Finite Group Databasebeta

← C127×#19830 #44583503

Subgroups — C127×#19830 #44583503

Order 32512.

572 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×SD16×C127C211yesmaximal, characteristic
2C127×#3364C211yesmaximal, characteristic
3C127×#3363C211yesmaximal, characteristic, complemented
4C127×#3328C211yesmaximal, characteristic
5C127×#1718C211yesmaximal, characteristic, complemented
6C127×#1703C211yesmaximal, characteristic
7C127×#1680C211yesmaximal, characteristic, complemented
8C127×#1680C211yesmaximal, characteristic, complemented
9C127×#1672C211yesmaximal, characteristic, complemented
10C127×#1649C211yesmaximal, characteristic
11C127×#1648C211yesmaximal, characteristic, complemented
12C127×#1645C211yesmaximal, characteristic, complemented
13C127×#1638C211yesmaximal, characteristic
14C127×#1583C211yesmaximal, characteristic
15C127×#1579C211yesmaximal, characteristic, complemented
16Q82×C127C2211yescharacteristic
17#557×C127C2211yescharacteristic
18#556×C127C2211yescharacteristic
19D4×Q8×C127C2211yescharacteristic
20#500×C127C2211yescharacteristic
21#498×C127—21no—
22#498×C127C2211yescharacteristic
23#488×C127—21no—
24#487×C127—21no—
25#487×C127C2211yescharacteristic
26#487×C127C2211yescharacteristic
27#487×C127C2211yescharacteristic
28#487×C127C2211yescharacteristic
29#485×C127—21no—
30#479×C127—21no—
31#477×C127—21no—
32#477×C127C2211yescharacteristic
33#476×C127—21no—
34#476×C127C2211yescharacteristic
35#475×C127—21no—
36#475×C127C2211yescharacteristic
37#475×C127C2211yescharacteristic
38#474×C127C2211yescharacteristic
39#470×C127—21no—
40#464×C127—21no—
41#462×C127—21no—
42#462×C127C2211yescharacteristic
43#462×C127C2211yescharacteristic
44#462×C127C2211yescharacteristic
45#451×C127—21no—
46C8×Q8×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48C8×Q8×C127C2211yescharacteristic
49C4×Q16×C127—21no—
50C4×Q16×C127—21no—
51C4×Q16×C127C2211yescharacteristic
52C4×SD16×C127—21no—
53C4×SD16×C127C2211yescharacteristic
54#436×C127C2211yescharacteristic
55#419×C127—21no—
56#334×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64Q8⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C22×Q8×C127—21no—
68C2×Q16×C127—21no—
69C2×Q16×C127—21no—
70C2×Q16×C127—21no—
71C2×Q16×C127D411yescharacteristic
72C2×SD16×C127D411yescharacteristic
73C2×M16×C127—21no—
74C4⋊Q8×C127—21no—
75C4⋊Q8×C127—21no—
76C4⋊Q8×C127—21no—
77C4⋊Q8×C127—21no—
78C4⋊Q8×C127—41no—
79C4⋊Q8×C127C2311yescharacteristic
80C4⋊Q8×C127C2311yescharacteristic
81C4⋊Q8×C127C2311yescharacteristic
82C4⋊Q8×C127C2311yescharacteristic
83#126×C127—41no—
84#125×C127—21no—
85#125×C127—41no—
86#124×C127—21no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127—21no—
89C22⋊Q8×C127—41no—
90C4×Q8×C127—21no—
91C4×Q8×C127—21no—
92C4×Q8×C127—21no—
93C4×Q8×C127—21no—
94C4×Q8×C127—21no—
95C4×Q8×C127C2311yescharacteristic
96C4×Q8×C127C2311yescharacteristic
97C4×Q8×C127C2311yescharacteristic
98C4×D4×C127—21no—
99C4×D4×C127C2311yescharacteristic
100#117×C127—21no—
101#107×C127—21no—
102#107×C127—21no—
103#107×C127—41no—
104#107×C127D411yescharacteristic
105#106×C127—21no—
106#106×C127—21no—
107#106×C127—21no—
108#106×C127—21no—
109#106×C127—21no—
110#106×C127D411yescharacteristic
111C4⋊C8×C127—21no—
112C4⋊C8×C127—21no—
113C4⋊C8×C127—21no—
114C4⋊C8×C127C2311yescharacteristic
115C4⋊C8×C127C2311yescharacteristic
116C4⋊C8×C127C2311yescharacteristic
117C4⋊C8×C127C2311yescharacteristic
118#103×C127—21no—
119#103×C127—21no—
120#103×C127—21no—
121#103×C127—21no—
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—41no—
131#103×C127D411yescharacteristic
132#103×C127D411yescharacteristic
133#103×C127D411yescharacteristic
134#102×C127—21no—
135#102×C127—21no—
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C4×C8×C127—21no—
139C4×C8×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127C2311yescharacteristic
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—41no—
150C2×Q8×C127—42no—
151C2×Q8×C127—81no—
152C2×Q8×C127C2×D411yescharacteristic
153C2×Q8×C127C2×D411yescharacteristic
154C2×Q8×C127C2×D411yescharacteristic
155C2×D4×C127C2×D411yescharacteristic
156C22×C4×C127—21no—
157C22×C4×C127—41no—
158Q16×C127—22no—
159Q16×C127—42no—
160Q16×C127—42no—
161Q16×C127—81no—
162SD16×C127—22no—
163M16×C127—81no—
164C2×C8×C127—21no—
165C2×C8×C127—21no—
166C2×C8×C127—21no—
167C2×C8×C127—21no—
168C2×C8×C127—21no—
169C2×C8×C127C2×D411yescharacteristic
170C2×C8×C127C2×D411yescharacteristic
171C2×C8×C127C2×D411yescharacteristic
172C2×C8×C127C2×D411yescharacteristic
173C4⋊C4×C127—21no—
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—41no—
185C4⋊C4×C127—41no—
186C4⋊C4×C127—41no—
187C4⋊C4×C127—41no—
188C4⋊C4×C127—41no—
189C4⋊C4×C127—41no—
190C4⋊C4×C127—41no—
191C4⋊C4×C127C2×D411yescharacteristic
192C4⋊C4×C127C2×D411yescharacteristic
193C4⋊C4×C127C2×D411yescharacteristic
194C4⋊C4×C127C2×D411yescharacteristic
195C22⋊C4×C127—21no—
196C22⋊C4×C127—41no—
197C22⋊C4×C127—41no—
198C22⋊C4×C127—41no—
199C42×C127—21no—
200C42×C127—21no—
201C42×C127—21no—
202C42×C127—41no—
203C42×C127—41no—
204C42×C127—41no—
205C42×C127C2411yescharacteristic
206C23×C127—21no—
207Q8×C127—21no—
208Q8×C127—21no—
209Q8×C127—21no—
210Q8×C127—21no—
211Q8×C127—41no—
212Q8×C127—41no—
213Q8×C127—41no—
214Q8×C127—41no—
215Q8×C127—41no—
216Q8×C127—41no—
217Q8×C127—82no—
218Q8×C127—81no—
219Q8×C127—161no—
220Q8×C127#13512yes—
221Q8×C127#13712yes—
222D4×C127—21no—
223D4×C127—21no—
224C2×C4×C127—21no—
225C2×C4×C127—21no—
226C2×C4×C127—21no—
227C2×C4×C127—21no—
228C2×C4×C127—21no—
229C2×C4×C127—21no—
230C2×C4×C127—21no—
231C2×C4×C127—41no—
232C2×C4×C127—41no—
233C2×C4×C127—41no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—41no—
237C2×C4×C127—82no—
238C2×C4×C127C22×D411yescharacteristic
239C2×C4×C127C22×D411yescharacteristic
240C2×C4×C127H(5,𝔽2)11yescharacteristic
241C8×C127—21no—
242C8×C127—21no—
243C8×C127—21no—
244C8×C127—21no—
245C8×C127—41no—
246C8×C127—41no—
247C8×C127—41no—
248C8×C127—41no—
249C8×C127—41no—
250C22×C127—41no—
251C22×C127—41no—
252C22×C127—41no—
253C22×C127D4211yescharacteristic
254C4×C127—22no—
255C4×C127—22no—
256C4×C127—21no—
257C4×C127—41no—
258C4×C127—41no—
259C4×C127—41no—
260C4×C127—41no—
261C4×C127—41no—
262C4×C127—81no—
263C4×C127—81no—
264C4×C127—81no—
265C4×C127—81no—
266C4×C127C2×#13511yescharacteristic
267C4×C127C2×#13711yescharacteristic
268C4×C127#57711yescharacteristic
269C4×C127#57811yescharacteristic
270#19830C12711yesmaximal, characteristic, direct product factor, Sylow
271C2×C127—81no—
272C2×C127#327011yescharacteristic
273C2×C127#328211yescharacteristic
274C2×C127#328911yescharacteristic
275Q8×SD16C2×C12711yescharacteristic
276#3364C2×C12711yescharacteristic
277#3363C2×C12711yescharacteristic, complemented
278#3328C2×C12711yescharacteristic
279#1718C2×C12711yescharacteristic, complemented
280#1703C2×C12711yescharacteristic
281#1680C2×C12711yescharacteristic, complemented
282#1680C2×C12711yescharacteristic, complemented
283#1672C2×C12711yescharacteristic, complemented
284#1649C2×C12711yescharacteristic
285#1648C2×C12711yescharacteristic, complemented
286#1645C2×C12711yescharacteristic, complemented
287#1638C2×C12711yescharacteristic
288#1583C2×C12711yescharacteristic
289#1579C2×C12711yescharacteristic, complemented
290C127#1983011yescharacteristic, direct product factor, Sylow
291Q82C22×C12711yescharacteristic
292#557C22×C12711yescharacteristic
293#556C22×C12711yescharacteristic
294D4×Q8C22×C12711yescharacteristic
295#500C22×C12711yescharacteristic
296#498—21no—
297#498C22×C12711yescharacteristic
298#488—21no—
299#487—21no—
300#487C22×C12711yescharacteristic
301#487C22×C12711yescharacteristic
302#487C22×C12711yescharacteristic
303#487C22×C12711yescharacteristic
304#485—21no—
305#479—21no—
306#477—21no—
307#477C22×C12711yescharacteristic
308#476—21no—
309#476C22×C12711yescharacteristic
310#475—21no—
311#475C22×C12711yescharacteristic
312#475C22×C12711yescharacteristic
313#474C22×C12711yescharacteristic
314#470—21no—
315#464—21no—
316#462—21no—
317#462C22×C12711yescharacteristic
318#462C22×C12711yescharacteristic
319#462C22×C12711yescharacteristic
320#451—21no—
321C8×Q8C22×C12711yescharacteristic
322C8×Q8C22×C12711yescharacteristic
323C8×Q8C22×C12711yescharacteristic
324C4×Q16—21no—
325C4×Q16—21no—
326C4×Q16C22×C12711yescharacteristic
327C4×SD16—21no—
328C4×SD16C22×C12711yescharacteristic
329#436C22×C12711yescharacteristic
330#419—21no—
331#334C22×C12711yescharacteristic
332#334C22×C12711yescharacteristic
333#333C22×C12711yescharacteristic
334#332C22×C12711yescharacteristic
335#332C22×C12711yescharacteristic
336#332C22×C12711yescharacteristic
337Q8⋊C8C22×C12711yescharacteristic
338Q8⋊C8C22×C12711yescharacteristic
339Q8⋊C8C22×C12711yescharacteristic
340D4⋊C8C22×C12711yescharacteristic
341#322C22×C12711yescharacteristic
342C22×Q8—21no—
343C2×Q16—21no—
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16D4×C12711yescharacteristic
347C2×SD16D4×C12711yescharacteristic
348C2×M16—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—41no—
354C4⋊Q8C23×C12711yescharacteristic
355C4⋊Q8C23×C12711yescharacteristic
356C4⋊Q8C23×C12711yescharacteristic
357C4⋊Q8C23×C12711yescharacteristic
358#126—41no—
359#125—21no—
360#125—41no—
361#124—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—41no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8C23×C12711yescharacteristic
371C4×Q8C23×C12711yescharacteristic
372C4×Q8C23×C12711yescharacteristic
373C4×D4—21no—
374C4×D4C23×C12711yescharacteristic
375#117—21no—
376#107—21no—
377#107—21no—
378#107—41no—
379#107D4×C12711yescharacteristic
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106D4×C12711yescharacteristic
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8C23×C12711yescharacteristic
390C4⋊C8C23×C12711yescharacteristic
391C4⋊C8C23×C12711yescharacteristic
392C4⋊C8C23×C12711yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—41no—
406#103D4×C12711yescharacteristic
407#103D4×C12711yescharacteristic
408#103D4×C12711yescharacteristic
409#102—21no—
410#102—21no—
411#102D4×C12711yescharacteristic
412C22⋊C8—21no—
413C4×C8—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C12711yescharacteristic
417C4×C8C23×C12711yescharacteristic
418C4×C8C23×C12711yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—41no—
424C2×Q8—41no—
425C2×Q8—42no—
426C2×Q8—81no—
427C2×Q8C2×D4×C12711yescharacteristic
428C2×Q8C2×D4×C12711yescharacteristic
429C2×Q8C2×D4×C12711yescharacteristic
430C2×D4C2×D4×C12711yescharacteristic
431C22×C4—21no—
432C22×C4—41no—
433Q16—22no—
434Q16—42no—
435Q16—42no—
436Q16—81no—
437SD16—22no—
438M16—81no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8C2×D4×C12711yescharacteristic
445C2×C8C2×D4×C12711yescharacteristic
446C2×C8C2×D4×C12711yescharacteristic
447C2×C8C2×D4×C12711yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
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—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×D4×C12711yescharacteristic
467C4⋊C4C2×D4×C12711yescharacteristic
468C4⋊C4C2×D4×C12711yescharacteristic
469C4⋊C4C2×D4×C12711yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42—41no—
480C42C24×C12711yescharacteristic
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—82no—
493Q8—81no—
494Q8—161no—
495Q8#135×C12712yes—
496Q8#137×C12712yes—
497D4—21no—
498D4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—82no—
513C2×C4C22×D4×C12711yescharacteristic
514C2×C4C22×D4×C12711yescharacteristic
515C2×C4H(5,𝔽2)×C12711yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22D42×C12711yescharacteristic
529C4—22no—
530C4—22no—
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4C2×#135×C12711yescharacteristic
542C4C2×#137×C12711yescharacteristic
543C4#577×C12711yescharacteristic
544C4#578×C12711yescharacteristic
545C2—81no—
546C2C127×#327011yescharacteristic
547C2C127×#328211yescharacteristic
548C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×D4×C127C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#3363C2semidirect
5. C127×#1718C2semidirect
7. C127×#1680C2semidirect
8. C127×#1680C2semidirect
9. C127×#1672C2semidirect
11. C127×#1648C2semidirect
12. C127×#1645C2semidirect
15. C127×#1579C2semidirect
270. #19830C127direct (N × H)
277. #3363C2×C127semidirect
279. #1718C2×C127semidirect
281. #1680C2×C127semidirect
282. #1680C2×C127semidirect
283. #1672C2×C127semidirect
285. #1648C2×C127semidirect
286. #1645C2×C127semidirect
289. #1579C2×C127semidirect
290. C127#19830direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×SD16×C1272
C127×#33642
C127×#33632
C127×#33282
C127×#17182
C127×#17032
C127×#16802
C127×#16722
C127×#16492
C127×#16482
C127×#16452
C127×#16382
C127×#15832
C127×#15792
#19830127