor, Sylow
293#533C22×C12711yescharacteristic
294C2×C4⋊Q8C22×C12711yescharacteristic
295#529C22×C12711yescharacteristic
296#501—21no—
297#498C22×C12711yescharacteristic
298#498C22×C12711yescharacteristic
299#489—21no—
300#487C22×C12711yescharacteristic
301#487C22×C12711yescharacteristic
302#483—21no—
303#483—21no—
304#483—21no—
305#480—21no—
306#479—21no—
307#477C22×C12711yescharacteristic
308#477C22×C12711yescharacteristic
309#476C22×C12711yescharacteristic
310#476C22×C12711yescharacteristic
311#475—21no—
312#475—21no—
313#475C22×C12711yescharacteristic
314#474C22×C12711yescharacteristic
315#467—21no—
316#465—21no—
317#464—21no—
318#462C22×C12711yescharacteristic
319#461C22×C12711yescharacteristic
320#446C22×C12711yescharacteristic
321C8×Q8C22×C12711yescharacteristic
322#436C22×C12711yescharacteristic
323#435—21no—
324C8×D4—21no—
325C8×D4C22×C12711yescharacteristic
326#433—21no—
327#432C22×C12711yescharacteristic
328#431C22×C12711yescharacteristic
329#424—21no—
330C2×C4⋊C8C22×C12711yescharacteristic
331C2×C4⋊C8C22×C12711yescharacteristic
332#335C22×C12711yescharacteristic
333#335C22×C12711yescharacteristic
334#334C22×C12711yescharacteristic
335#334C22×C12711yescharacteristic
336#333C22×C12711yescharacteristic
337#333C22×C12711yescharacteristic
338#333C22×C12711yescharacteristic
339#333C22×C12711yescharacteristic
340#332C22×C12711yescharacteristic
341#332C22×C12711yescharacteristic
342#332C22×C12711yescharacteristic
343#332C22×C12711yescharacteristic
344C22×Q8—21no—
345C2×Q16—21no—
346C2×SD16—21no—
347C2×M16—21no—
348C22×C8—21no—
349C22×C8—21no—
350C22×C8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C12711yescharacteristic
355C4⋊Q8C23×C12711yescharacteristic
356C4⋊Q8C23×C12711yescharacteristic
357C4⋊Q8C23×C12711yescharacteristic
358#126—21no—
359#125—21no—
360#125D4×C12711yescharacteristic
361#124D4×C12711yescharacteristic
362#123—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8D4×C12711yescharacteristic
366#121D4×C12711yescharacteristic
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C12711yescharacteristic
370C4×D4—21no—
371C4×D4C23×C12711yescharacteristic
372#117—21no—
373#117—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C42C23×C12711yescharacteristic
377#107—21no—
378#107—21no—
379#107—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8D4×C12711yescharacteristic
392C4⋊C8D4×C12711yescharacteristic
393C4⋊C8C23×C12711yescharacteristic
394C4⋊C8C23×C12711yescharacteristic
395C4⋊C8C23×C12711yescharacteristic
396C4⋊C8C23×C12711yescharacteristic
397C4⋊C8C23×C12711yescharacteristic
398C4⋊C8C23×C12711yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8D4×C12711yescharacteristic
415C22⋊C8D4×C12711yescharacteristic
416#97—21no—
417#97—21no—
418C4×C8—21no—
419C4×C8C23×C12711yescharacteristic
420C4×C8C23×C12711yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—82no—
427C2×Q8C2×D4×C12711yescharacteristic
428C2×D4—21no—
429C2×D4C2×D4×C12711yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4C2×D4×C12711yescharacteristic
433C22×C4C2×D4×C12711yescharacteristic
434C22×C4#41×C12711yescharacteristic
435Q16—81no—
436SD16—81no—
437M16—81no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—81no—
445C2×C8—81no—
446C2×C8—81no—
447C2×C8C2×D4×C12711yescharacteristic
448C2×C8C2×D4×C12711yescharacteristic
449C2×C8C2×D4×C12711yescharacteristic
450C2×C8C2×D4×C12711yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C12711yescharacteristic
468C4⋊C4C2×D4×C12711yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—41no—
475C42—21no—
476C42—41no—
477C42C2×D4×C12711yescharacteristic
478C42C2×D4×C12711yescharacteristic
479C42#41×C12711yescharacteristic
480C42C24×C12711yescharacteristic
481C23—21no—
482C23#121×C12711yescharacteristic
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—81no—
490Q8—81no—
491Q8—82no—
492D4—21no—
493D4—21no—
494D4—42no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—82no—
510C2×C4#121×C12711yescharacteristic
511C2×C4#121×C12711yescharacteristic
512C2×C4#121×C12711yescharacteristic
513C2×C4C22×D4×C12711yescharacteristic
514C2×C4C22×D4×C12711yescharacteristic
515C2×C4C2×#41×C12711yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22#471×C12712yes—
532C22C2×#121×C12711yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4#577×C12711yescharacteristic
545C4#577×C12711yescharacteristic
546C4#578×C12711yescharacteristic
547C4#578×C12711yescharacteristic
548C2—22no—
549C2—81no—
550C2C127×#304611yescharacteristic
551C2C127×#306311yescharacteristic
552C2C2×#471×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radical#121×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
3. C127×#3229C2semidirect
5. C127×#1704C2semidirect
6. C127×#1703C2semidirect
7. C127×#1692C2semidirect
8. C127×#1691C2semidirect
9. C127×#1684C2semidirect
10. C127×#1683C2semidirect
11. C127×#1672C2semidirect
12. C127×#1671C2semidirect
13. C127×#1573C2semidirect
14. C127×#1552C2semidirect
15. C2×#333×C127C2semidirect
271. #19588C127direct (N × H)
279. #3229C2×C127semidirect
281. #1704C2×C127semidirect
282. #1703C2×C127semidirect
283. #1692C2×C127semidirect
284. #1691C2×C127semidirect
285. #1684C2×C127semidirect
286. #1683C2×C127semidirect
287. #1672C2×C127semidirect
288. #1671C2×C127semidirect
289. #1573C2×C127semidirect
290. #1552C2×C127semidirect
291. C2×#333C2×C127semidirect
292. C127#19588direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32482
C127×#32382
C127×#32292
C127×#29942
C127×#17042
C127×#17032
C127×#16922
C127×#16912
C127×#16842
C127×#16832
C127×#16722
C127×#16712
C127×#15732
C127×#15522
C2×#333×C1272
#19588127