Finite Group Databasebeta

← C127×#10322 #44573995

Subgroups — C127×#10322 #44573995

Order 32512.

988 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3187C211yesmaximal, characteristic, complemented
2C127×#2848C211yesmaximal, characteristic, complemented
3C127×#2847C211yesmaximal, characteristic
4C127×#1779C211yesmaximal, characteristic, complemented
5C127×#1520C211yesmaximal, characteristic, complemented
6C127×#1519C211yesmaximal, characteristic, complemented
7C127×#1289C211yesmaximal, characteristic, complemented
8C24×C4×C127C2211yescharacteristic
9C2×C22⋊Q8×C127—21no—
10C2×C22⋊Q8×C127C2211yescharacteristic
11C2×#121×C127—21no—
12C2×#121×C127C2211yescharacteristic
13C2×#120×C127—21no—
14#483×C127—21no—
15#481×C127—21no—
16#465×C127—22no—
17#450×C127—21no—
18#448×C127—21no—
19C2×C22⋊C8×C127—22no—
20C2×C22⋊C8×C127C2211yescharacteristic
21C2×C22⋊C8×C127C2211yescharacteristic
22#386×C127—21no—
23#386×C127—22no—
24#385×C127—21no—
25#385×C127—22no—
26#380×C127—21no—
27#380×C127—21no—
28#380×C127C2211yescharacteristic
29#380×C127C2211yescharacteristic
30#379×C127—21no—
31#328×C127—22no—
32#327×C127—22no—
33C25×C127D411yescharacteristic
34C22×Q8×C127D411yescharacteristic, complemented
35C22×D4×C127—22no—
36C22×D4×C127—21no—
37C22×D4×C127D411yescharacteristic
38C23×C4×C127—21no—
39C23×C4×C127—21no—
40C23×C4×C127—21no—
41C23×C4×C127—21no—
42C23×C4×C127—21no—
43C23×C4×C127—21no—
44C23×C4×C127—44no—
45C23×C4×C127D411yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C2×SD16×C127—22no—
48C22×C8×C127—21no—
49C22×C8×C127D412yescomplemented
50C22⋊Q8×C127—21no—
51C22⋊Q8×C127—21no—
52C22⋊Q8×C127—21no—
53C22⋊Q8×C127—21no—
54C22⋊Q8×C127—44no—
55#121×C127—21no—
56#121×C127—21no—
57#121×C127—21no—
58#121×C127—21no—
59#121×C127—44no—
60#120×C127—42no—
61#120×C127—42no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—21no—
64C2×C4⋊C4×C127—21no—
65C2×C4⋊C4×C127—21no—
66C2×C4⋊C4×C127D411yescharacteristic
67C2×C4⋊C4×C127D411yescharacteristic, complemented
68C2×C22⋊C4×C127—22no—
69C2×C22⋊C4×C127—22no—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—21no—
73C2×C22⋊C4×C127—21no—
74C2×C22⋊C4×C127—21no—
75C2×C22⋊C4×C127—21no—
76#106×C127—22no—
77#103×C127—22no—
78#102×C127—22no—
79C22⋊C8×C127—21no—
80C22⋊C8×C127—21no—
81C22⋊C8×C127—21no—
82C22⋊C8×C127—21no—
83C22⋊C8×C127—44no—
84#95×C127—22no—
85#95×C127—22no—
86#95×C127D412yes—
87#95×C127D412yescomplemented
88C24×C127—21no—
89C24×C127—21no—
90C24×C127—21no—
91C24×C127—21no—
92C24×C127—21no—
93C24×C127—21no—
94C24×C127—21no—
95C24×C127—42no—
96C24×C127—42no—
97C24×C127SD1612yescomplemented
98C24×C127C2×D411yescharacteristic
99C2×Q8×C127—21no—
100C2×Q8×C127—21no—
101C2×Q8×C127—42no—
102C2×D4×C127—21no—
103C2×D4×C127—21no—
104C2×D4×C127—42no—
105C2×D4×C127—44no—
106C2×D4×C127—44no—
107C2×D4×C127—44no—
108C2×D4×C127—41no—
109C2×D4×C127—41no—
110C2×D4×C127—41no—
111C2×D4×C127—41no—
112C2×D4×C127—41no—
113C2×D4×C127—41no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127—24no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—21no—
125C22×C4×C127—42no—
126C22×C4×C127—42no—
127C22×C4×C127—42no—
128C22×C4×C127—42no—
129C22×C4×C127—42no—
130C22×C4×C127—42no—
131C22×C4×C127—42no—
132C22×C4×C127—42no—
133C22×C4×C127—42no—
134C22×C4×C127—42no—
135C22×C4×C127—42no—
136C22×C4×C127—41no—
137C22×C4×C127—41no—
138C22×C4×C127—41no—
139C22×C4×C127—41no—
140C22×C4×C127C2×D411yescharacteristic
141C22×C4×C127C2×D411yescharacteristic
142C22×C4×C127C2×D411yescharacteristic
143C22×C4×C127C2×D411yescharacteristic
144C22×C4×C127C2×D411yescharacteristic
145C22×C4×C127#4111yescharacteristic
146SD16×C127—82no—
147C2×C8×C127—22no—
148C2×C8×C127—42no—
149C2×C8×C127—42no—
150C2×C8×C127—41no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—21no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—21no—
155C4⋊C4×C127—42no—
156C4⋊C4×C127—42no—
157C4⋊C4×C127—44no—
158C4⋊C4×C127—41no—
159C4⋊C4×C127—41no—
160C22⋊C4×C127—44no—
161C22⋊C4×C127—44no—
162C22⋊C4×C127—44no—
163C22⋊C4×C127—44no—
164C22⋊C4×C127—41no—
165C22⋊C4×C127—41no—
166C22⋊C4×C127—41no—
167C22⋊C4×C127—41no—
168C22⋊C4×C127—41no—
169C22⋊C4×C127—41no—
170C22⋊C4×C127—41no—
171C22⋊C4×C127—41no—
172C23×C127—22no—
173C23×C127—22no—
174C23×C127—22no—
175C23×C127—22no—
176C23×C127—22no—
177C23×C127—22no—
178C23×C127—22no—
179C23×C127—22no—
180C23×C127—22no—
181C23×C127—41no—
182C23×C127—44no—
183C23×C127—41no—
184C23×C127—41no—
185C23×C127—41no—
186C23×C127—41no—
187C23×C127—41no—
188C23×C127—41no—
189C23×C127—41no—
190C23×C127—44no—
191C23×C127—44no—
192C23×C127—44no—
193C23×C127—42no—
194C23×C127—42no—
195C23×C127—41no—
196C23×C127—41no—
197C23×C127—41no—
198C23×C127—41no—
199C23×C127—41no—
200C23×C127—41no—
201C23×C127—41no—
202C23×C127#12011yescharacteristic
203C23×C127#12011yescharacteristic
204C23×C127#12111yescharacteristic
205C23×C127C2×SD1611yescharacteristic
206C23×C127#13511yescharacteristic
207C23×C127AGL(1,ℤ/8)11yescharacteristic
208C23×C127#13711yescharacteristic
209Q8×C127—42no—
210Q8×C127—81no—
211D4×C127—42no—
212D4×C127—81no—
213D4×C127—88no—
214D4×C127—81no—
215D4×C127—81no—
216D4×C127—81no—
217D4×C127—81no—
218C2×C4×C127—22no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—22no—
223C2×C4×C127—22no—
224C2×C4×C127—41no—
225C2×C4×C127—41no—
226C2×C4×C127—41no—
227C2×C4×C127—44no—
228C2×C4×C127—44no—
229C2×C4×C127—44no—
230C2×C4×C127—41no—
231C2×C4×C127—41no—
232C2×C4×C127—41no—
233C2×C4×C127—41no—
234C2×C4×C127—44no—
235C2×C4×C127—42no—
236C2×C4×C127—42no—
237C2×C4×C127—42no—
238C2×C4×C127—42no—
239C2×C4×C127—42no—
240C2×C4×C127—42no—
241C2×C4×C127—41no—
242C2×C4×C127—41no—
243C2×C4×C127—41no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127—41no—
247C2×C4×C127—41no—
248C2×C4×C127#12011yescharacteristic
249C2×C4×C127#12111yescharacteristic
250C2×C4×C127#12111yescharacteristic
251C2×C4×C127#12711yescharacteristic
252C8×C127—42no—
253C8×C127—81no—
254C22×C127—21no—
255C22×C127—21no—
256C22×C127—21no—
257C22×C127—21no—
258C22×C127—21no—
259C22×C127—21no—
260C22×C127—24no—
261C22×C127—24no—
262C22×C127—24no—
263C22×C127—41no—
264C22×C127—41no—
265C22×C127—41no—
266C22×C127—41no—
267C22×C127—42no—
268C22×C127—42no—
269C22×C127—42no—
270C22×C127—42no—
271C22×C127—42no—
272C22×C127—42no—
273C22×C127—42no—
274C22×C127—42no—
275C22×C127—42no—
276C22×C127—42no—
277C22×C127—42no—
278C22×C127—42no—
279C22×C127—82no—
280C22×C127—82no—
281C22×C127—81no—
282C22×C127—81no—
283C22×C127—81no—
284C22×C127#39211yescharacteristic
285C22×C127#44811yescharacteristic
286C22×C127#44911yescharacteristic
287C22×C127#45011yescharacteristic
288C22×C127#45211yescharacteristic
289C22×C127#46511yescharacteristic
290C22×C127#46811yescharacteristic
291C4×C127—21no—
292C4×C127—21no—
293C4×C127—21no—
294C4×C127—42no—
295C4×C127—82no—
296C4×C127—82no—
297C4×C127—81no—
298C4×C127—81no—
299C4×C127—81no—
300C4×C127B(4,𝔽2)12yes—
301#10322C12711yesmaximal, characteristic, direct product factor, Sylow
302C2×C127—21no—
303C2×C127—21no—
304C2×C127—21no—
305C2×C127—21no—
306C2×C127—21no—
307C2×C127—21no—
308C2×C127—44no—
309C2×C127—161no—
310C2×C127#200011yescharacteristic
311C2×C127#201011yescharacteristic
312C2×C127#202111yescharacteristic
313#3187C2×C12711yescharacteristic, complemented
314#2848C2×C12711yescharacteristic, complemented
315#2847C2×C12711yescharacteristic
316#1779C2×C12711yescharacteristic, complemented
317#1520C2×C12711yescharacteristic, complemented
318#1519C2×C12711yescharacteristic, complemented
319#1289C2×C12711yescharacteristic, complemented
320C127#1032211yescharacteristic, direct product factor, Sylow
321C24×C4C22×C12711yescharacteristic
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8C22×C12711yescharacteristic
324C2×#121—21no—
325C2×#121C22×C12711yescharacteristic
326C2×#120—21no—
327#483—21no—
328#481—21no—
329#465—22no—
330#450—21no—
331#448—21no—
332C2×C22⋊C8—22no—
333C2×C22⋊C8C22×C12711yescharacteristic
334C2×C22⋊C8C22×C12711yescharacteristic
335#386—21no—
336#386—22no—
337#385—21no—
338#385—22no—
339#380—21no—
340#380—21no—
341#380C22×C12711yescharacteristic
342#380C22×C12711yescharacteristic
343#379—21no—
344#328—22no—
345#327—22no—
346C25D4×C12711yescharacteristic
347C22×Q8D4×C12711yescharacteristic, complemented
348C22×D4—22no—
349C22×D4—21no—
350C22×D4D4×C12711yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—44no—
358C23×C4D4×C12711yescharacteristic
359C23×C4C23×C12711yescharacteristic
360C2×SD16—22no—
361C22×C8—21no—
362C22×C8D4×C12712yescomplemented
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—44no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—44no—
373#120—42no—
374#120—42no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4D4×C12711yescharacteristic
380C2×C4⋊C4D4×C12711yescharacteristic, complemented
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389#106—22no—
390#103—22no—
391#102—22no—
392C22⋊C8—21no—
393C22⋊C8—21no—
394C22⋊C8—21no—
395C22⋊C8—21no—
396C22⋊C8—44no—
397#95—22no—
398#95—22no—
399#95D4×C12712yes—
400#95D4×C12712yescomplemented
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—42no—
409C24—42no—
410C24SD16×C12712yescomplemented
411C24C2×D4×C12711yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—42no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—42no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C12711yescharacteristic
454C22×C4C2×D4×C12711yescharacteristic
455C22×C4C2×D4×C12711yescharacteristic
456C22×C4C2×D4×C12711yescharacteristic
457C22×C4C2×D4×C12711yescharacteristic
458C22×C4#41×C12711yescharacteristic
459SD16—82no—
460C2×C8—22no—
461C2×C8—42no—
462C2×C8—42no—
463C2×C8—41no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—44no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—44no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—44no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—41no—
495C23—44no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—44no—
504C23—44no—
505C23—44no—
506C23—42no—
507C23—42no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23#120×C12711yescharacteristic
516C23#120×C12711yescharacteristic
517C23#121×C12711yescharacteristic
518C23C2×SD16×C12711yescharacteristic
519C23#135×C12711yescharacteristic
520C23AGL(1,ℤ/8)×C12711yescharacteristic
521C23#137×C12711yescharacteristic
522Q8—42no—
523Q8—81no—
524D4—42no—
525D4—81no—
526D4—88no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4#120×C12711yescharacteristic
562C2×C4#121×C12711yescharacteristic
563C2×C4#121×C12711yescharacteristic
564C2×C4#127×C12711yescharacteristic
565C8—42no—
566C8—81no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—82no—
593C22—82no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22#392×C12711yescharacteristic
598C22#448×C12711yescharacteristic
599C22#449×C12711yescharacteristic
600C22#450×C12711yescharacteristic
601C22#452×C12711yescharacteristic
602C22#465×C12711yescharacteristic
603C22#468×C12711yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—82no—
609C4—82no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4B(4,𝔽2)×C12712yes—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—44no—
621C2—161no—
622C2C127×#200011yescharacteristic
623C2C127×#201011yescharacteristic
624C2C127×#202111yescharacteristic
subgroupG/H
center, socleC22×C127#392
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC127×#2847C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3187C2semidirect
2. C127×#2848C2semidirect
4. C127×#1779C2semidirect
5. C127×#1520C2semidirect
6. C127×#1519C2semidirect
7. C127×#1289C2semidirect
34. C22×Q8×C127D4semidirect
49. C22×C8×C127D4semidirect
67. C2×C4⋊C4×C127D4semidirect
87. #95×C127D4semidirect
97. C24×C127SD16semidirect
301. #10322C127direct (N × H)
313. #3187C2×C127semidirect
314. #2848C2×C127semidirect
316. #1779C2×C127semidirect
317. #1520C2×C127semidirect
318. #1519C2×C127semidirect
319. #1289C2×C127semidirect
320. C127#10322direct (N × H)
347. C22×Q8D4×C127semidirect
362. C22×C8D4×C127semidirect
380. C2×C4⋊C4D4×C127semidirect
400. #95D4×C127semidirect
410. C24SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31872
C127×#28482
C127×#28472
C127×#17792
C127×#15202
C127×#15192
C127×#12892
#10322127