Finite Group Databasebeta

← C127×#19832 #44583505

Subgroups — C127×#19832 #44583505

Order 32512.

580 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3364C211yesmaximal, characteristic, complemented
2C127×#3359C211yesmaximal, characteristic, complemented
3C127×#3340C211yesmaximal, characteristic
4C127×#3329C211yesmaximal, characteristic
5C127×#1718C211yesmaximal, characteristic, complemented
6C127×#1699C211yesmaximal, characteristic, complemented
7C127×#1684C211yesmaximal, characteristic, complemented
8C127×#1679C211yesmaximal, characteristic, complemented
9C127×#1672C211yesmaximal, characteristic, complemented
10C127×#1650C211yesmaximal, characteristic, complemented
11C127×#1649C211yesmaximal, characteristic, complemented
12C127×#1646C211yesmaximal, characteristic
13C127×#1636C211yesmaximal, characteristic, complemented
14C127×#1583C211yesmaximal, characteristic, complemented
15C127×SD16⋊C8C211yesmaximal, characteristic, complemented
16#557×C127C2211yescharacteristic
17#556×C127C2211yescharacteristic
18#555×C127C2211yescharacteristic
19D4×Q8×C127C2211yescharacteristic
20#500×C127C2211yescharacteristic
21#498×C127C2211yescharacteristic
22#488×C127—21no—
23#487×C127—21no—
24#487×C127C2211yescharacteristic
25#487×C127C2211yescharacteristic
26#487×C127C2211yescharacteristic
27#487×C127C2211yescharacteristic
28#485×C127—21no—
29#485×C127—21no—
30#482×C127—21no—
31#479×C127—21no—
32#477×C127C2211yescharacteristic
33#477×C127C2211yescharacteristic
34#475×C127—21no—
35#475×C127C2211yescharacteristic
36#474×C127C2211yescharacteristic
37#474×C127C2211yescharacteristic
38#468×C127—21no—
39#465×C127—21no—
40#464×C127—21no—
41#462×C127C2211yescharacteristic
42#461×C127—21no—
43#461×C127C2211yescharacteristic
44#461×C127C2211yescharacteristic
45#448×C127—21no—
46C8×Q8×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48C4×Q16×C127—21no—
49C4×SD16×C127—21no—
50C4×SD16×C127C2211yescharacteristic
51C4×SD16×C127C2211yescharacteristic
52#436×C127C2211yescharacteristic
53C8×D4×C127C2211yescharacteristic
54#427×C127—21no—
55#419×C127—21no—
56#335×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64D4⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C22×Q8×C127—21no—
68C2×Q16×C127—21no—
69C2×SD16×C127—21no—
70C2×SD16×C127—21no—
71C2×SD16×C127D411yescharacteristic
72C2×SD16×C127D411yescharacteristic
73C2×M16×C127—21no—
74C22×C8×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—41no—
82#125×C127—21no—
83#125×C127—41no—
84#124×C127—21no—
85#124×C127—41no—
86C22⋊Q8×C127—21no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127—41no—
89#121×C127—21no—
90#121×C127—21no—
91C4×Q8×C127—21no—
92C4×Q8×C127—21no—
93C4×Q8×C127—21no—
94C4×Q8×C127C2311yescharacteristic
95C4×Q8×C127C2311yescharacteristic
96C4×D4×C127—21no—
97C4×D4×C127C2311yescharacteristic
98C4×D4×C127C2311yescharacteristic
99#117×C127—21no—
100#117×C127—21no—
101#117×C127—21no—
102#107×C127—21no—
103#107×C127—21no—
104#107×C127—21no—
105#107×C127—21no—
106#107×C127—41no—
107#106×C127—21no—
108#106×C127—21no—
109#106×C127—21no—
110#106×C127D411yescharacteristic
111#106×C127D411yescharacteristic
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#102×C127—21no—
134#102×C127—21no—
135#102×C127D411yescharacteristic
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C22⋊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—42no—
150C2×Q8×C127—81no—
151C2×Q8×C127C2×D411yescharacteristic
152C2×Q8×C127C2×D411yescharacteristic
153C2×D4×C127—41no—
154C2×D4×C127C2×D411yescharacteristic
155C2×D4×C127C2×D411yescharacteristic
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—41no—
159Q16×C127—42no—
160SD16×C127—22no—
161SD16×C127—41no—
162SD16×C127—42no—
163SD16×C127—81no—
164M16×C127—81no—
165C2×C8×C127—21no—
166C2×C8×C127—21no—
167C2×C8×C127—21no—
168C2×C8×C127—21no—
169C2×C8×C127—21no—
170C2×C8×C127—42no—
171C2×C8×C127C2×D411yescharacteristic
172C2×C8×C127C2×D411yescharacteristic
173C2×C8×C127C2×D411yescharacteristic
174C2×C8×C127C2×D411yescharacteristic
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—41no—
186C4⋊C4×C127—41no—
187C4⋊C4×C127—41no—
188C4⋊C4×C127—41no—
189C4⋊C4×C127—41no—
190C4⋊C4×C127C2×D411yescharacteristic
191C4⋊C4×C127C2×D411yescharacteristic
192C4⋊C4×C127C2×D411yescharacteristic
193C4⋊C4×C127C2×D411yescharacteristic
194C22⋊C4×C127—21no—
195C22⋊C4×C127—21no—
196C22⋊C4×C127—41no—
197C22⋊C4×C127—41no—
198C22⋊C4×C127—41no—
199C22⋊C4×C127—41no—
200C22⋊C4×C127—41no—
201C42×C127—21no—
202C42×C127—21no—
203C42×C127—41no—
204C42×C127—41no—
205C42×C127—41no—
206C42×C127C2411yescharacteristic
207C23×C127—21no—
208C23×C127—21no—
209Q8×C127—21no—
210Q8×C127—21no—
211Q8×C127—21no—
212Q8×C127—41no—
213Q8×C127—41no—
214Q8×C127—41no—
215Q8×C127—41no—
216Q8×C127—41no—
217Q8×C127—41no—
218Q8×C127—82no—
219Q8×C127—81no—
220Q8×C127#13512yes—
221D4×C127—21no—
222D4×C127—21no—
223D4×C127—21no—
224D4×C127—21no—
225D4×C127—161no—
226C2×C4×C127—21no—
227C2×C4×C127—21no—
228C2×C4×C127—21no—
229C2×C4×C127—21no—
230C2×C4×C127—21no—
231C2×C4×C127—21no—
232C2×C4×C127—41no—
233C2×C4×C127—41no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—41no—
237C2×C4×C127—41no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—82no—
241C2×C4×C127C22×D411yescharacteristic
242C2×C4×C127C22×D411yescharacteristic
243C2×C4×C127H(5,𝔽2)11yescharacteristic
244C8×C127—21no—
245C8×C127—21no—
246C8×C127—21no—
247C8×C127—21no—
248C8×C127—41no—
249C8×C127—41no—
250C8×C127—41no—
251C8×C127—41no—
252C8×C127—41no—
253C22×C127—41no—
254C22×C127—41no—
255C22×C127—41no—
256C22×C127—41no—
257C22×C127—41no—
258C22×C127—41no—
259C22×C127D4211yescharacteristic
260C4×C127—22no—
261C4×C127—21no—
262C4×C127—41no—
263C4×C127—41no—
264C4×C127—41no—
265C4×C127—41no—
266C4×C127—41no—
267C4×C127—81no—
268C4×C127—81no—
269C4×C127—81no—
270C4×C127—81no—
271C4×C127C2×#13511yescharacteristic
272C4×C127#57511yescharacteristic
273C4×C127#57711yescharacteristic
274C4×C127#57811yescharacteristic
275#19832C12711yesmaximal, characteristic, direct product factor, Sylow
276C2×C127—81no—
277C2×C127—81no—
278C2×C127#326911yescharacteristic
279C2×C127#328211yescharacteristic
280C2×C127#328911yescharacteristic
281#3364C2×C12711yescharacteristic, complemented
282#3359C2×C12711yescharacteristic, complemented
283#3340C2×C12711yescharacteristic
284#3329C2×C12711yescharacteristic
285#1718C2×C12711yescharacteristic, complemented
286#1699C2×C12711yescharacteristic, complemented
287#1684C2×C12711yescharacteristic, complemented
288#1679C2×C12711yescharacteristic, complemented
289#1672C2×C12711yescharacteristic, complemented
290#1650C2×C12711yescharacteristic, complemented
291#1649C2×C12711yescharacteristic, complemented
292#1646C2×C12711yescharacteristic
293#1636C2×C12711yescharacteristic, complemented
294#1583C2×C12711yescharacteristic, complemented
295SD16⋊C8C2×C12711yescharacteristic, complemented
296C127#1983211yescharacteristic, direct product factor, Sylow
297#557C22×C12711yescharacteristic
298#556C22×C12711yescharacteristic
299#555C22×C12711yescharacteristic
300D4×Q8C22×C12711yescharacteristic
301#500C22×C12711yescharacteristic
302#498C22×C12711yescharacteristic
303#488—21no—
304#487—21no—
305#487C22×C12711yescharacteristic
306#487C22×C12711yescharacteristic
307#487C22×C12711yescharacteristic
308#487C22×C12711yescharacteristic
309#485—21no—
310#485—21no—
311#482—21no—
312#479—21no—
313#477C22×C12711yescharacteristic
314#477C22×C12711yescharacteristic
315#475—21no—
316#475C22×C12711yescharacteristic
317#474C22×C12711yescharacteristic
318#474C22×C12711yescharacteristic
319#468—21no—
320#465—21no—
321#464—21no—
322#462C22×C12711yescharacteristic
323#461—21no—
324#461C22×C12711yescharacteristic
325#461C22×C12711yescharacteristic
326#448—21no—
327C8×Q8C22×C12711yescharacteristic
328C8×Q8C22×C12711yescharacteristic
329C4×Q16—21no—
330C4×SD16—21no—
331C4×SD16C22×C12711yescharacteristic
332C4×SD16C22×C12711yescharacteristic
333#436C22×C12711yescharacteristic
334C8×D4C22×C12711yescharacteristic
335#427—21no—
336#419—21no—
337#335C22×C12711yescharacteristic
338#334C22×C12711yescharacteristic
339#333C22×C12711yescharacteristic
340#332C22×C12711yescharacteristic
341#332C22×C12711yescharacteristic
342#332C22×C12711yescharacteristic
343Q8⋊C8C22×C12711yescharacteristic
344Q8⋊C8C22×C12711yescharacteristic
345D4⋊C8C22×C12711yescharacteristic
346D4⋊C8C22×C12711yescharacteristic
347#322C22×C12711yescharacteristic
348C22×Q8—21no—
349C2×Q16—21no—
350C2×SD16—21no—
351C2×SD16—21no—
352C2×SD16D4×C12711yescharacteristic
353C2×SD16D4×C12711yescharacteristic
354C2×M16—21no—
355C22×C8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8C23×C12711yescharacteristic
359C4⋊Q8C23×C12711yescharacteristic
360C4⋊Q8C23×C12711yescharacteristic
361C4⋊Q8C23×C12711yescharacteristic
362#126—41no—
363#125—21no—
364#125—41no—
365#124—21no—
366#124—41no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—41no—
370#121—21no—
371#121—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C23×C12711yescharacteristic
376C4×Q8C23×C12711yescharacteristic
377C4×D4—21no—
378C4×D4C23×C12711yescharacteristic
379C4×D4C23×C12711yescharacteristic
380#117—21no—
381#117—21no—
382#117—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—41no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106D4×C12711yescharacteristic
392#106D4×C12711yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—21no—
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#103—21no—
409#103—21no—
410#103—21no—
411#103—41no—
412#103D4×C12711yescharacteristic
413#103D4×C12711yescharacteristic
414#102—21no—
415#102—21no—
416#102D4×C12711yescharacteristic
417#102D4×C12711yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—21no—
420C4×C8—21no—
421C4×C8—21no—
422C4×C8C23×C12711yescharacteristic
423C4×C8C23×C12711yescharacteristic
424C4×C8C23×C12711yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—42no—
431C2×Q8—81no—
432C2×Q8C2×D4×C12711yescharacteristic
433C2×Q8C2×D4×C12711yescharacteristic
434C2×D4—41no—
435C2×D4C2×D4×C12711yescharacteristic
436C2×D4C2×D4×C12711yescharacteristic
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—41no—
440Q16—42no—
441SD16—22no—
442SD16—41no—
443SD16—42no—
444SD16—81no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—42no—
452C2×C8C2×D4×C12711yescharacteristic
453C2×C8C2×D4×C12711yescharacteristic
454C2×C8C2×D4×C12711yescharacteristic
455C2×C8C2×D4×C12711yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C12711yescharacteristic
472C4⋊C4C2×D4×C12711yescharacteristic
473C4⋊C4C2×D4×C12711yescharacteristic
474C4⋊C4C2×D4×C12711yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—41no—
486C42—41no—
487C42C24×C12711yescharacteristic
488C23—21no—
489C23—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—82no—
500Q8—81no—
501Q8#135×C12712yes—
502D4—21no—
503D4—21no—
504D4—21no—
505D4—21no—
506D4—161no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4C22×D4×C12711yescharacteristic
523C2×C4C22×D4×C12711yescharacteristic
524C2×C4H(5,𝔽2)×C12711yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22D42×C12711yescharacteristic
541C4—22no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×#135×C12711yescharacteristic
553C4#575×C12711yescharacteristic
554C4#577×C12711yescharacteristic
555C4#578×C12711yescharacteristic
556C2—81no—
557C2—81no—
558C2C127×#326911yescharacteristic
559C2C127×#328211yescharacteristic
560C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radical#555×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3364C2semidirect
2. C127×#3359C2semidirect
5. C127×#1718C2semidirect
6. C127×#1699C2semidirect
7. C127×#1684C2semidirect
8. C127×#1679C2semidirect
9. C127×#1672C2semidirect
10. C127×#1650C2semidirect
11. C127×#1649C2semidirect
13. C127×#1636C2semidirect
14. C127×#1583C2semidirect
15. C127×SD16⋊C8C2semidirect
275. #19832C127direct (N × H)
281. #3364C2×C127semidirect
282. #3359C2×C127semidirect
285. #1718C2×C127semidirect
286. #1699C2×C127semidirect
287. #1684C2×C127semidirect
288. #1679C2×C127semidirect
289. #1672C2×C127semidirect
290. #1650C2×C127semidirect
291. #1649C2×C127semidirect
293. #1636C2×C127semidirect
294. #1583C2×C127semidirect
295. SD16⋊C8C2×C127semidirect
296. C127#19832direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#33642
C127×#33592
C127×#33402
C127×#33292
C127×#17182
C127×#16992
C127×#16842
C127×#16792
C127×#16722
C127×#16502
C127×#16492
C127×#16462
C127×#16362
C127×#15832
C127×SD16⋊C82
#19832127