Finite Group Databasebeta

← C2×C127×#1639 #44582154

Subgroups — C2×C127×#1639 #44582154

Order 32512.

1690 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C127C211yesmaximal, characteristic
2C2×#486×C127C211yesmaximal, characteristic, complemented
3C2×#474×C127C211yesmaximal, characteristic, complemented
4C2×#461×C127C211yesmaximal, characteristic, complemented
5C127×#1639C218yesmaximal, direct product factor
6C2×#331×C127C211yesmaximal, characteristic, complemented
7C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
9C23×D4×C127—21no—
10C23×D4×C127—21no—
11C22×SD16×C127—21no—
12D42×C127—22no—
13D42×C127—22no—
14D42×C127—22no—
15D42×C127C2214yes—
16C2×C4⋊Q8×C127C2211yescharacteristic, complemented
17C2×#127×C127C2211yescharacteristic
18C2×#121×C127—21no—
19C2×#121×C127—21no—
20C2×#120×C127—22no—
21C2×C4×D4×C127C2211yescharacteristic
22C2×C4×D4×C127C2211yescharacteristic
23#486×C127—22no—
24#486×C127C2214yescomplemented
25#474×C127—22no—
26#474×C127C2214yescomplemented
27#461×C127—22no—
28#461×C127C2214yescomplemented
29C2×#107×C127—21no—
30C2×C4⋊C8×C127C2211yescharacteristic, complemented
31C2×C4⋊C8×C127C2211yescharacteristic, complemented
32C2×#103×C127—21no—
33C2×#102×C127—22no—
34C2×#102×C127—21no—
35C2×C4×C8×C127C2211yescharacteristic, complemented
36#331×C127C2214yescomplemented
37D4⋊C8×C127C2214yescomplemented
38D4⋊C8×C127C2214yescomplemented
39C25×C127—22no—
40C22×Q8×C127—21no—
41C22×D4×C127—22no—
42C22×D4×C127—22no—
43C22×D4×C127—24no—
44C22×D4×C127—24no—
45C22×D4×C127—24no—
46C22×D4×C127—24no—
47C22×D4×C127—21no—
48C22×D4×C127—21no—
49C22×D4×C127—44no—
50C22×D4×C127—44no—
51C22×D4×C127—44no—
52C22×D4×C127—44no—
53C22×D4×C127D411yescharacteristic
54C22×D4×C127D411yescharacteristic
55C22×D4×C127D412yes—
56C23×C4×C127—21no—
57C23×C4×C127—21no—
58C2×SD16×C127—24no—
59C2×SD16×C127—44no—
60C22×C8×C127—21no—
61C22×C8×C127—21no—
62C22×C8×C127—21no—
63C4⋊Q8×C127—21no—
64C4⋊Q8×C127—21no—
65C4⋊Q8×C127—21no—
66C4⋊Q8×C127C2312yescomplemented
67#127×C127—21no—
68#127×C127—21no—
69#127×C127D412yes—
70#127×C127C2312yes—
71#121×C127—24no—
72#121×C127—24no—
73#121×C127—24no—
74#121×C127—24no—
75#120×C127—28no—
76#120×C127—28no—
77C4×D4×C127—21no—
78C4×D4×C127—21no—
79C4×D4×C127—21no—
80C4×D4×C127—21no—
81C4×D4×C127D412yes—
82C4×D4×C127D412yes—
83C4×D4×C127C2312yes—
84C4×D4×C127C2312yes—
85C2×C4⋊C4×C127—21no—
86C2×C4⋊C4×C127—21no—
87C2×C4⋊C4×C127D411yescharacteristic
88C2×C4⋊C4×C127D411yescharacteristic
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—21no—
91C2×C22⋊C4×C127—21no—
92C2×C42×C127C2311yescharacteristic
93#107×C127—24no—
94C4⋊C8×C127—21no—
95C4⋊C8×C127—21no—
96C4⋊C8×C127C2312yescomplemented
97C4⋊C8×C127C2312yescomplemented
98#103×C127—24no—
99#102×C127—24no—
100#102×C127—28no—
101C4×C8×C127—21no—
102C4×C8×C127C2312yescomplemented
103C24×C127—21no—
104C24×C127—21no—
105C24×C127—28no—
106C24×C127—22no—
107C24×C127—48no—
108C24×C127—48no—
109C24×C127—84no—
110C2×Q8×C127—22no—
111C2×Q8×C127—41no—
112C2×Q8×C127—42no—
113C2×Q8×C127—42no—
114C2×D4×C127—28no—
115C2×D4×C127—28no—
116C2×D4×C127—21no—
117C2×D4×C127—21no—
118C2×D4×C127—22no—
119C2×D4×C127—22no—
120C2×D4×C127—22no—
121C2×D4×C127—22no—
122C2×D4×C127—22no—
123C2×D4×C127—22no—
124C2×D4×C127—22no—
125C2×D4×C127—44no—
126C2×D4×C127—48no—
127C2×D4×C127—48no—
128C2×D4×C127—416no—
129C2×D4×C127—416no—
130C2×D4×C127—48no—
131C2×D4×C127—48no—
132C2×D4×C127—48no—
133C2×D4×C127—48no—
134C2×D4×C127—42no—
135C2×D4×C127—42no—
136C2×D4×C127—42no—
137C2×D4×C127—42no—
138C2×D4×C127D814yes—
139C2×D4×C127SD1614yescomplemented
140C2×D4×C127C2×D412yes—
141C2×D4×C127C2×D412yes—
142C2×D4×C127C2×D414yes—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—42no—
150C22×C4×C127—42no—
151C22×C4×C127—42no—
152C22×C4×C127—42no—
153C22×C4×C127—41no—
154C22×C4×C127C2×D411yescharacteristic
155C22×C4×C127C2×D411yescharacteristic
156C22×C4×C127C2×D411yescharacteristic
157SD16×C127—48no—
158C2×C8×C127—22no—
159C2×C8×C127—22no—
160C2×C8×C127—22no—
161C2×C8×C127—42no—
162C2×C8×C127—42no—
163C2×C8×C127—42no—
164C4⋊C4×C127—21no—
165C4⋊C4×C127—21no—
166C4⋊C4×C127—22no—
167C4⋊C4×C127—22no—
168C4⋊C4×C127—41no—
169C4⋊C4×C127—41no—
170C4⋊C4×C127C2×D412yes—
171C4⋊C4×C127C2×D412yes—
172C22⋊C4×C127—28no—
173C22⋊C4×C127—22no—
174C22⋊C4×C127—22no—
175C22⋊C4×C127—22no—
176C22⋊C4×C127—22no—
177C42×C127C2×D411yescharacteristic
178C42×C127C2×D411yescharacteristic
179C42×C127C2×D411yescharacteristic
180C42×C127C2411yescharacteristic
181C23×C127—22no—
182C23×C127—22no—
183C23×C127—24no—
184C23×C127—24no—
185C23×C127—24no—
186C23×C127—416no—
187C23×C127—416no—
188C23×C127—42no—
189C23×C127—42no—
190C23×C127—42no—
191C23×C127—42no—
192C23×C127—44no—
193C23×C127—44no—
194C23×C127—44no—
195C23×C127—88no—
196C23×C127—832no—
197C23×C127#12011yescharacteristic
198Q8×C127—42no—
199Q8×C127—42no—
200Q8×C127—82no—
201D4×C127—22no—
202D4×C127—22no—
203D4×C127—24no—
204D4×C127—24no—
205D4×C127—44no—
206D4×C127—416no—
207D4×C127—416no—
208D4×C127—42no—
209D4×C127—42no—
210D4×C127—42no—
211D4×C127—42no—
212D4×C127—44no—
213D4×C127—44no—
214D4×C127—82no—
215D4×C127C2×D814yes—
216D4×C127C2×SD1614yescomplemented
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—22no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—44no—
227C2×C4×C127—44no—
228C2×C4×C127—42no—
229C2×C4×C127—82no—
230C2×C4×C127#12011yescharacteristic
231C2×C4×C127#12011yescharacteristic
232C2×C4×C127#12011yescharacteristic
233C2×C4×C127C2×D812yes—
234C2×C4×C127C2×SD1612yes—
235C2×C4×C127AGL(1,ℤ/8)12yes—
236C2×C4×C127AGL(1,ℤ/8)12yes—
237C2×C4×C127C22×D411yescharacteristic
238C2×C4×C127C22×D411yescharacteristic
239C2×C4×C127C22×D411yescharacteristic
240C8×C127—42no—
241C8×C127—42no—
242C8×C127—42no—
243C22×C127—24no—
244C22×C127—24no—
245C22×C127—48no—
246C22×C127—48no—
247C22×C127—42no—
248C22×C127—42no—
249C22×C127—42no—
250C22×C127—42no—
251C22×C127—44no—
252C22×C127—44no—
253C22×C127—44no—
254C22×C127—832no—
255C22×C127—88no—
256C22×C127#44712yes—
257C22×C127#45012yes—
258C22×C127#45512yes—
259C22×C127C2×#12011yescharacteristic
260C4×C127—21no—
261C4×C127—21no—
262C4×C127—42no—
263C4×C127—42no—
264C4×C127—82no—
265C4×C127#44712yes—
266C4×C127#45012yes—
267C4×C127C22×D811yescharacteristic
268C4×C127C22×SD1611yescharacteristic
269C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
270C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
271C2×#1639C12711yesmaximal, characteristic, direct product factor, Sylow
272C2×C127—44no—
273C2×C127—44no—
274C2×C127—84no—
275C2×C127#163914yesdirect product factor
276C2×C127C2×#44711yescharacteristic
277C2×C127C2×#45011yescharacteristic
278C2×C127C2×#45511yescharacteristic
279C2×D42C2×C12711yescharacteristic
280C2×#486C2×C12711yescharacteristic, complemented
281C2×#474C2×C12711yescharacteristic, complemented
282C2×#461C2×C12711yescharacteristic, complemented
283#1639C2×C12718yesdirect product factor
284C2×#331C2×C12711yescharacteristic, complemented
285C2×D4⋊C8C2×C12711yescharacteristic, complemented
286C2×D4⋊C8C2×C12711yescharacteristic, complemented
287C127C2×#163911yescharacteristic, direct product factor, Sylow
288C23×D4—21no—
289C23×D4—21no—
290C22×SD16—21no—
291D42—22no—
292D42—22no—
293D42—22no—
294D42C22×C12714yes—
295C2×C4⋊Q8C22×C12711yescharacteristic, complemented
296C2×#127C22×C12711yescharacteristic
297C2×#121—21no—
298C2×#121—21no—
299C2×#120—22no—
300C2×C4×D4C22×C12711yescharacteristic
301C2×C4×D4C22×C12711yescharacteristic
302#486—22no—
303#486C22×C12714yescomplemented
304#474—22no—
305#474C22×C12714yescomplemented
306#461—22no—
307#461C22×C12714yescomplemented
308C2×#107—21no—
309C2×C4⋊C8C22×C12711yescharacteristic, complemented
310C2×C4⋊C8C22×C12711yescharacteristic, complemented
311C2×#103—21no—
312C2×#102—22no—
313C2×#102—21no—
314C2×C4×C8C22×C12711yescharacteristic, complemented
315#331C22×C12714yescomplemented
316D4⋊C8C22×C12714yescomplemented
317D4⋊C8C22×C12714yescomplemented
318C25—22no—
319C22×Q8—21no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—44no—
329C22×D4—44no—
330C22×D4—44no—
331C22×D4—44no—
332C22×D4D4×C12711yescharacteristic
333C22×D4D4×C12711yescharacteristic
334C22×D4D4×C12712yes—
335C23×C4—21no—
336C23×C4—21no—
337C2×SD16—24no—
338C2×SD16—44no—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8C23×C12712yescomplemented
346#127—21no—
347#127—21no—
348#127D4×C12712yes—
349#127C23×C12712yes—
350#121—24no—
351#121—24no—
352#121—24no—
353#121—24no—
354#120—28no—
355#120—28no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4D4×C12712yes—
361C4×D4D4×C12712yes—
362C4×D4C23×C12712yes—
363C4×D4C23×C12712yes—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4D4×C12711yescharacteristic
367C2×C4⋊C4D4×C12711yescharacteristic
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C42C23×C12711yescharacteristic
372#107—24no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8C23×C12712yescomplemented
376C4⋊C8C23×C12712yescomplemented
377#103—24no—
378#102—24no—
379#102—28no—
380C4×C8—21no—
381C4×C8C23×C12712yescomplemented
382C24—21no—
383C24—21no—
384C24—28no—
385C24—22no—
386C24—48no—
387C24—48no—
388C24—84no—
389C2×Q8—22no—
390C2×Q8—41no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×D4—28no—
394C2×D4—28no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—44no—
405C2×D4—48no—
406C2×D4—48no—
407C2×D4—416no—
408C2×D4—416no—
409C2×D4—48no—
410C2×D4—48no—
411C2×D4—48no—
412C2×D4—48no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4D8×C12714yes—
418C2×D4SD16×C12714yescomplemented
419C2×D4C2×D4×C12712yes—
420C2×D4C2×D4×C12712yes—
421C2×D4C2×D4×C12714yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4C2×D4×C12711yescharacteristic
434C22×C4C2×D4×C12711yescharacteristic
435C22×C4C2×D4×C12711yescharacteristic
436SD16—48no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—42no—
441C2×C8—42no—
442C2×C8—42no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4C2×D4×C12712yes—
450C4⋊C4C2×D4×C12712yes—
451C22⋊C4—28no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C42C2×D4×C12711yescharacteristic
457C42C2×D4×C12711yescharacteristic
458C42C2×D4×C12711yescharacteristic
459C42C24×C12711yescharacteristic
460C23—22no—
461C23—22no—
462C23—24no—
463C23—24no—
464C23—24no—
465C23—416no—
466C23—416no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—42no—
471C23—44no—
472C23—44no—
473C23—44no—
474C23—88no—
475C23—832no—
476C23#120×C12711yescharacteristic
477Q8—42no—
478Q8—42no—
479Q8—82no—
480D4—22no—
481D4—22no—
482D4—24no—
483D4—24no—
484D4—44no—
485D4—416no—
486D4—416no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—44no—
492D4—44no—
493D4—82no—
494D4C2×D8×C12714yes—
495D4C2×SD16×C12714yescomplemented
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—82no—
509C2×C4#120×C12711yescharacteristic
510C2×C4#120×C12711yescharacteristic
511C2×C4#120×C12711yescharacteristic
512C2×C4C2×D8×C12712yes—
513C2×C4C2×SD16×C12712yes—
514C2×C4AGL(1,ℤ/8)×C12712yes—
515C2×C4AGL(1,ℤ/8)×C12712yes—
516C2×C4C22×D4×C12711yescharacteristic
517C2×C4C22×D4×C12711yescharacteristic
518C2×C4C22×D4×C12711yescharacteristic
519C8—42no—
520C8—42no—
521C8—42no—
522C22—24no—
523C22—24no—
524C22—48no—
525C22—48no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—44no—
531C22—44no—
532C22—44no—
533C22—832no—
534C22—88no—
535C22#447×C12712yes—
536C22#450×C12712yes—
537C22#455×C12712yes—
538C22C2×#120×C12711yescharacteristic
539C4—21no—
540C4—21no—
541C4—42no—
542C4—42no—
543C4—82no—
544C4#447×C12712yes—
545C4#450×C12712yes—
546C4C22×D8×C12711yescharacteristic
547C4C22×SD16×C12711yescharacteristic
548C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
549C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
550C2—44no—
551C2—44no—
552C2—84no—
553C2C127×#163914yesdirect product factor
554C2C2×#447×C12711yescharacteristic
555C2C2×#450×C12711yescharacteristic
556C2C2×#455×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×D42×C127C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#486×C127C2semidirect
3. C2×#474×C127C2semidirect
4. C2×#461×C127C2semidirect
5. C127×#1639C2direct (N × H)
6. C2×#331×C127C2semidirect
7. C2×D4⋊C8×C127C2semidirect
8. C2×D4⋊C8×C127C2semidirect
16. C2×C4⋊Q8×C127C22semidirect
24. #486×C127C22semidirect
26. #474×C127C22semidirect
28. #461×C127C22semidirect
30. C2×C4⋊C8×C127C22semidirect
31. C2×C4⋊C8×C127C22semidirect
35. C2×C4×C8×C127C22semidirect
36. #331×C127C22semidirect
37. D4⋊C8×C127C22semidirect
38. D4⋊C8×C127C22semidirect
66. C4⋊Q8×C127C23semidirect
96. C4⋊C8×C127C23semidirect
97. C4⋊C8×C127C23semidirect
102. C4×C8×C127C23semidirect
139. C2×D4×C127SD16semidirect
216. D4×C127C2×SD16semidirect
271. C2×#1639C127direct (N × H)
275. C2×C127#1639direct (N × H)
280. C2×#486C2×C127semidirect
281. C2×#474C2×C127semidirect
282. C2×#461C2×C127semidirect
283. #1639C2×C127direct (N × H)
284. C2×#331C2×C127semidirect
285. C2×D4⋊C8C2×C127semidirect
286. C2×D4⋊C8C2×C127semidirect
287. C127C2×#1639direct (N × H)
295. C2×C4⋊Q8C22×C127semidirect
303. #486C22×C127semidirect
305. #474C22×C127semidirect
307. #461C22×C127semidirect
309. C2×C4⋊C8C22×C127semidirect
310. C2×C4⋊C8C22×C127semidirect
314. C2×C4×C8C22×C127semidirect
315. #331C22×C127semidirect
316. D4⋊C8C22×C127semidirect
317. D4⋊C8C22×C127semidirect
345. C4⋊Q8C23×C127semidirect
375. C4⋊C8C23×C127semidirect
376. C4⋊C8C23×C127semidirect
381. C4×C8C23×C127semidirect
418. C2×D4SD16×C127semidirect
495. D4C2×SD16×C127semidirect
553. C2C127×#1639direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D42×C1272
C2×#486×C1272
C2×#474×C1272
C2×#461×C1272
C127×#16392
C2×#331×C1272
C2×D4⋊C8×C1272
C2×#1639127