Finite Group Databasebeta

← C127×#19649 #44583322

Subgroups — C127×#19649 #44583322

Order 32512.

720 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3231C211yesmaximal, characteristic, complemented
2C127×#3207C211yesmaximal, characteristic
3C127×#3182C211yesmaximal, characteristic, complemented
4C127×#3182C211yesmaximal, characteristic, complemented
5C127×#3167C211yesmaximal, characteristic, complemented
6C127×#3131C211yesmaximal, characteristic, complemented
7C127×#1718C211yesmaximal, characteristic, complemented
8C127×#1717C211yesmaximal, characteristic, complemented
9C127×#1714C211yesmaximal, characteristic, complemented
10C127×#1714C211yesmaximal, characteristic, complemented
11C127×#1711C211yesmaximal, characteristic, complemented
12C127×#1710C211yesmaximal, characteristic, complemented
13C127×#1708C211yesmaximal, characteristic, complemented
14C127×#1706C211yesmaximal, characteristic, complemented
15C8×M16×C127C211yesmaximal, characteristic, complemented
16#533×C127C2211yescharacteristic
17#533×C127C2211yescharacteristic
18#532×C127C2211yescharacteristic
19#532×C127C2211yescharacteristic
20#500×C127C2211yescharacteristic
21#500×C127C2211yescharacteristic
22#500×C127C2211yescharacteristic
23#498×C127C2211yescharacteristic
24#498×C127C2211yescharacteristic
25#493×C127C2211yescharacteristic
26#492×C127C2211yescharacteristic
27#492×C127C2211yescharacteristic
28#492×C127C2211yescharacteristic
29#492×C127C2211yescharacteristic
30#488×C127—22no—
31#487×C127C2211yescharacteristic
32#487×C127C2211yescharacteristic
33#487×C127C2211yescharacteristic
34#487×C127C2211yescharacteristic
35#487×C127C2211yescharacteristic
36#487×C127C2211yescharacteristic
37#487×C127C2211yescharacteristic
38#487×C127C2211yescharacteristic
39#486×C127C2211yescharacteristic
40#486×C127C2211yescharacteristic
41#486×C127C2211yescharacteristic
42#486×C127C2211yescharacteristic
43#486×C127C2211yescharacteristic
44#486×C127C2211yescharacteristic
45#485×C127—22no—
46#479×C127—22no—
47#468×C127—22no—
48#468×C127—22no—
49#465×C127—22no—
50#463×C127—22no—
51#449×C127—22no—
52#440×C127—22no—
53#440×C127—22no—
54C4×SD16×C127—22no—
55#431×C127C2211yescharacteristic
56#416×C127—22no—
57C4×M16×C127C2211yescharacteristic
58C2×C4×C8×C127C2211yescharacteristic
59#322×C127C2211yescharacteristic
60#322×C127C2211yescharacteristic
61C82×C127C2211yescharacteristic
62C82×C127C2211yescharacteristic
63C2×#41×C127—21no—
64C2×#41×C127—21no—
65C2×SD16×C127—22no—
66C2×SD16×C127—22no—
67C2×SD16×C127—22no—
68C2×SD16×C127—22no—
69C2×D8×C127—22no—
70C2×M16×C127D412yes—
71C22×C8×C127D412yes—
72C4⋊Q8×C127C2311yescharacteristic
73C4⋊Q8×C127C2311yescharacteristic
74C4⋊Q8×C127C2311yescharacteristic
75C4⋊Q8×C127C2311yescharacteristic
76C4⋊Q8×C127C2311yescharacteristic
77C4⋊Q8×C127C2311yescharacteristic
78#127×C127C2311yescharacteristic
79#127×C127C2311yescharacteristic
80#125×C127—21no—
81#125×C127—21no—
82#124×C127—21no—
83#124×C127—21no—
84C22⋊Q8×C127—21no—
85C22⋊Q8×C127—21no—
86C22⋊Q8×C127—21no—
87C22⋊Q8×C127—21no—
88#121×C127—21no—
89#121×C127—21no—
90#121×C127—21no—
91#121×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×C127—21no—
99C4×D4×C127—21no—
100#117×C127—21no—
101#117×C127—21no—
102C2×C42×C127C2311yescharacteristic
103#107×C127—22no—
104#107×C127—22no—
105#107×C127—22no—
106#106×C127—22no—
107#106×C127—22no—
108C4⋊C8×C127D412yes—
109#103×C127—22no—
110#103×C127—22no—
111#103×C127—22no—
112#103×C127—22no—
113#103×C127—22no—
114#103×C127—22no—
115#103×C127—22no—
116#103×C127—22no—
117#102×C127—22no—
118#102×C127—22no—
119#102×C127—22no—
120#102×C127—22no—
121#102×C127—22no—
122#102×C127—22no—
123C22⋊C8×C127D412yes—
124#97×C127D412yes—
125C4×C8×C127D412yes—
126C4×C8×C127C2311yescharacteristic
127C4×C8×C127C2311yescharacteristic
128C4×C8×C127C2311yescharacteristic
129C4×C8×C127C2311yescharacteristic
130C4×C8×C127C2311yescharacteristic
131C4×C8×C127C2311yescharacteristic
132#41×C127—44no—
133#41×C127—82no—
134C2×Q8×C127—21no—
135C2×Q8×C127—21no—
136C2×Q8×C127—21no—
137C2×Q8×C127—21no—
138C2×Q8×C127—21no—
139C2×Q8×C127—21no—
140C2×D4×C127—21no—
141C2×D4×C127—21no—
142C2×D4×C127—21no—
143C2×D4×C127—21no—
144C2×D4×C127—21no—
145C2×D4×C127—21no—
146C2×D4×C127—41no—
147C2×D4×C127—41no—
148C22×C4×C127—41no—
149C22×C4×C127—41no—
150C22×C4×C127C2×D411yescharacteristic
151C22×C4×C127C2×D411yescharacteristic
152C22×C4×C127C2×D411yescharacteristic
153SD16×C127—44no—
154SD16×C127—44no—
155SD16×C127—44no—
156SD16×C127—82no—
157D8×C127—82no—
158M16×C127—24no—
159C2×C8×C127—42no—
160C2×C8×C127C2×D412yes—
161C2×C8×C127C2×D412yes—
162C2×C8×C127C2×D412yes—
163C2×C8×C127C2×D412yes—
164C2×C8×C127C2×D412yes—
165C2×C8×C127C2×D412yes—
166C4⋊C4×C127—21no—
167C4⋊C4×C127—21no—
168C4⋊C4×C127—21no—
169C4⋊C4×C127—21no—
170C4⋊C4×C127—21no—
171C4⋊C4×C127—21no—
172C4⋊C4×C127—21no—
173C4⋊C4×C127—21no—
174C4⋊C4×C127—21no—
175C4⋊C4×C127—21no—
176C4⋊C4×C127—21no—
177C4⋊C4×C127—21no—
178C4⋊C4×C127—41no—
179C4⋊C4×C127—41no—
180C4⋊C4×C127—41no—
181C4⋊C4×C127—41no—
182C22⋊C4×C127—41no—
183C22⋊C4×C127—41no—
184C22⋊C4×C127—41no—
185C22⋊C4×C127—41no—
186C22⋊C4×C127—41no—
187C22⋊C4×C127—41no—
188C42×C127—41no—
189C42×C127—41no—
190C42×C127C2×D411yescharacteristic
191C42×C127C2×D411yescharacteristic
192C42×C127C2×D411yescharacteristic
193C42×C127C2411yescharacteristic
194C23×C127—41no—
195C23×C127—41no—
196C23×C127#12711yescharacteristic
197Q8×C127—42no—
198Q8×C127—42no—
199Q8×C127—42no—
200Q8×C127—42no—
201Q8×C127—42no—
202Q8×C127—42no—
203D4×C127—42no—
204D4×C127—42no—
205D4×C127—42no—
206D4×C127—42no—
207D4×C127—42no—
208D4×C127—42no—
209D4×C127—82no—
210D4×C127—82no—
211C2×C4×C127—22no—
212C2×C4×C127—22no—
213C2×C4×C127—22no—
214C2×C4×C127—41no—
215C2×C4×C127—41no—
216C2×C4×C127—41no—
217C2×C4×C127—41no—
218C2×C4×C127—41no—
219C2×C4×C127—41no—
220C2×C4×C127—82no—
221C2×C4×C127—82no—
222C2×C4×C127#12711yescharacteristic
223C2×C4×C127#12711yescharacteristic
224C2×C4×C127#12711yescharacteristic
225C2×C4×C127C22×D411yescharacteristic
226C2×C4×C127C22×D411yescharacteristic
227C2×C4×C127C22×D411yescharacteristic
228C8×C127—22no—
229C8×C127—22no—
230C8×C127—22no—
231C8×C127—22no—
232C8×C127—22no—
233C8×C127#13514yes—
234C22×C127—21no—
235C22×C127—21no—
236C22×C127—21no—
237C22×C127—81no—
238C22×C127—81no—
239C22×C127—81no—
240C22×C127—81no—
241C22×C127—81no—
242C22×C127—81no—
243C22×C127C2×#12711yescharacteristic
244C4×C127—21no—
245C4×C127—21no—
246C4×C127—21no—
247C4×C127—81no—
248C4×C127—81no—
249C4×C127—81no—
250C4×C127—81no—
251C4×C127—81no—
252C4×C127—81no—
253C4×C127C2×#13512yes—
254C4×C127#57512yes—
255C4×C127#57712yes—
256#19649C12711yesmaximal, characteristic, direct product factor, Sylow
257C2×C127—41no—
258C2×C127—161no—
259C2×C127—161no—
260C2×C127#314711yescharacteristic
261C2×C127#315311yescharacteristic
262C2×C127#315411yescharacteristic
263#3231C2×C12711yescharacteristic, complemented
264#3207C2×C12711yescharacteristic
265#3182C2×C12711yescharacteristic, complemented
266#3182C2×C12711yescharacteristic, complemented
267#3167C2×C12711yescharacteristic, complemented
268#3131C2×C12711yescharacteristic, complemented
269#1718C2×C12711yescharacteristic, complemented
270#1717C2×C12711yescharacteristic, complemented
271#1714C2×C12711yescharacteristic, complemented
272#1714C2×C12711yescharacteristic, complemented
273#1711C2×C12711yescharacteristic, complemented
274#1710C2×C12711yescharacteristic, complemented
275#1708C2×C12711yescharacteristic, complemented
276#1706C2×C12711yescharacteristic, complemented
277C8×M16C2×C12711yescharacteristic, complemented
278C127#1964911yescharacteristic, direct product factor, Sylow
279#533C22×C12711yescharacteristic
280#533C22×C12711yescharacteristic
281#532C22×C12711yescharacteristic
282#532C22×C12711yescharacteristic
283#500C22×C12711yescharacteristic
284#500C22×C12711yescharacteristic
285#500C22×C12711yescharacteristic
286#498C22×C12711yescharacteristic
287#498C22×C12711yescharacteristic
288#493C22×C12711yescharacteristic
289#492C22×C12711yescharacteristic
290#492C22×C12711yescharacteristic
291#492C22×C12711yescharacteristic
292#492C22×C12711yescharacteristic
293#488—22no—
294#487C22×C12711yescharacteristic
295#487C22×C12711yescharacteristic
296#487C22×C12711yescharacteristic
297#487C22×C12711yescharacteristic
298#487C22×C12711yescharacteristic
299#487C22×C12711yescharacteristic
300#487C22×C12711yescharacteristic
301#487C22×C12711yescharacteristic
302#486C22×C12711yescharacteristic
303#486C22×C12711yescharacteristic
304#486C22×C12711yescharacteristic
305#486C22×C12711yescharacteristic
306#486C22×C12711yescharacteristic
307#486C22×C12711yescharacteristic
308#485—22no—
309#479—22no—
310#468—22no—
311#468—22no—
312#465—22no—
313#463—22no—
314#449—22no—
315#440—22no—
316#440—22no—
317C4×SD16—22no—
318#431C22×C12711yescharacteristic
319#416—22no—
320C4×M16C22×C12711yescharacteristic
321C2×C4×C8C22×C12711yescharacteristic
322#322C22×C12711yescharacteristic
323#322C22×C12711yescharacteristic
324C82C22×C12711yescharacteristic
325C82C22×C12711yescharacteristic
326C2×#41—21no—
327C2×#41—21no—
328C2×SD16—22no—
329C2×SD16—22no—
330C2×SD16—22no—
331C2×SD16—22no—
332C2×D8—22no—
333C2×M16D4×C12712yes—
334C22×C8D4×C12712yes—
335C4⋊Q8C23×C12711yescharacteristic
336C4⋊Q8C23×C12711yescharacteristic
337C4⋊Q8C23×C12711yescharacteristic
338C4⋊Q8C23×C12711yescharacteristic
339C4⋊Q8C23×C12711yescharacteristic
340C4⋊Q8C23×C12711yescharacteristic
341#127C23×C12711yescharacteristic
342#127C23×C12711yescharacteristic
343#125—21no—
344#125—21no—
345#124—21no—
346#124—21no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351#121—21no—
352#121—21no—
353#121—21no—
354#121—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363#117—21no—
364#117—21no—
365C2×C42C23×C12711yescharacteristic
366#107—22no—
367#107—22no—
368#107—22no—
369#106—22no—
370#106—22no—
371C4⋊C8D4×C12712yes—
372#103—22no—
373#103—22no—
374#103—22no—
375#103—22no—
376#103—22no—
377#103—22no—
378#103—22no—
379#103—22no—
380#102—22no—
381#102—22no—
382#102—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386C22⋊C8D4×C12712yes—
387#97D4×C12712yes—
388C4×C8D4×C12712yes—
389C4×C8C23×C12711yescharacteristic
390C4×C8C23×C12711yescharacteristic
391C4×C8C23×C12711yescharacteristic
392C4×C8C23×C12711yescharacteristic
393C4×C8C23×C12711yescharacteristic
394C4×C8C23×C12711yescharacteristic
395#41—44no—
396#41—82no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—41no—
410C2×D4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4C2×D4×C12711yescharacteristic
414C22×C4C2×D4×C12711yescharacteristic
415C22×C4C2×D4×C12711yescharacteristic
416SD16—44no—
417SD16—44no—
418SD16—44no—
419SD16—82no—
420D8—82no—
421M16—24no—
422C2×C8—42no—
423C2×C8C2×D4×C12712yes—
424C2×C8C2×D4×C12712yes—
425C2×C8C2×D4×C12712yes—
426C2×C8C2×D4×C12712yes—
427C2×C8C2×D4×C12712yes—
428C2×C8C2×D4×C12712yes—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C42—41no—
452C42—41no—
453C42C2×D4×C12711yescharacteristic
454C42C2×D4×C12711yescharacteristic
455C42C2×D4×C12711yescharacteristic
456C42C24×C12711yescharacteristic
457C23—41no—
458C23—41no—
459C23#127×C12711yescharacteristic
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—42no—
466D4—42no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—82no—
473D4—82no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—82no—
485C2×C4#127×C12711yescharacteristic
486C2×C4#127×C12711yescharacteristic
487C2×C4#127×C12711yescharacteristic
488C2×C4C22×D4×C12711yescharacteristic
489C2×C4C22×D4×C12711yescharacteristic
490C2×C4C22×D4×C12711yescharacteristic
491C8—22no—
492C8—22no—
493C8—22no—
494C8—22no—
495C8—22no—
496C8#135×C12714yes—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22C2×#127×C12711yescharacteristic
507C4—21no—
508C4—21no—
509C4—21no—
510C4—81no—
511C4—81no—
512C4—81no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4C2×#135×C12712yes—
517C4#575×C12712yes—
518C4#577×C12712yes—
519C2—41no—
520C2—161no—
521C2—161no—
522C2C127×#314711yescharacteristic
523C2C127×#315311yescharacteristic
524C2C127×#315411yescharacteristic
subgroupG/H
center, socleC22×C127C2×#127
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3207C2
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×#3231C2semidirect
3. C127×#3182C2semidirect
4. C127×#3182C2semidirect
5. C127×#3167C2semidirect
6. C127×#3131C2semidirect
7. C127×#1718C2semidirect
8. C127×#1717C2semidirect
9. C127×#1714C2semidirect
10. C127×#1714C2semidirect
11. C127×#1711C2semidirect
12. C127×#1710C2semidirect
13. C127×#1708C2semidirect
14. C127×#1706C2semidirect
15. C8×M16×C127C2semidirect
256. #19649C127direct (N × H)
263. #3231C2×C127semidirect
265. #3182C2×C127semidirect
266. #3182C2×C127semidirect
267. #3167C2×C127semidirect
268. #3131C2×C127semidirect
269. #1718C2×C127semidirect
270. #1717C2×C127semidirect
271. #1714C2×C127semidirect
272. #1714C2×C127semidirect
273. #1711C2×C127semidirect
274. #1710C2×C127semidirect
275. #1708C2×C127semidirect
276. #1706C2×C127semidirect
277. C8×M16C2×C127semidirect
278. C127#19649direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32312
C127×#32072
C127×#31822
C127×#31672
C127×#31312
C127×#17182
C127×#17172
C127×#17142
C127×#17112
C127×#17102
C127×#17082
C127×#17062
C8×M16×C1272
#19649127