Finite Group Databasebeta

← C127×#19068 #44582741

Subgroups — C127×#19068 #44582741

Order 32512.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3545C211yesmaximal, characteristic, complemented
2C127×#3219C211yesmaximal, characteristic, complemented
3C127×#3213C211yesmaximal, characteristic, complemented
4C127×#3171C211yesmaximal, characteristic, complemented
5C127×#1664C211yesmaximal, characteristic, complemented
6C127×#1662C211yesmaximal, characteristic, complemented
7C127×#1661C211yesmaximal, characteristic, complemented
8C127×#1659C211yesmaximal, characteristic, complemented
9C127×#1657C211yesmaximal, characteristic, complemented
10C127×#1656C211yesmaximal, characteristic, complemented
11C127×#1656C211yesmaximal, characteristic, complemented
12C127×#1655C211yesmaximal, characteristic, complemented
13C127×#1535C211yesmaximal, characteristic, complemented
14C127×#1529C211yesmaximal, characteristic, complemented
15C127×#1527C211yesmaximal, characteristic, complemented
16#563×C127C2211yescharacteristic
17#562×C127C2211yescharacteristic
18#562×C127C2211yescharacteristic
19H(3,𝔽4)×C127C2211yescharacteristic
20#555×C127—21no—
21#551×C127—21no—
22#551×C127—21no—
23#551×C127—21no—
24#546×C127—21no—
25#546×C127—21no—
26#542×C127—21no—
27#542×C127—21no—
28#538×C127—21no—
29#538×C127—21no—
30#536×C127—21no—
31#534×C127—21no—
32#532×C127C2211yescharacteristic, complemented
33#529×C127C2211yescharacteristic
34#529×C127C2211yescharacteristic
35C2×#124×C127C2211yescharacteristic
36#501×C127C2211yescharacteristic, complemented
37#497×C127C2211yescharacteristic, complemented
38#496×C127C2211yescharacteristic
39#496×C127C2211yescharacteristic, complemented
40#496×C127C2211yescharacteristic, complemented
41#496×C127C2211yescharacteristic, complemented
42#491×C127C2211yescharacteristic, complemented
43#490×C127C2211yescharacteristic, complemented
44#490×C127C2211yescharacteristic, complemented
45#489×C127C2211yescharacteristic
46#489×C127C2211yescharacteristic, complemented
47#489×C127C2211yescharacteristic, complemented
48#469×C127—21no—
49#468×C127—21no—
50#464×C127—21no—
51#463×C127—21no—
52#463×C127—21no—
53#463×C127—21no—
54#452×C127—21no—
55#449×C127—21no—
56#448×C127—21no—
57#447×C127—21no—
58C4×SD16×C127—21no—
59C4×D8×C127—21no—
60#432×C127C2211yescharacteristic, complemented
61#432×C127C2211yescharacteristic, complemented
62C4×M16×C127C2211yescharacteristic, complemented
63#330×C127C2211yescharacteristic, complemented
64#330×C127C2211yescharacteristic, complemented
65#330×C127C2211yescharacteristic, complemented
66#330×C127C2211yescharacteristic, complemented
67#329×C127C2211yescharacteristic
68#329×C127C2211yescharacteristic
69#329×C127C2211yescharacteristic, complemented
70#329×C127C2211yescharacteristic, complemented
71#329×C127C2211yescharacteristic, complemented
72#329×C127C2211yescharacteristic, complemented
73#329×C127C2211yescharacteristic, complemented
74#329×C127C2211yescharacteristic, complemented
75C2×#41×C127—21no—
76C2×#41×C127—21no—
77C22×Q8×C127D411yescharacteristic
78C22×D4×C127—21no—
79C22×D4×C127D411yescharacteristic
80C2×Q16×C127—21no—
81C2×SD16×C127—21no—
82C2×SD16×C127—21no—
83C2×SD16×C127—21no—
84C2×SD16×C127—21no—
85C2×SD16×C127—21no—
86C2×D8×C127—21no—
87C2×D8×C127—21no—
88C2×D8×C127—21no—
89C2×D8×C127—21no—
90C2×M16×C127—21no—
91C4⋊Q8×C127—21no—
92C4⋊Q8×C127—21no—
93C4⋊Q8×C127C2311yescharacteristic
94#127×C127C2311yescharacteristic
95#126×C127—21no—
96#126×C127—21no—
97#126×C127—21no—
98#126×C127—21no—
99#126×C127—21no—
100#126×C127—21no—
101#125×C127C2311yescharacteristic
102#125×C127C2311yescharacteristic
103#124×C127—21no—
104#124×C127—21no—
105#124×C127—21no—
106#124×C127—21no—
107#124×C127—21no—
108#124×C127—21no—
109#124×C127—21no—
110#124×C127—21no—
111#124×C127—21no—
112#124×C127D411yescharacteristic
113#124×C127D411yescharacteristic
114#124×C127C2311yescharacteristic
115#124×C127C2311yescharacteristic
116#124×C127C2311yescharacteristic
117#124×C127C2311yescharacteristic
118#123×C127—21no—
119#123×C127—21no—
120#123×C127—21no—
121#123×C127—21no—
122#123×C127—21no—
123#123×C127—21no—
124#123×C127—21no—
125#123×C127—21no—
126#123×C127—21no—
127#123×C127—21no—
128#123×C127—21no—
129#123×C127—21no—
130C22⋊Q8×C127—21no—
131C22⋊Q8×C127—21no—
132C22⋊Q8×C127—21no—
133C22⋊Q8×C127—21no—
134C22⋊Q8×C127—21no—
135C22⋊Q8×C127—21no—
136C22⋊Q8×C127—21no—
137C22⋊Q8×C127—21no—
138C22⋊Q8×C127D411yescharacteristic
139C22⋊Q8×C127D411yescharacteristic
140#121×C127—21no—
141#121×C127—21no—
142#121×C127—21no—
143#121×C127—21no—
144#121×C127—21no—
145#121×C127—21no—
146#121×C127—21no—
147#121×C127—21no—
148#121×C127—21no—
149#121×C127—21no—
150#121×C127D411yescharacteristic
151#121×C127D411yescharacteristic
152#120×C127—21no—
153#120×C127—21no—
154#120×C127—21no—
155#120×C127—21no—
156#120×C127—21no—
157#120×C127—21no—
158C4×Q8×C127D411yescharacteristic
159C4×Q8×C127D411yescharacteristic
160C4×D4×C127—21no—
161C4×D4×C127—21no—
162C4×D4×C127—21no—
163C4×D4×C127—21no—
164C4×D4×C127—21no—
165C4×D4×C127—21no—
166C4×D4×C127—21no—
167C4×D4×C127—21no—
168C4×D4×C127D411yescharacteristic
169C4×D4×C127D411yescharacteristic
170#117×C127—21no—
171#117×C127—21no—
172#117×C127—21no—
173#117×C127—21no—
174#117×C127—21no—
175C2×C22⋊C4×C127—21no—
176C2×C22⋊C4×C127—21no—
177C2×C22⋊C4×C127—21no—
178C2×C22⋊C4×C127—21no—
179C2×C22⋊C4×C127—21no—
180C2×C42×C127C2311yescharacteristic
181#107×C127—21no—
182#106×C127—21no—
183C4⋊C8×C127—21no—
184C4⋊C8×C127—21no—
185#103×C127—21no—
186#103×C127—21no—
187#103×C127—21no—
188#103×C127—21no—
189#103×C127—21no—
190#102×C127—21no—
191#102×C127—21no—
192#102×C127—21no—
193#102×C127—21no—
194#102×C127—21no—
195#102×C127—21no—
196#102×C127—21no—
197C22⋊C8×C127—21no—
198C22⋊C8×C127—21no—
199#97×C127C2311yescharacteristic
200#97×C127C2311yescharacteristic
201#97×C127C2311yescharacteristic
202#97×C127C2311yescharacteristic
203#97×C127C2311yescharacteristic
204#97×C127C2311yescharacteristic
205C4×C8×C127—21no—
206C24×C127—21no—
207C24×C127—21no—
208#41×C127—82no—
209#41×C127—81no—
210#41×C127—81no—
211C2×Q8×C127—21no—
212C2×Q8×C127—21no—
213C2×Q8×C127—21no—
214C2×Q8×C127—81no—
215C2×Q8×C127C2×D411yescharacteristic
216C2×Q8×C127C2×D411yescharacteristic
217C2×Q8×C127C2×D411yescharacteristic
218C2×Q8×C127C2×D411yescharacteristic
219C2×D4×C127—21no—
220C2×D4×C127—21no—
221C2×D4×C127—21no—
222C2×D4×C127—21no—
223C2×D4×C127—21no—
224C2×D4×C127—21no—
225C2×D4×C127—21no—
226C2×D4×C127—21no—
227C2×D4×C127—21no—
228C2×D4×C127—21no—
229C2×D4×C127—21no—
230C2×D4×C127—21no—
231C2×D4×C127—21no—
232C2×D4×C127—41no—
233C2×D4×C127—81no—
234C2×D4×C127—82no—
235C2×D4×C127C2×D411yescharacteristic
236C2×D4×C127C2×D411yescharacteristic
237C2×D4×C127C2×D411yescharacteristic
238C2×D4×C127C2×D411yescharacteristic
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—41no—
248C22×C4×C127C2×D411yescharacteristic
249C22×C4×C127C2×D411yescharacteristic
250C22×C4×C127C2×D411yescharacteristic
251Q16×C127—81no—
252SD16×C127—42no—
253SD16×C127—81no—
254SD16×C127—81no—
255SD16×C127—81no—
256SD16×C127—81no—
257D8×C127—42no—
258D8×C127—81no—
259D8×C127—81no—
260D8×C127—81no—
261M16×C127—42no—
262C2×C8×C127—21no—
263C2×C8×C127—21no—
264C2×C8×C127—21no—
265C2×C8×C127—21no—
266C2×C8×C127—21no—
267C2×C8×C127—21no—
268C4⋊C4×C127—21no—
269C4⋊C4×C127—21no—
270C4⋊C4×C127—21no—
271C4⋊C4×C127—21no—
272C4⋊C4×C127—21no—
273C4⋊C4×C127—21no—
274C4⋊C4×C127—21no—
275C4⋊C4×C127—21no—
276C4⋊C4×C127—21no—
277C4⋊C4×C127—21no—
278C4⋊C4×C127—21no—
279C4⋊C4×C127—21no—
280C4⋊C4×C127—21no—
281C4⋊C4×C127—21no—
282C4⋊C4×C127—21no—
283C4⋊C4×C127—21no—
284C4⋊C4×C127C2×D411yescharacteristic
285C4⋊C4×C127C2×D411yescharacteristic
286C4⋊C4×C127C2×D411yescharacteristic
287C4⋊C4×C127C2×D411yescharacteristic
288C22⋊C4×C127—21no—
289C22⋊C4×C127—21no—
290C22⋊C4×C127—21no—
291C22⋊C4×C127—21no—
292C22⋊C4×C127—21no—
293C22⋊C4×C127—21no—
294C22⋊C4×C127—21no—
295C22⋊C4×C127—21no—
296C22⋊C4×C127—21no—
297C22⋊C4×C127—21no—
298C22⋊C4×C127—21no—
299C22⋊C4×C127—21no—
300C22⋊C4×C127—21no—
301C22⋊C4×C127—21no—
302C22⋊C4×C127—21no—
303C22⋊C4×C127—21no—
304C22⋊C4×C127—21no—
305C22⋊C4×C127—21no—
306C22⋊C4×C127—21no—
307C22⋊C4×C127—21no—
308C22⋊C4×C127—21no—
309C22⋊C4×C127—21no—
310C22⋊C4×C127—21no—
311C22⋊C4×C127—21no—
312C22⋊C4×C127—21no—
313C22⋊C4×C127—21no—
314C22⋊C4×C127—21no—
315C22⋊C4×C127—21no—
316C22⋊C4×C127—41no—
317C22⋊C4×C127—41no—
318C42×C127—21no—
319C42×C127—21no—
320C42×C127—21no—
321C42×C127—21no—
322C42×C127C2×D411yescharacteristic
323C42×C127C2×D411yescharacteristic
324C42×C127C2×D411yescharacteristic
325C42×C127C2411yescharacteristic
326C23×C127—21no—
327C23×C127—21no—
328C23×C127—21no—
329C23×C127—21no—
330C23×C127—42no—
331C23×C127—41no—
332C23×C127—81no—
333C23×C127—81no—
334C23×C127—81no—
335C23×C127—81no—
336C23×C127—81no—
337C23×C127#12011yescharacteristic
338Q8×C127—41no—
339Q8×C127—41no—
340Q8×C127—41no—
341Q8×C127—41no—
342Q8×C127—41no—
343Q8×C127—41no—
344Q8×C127—81no—
345Q8×C127—81no—
346D4×C127—41no—
347D4×C127—41no—
348D4×C127—41no—
349D4×C127—41no—
350D4×C127—41no—
351D4×C127—41no—
352D4×C127—41no—
353D4×C127—41no—
354D4×C127—41no—
355D4×C127—41no—
356D4×C127—42no—
357D4×C127—42no—
358D4×C127—81no—
359D4×C127—81no—
360D4×C127—81no—
361D4×C127—81no—
362D4×C127—81no—
363D4×C127—81no—
364D4×C127—81no—
365D4×C127—81no—
366D4×C127—82no—
367C2×C4×C127—21no—
368C2×C4×C127—21no—
369C2×C4×C127—21no—
370C2×C4×C127—21no—
371C2×C4×C127—21no—
372C2×C4×C127—21no—
373C2×C4×C127—21no—
374C2×C4×C127—21no—
375C2×C4×C127—41no—
376C2×C4×C127—41no—
377C2×C4×C127—41no—
378C2×C4×C127—42no—
379C2×C4×C127—41no—
380C2×C4×C127—81no—
381C2×C4×C127—81no—
382C2×C4×C127—82no—
383C2×C4×C127—81no—
384C2×C4×C127—81no—
385C2×C4×C127—81no—
386C2×C4×C127—81no—
387C2×C4×C127—81no—
388C2×C4×C127#12011yescharacteristic
389C2×C4×C127#12011yescharacteristic
390C2×C4×C127#12011yescharacteristic
391C2×C4×C127C22×D411yescharacteristic
392C2×C4×C127C22×D411yescharacteristic
393C2×C4×C127C22×D411yescharacteristic
394C8×C127—22no—
395C8×C127—41no—
396C8×C127—41no—
397C8×C127—41no—
398C8×C127—41no—
399C8×C127—41no—
400C22×C127—21no—
401C22×C127—21no—
402C22×C127—21no—
403C22×C127—41no—
404C22×C127—41no—
405C22×C127—41no—
406C22×C127—41no—
407C22×C127—41no—
408C22×C127—41no—
409C22×C127—41no—
410C22×C127—41no—
411C22×C127—41no—
412C22×C127—41no—
413C22×C127—41no—
414C22×C127—41no—
415C22×C127—81no—
416C22×C127—81no—
417C22×C127—81no—
418C22×C127—162no—
419C22×C127—162no—
420C22×C127C2×#12011yescharacteristic
421C4×C127—21no—
422C4×C127—21no—
423C4×C127—21no—
424C4×C127—21no—
425C4×C127—21no—
426C4×C127—21no—
427C4×C127—41no—
428C4×C127—41no—
429C4×C127—41no—
430C4×C127—41no—
431C4×C127—41no—
432C4×C127—41no—
433C4×C127—41no—
434C4×C127—41no—
435C4×C127—81no—
436#19068C12711yesmaximal, characteristic, direct product factor, Sylow
437C2×C127—41no—
438C2×C127—81no—
439C2×C127—81no—
440C2×C127—81no—
441C2×C127—81no—
442C2×C127—161no—
443C2×C127#301811yescharacteristic
444C2×C127#301911yescharacteristic
445C2×C127#302111yescharacteristic
446#3545C2×C12711yescharacteristic, complemented
447#3219C2×C12711yescharacteristic, complemented
448#3213C2×C12711yescharacteristic, complemented
449#3171C2×C12711yescharacteristic, complemented
450#1664C2×C12711yescharacteristic, complemented
451#1662C2×C12711yescharacteristic, complemented
452#1661C2×C12711yescharacteristic, complemented
453#1659C2×C12711yescharacteristic, complemented
454#1657C2×C12711yescharacteristic, complemented
455#1656C2×C12711yescharacteristic, complemented
456#1656C2×C12711yescharacteristic, complemented
457#1655C2×C12711yescharacteristic, complemented
458#1535C2×C12711yescharacteristic, complemented
459#1529C2×C12711yescharacteristic, complemented
460#1527C2×C12711yescharacteristic, complemented
461C127#1906811yescharacteristic, direct product factor, Sylow
462#563C22×C12711yescharacteristic
463#562C22×C12711yescharacteristic
464#562C22×C12711yescharacteristic
465H(3,𝔽4)C22×C12711yescharacteristic
466#555—21no—
467#551—21no—
468#551—21no—
469#551—21no—
470#546—21no—
471#546—21no—
472#542—21no—
473#542—21no—
474#538—21no—
475#538—21no—
476#536—21no—
477#534—21no—
478#532C22×C12711yescharacteristic, complemented
479#529C22×C12711yescharacteristic
480#529C22×C12711yescharacteristic
481C2×#124C22×C12711yescharacteristic
482#501C22×C12711yescharacteristic, complemented
483#497C22×C12711yescharacteristic, complemented
484#496C22×C12711yescharacteristic
485#496C22×C12711yescharacteristic, complemented
486#496C22×C12711yescharacteristic, complemented
487#496C22×C12711yescharacteristic, complemented
488#491C22×C12711yescharacteristic, complemented
489#490C22×C12711yescharacteristic, complemented
490#490C22×C12711yescharacteristic, complemented
491#489C22×C12711yescharacteristic
492#489C22×C12711yescharacteristic, complemented
493#489C22×C12711yescharacteristic, complemented
494#469—21no—
495#468—21no—
496#464—21no—
497#463—21no—
498#463—21no—
499#463—21no—
500#452—21no—
501#449—21no—
502#448—21no—
503#447—21no—
504C4×SD16—21no—
505C4×D8—21no—
506#432C22×C12711yescharacteristic, complemented
507#432C22×C12711yescharacteristic, complemented
508C4×M16C22×C12711yescharacteristic, complemented
509#330C22×C12711yescharacteristic, complemented
510#330C22×C12711yescharacteristic, complemented
511#330C22×C12711yescharacteristic, complemented
512#330C22×C12711yescharacteristic, complemented
513#329C22×C12711yescharacteristic
514#329C22×C12711yescharacteristic
515#329C22×C12711yescharacteristic, complemented
516#329C22×C12711yescharacteristic, complemented
517#329C22×C12711yescharacteristic, complemented
518#329C22×C12711yescharacteristic, complemented
519#329C22×C12711yescharacteristic, complemented
520#329C22×C12711yescharacteristic, complemented
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C12711yescharacteristic
524C22×D4—21no—
525C22×D4D4×C12711yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C12711yescharacteristic
540#127C23×C12711yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C12711yescharacteristic
548#125C23×C12711yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C12711yescharacteristic
559#124D4×C12711yescharacteristic
560#124C23×C12711yescharacteristic
561#124C23×C12711yescharacteristic
562#124C23×C12711yescharacteristic
563#124C23×C12711yescharacteristic
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C12711yescharacteristic
585C22⋊Q8D4×C12711yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121D4×C12711yescharacteristic
597#121D4×C12711yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C12711yescharacteristic
605C4×Q8D4×C12711yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C12711yescharacteristic
615C4×D4D4×C12711yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C12711yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C12711yescharacteristic
646#97C23×C12711yescharacteristic
647#97C23×C12711yescharacteristic
648#97C23×C12711yescharacteristic
649#97C23×C12711yescharacteristic
650#97C23×C12711yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C12711yescharacteristic
662C2×Q8C2×D4×C12711yescharacteristic
663C2×Q8C2×D4×C12711yescharacteristic
664C2×Q8C2×D4×C12711yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C12711yescharacteristic
682C2×D4C2×D4×C12711yescharacteristic
683C2×D4C2×D4×C12711yescharacteristic
684C2×D4C2×D4×C12711yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4C2×D4×C12711yescharacteristic
695C22×C4C2×D4×C12711yescharacteristic
696C22×C4C2×D4×C12711yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C2×D4×C12711yescharacteristic
731C4⋊C4C2×D4×C12711yescharacteristic
732C4⋊C4C2×D4×C12711yescharacteristic
733C4⋊C4C2×D4×C12711yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C12711yescharacteristic
769C42C2×D4×C12711yescharacteristic
770C42C2×D4×C12711yescharacteristic
771C42C24×C12711yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C12711yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C12711yescharacteristic
835C2×C4#120×C12711yescharacteristic
836C2×C4#120×C12711yescharacteristic
837C2×C4C22×D4×C12711yescharacteristic
838C2×C4C22×D4×C12711yescharacteristic
839C2×C4C22×D4×C12711yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C12711yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C127×#301811yescharacteristic
889C2C127×#301911yescharacteristic
890C2C127×#302111yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3545C2semidirect
2. C127×#3219C2semidirect
3. C127×#3213C2semidirect
4. C127×#3171C2semidirect
5. C127×#1664C2semidirect
6. C127×#1662C2semidirect
7. C127×#1661C2semidirect
8. C127×#1659C2semidirect
9. C127×#1657C2semidirect
10. C127×#1656C2semidirect
11. C127×#1656C2semidirect
12. C127×#1655C2semidirect
13. C127×#1535C2semidirect
14. C127×#1529C2semidirect
15. C127×#1527C2semidirect
32. #532×C127C22semidirect
36. #501×C127C22semidirect
37. #497×C127C22semidirect
39. #496×C127C22semidirect
40. #496×C127C22semidirect
41. #496×C127C22semidirect
42. #491×C127C22semidirect
43. #490×C127C22semidirect
44. #490×C127C22semidirect
46. #489×C127C22semidirect
47. #489×C127C22semidirect
60. #432×C127C22semidirect
61. #432×C127C22semidirect
62. C4×M16×C127C22semidirect
63. #330×C127C22semidirect
64. #330×C127C22semidirect
65. #330×C127C22semidirect
66. #330×C127C22semidirect
69. #329×C127C22semidirect
70. #329×C127C22semidirect
71. #329×C127C22semidirect
72. #329×C127C22semidirect
73. #329×C127C22semidirect
74. #329×C127C22semidirect
436. #19068C127direct (N × H)
446. #3545C2×C127semidirect
447. #3219C2×C127semidirect
448. #3213C2×C127semidirect
449. #3171C2×C127semidirect
450. #1664C2×C127semidirect
451. #1662C2×C127semidirect
452. #1661C2×C127semidirect
453. #1659C2×C127semidirect
454. #1657C2×C127semidirect
455. #1656C2×C127semidirect
456. #1656C2×C127semidirect
457. #1655C2×C127semidirect
458. #1535C2×C127semidirect
459. #1529C2×C127semidirect
460. #1527C2×C127semidirect
461. C127#19068direct (N × H)
478. #532C22×C127semidirect
482. #501C22×C127semidirect
483. #497C22×C127semidirect
485. #496C22×C127semidirect
486. #496C22×C127semidirect
487. #496C22×C127semidirect
488. #491C22×C127semidirect
489. #490C22×C127semidirect
490. #490C22×C127semidirect
492. #489C22×C127semidirect
493. #489C22×C127semidirect
506. #432C22×C127semidirect
507. #432C22×C127semidirect
508. C4×M16C22×C127semidirect
509. #330C22×C127semidirect
510. #330C22×C127semidirect
511. #330C22×C127semidirect
512. #330C22×C127semidirect
515. #329C22×C127semidirect
516. #329C22×C127semidirect
517. #329C22×C127semidirect
518. #329C22×C127semidirect
519. #329C22×C127semidirect
520. #329C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35452
C127×#32192
C127×#32132
C127×#31712
C127×#16642
C127×#16622
C127×#16612
C127×#16592
C127×#16572
C127×#16562
C127×#16552
C127×#15352
C127×#15292
C127×#15272
#19068127