Finite Group Databasebeta

← C127×#10778 #44574451

Subgroups — C127×#10778 #44574451

Order 32512.

1164 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C127C211yesmaximal, characteristic
2C2×#421×C127C211yesmaximal, characteristic
3C127×#2896C211yesmaximal, characteristic
4C2×#344×C127C211yesmaximal, characteristic, complemented
5C2×#344×C127C211yesmaximal, characteristic, complemented
6C127×#1738C211yesmaximal, characteristic, complemented
7C127×#1733C211yesmaximal, characteristic, complemented
8C22×#41×C127C2211yescharacteristic
9#568×C127—22no—
10#568×C127—22no—
11#568×C127—22no—
12#568×C127—22no—
13C2×#131×C127—22no—
14C2×#131×C127C414yescomplemented
15C22×M16×C127—22no—
16C22×M16×C127C2211yescharacteristic
17C22×M16×C127C2211yescharacteristic
18C22×M16×C127C2211yescharacteristic
19C22×M16×C127C2211yescharacteristic
20C2×#117×C127C2211yescharacteristic
21C2×#117×C127C2211yescharacteristic
22#421×C127—22no—
23#421×C127C414yescomplemented
24C2×#104×C127—22no—
25#419×C127C412yescomplemented
26#418×C127C412yescomplemented
27#417×C127—22no—
28#416×C127—22no—
29#344×C127—22no—
30#344×C127—22no—
31#341×C127—22no—
32#339×C127—22no—
33C2×#41×C127—21no—
34C2×#41×C127—21no—
35C2×#41×C127—21no—
36C2×#41×C127—21no—
37C2×#41×C127—21no—
38C2×#41×C127—21no—
39C2×#41×C127C2×C412yes—
40C2×#41×C127C2×C412yes—
41C2×#41×C127D412yes—
42C2×#41×C127D412yes—
43C2×#41×C127D412yes—
44C2×#41×C127Q812yes—
45C22×Q8×C127C2×C411yescharacteristic
46C22×D4×C127—21no—
47C22×D4×C127C2×C411yescharacteristic
48C23×C4×C127—21no—
49C23×C4×C127C2311yescharacteristic
50#131×C127—28no—
51#131×C127—28no—
52#131×C127—28no—
53#131×C127—28no—
54C2×M16×C127—28no—
55C2×M16×C127—28no—
56C2×M16×C127—21no—
57C2×M16×C127—21no—
58C2×M16×C127—21no—
59C2×M16×C127—21no—
60C2×M16×C127—21no—
61C2×M16×C127—21no—
62C2×M16×C127—21no—
63C2×M16×C127—21no—
64C2×M16×C127—21no—
65C2×M16×C127—24no—
66C2×M16×C127—21no—
67C2×M16×C127—21no—
68C2×M16×C127—21no—
69C2×M16×C127—21no—
70C2×M16×C127—21no—
71C2×M16×C127—21no—
72C2×M16×C127—21no—
73C2×M16×C127—21no—
74C2×M16×C127C2×C412yes—
75C2×M16×C127C2×C412yes—
76C2×M16×C127C2×C412yes—
77C2×M16×C127D412yes—
78C2×M16×C127D412yes—
79C2×M16×C127D412yes—
80C2×M16×C127D412yes—
81C22×C8×C127—21no—
82C22×C8×C127—24no—
83C22×C8×C127—21no—
84C22×C8×C127—21no—
85C22×C8×C127C2×C412yes—
86#117×C127—21no—
87#117×C127—21no—
88#117×C127—21no—
89#117×C127—21no—
90#117×C127—21no—
91#117×C127—21no—
92#117×C127C2×C412yes—
93#117×C127C2×C412yes—
94C2×C4⋊C4×C127—21no—
95C2×C4⋊C4×C127—21no—
96C2×C22⋊C4×C127—21no—
97C2×C22⋊C4×C127—21no—
98C2×C42×C127—21no—
99C2×C42×C127—21no—
100#104×C127—28no—
101#103×C127—24no—
102#102×C127—24no—
103C24×C127—21no—
104C24×C127#4111yescharacteristic
105#41×C127—22no—
106#41×C127—22no—
107#41×C127—22no—
108#41×C127—22no—
109#41×C127—22no—
110#41×C127—22no—
111#41×C127—22no—
112#41×C127—22no—
113#41×C127—22no—
114#41×C127—22no—
115#41×C127—22no—
116#41×C127—22no—
117#41×C127C22⋊C414yes—
118#41×C127C22⋊C414yes—
119#41×C127C4⋊C414yes—
120#41×C127C4⋊C414yes—
121C2×Q8×C127—21no—
122C2×Q8×C127—21no—
123C2×Q8×C127—21no—
124C2×Q8×C127C4212yes—
125C2×Q8×C127C22⋊C412yes—
126C2×Q8×C127C4⋊C412yes—
127C2×D4×C127—22no—
128C2×D4×C127—22no—
129C2×D4×C127—22no—
130C2×D4×C127—22no—
131C2×D4×C127—22no—
132C2×D4×C127—22no—
133C2×D4×C127—21no—
134C2×D4×C127—21no—
135C2×D4×C127—21no—
136C2×D4×C127C4212yes—
137C2×D4×C127C22⋊C412yes—
138C2×D4×C127C4⋊C412yes—
139C22×C4×C127—21no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—41no—
147C22×C4×C127—41no—
148C22×C4×C127C22×C411yescharacteristic
149C22×C4×C127C22×C411yescharacteristic
150C22×C4×C127C22×C411yescharacteristic
151C22×C4×C127C2×D411yescharacteristic
152C22×C4×C127C2×D411yescharacteristic
153C22×C4×C127C2×D411yescharacteristic
154C22×C4×C127C2×D411yescharacteristic
155C22×C4×C127C2×D411yescharacteristic
156C22×C4×C127C2×D411yescharacteristic
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×Q811yescharacteristic
159C22×C4×C127#4111yescharacteristic
160C22×C4×C127#4111yescharacteristic
161C22×C4×C127#4111yescharacteristic
162M16×C127—216no—
163M16×C127—22no—
164M16×C127—22no—
165M16×C127—22no—
166M16×C127—22no—
167M16×C127—22no—
168M16×C127—22no—
169M16×C127—22no—
170M16×C127—22no—
171M16×C127—22no—
172M16×C127—22no—
173M16×C127—22no—
174M16×C127—41no—
175M16×C127—41no—
176M16×C127—41no—
177M16×C127—41no—
178M16×C127C22⋊C414yes—
179C2×C8×C127—216no—
180C2×C8×C127—22no—
181C2×C8×C127—22no—
182C2×C8×C127—22no—
183C2×C8×C127—22no—
184C2×C8×C127—22no—
185C2×C8×C127—22no—
186C2×C8×C127—22no—
187C2×C8×C127—41no—
188C2×C8×C127—41no—
189C2×C8×C127—41no—
190C2×C8×C127—41no—
191C2×C8×C127C22⋊C414yes—
192C4⋊C4×C127—22no—
193C4⋊C4×C127—22no—
194C4⋊C4×C127—41no—
195C4⋊C4×C127—41no—
196C22⋊C4×C127—22no—
197C22⋊C4×C127—22no—
198C22⋊C4×C127—41no—
199C22⋊C4×C127—41no—
200C42×C127—22no—
201C42×C127—22no—
202C42×C127—41no—
203C42×C127—41no—
204C23×C127—22no—
205C23×C127—22no—
206C23×C127—22no—
207C23×C127—81no—
208C23×C127—82no—
209C23×C127#11711yescharacteristic
210C23×C127C4×D411yescharacteristic
211C23×C127C4×D411yescharacteristic
212C23×C127#12111yescharacteristic
213C23×C127C22⋊Q811yescharacteristic
214C23×C127#12311yescharacteristic
215C23×C127#12311yescharacteristic
216Q8×C127—22no—
217Q8×C127—22no—
218Q8×C127—22no—
219Q8×C127#9514yes—
220D4×C127—24no—
221D4×C127—24no—
222D4×C127—24no—
223D4×C127—24no—
224D4×C127—22no—
225D4×C127—22no—
226D4×C127—22no—
227D4×C127#9514yes—
228C2×C4×C127—22no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—24no—
232C2×C4×C127—24no—
233C2×C4×C127—24no—
234C2×C4×C127—24no—
235C2×C4×C127—42no—
236C2×C4×C127—42no—
237C2×C4×C127—82no—
238C2×C4×C127—82no—
239C2×C4×C127C2×C4211yescharacteristic
240C2×C4×C127C2×C22⋊C411yescharacteristic
241C2×C4×C127C2×C22⋊C411yescharacteristic
242C2×C4×C127C2×C22⋊C411yescharacteristic
243C2×C4×C127C2×C22⋊C411yescharacteristic
244C2×C4×C127C2×C22⋊C411yescharacteristic
245C2×C4×C127C2×C4⋊C411yescharacteristic
246C2×C4×C127C2×C4⋊C411yescharacteristic
247C2×C4×C127C2×C4⋊C411yescharacteristic
248C2×C4×C127#11711yescharacteristic
249C2×C4×C127C4×D411yescharacteristic
250C2×C4×C127C4×D411yescharacteristic
251C2×C4×C127C4×D411yescharacteristic
252C2×C4×C127C4×D411yescharacteristic
253C2×C4×C127C4×D411yescharacteristic
254C2×C4×C127C4×D411yescharacteristic
255C2×C4×C127#12011yescharacteristic
256C2×C4×C127#12011yescharacteristic
257C2×C4×C127#12011yescharacteristic
258C2×C4×C127#12011yescharacteristic
259C2×C4×C127#12111yescharacteristic
260C2×C4×C127#12111yescharacteristic
261C2×C4×C127#12111yescharacteristic
262C2×C4×C127C22⋊Q811yescharacteristic
263C2×C4×C127C22⋊Q811yescharacteristic
264C2×C4×C127C22⋊Q811yescharacteristic
265C2×C4×C127#12311yescharacteristic
266C2×C4×C127#12311yescharacteristic
267C8×C127—24no—
268C8×C127—24no—
269C8×C127—42no—
270C8×C127—42no—
271C22×C127—24no—
272C22×C127—41no—
273C22×C127—41no—
274C22×C127—41no—
275C22×C127—41no—
276C22×C127—41no—
277C22×C127—41no—
278C22×C127—41no—
279C22×C127—44no—
280C22×C127—82no—
281C22×C127—82no—
282C22×C127C4×C22⋊C411yescharacteristic
283C22×C127#38011yescharacteristic
284C22×C127#38111yescharacteristic
285C22×C127#38511yescharacteristic
286C22×C127#38511yescharacteristic
287C22×C127#38611yescharacteristic
288C22×C127#38611yescharacteristic
289C4×C127—24no—
290C4×C127—82no—
291C4×C127—82no—
292C4×C127C2×#9511yescharacteristic
293C4×C127C4×C22⋊C411yescharacteristic
294C4×C127#37911yescharacteristic
295C4×C127#38011yescharacteristic
296C4×C127#38511yescharacteristic
297C4×C127#38511yescharacteristic
298C4×C127#38611yescharacteristic
299C4×C127#38611yescharacteristic
300#10778C12711yesmaximal, characteristic, direct product factor, Sylow
301C2×C127—21no—
302C2×C127—21no—
303C2×C127—21no—
304C2×C127—21no—
305C2×C127—21no—
306C2×C127—21no—
307C2×C127—21no—
308C2×C127—44no—
309C2×C127C22⋊#9511yescharacteristic
310C2×#568C2×C12711yescharacteristic
311C2×#421C2×C12711yescharacteristic
312#2896C2×C12711yescharacteristic
313C2×#344C2×C12711yescharacteristic, complemented
314C2×#344C2×C12711yescharacteristic, complemented
315#1738C2×C12711yescharacteristic, complemented
316#1733C2×C12711yescharacteristic, complemented
317C127#1077811yescharacteristic, direct product factor, Sylow
318C22×#41C22×C12711yescharacteristic
319#568—22no—
320#568—22no—
321#568—22no—
322#568—22no—
323C2×#131—22no—
324C2×#131C4×C12714yescomplemented
325C22×M16—22no—
326C22×M16C22×C12711yescharacteristic
327C22×M16C22×C12711yescharacteristic
328C22×M16C22×C12711yescharacteristic
329C22×M16C22×C12711yescharacteristic
330C2×#117C22×C12711yescharacteristic
331C2×#117C22×C12711yescharacteristic
332#421—22no—
333#421C4×C12714yescomplemented
334C2×#104—22no—
335#419C4×C12712yescomplemented
336#418C4×C12712yescomplemented
337#417—22no—
338#416—22no—
339#344—22no—
340#344—22no—
341#341—22no—
342#339—22no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41C2×C4×C12712yes—
350C2×#41C2×C4×C12712yes—
351C2×#41D4×C12712yes—
352C2×#41D4×C12712yes—
353C2×#41D4×C12712yes—
354C2×#41Q8×C12712yes—
355C22×Q8C2×C4×C12711yescharacteristic
356C22×D4—21no—
357C22×D4C2×C4×C12711yescharacteristic
358C23×C4—21no—
359C23×C4C23×C12711yescharacteristic
360#131—28no—
361#131—28no—
362#131—28no—
363#131—28no—
364C2×M16—28no—
365C2×M16—28no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—24no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16C2×C4×C12712yes—
385C2×M16C2×C4×C12712yes—
386C2×M16C2×C4×C12712yes—
387C2×M16D4×C12712yes—
388C2×M16D4×C12712yes—
389C2×M16D4×C12712yes—
390C2×M16D4×C12712yes—
391C22×C8—21no—
392C22×C8—24no—
393C22×C8—21no—
394C22×C8—21no—
395C22×C8C2×C4×C12712yes—
396#117—21no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117C2×C4×C12712yes—
403#117C2×C4×C12712yes—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42—21no—
410#104—28no—
411#103—24no—
412#102—24no—
413C24—21no—
414C24#41×C12711yescharacteristic
415#41—22no—
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—22no—
422#41—22no—
423#41—22no—
424#41—22no—
425#41—22no—
426#41—22no—
427#41C22⋊C4×C12714yes—
428#41C22⋊C4×C12714yes—
429#41C4⋊C4×C12714yes—
430#41C4⋊C4×C12714yes—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C42×C12712yes—
435C2×Q8C22⋊C4×C12712yes—
436C2×Q8C4⋊C4×C12712yes—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4C42×C12712yes—
447C2×D4C22⋊C4×C12712yes—
448C2×D4C4⋊C4×C12712yes—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4C22×C4×C12711yescharacteristic
459C22×C4C22×C4×C12711yescharacteristic
460C22×C4C22×C4×C12711yescharacteristic
461C22×C4C2×D4×C12711yescharacteristic
462C22×C4C2×D4×C12711yescharacteristic
463C22×C4C2×D4×C12711yescharacteristic
464C22×C4C2×D4×C12711yescharacteristic
465C22×C4C2×D4×C12711yescharacteristic
466C22×C4C2×D4×C12711yescharacteristic
467C22×C4C2×D4×C12711yescharacteristic
468C22×C4C2×Q8×C12711yescharacteristic
469C22×C4#41×C12711yescharacteristic
470C22×C4#41×C12711yescharacteristic
471C22×C4#41×C12711yescharacteristic
472M16—216no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—22no—
482M16—22no—
483M16—22no—
484M16—41no—
485M16—41no—
486M16—41no—
487M16—41no—
488M16C22⋊C4×C12714yes—
489C2×C8—216no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8C22⋊C4×C12714yes—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C42—22no—
511C42—22no—
512C42—41no—
513C42—41no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—81no—
518C23—82no—
519C23#117×C12711yescharacteristic
520C23C4×D4×C12711yescharacteristic
521C23C4×D4×C12711yescharacteristic
522C23#121×C12711yescharacteristic
523C23C22⋊Q8×C12711yescharacteristic
524C23#123×C12711yescharacteristic
525C23#123×C12711yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—22no—
529Q8#95×C12714yes—
530D4—24no—
531D4—24no—
532D4—24no—
533D4—24no—
534D4—22no—
535D4—22no—
536D4—22no—
537D4#95×C12714yes—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4C2×C42×C12711yescharacteristic
550C2×C4C2×C22⋊C4×C12711yescharacteristic
551C2×C4C2×C22⋊C4×C12711yescharacteristic
552C2×C4C2×C22⋊C4×C12711yescharacteristic
553C2×C4C2×C22⋊C4×C12711yescharacteristic
554C2×C4C2×C22⋊C4×C12711yescharacteristic
555C2×C4C2×C4⋊C4×C12711yescharacteristic
556C2×C4C2×C4⋊C4×C12711yescharacteristic
557C2×C4C2×C4⋊C4×C12711yescharacteristic
558C2×C4#117×C12711yescharacteristic
559C2×C4C4×D4×C12711yescharacteristic
560C2×C4C4×D4×C12711yescharacteristic
561C2×C4C4×D4×C12711yescharacteristic
562C2×C4C4×D4×C12711yescharacteristic
563C2×C4C4×D4×C12711yescharacteristic
564C2×C4C4×D4×C12711yescharacteristic
565C2×C4#120×C12711yescharacteristic
566C2×C4#120×C12711yescharacteristic
567C2×C4#120×C12711yescharacteristic
568C2×C4#120×C12711yescharacteristic
569C2×C4#121×C12711yescharacteristic
570C2×C4#121×C12711yescharacteristic
571C2×C4#121×C12711yescharacteristic
572C2×C4C22⋊Q8×C12711yescharacteristic
573C2×C4C22⋊Q8×C12711yescharacteristic
574C2×C4C22⋊Q8×C12711yescharacteristic
575C2×C4#123×C12711yescharacteristic
576C2×C4#123×C12711yescharacteristic
577C8—24no—
578C8—24no—
579C8—42no—
580C8—42no—
581C22—24no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—44no—
590C22—82no—
591C22—82no—
592C22C4×C22⋊C4×C12711yescharacteristic
593C22#380×C12711yescharacteristic
594C22#381×C12711yescharacteristic
595C22#385×C12711yescharacteristic
596C22#385×C12711yescharacteristic
597C22#386×C12711yescharacteristic
598C22#386×C12711yescharacteristic
599C4—24no—
600C4—82no—
601C4—82no—
602C4C2×#95×C12711yescharacteristic
603C4C4×C22⋊C4×C12711yescharacteristic
604C4#379×C12711yescharacteristic
605C4#380×C12711yescharacteristic
606C4#385×C12711yescharacteristic
607C4#385×C12711yescharacteristic
608C4#386×C12711yescharacteristic
609C4#386×C12711yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—44no—
618C2C127×C22⋊#9511yescharacteristic
subgroupG/H
centerC4×C127#379
commutatorC2×C4C2×C42×C127
Frattini, cosocleC23×C4C23×C127
socleC2×C127C22⋊#95
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#344×C127C2semidirect
5. C2×#344×C127C2semidirect
6. C127×#1738C2semidirect
7. C127×#1733C2semidirect
14. C2×#131×C127C4semidirect
23. #421×C127C4semidirect
25. #419×C127C4semidirect
26. #418×C127C4semidirect
300. #10778C127direct (N × H)
313. C2×#344C2×C127semidirect
314. C2×#344C2×C127semidirect
315. #1738C2×C127semidirect
316. #1733C2×C127semidirect
317. C127#10778direct (N × H)
324. C2×#131C4×C127semidirect
333. #421C4×C127semidirect
335. #419C4×C127semidirect
336. #418C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#568×C1272
C2×#421×C1272
C127×#28962
C2×#344×C1272
C127×#17382
C127×#17332
#10778127