Finite Group Databasebeta

← C127×#8375 #44572048

Subgroups — C127×#8375 #44572048

Order 32512.

1518 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C127C211yesmaximal, characteristic
2C127×#1799C211yesmaximal, characteristic, complemented
3C127×#1786C212yesmaximal, complemented
4C127×#1519C212yesmaximal, complemented
5C127×#1459C211yesmaximal, characteristic, complemented
6C23×D4×C127—21no—
7C23×D4×C127C411yescharacteristic, complemented
8C23×D4×C127C2211yescharacteristic
9D42×C127—24no—
10D42×C127—24no—
11C2×#127×C127C411yescharacteristic, complemented
12C2×#121×C127—21no—
13C2×#121×C127C411yescharacteristic, complemented
14C2×#121×C127C2211yescharacteristic
15C2×#120×C127—21no—
16C2×#120×C127—21no—
17C2×C4×D4×C127C411yescharacteristic, complemented
18C2×C4×D4×C127C2211yescharacteristic
19C2×#102×C127—24no—
20C2×#99×C127—21no—
21C2×C22⋊C8×C127C2212yescomplemented
22#380×C127C2212yescomplemented
23#342×C127—21no—
24#327×C127—24no—
25#324×C127—21no—
26#323×C127—21no—
27C25×C127—21no—
28C25×C127—21no—
29C22×D4×C127—28no—
30C22×D4×C127—21no—
31C22×D4×C127—21no—
32C22×D4×C127—22no—
33C22×D4×C127—22no—
34C22×D4×C127—21no—
35C22×D4×C127—21no—
36C22×D4×C127—21no—
37C22×D4×C127—21no—
38C22×D4×C127—22no—
39C22×D4×C127—44no—
40C22×D4×C127—44no—
41C22×D4×C127—44no—
42C22×D4×C127—42no—
43C22×D4×C127—42no—
44C22×D4×C127C2×C411yescharacteristic
45C22×D4×C127C2×C411yescharacteristic
46C22×D4×C127C2×C411yescharacteristic
47C22×D4×C127D411yescharacteristic
48C22×D4×C127D414yes—
49C23×C4×C127—21no—
50C23×C4×C127C2×C411yescharacteristic
51C23×C4×C127C2311yescharacteristic
52C22×C8×C127—22no—
53#127×C127—22no—
54#127×C127—22no—
55#121×C127—28no—
56#121×C127—22no—
57#121×C127—22no—
58#121×C127—22no—
59#121×C127D414yes—
60#120×C127—28no—
61#120×C127—28no—
62C4×D4×C127—22no—
63C4×D4×C127—22no—
64C4×D4×C127—22no—
65C4×D4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127C2×C411yescharacteristic
68C2×C4⋊C4×C127D411yescharacteristic
69C2×C22⋊C4×C127—21no—
70C2×C22⋊C4×C127—21no—
71C2×C22⋊C4×C127—21no—
72C2×C22⋊C4×C127—22no—
73C2×C22⋊C4×C127D411yescharacteristic
74C2×C22⋊C4×C127D411yescharacteristic
75C2×C42×C127C2×C411yescharacteristic
76#102×C127—48no—
77#99×C127—42no—
78C22⋊C8×C127—22no—
79C22⋊C8×C127—22no—
80#95×C127—22no—
81C24×C127—21no—
82C24×C127—24no—
83C24×C127—21no—
84C24×C127—21no—
85C24×C127—24no—
86C24×C127—44no—
87C24×C127—44no—
88C24×C127—42no—
89C24×C127—42no—
90C24×C127—41no—
91C24×C127—41no—
92C24×C127—42no—
93C24×C127—82no—
94C24×C127—82no—
95C24×C127C22⋊C411yescharacteristic
96C24×C127C2×D411yescharacteristic
97C2×D4×C127—22no—
98C2×D4×C127—22no—
99C2×D4×C127—24no—
100C2×D4×C127—28no—
101C2×D4×C127—24no—
102C2×D4×C127—24no—
103C2×D4×C127—24no—
104C2×D4×C127—24no—
105C2×D4×C127—24no—
106C2×D4×C127—21no—
107C2×D4×C127—21no—
108C2×D4×C127—21no—
109C2×D4×C127—24no—
110C2×D4×C127—42no—
111C2×D4×C127—44no—
112C2×D4×C127—42no—
113C2×D4×C127—42no—
114C2×D4×C127—48no—
115C2×D4×C127—48no—
116C2×D4×C127—416no—
117C2×D4×C127—416no—
118C2×D4×C127—44no—
119C2×D4×C127—44no—
120C2×D4×C127—42no—
121C2×D4×C127—44no—
122C2×D4×C127—42no—
123C2×D4×C127—41no—
124C2×D4×C127—41no—
125C2×D4×C127—42no—
126C2×D4×C127—44no—
127C2×D4×C127—42no—
128C2×D4×C127—82no—
129C2×D4×C127C22⋊C412yes—
130C2×D4×C127C22⋊C412yes—
131C2×D4×C127C22⋊C412yes—
132C2×D4×C127D812yes—
133C2×D4×C127SD1612yes—
134C22×C4×C127—24no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127—42no—
139C22×C4×C127—42no—
140C22×C4×C127—42no—
141C22×C4×C127—42no—
142C22×C4×C127—42no—
143C22×C4×C127C22⋊C411yescharacteristic
144C22×C4×C127C22⋊C411yescharacteristic
145C22×C4×C127C22⋊C411yescharacteristic
146C22×C4×C127C22×C411yescharacteristic
147C22×C4×C127C2×D412yes—
148C22×C4×C127C2×D412yes—
149C22×C4×C127C2×D411yescharacteristic
150C2×C8×C127—44no—
151C2×C8×C127—42no—
152C4⋊C4×C127—21no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—44no—
155C4⋊C4×C127C22⋊C412yes—
156C22⋊C4×C127—24no—
157C22⋊C4×C127—24no—
158C22⋊C4×C127—22no—
159C22⋊C4×C127—24no—
160C22⋊C4×C127—22no—
161C22⋊C4×C127—42no—
162C22⋊C4×C127—42no—
163C42×C127—21no—
164C42×C127—21no—
165C23×C127—24no—
166C23×C127—21no—
167C23×C127—22no—
168C23×C127—21no—
169C23×C127—22no—
170C23×C127—22no—
171C23×C127—41no—
172C23×C127—41no—
173C23×C127—48no—
174C23×C127—41no—
175C23×C127—41no—
176C23×C127—42no—
177C23×C127—42no—
178C23×C127—42no—
179C23×C127—48no—
180C23×C127—48no—
181C23×C127—42no—
182C23×C127—42no—
183C23×C127—41no—
184C23×C127—41no—
185C23×C127—41no—
186C23×C127—41no—
187C23×C127—41no—
188C23×C127—41no—
189C23×C127—44no—
190C23×C127—44no—
191C23×C127—84no—
192C23×C127—84no—
193C23×C127—84no—
194C23×C127—84no—
195C23×C127—88no—
196C23×C127—88no—
197C23×C127—88no—
198C23×C127#10212yescomplemented
199C23×C127C2×C22⋊C411yescharacteristic
200C23×C127#12012yes—
201C23×C127C2×D811yescharacteristic
202C23×C127C2×SD1611yescharacteristic
203C23×C127AGL(1,ℤ/8)12yes—
204D4×C127—24no—
205D4×C127—24no—
206D4×C127—24no—
207D4×C127—22no—
208D4×C127—24no—
209D4×C127—48no—
210D4×C127—42no—
211D4×C127—42no—
212D4×C127—48no—
213D4×C127—48no—
214D4×C127—48no—
215D4×C127—44no—
216D4×C127—44no—
217D4×C127—42no—
218D4×C127—84no—
219D4×C127#9914yescomplemented
220C2×C4×C127—21no—
221C2×C4×C127—21no—
222C2×C4×C127—24no—
223C2×C4×C127—22no—
224C2×C4×C127—21no—
225C2×C4×C127—21no—
226C2×C4×C127—22no—
227C2×C4×C127—41no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—48no—
231C2×C4×C127—41no—
232C2×C4×C127—41no—
233C2×C4×C127—42no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—82no—
237C2×C4×C127—82no—
238C2×C4×C127—82no—
239C2×C4×C127#10212yescomplemented
240C2×C4×C127C2×C22⋊C411yescharacteristic
241C2×C4×C127C2×C22⋊C411yescharacteristic
242C2×C4×C127#12012yes—
243C8×C127—82no—
244C22×C127—21no—
245C22×C127—22no—
246C22×C127—21no—
247C22×C127—22no—
248C22×C127—24no—
249C22×C127—22no—
250C22×C127—41no—
251C22×C127—41no—
252C22×C127—42no—
253C22×C127—42no—
254C22×C127—44no—
255C22×C127—44no—
256C22×C127—42no—
257C22×C127—42no—
258C22×C127—41no—
259C22×C127—41no—
260C22×C127—42no—
261C22×C127—42no—
262C22×C127—42no—
263C22×C127—42no—
264C22×C127—42no—
265C22×C127—42no—
266C22×C127—42no—
267C22×C127—88no—
268C22×C127—88no—
269C22×C127—82no—
270C22×C127—82no—
271C22×C127—82no—
272C22×C127—82no—
273C22×C127—816no—
274C22×C127#37911yescharacteristic
275C22×C127C2×#10211yescharacteristic
276C22×C127#41811yescharacteristic
277C22×C127#44712yes—
278C22×C127#45012yes—
279C4×C127—22no—
280C4×C127—21no—
281C4×C127—22no—
282C4×C127—41no—
283C4×C127—41no—
284C4×C127—42no—
285C4×C127—162no—
286C4×C127C2×#9912yes—
287#8375C12711yesmaximal, characteristic, direct product factor, Sylow
288C2×C127—22no—
289C2×C127—21no—
290C2×C127—21no—
291C2×C127—22no—
292C2×C127—44no—
293C2×C127—42no—
294C2×C127—82no—
295C2×C127—82no—
296C2×C127#178111yescharacteristic
297C2×C127#178611yescharacteristic
298C2×C127#179511yescharacteristic
299C2×D42C2×C12711yescharacteristic
300#1799C2×C12711yescharacteristic, complemented
301#1786C2×C12712yescomplemented
302#1519C2×C12712yescomplemented
303#1459C2×C12711yescharacteristic, complemented
304C127#837511yescharacteristic, direct product factor, Sylow
305C23×D4—21no—
306C23×D4C4×C12711yescharacteristic, complemented
307C23×D4C22×C12711yescharacteristic
308D42—24no—
309D42—24no—
310C2×#127C4×C12711yescharacteristic, complemented
311C2×#121—21no—
312C2×#121C4×C12711yescharacteristic, complemented
313C2×#121C22×C12711yescharacteristic
314C2×#120—21no—
315C2×#120—21no—
316C2×C4×D4C4×C12711yescharacteristic, complemented
317C2×C4×D4C22×C12711yescharacteristic
318C2×#102—24no—
319C2×#99—21no—
320C2×C22⋊C8C22×C12712yescomplemented
321#380C22×C12712yescomplemented
322#342—21no—
323#327—24no—
324#324—21no—
325#323—21no—
326C25—21no—
327C25—21no—
328C22×D4—28no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4—22no—
338C22×D4—44no—
339C22×D4—44no—
340C22×D4—44no—
341C22×D4—42no—
342C22×D4—42no—
343C22×D4C2×C4×C12711yescharacteristic
344C22×D4C2×C4×C12711yescharacteristic
345C22×D4C2×C4×C12711yescharacteristic
346C22×D4D4×C12711yescharacteristic
347C22×D4D4×C12714yes—
348C23×C4—21no—
349C23×C4C2×C4×C12711yescharacteristic
350C23×C4C23×C12711yescharacteristic
351C22×C8—22no—
352#127—22no—
353#127—22no—
354#121—28no—
355#121—22no—
356#121—22no—
357#121—22no—
358#121D4×C12714yes—
359#120—28no—
360#120—28no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4C2×C4×C12711yescharacteristic
367C2×C4⋊C4D4×C12711yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4D4×C12711yescharacteristic
373C2×C22⋊C4D4×C12711yescharacteristic
374C2×C42C2×C4×C12711yescharacteristic
375#102—48no—
376#99—42no—
377C22⋊C8—22no—
378C22⋊C8—22no—
379#95—22no—
380C24—21no—
381C24—24no—
382C24—21no—
383C24—21no—
384C24—24no—
385C24—44no—
386C24—44no—
387C24—42no—
388C24—42no—
389C24—41no—
390C24—41no—
391C24—42no—
392C24—82no—
393C24—82no—
394C24C22⋊C4×C12711yescharacteristic
395C24C2×D4×C12711yescharacteristic
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—24no—
399C2×D4—28no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—24no—
409C2×D4—42no—
410C2×D4—44no—
411C2×D4—42no—
412C2×D4—42no—
413C2×D4—48no—
414C2×D4—48no—
415C2×D4—416no—
416C2×D4—416no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—42no—
420C2×D4—44no—
421C2×D4—42no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—44no—
426C2×D4—42no—
427C2×D4—82no—
428C2×D4C22⋊C4×C12712yes—
429C2×D4C22⋊C4×C12712yes—
430C2×D4C22⋊C4×C12712yes—
431C2×D4D8×C12712yes—
432C2×D4SD16×C12712yes—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4C22⋊C4×C12711yescharacteristic
443C22×C4C22⋊C4×C12711yescharacteristic
444C22×C4C22⋊C4×C12711yescharacteristic
445C22×C4C22×C4×C12711yescharacteristic
446C22×C4C2×D4×C12712yes—
447C22×C4C2×D4×C12712yes—
448C22×C4C2×D4×C12711yescharacteristic
449C2×C8—44no—
450C2×C8—42no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—44no—
454C4⋊C4C22⋊C4×C12712yes—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—42no—
461C22⋊C4—42no—
462C42—21no—
463C42—21no—
464C23—24no—
465C23—21no—
466C23—22no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—41no—
471C23—41no—
472C23—48no—
473C23—41no—
474C23—41no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—48no—
479C23—48no—
480C23—42no—
481C23—42no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—44no—
489C23—44no—
490C23—84no—
491C23—84no—
492C23—84no—
493C23—84no—
494C23—88no—
495C23—88no—
496C23—88no—
497C23#102×C12712yescomplemented
498C23C2×C22⋊C4×C12711yescharacteristic
499C23#120×C12712yes—
500C23C2×D8×C12711yescharacteristic
501C23C2×SD16×C12711yescharacteristic
502C23AGL(1,ℤ/8)×C12712yes—
503D4—24no—
504D4—24no—
505D4—24no—
506D4—22no—
507D4—24no—
508D4—48no—
509D4—42no—
510D4—42no—
511D4—48no—
512D4—48no—
513D4—48no—
514D4—44no—
515D4—44no—
516D4—42no—
517D4—84no—
518D4#99×C12714yescomplemented
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—48no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4#102×C12712yescomplemented
539C2×C4C2×C22⋊C4×C12711yescharacteristic
540C2×C4C2×C22⋊C4×C12711yescharacteristic
541C2×C4#120×C12712yes—
542C8—82no—
543C22—21no—
544C22—22no—
545C22—21no—
546C22—22no—
547C22—24no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—44no—
554C22—44no—
555C22—42no—
556C22—41no—
557C22—42no—
558C22—42no—
559C22—41no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—88no—
567C22—88no—
568C22—82no—
569C22—82no—
570C22—82no—
571C22—82no—
572C22—816no—
573C22#379×C12711yescharacteristic
574C22C2×#102×C12711yescharacteristic
575C22#418×C12711yescharacteristic
576C22#447×C12712yes—
577C22#450×C12712yes—
578C4—22no—
579C4—21no—
580C4—22no—
581C4—41no—
582C4—42no—
583C4—41no—
584C4—162no—
585C4C2×#99×C12712yes—
586C2—22no—
587C2—21no—
588C2—21no—
589C2—22no—
590C2—44no—
591C2—42no—
592C2—82no—
593C2—82no—
594C2C127×#178111yescharacteristic
595C2C127×#178611yescharacteristic
596C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC2×D42×C127C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1799C2semidirect
3. C127×#1786C2semidirect
4. C127×#1519C2semidirect
5. C127×#1459C2semidirect
7. C23×D4×C127C4semidirect
11. C2×#127×C127C4semidirect
13. C2×#121×C127C4semidirect
17. C2×C4×D4×C127C4semidirect
21. C2×C22⋊C8×C127C22semidirect
22. #380×C127C22semidirect
198. C23×C127#102semidirect
219. D4×C127#99semidirect
239. C2×C4×C127#102semidirect
287. #8375C127direct (N × H)
300. #1799C2×C127semidirect
301. #1786C2×C127semidirect
302. #1519C2×C127semidirect
303. #1459C2×C127semidirect
304. C127#8375direct (N × H)
306. C23×D4C4×C127semidirect
310. C2×#127C4×C127semidirect
312. C2×#121C4×C127semidirect
316. C2×C4×D4C4×C127semidirect
320. C2×C22⋊C8C22×C127semidirect
321. #380C22×C127semidirect
497. C23#102×C127semidirect
518. D4#99×C127semidirect
538. C2×C4#102×C127semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1272
C127×#17992
C127×#17862
C127×#15192
C127×#14592
#8375127