Finite Group Databasebeta

← C127×#18429 #44582102

Subgroups — C127×#18429 #44582102

Order 32512.

932 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3561C211yesmaximal, characteristic
2C127×#3218C211yesmaximal, characteristic, complemented
3C127×#3209C211yesmaximal, characteristic, complemented
4C127×#2640C211yesmaximal, characteristic, complemented
5C127×#1606C214yesmaximal, complemented
6C127×#1602C214yesmaximal, complemented
7C127×#1506C211yesmaximal, characteristic, complemented
8C127×#1500C211yesmaximal, characteristic, complemented
9C127×#1469C211yesmaximal, characteristic, complemented
10#563×C127—21no—
11#562×C127—21no—
12#556×C127—21no—
13#551×C127—22no—
14D4×Q8×C127—21no—
15#548×C127—21no—
16#546×C127—21no—
17#543×C127C2212yes—
18#542×C127—21no—
19#542×C127—22no—
20#538×C127C2212yes—
21#536×C127—21no—
22#533×C127C2211yescharacteristic
23C2×C4⋊Q8×C127C2211yescharacteristic
24#529×C127C2211yescharacteristic
25C2×#124×C127C2211yescharacteristic
26#497×C127—21no—
27#494×C127—21no—
28#491×C127—21no—
29#487×C127—21no—
30#462×C127—22no—
31#462×C127—21no—
32#461×C127—21no—
33#451×C127C2212yes—
34#451×C127C2214yes—
35#448×C127C2212yes—
36#432×C127C2211yescharacteristic
37#431×C127C2211yescharacteristic
38#397×C127—22no—
39#393×C127C2214yes—
40#391×C127—21no—
41#390×C127—21no—
42#376×C127C2211yescharacteristic
43#328×C127C2212yes—
44#328×C127C2214yes—
45#327×C127C2212yes—
46#323×C127C2214yes—
47C2×#41×C127—21no—
48C22×Q8×C127—21no—
49C22×Q8×C127D411yescharacteristic
50C22×Q8×C127C2312yes—
51C22×D4×C127D411yescharacteristic
52C2×Q16×C127—22no—
53C2×Q16×C127—24no—
54C2×SD16×C127—22no—
55C4⋊Q8×C127—21no—
56C4⋊Q8×C127—22no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127—21no—
60C4⋊Q8×C127—21no—
61C4⋊Q8×C127D411yescharacteristic
62C4⋊Q8×C127D411yescharacteristic
63#126×C127—22no—
64#126×C127—22no—
65#126×C127—22no—
66#126×C127—21no—
67#125×C127—21no—
68#125×C127D411yescharacteristic
69#124×C127—21no—
70#124×C127—22no—
71#124×C127—22no—
72#124×C127—21no—
73#124×C127—21no—
74#124×C127—21no—
75#124×C127—21no—
76#124×C127D411yescharacteristic
77#123×C127—22no—
78#123×C127—22no—
79#123×C127—22no—
80#123×C127—21no—
81#123×C127—22no—
82C22⋊Q8×C127—22no—
83C22⋊Q8×C127—21no—
84C22⋊Q8×C127—22no—
85C22⋊Q8×C127—22no—
86C22⋊Q8×C127—22no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127—22no—
89C22⋊Q8×C127—22no—
90C22⋊Q8×C127—22no—
91C22⋊Q8×C127C2311yescharacteristic
92C22⋊Q8×C127C2312yes—
93#121×C127—21no—
94#121×C127—22no—
95#121×C127—22no—
96#121×C127C2311yescharacteristic
97#120×C127—22no—
98C4×Q8×C127—21no—
99C4×Q8×C127—21no—
100C4×Q8×C127D411yescharacteristic
101C4×Q8×C127D412yes—
102C4×D4×C127—21no—
103C4×D4×C127—22no—
104C4×D4×C127—21no—
105C4×D4×C127—22no—
106C4×D4×C127D411yescharacteristic
107#117×C127—22no—
108#117×C127—21no—
109#117×C127—21no—
110C2×C4⋊C4×C127—21no—
111C2×C4⋊C4×C127—21no—
112C2×C22⋊C4×C127—22no—
113C2×C22⋊C4×C127—24no—
114C2×C22⋊C4×C127D412yes—
115C2×C22⋊C4×C127C2312yes—
116C2×C42×C127—21no—
117C2×C42×C127C2311yescharacteristic
118C4⋊C8×C127—21no—
119C4⋊C8×C127—21no—
120#103×C127—22no—
121#103×C127—22no—
122#103×C127—24no—
123C22⋊C8×C127C2312yes—
124C22⋊C8×C127C2312yes—
125#97×C127—21no—
126C4×C8×C127—21no—
127#95×C127—21no—
128#95×C127—24no—
129#95×C127C2312yes—
130C24×C127C2×D412yes—
131#41×C127—82no—
132C2×Q8×C127—22no—
133C2×Q8×C127—21no—
134C2×Q8×C127—21no—
135C2×Q8×C127—21no—
136C2×Q8×C127—22no—
137C2×Q8×C127—22no—
138C2×Q8×C127—42no—
139C2×Q8×C127—82no—
140C2×Q8×C127—82no—
141C2×Q8×C127C2×D411yescharacteristic
142C2×Q8×C127C2×D412yes—
143C2×D4×C127—21no—
144C2×D4×C127—22no—
145C2×D4×C127—22no—
146C2×D4×C127—21no—
147C2×D4×C127—21no—
148C2×D4×C127—42no—
149C2×D4×C127C2×D411yescharacteristic
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—21no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127C2×D411yescharacteristic
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2411yescharacteristic
160Q16×C127—82no—
161Q16×C127—84no—
162SD16×C127—82no—
163C2×C8×C127—22no—
164C2×C8×C127—22no—
165C4⋊C4×C127—22no—
166C4⋊C4×C127—22no—
167C4⋊C4×C127—22no—
168C4⋊C4×C127—22no—
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—22no—
176C4⋊C4×C127—21no—
177C4⋊C4×C127—22no—
178C4⋊C4×C127—41no—
179C4⋊C4×C127—41no—
180C4⋊C4×C127—41no—
181C4⋊C4×C127—41no—
182C4⋊C4×C127C2×D411yescharacteristic
183C4⋊C4×C127C2×D411yescharacteristic
184C4⋊C4×C127C2×D412yes—
185C22⋊C4×C127—22no—
186C22⋊C4×C127—22no—
187C22⋊C4×C127—22no—
188C22⋊C4×C127—22no—
189C22⋊C4×C127—22no—
190C22⋊C4×C127—21no—
191C22⋊C4×C127—22no—
192C22⋊C4×C127—22no—
193C22⋊C4×C127—22no—
194C22⋊C4×C127—21no—
195C22⋊C4×C127—21no—
196C22⋊C4×C127—21no—
197C22⋊C4×C127—22no—
198C22⋊C4×C127—22no—
199C22⋊C4×C127—21no—
200C22⋊C4×C127—84no—
201C42×C127—22no—
202C42×C127—22no—
203C42×C127—21no—
204C42×C127—42no—
205C42×C127C2×D411yescharacteristic
206C42×C127C2×D411yescharacteristic
207C42×C127C2×D411yescharacteristic
208C42×C127C2×D411yescharacteristic
209C23×C127—22no—
210C23×C127—21no—
211C23×C127—24no—
212C23×C127—42no—
213C23×C127—42no—
214C23×C127C22×D411yescharacteristic
215Q8×C127—41no—
216Q8×C127—42no—
217Q8×C127—42no—
218Q8×C127—42no—
219Q8×C127—44no—
220Q8×C127—42no—
221Q8×C127—42no—
222Q8×C127—81no—
223Q8×C127—82no—
224D4×C127—41no—
225D4×C127—42no—
226D4×C127—42no—
227D4×C127—81no—
228D4×C127—82no—
229D4×C127—82no—
230C2×C4×C127—22no—
231C2×C4×C127—22no—
232C2×C4×C127—21no—
233C2×C4×C127—22no—
234C2×C4×C127—21no—
235C2×C4×C127—22no—
236C2×C4×C127—22no—
237C2×C4×C127—21no—
238C2×C4×C127—41no—
239C2×C4×C127—42no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127—42no—
243C2×C4×C127—44no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127—82no—
247C2×C4×C127—82no—
248C2×C4×C127—82no—
249C2×C4×C127#12011yescharacteristic
250C2×C4×C127#12011yescharacteristic
251C2×C4×C127#12011yescharacteristic
252C2×C4×C127#12011yescharacteristic
253C2×C4×C127C22×D411yescharacteristic
254C2×C4×C127C22×D411yescharacteristic
255C8×C127—42no—
256C8×C127—42no—
257C22×C127—21no—
258C22×C127—21no—
259C22×C127—41no—
260C22×C127—42no—
261C22×C127—41no—
262C22×C127—42no—
263C22×C127—42no—
264C22×C127—41no—
265C22×C127—84no—
266C22×C127C2×#12011yescharacteristic
267C22×C127#57812yes—
268C4×C127—21no—
269C4×C127—21no—
270C4×C127—21no—
271C4×C127—21no—
272C4×C127—21no—
273C4×C127—41no—
274C4×C127—41no—
275C4×C127—42no—
276C4×C127—42no—
277C4×C127—41no—
278C4×C127—42no—
279C4×C127—82no—
280C4×C127—82no—
281C4×C127#45512yes—
282#18429C12711yesmaximal, characteristic, direct product factor, Sylow
283C2×C127—22no—
284C2×C127—81no—
285C2×C127—82no—
286C2×C127#301111yescharacteristic
287C2×C127C2×#45511yescharacteristic
288C2×C127#302711yescharacteristic
289#3561C2×C12711yescharacteristic
290#3218C2×C12711yescharacteristic, complemented
291#3209C2×C12711yescharacteristic, complemented
292#2640C2×C12711yescharacteristic, complemented
293#1606C2×C12714yescomplemented
294#1602C2×C12714yescomplemented
295#1506C2×C12711yescharacteristic, complemented
296#1500C2×C12711yescharacteristic, complemented
297#1469C2×C12711yescharacteristic, complemented
298C127#1842911yescharacteristic, direct product factor, Sylow
299#563—21no—
300#562—21no—
301#556—21no—
302#551—22no—
303D4×Q8—21no—
304#548—21no—
305#546—21no—
306#543C22×C12712yes—
307#542—21no—
308#542—22no—
309#538C22×C12712yes—
310#536—21no—
311#533C22×C12711yescharacteristic
312C2×C4⋊Q8C22×C12711yescharacteristic
313#529C22×C12711yescharacteristic
314C2×#124C22×C12711yescharacteristic
315#497—21no—
316#494—21no—
317#491—21no—
318#487—21no—
319#462—22no—
320#462—21no—
321#461—21no—
322#451C22×C12712yes—
323#451C22×C12714yes—
324#448C22×C12712yes—
325#432C22×C12711yescharacteristic
326#431C22×C12711yescharacteristic
327#397—22no—
328#393C22×C12714yes—
329#391—21no—
330#390—21no—
331#376C22×C12711yescharacteristic
332#328C22×C12712yes—
333#328C22×C12714yes—
334#327C22×C12712yes—
335#323C22×C12714yes—
336C2×#41—21no—
337C22×Q8—21no—
338C22×Q8D4×C12711yescharacteristic
339C22×Q8C23×C12712yes—
340C22×D4D4×C12711yescharacteristic
341C2×Q16—24no—
342C2×Q16—22no—
343C2×SD16—22no—
344C4⋊Q8—21no—
345C4⋊Q8—22no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8D4×C12711yescharacteristic
351C4⋊Q8D4×C12711yescharacteristic
352#126—22no—
353#126—22no—
354#126—22no—
355#126—21no—
356#125—21no—
357#125D4×C12711yescharacteristic
358#124—21no—
359#124—22no—
360#124—22no—
361#124—21no—
362#124—21no—
363#124—21no—
364#124—21no—
365#124D4×C12711yescharacteristic
366#123—22no—
367#123—22no—
368#123—22no—
369#123—21no—
370#123—22no—
371C22⋊Q8—22no—
372C22⋊Q8—21no—
373C22⋊Q8—22no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8—21no—
377C22⋊Q8—22no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8C23×C12711yescharacteristic
381C22⋊Q8C23×C12712yes—
382#121—21no—
383#121—22no—
384#121—22no—
385#121C23×C12711yescharacteristic
386#120—22no—
387C4×Q8—21no—
388C4×Q8—21no—
389C4×Q8D4×C12711yescharacteristic
390C4×Q8D4×C12712yes—
391C4×D4—21no—
392C4×D4—22no—
393C4×D4—21no—
394C4×D4—22no—
395C4×D4D4×C12711yescharacteristic
396#117—22no—
397#117—21no—
398#117—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4D4×C12712yes—
404C2×C22⋊C4C23×C12712yes—
405C2×C42—21no—
406C2×C42C23×C12711yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—21no—
409#103—22no—
410#103—22no—
411#103—24no—
412C22⋊C8C23×C12712yes—
413C22⋊C8C23×C12712yes—
414#97—21no—
415C4×C8—21no—
416#95—21no—
417#95—24no—
418#95C23×C12712yes—
419C24C2×D4×C12712yes—
420#41—82no—
421C2×Q8—22no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—42no—
428C2×Q8—82no—
429C2×Q8—82no—
430C2×Q8C2×D4×C12711yescharacteristic
431C2×Q8C2×D4×C12712yes—
432C2×D4—21no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—42no—
438C2×D4C2×D4×C12711yescharacteristic
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4C2×D4×C12711yescharacteristic
446C22×C4C2×D4×C12711yescharacteristic
447C22×C4C2×D4×C12712yes—
448C22×C4C24×C12711yescharacteristic
449Q16—82no—
450Q16—84no—
451SD16—82no—
452C2×C8—22no—
453C2×C8—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4C2×D4×C12711yescharacteristic
472C4⋊C4C2×D4×C12711yescharacteristic
473C4⋊C4C2×D4×C12712yes—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—84no—
490C42—22no—
491C42—22no—
492C42—21no—
493C42—42no—
494C42C2×D4×C12711yescharacteristic
495C42C2×D4×C12711yescharacteristic
496C42C2×D4×C12711yescharacteristic
497C42C2×D4×C12711yescharacteristic
498C23—22no—
499C23—21no—
500C23—24no—
501C23—42no—
502C23—42no—
503C23C22×D4×C12711yescharacteristic
504Q8—41no—
505Q8—42no—
506Q8—42no—
507Q8—42no—
508Q8—44no—
509Q8—42no—
510Q8—42no—
511Q8—81no—
512Q8—82no—
513D4—41no—
514D4—42no—
515D4—42no—
516D4—81no—
517D4—82no—
518D4—82no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4#120×C12711yescharacteristic
539C2×C4#120×C12711yescharacteristic
540C2×C4#120×C12711yescharacteristic
541C2×C4#120×C12711yescharacteristic
542C2×C4C22×D4×C12711yescharacteristic
543C2×C4C22×D4×C12711yescharacteristic
544C8—42no—
545C8—42no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—42no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—84no—
555C22C2×#120×C12711yescharacteristic
556C22#578×C12712yes—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—42no—
568C4—82no—
569C4—82no—
570C4#455×C12712yes—
571C2—22no—
572C2—82no—
573C2—81no—
574C2C127×#301111yescharacteristic
575C2C2×#455×C12711yescharacteristic
576C2C127×#302711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#3561C2
LCSG ▷ C22×C4 ▷ 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×#3218C2semidirect
3. C127×#3209C2semidirect
4. C127×#2640C2semidirect
5. C127×#1606C2semidirect
6. C127×#1602C2semidirect
7. C127×#1506C2semidirect
8. C127×#1500C2semidirect
9. C127×#1469C2semidirect
282. #18429C127direct (N × H)
290. #3218C2×C127semidirect
291. #3209C2×C127semidirect
292. #2640C2×C127semidirect
293. #1606C2×C127semidirect
294. #1602C2×C127semidirect
295. #1506C2×C127semidirect
296. #1500C2×C127semidirect
297. #1469C2×C127semidirect
298. C127#18429direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35612
C127×#32182
C127×#32092
C127×#26402
C127×#16062
C127×#16022
C127×#15062
C127×#15002
C127×#14692
#18429127