Finite Group Databasebeta

← C127×#13043 #44576716

Subgroups — C127×#13043 #44576716

Order 32512.

844 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×B(4,𝔽2)×C127C211yesmaximal, characteristic
2C127×#2375C211yesmaximal, characteristic, complemented
3C2×AΣL(1,𝔽16)×C127C211yesmaximal, characteristic, complemented
4C127×#1792C211yesmaximal, characteristic, complemented
5C127×#1790C211yesmaximal, characteristic, complemented
6C127×#1393C211yesmaximal, characteristic, complemented
7C127×#1390C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C127C2211yescharacteristic
9C2×#120×C127—21no—
10C2×#120×C127C2211yescharacteristic
11B(4,𝔽2)×C127—22no—
12B(4,𝔽2)×C127C414yescomplemented
13C2×#104×C127—21no—
14#417×C127—21no—
15C2×#100×C127C2211yescharacteristic
16C2×#99×C127—21no—
17C2×#99×C127—21no—
18C2×#99×C127C2211yescharacteristic
19C2×#99×C127C2211yescharacteristic
20#390×C127—21no—
21#390×C127C2211yescharacteristic
22#388×C127—21no—
23#388×C127—21no—
24#388×C127—21no—
25#386×C127—21no—
26#386×C127—21no—
27#386×C127C2211yescharacteristic
28#379×C127—21no—
29AΣL(1,𝔽16)×C127—22no—
30C25×C127D411yescharacteristic
31H(5,𝔽2)×C127—21no—
32H(5,𝔽2)×C127—21no—
33H(5,𝔽2)×C127—21no—
34H(5,𝔽2)×C127—42no—
35H(5,𝔽2)×C127C2×C412yes—
36C2×#41×C127—21no—
37C2×#41×C127—41no—
38C22×D4×C127—21no—
39C22×D4×C127—21no—
40C22×D4×C127—21no—
41C22×D4×C127—41no—
42C22×D4×C127—41no—
43C22×D4×C127C2311yescharacteristic
44C23×C4×C127D411yescharacteristic, complemented
45C2×M16×C127—21no—
46#120×C127—21no—
47#120×C127—21no—
48#120×C127—24no—
49#120×C127—42no—
50#120×C127C2×C412yes—
51#120×C127D412yes—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127D411yescharacteristic, complemented
54C2×C22⋊C4×C127—21no—
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127—21no—
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—21no—
59C2×C22⋊C4×C127—21no—
60C2×C22⋊C4×C127—21no—
61C2×C22⋊C4×C127—21no—
62C2×C22⋊C4×C127—21no—
63C2×C22⋊C4×C127—21no—
64C2×C22⋊C4×C127—41no—
65C2×C22⋊C4×C127—41no—
66C2×C22⋊C4×C127D411yescharacteristic
67C2×C22⋊C4×C127D411yescharacteristic, complemented
68C2×C42×C127—21no—
69C2×C42×C127D411yescharacteristic, complemented
70#104×C127—42no—
71#103×C127—41no—
72#102×C127—41no—
73#100×C127—21no—
74#100×C127—21no—
75#99×C127—21no—
76#99×C127—24no—
77#99×C127—21no—
78#99×C127—21no—
79#99×C127—42no—
80#99×C127C2×C412yes—
81#95×C127—21no—
82#95×C127—21no—
83#95×C127—21no—
84#95×C127—41no—
85C24×C127—21no—
86C24×C127—21no—
87C24×C127—21no—
88C24×C127—21no—
89C24×C127—41no—
90C24×C127—41no—
91C24×C127—81no—
92C24×C127—81no—
93C24×C127C22⋊C412yescomplemented
94C24×C127C2×D411yescharacteristic
95C24×C127C2×D411yescharacteristic
96#41×C127—22no—
97#41×C127—22no—
98#41×C127—42no—
99#41×C127—41no—
100#41×C127—42no—
101#41×C127—42no—
102#41×C127—42no—
103#41×C127—41no—
104C2×Q8×C127—21no—
105C2×D4×C127—21no—
106C2×D4×C127—22no—
107C2×D4×C127—22no—
108C2×D4×C127—22no—
109C2×D4×C127—22no—
110C2×D4×C127—22no—
111C2×D4×C127—22no—
112C2×D4×C127—41no—
113C2×D4×C127—41no—
114C2×D4×C127—42no—
115C2×D4×C127—42no—
116C2×D4×C127—41no—
117C2×D4×C127—41no—
118C2×D4×C127—41no—
119C2×D4×C127—41no—
120C2×D4×C127—42no—
121C2×D4×C127—42no—
122C2×D4×C127—41no—
123C2×D4×C127—41no—
124C2×D4×C127—41no—
125C2×D4×C127—44no—
126C2×D4×C127—81no—
127C2×D4×C127—81no—
128C2×D4×C127—82no—
129C2×D4×C127—82no—
130C2×D4×C127C22×C411yescharacteristic
131C2×D4×C127C2×D411yescharacteristic
132C2×D4×C127#4111yescharacteristic
133C2×D4×C127#4111yescharacteristic
134C22×C4×C127—21no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—21no—
141C22×C4×C127—41no—
142C22×C4×C127—41no—
143C22×C4×C127—41no—
144C22×C4×C127—41no—
145C22×C4×C127—81no—
146C22×C4×C127C2×D411yescharacteristic
147M16×C127—41no—
148M16×C127—41no—
149C2×C8×C127—41no—
150C4⋊C4×C127—41no—
151C4⋊C4×C127—81no—
152C22⋊C4×C127—21no—
153C22⋊C4×C127—22no—
154C22⋊C4×C127—22no—
155C22⋊C4×C127—22no—
156C22⋊C4×C127—44no—
157C22⋊C4×C127—41no—
158C22⋊C4×C127—41no—
159C22⋊C4×C127—41no—
160C22⋊C4×C127—41no—
161C22⋊C4×C127—81no—
162C22⋊C4×C127—81no—
163C22⋊C4×C127—81no—
164C22⋊C4×C127—81no—
165C22⋊C4×C127—81no—
166C22⋊C4×C127—81no—
167C22⋊C4×C127—81no—
168C22⋊C4×C127—82no—
169C22⋊C4×C127C22⋊C412yescomplemented
170C42×C127—41no—
171C42×C127—81no—
172C23×C127—21no—
173C23×C127—21no—
174C23×C127—21no—
175C23×C127—21no—
176C23×C127—22no—
177C23×C127—22no—
178C23×C127—22no—
179C23×C127—42no—
180C23×C127—41no—
181C23×C127—41no—
182C23×C127—41no—
183C23×C127—41no—
184C23×C127—41no—
185C23×C127—41no—
186C23×C127—41no—
187C23×C127—41no—
188C23×C127—41no—
189C23×C127—41no—
190C23×C127—42no—
191C23×C127—42no—
192C23×C127—41no—
193C23×C127—41no—
194C23×C127—41no—
195C23×C127—81no—
196C23×C127—82no—
197C23×C127—82no—
198C23×C127—81no—
199C23×C127—81no—
200C23×C127—84no—
201C23×C127—81no—
202C23×C127—81no—
203C23×C127—81no—
204C23×C127—81no—
205C23×C127C2×C22⋊C411yescharacteristic
206C23×C127C4×D411yescharacteristic
207C23×C127#12011yescharacteristic
208C23×C127#12111yescharacteristic
209C23×C127#12311yescharacteristic
210Q8×C127—22no—
211Q8×C127—41no—
212D4×C127—22no—
213D4×C127—41no—
214D4×C127—41no—
215D4×C127—41no—
216D4×C127—41no—
217D4×C127—41no—
218D4×C127—42no—
219D4×C127—42no—
220D4×C127—42no—
221D4×C127—42no—
222D4×C127—42no—
223D4×C127—42no—
224D4×C127—82no—
225D4×C127—82no—
226D4×C127—88no—
227C2×C4×C127—21no—
228C2×C4×C127—21no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—22no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—41no—
237C2×C4×C127—41no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—42no—
242C2×C4×C127—41no—
243C2×C4×C127—41no—
244C2×C4×C127—41no—
245C2×C4×C127—41no—
246C2×C4×C127—41no—
247C2×C4×C127—41no—
248C2×C4×C127—42no—
249C2×C4×C127—41no—
250C2×C4×C127—41no—
251C2×C4×C127—41no—
252C2×C4×C127—41no—
253C2×C4×C127—81no—
254C2×C4×C127—81no—
255C2×C4×C127—81no—
256C2×C4×C127—81no—
257C2×C4×C127—81no—
258C2×C4×C127—81no—
259C2×C4×C127C4×D411yescharacteristic
260C2×C4×C127#12111yescharacteristic
261C8×C127—81no—
262C22×C127—21no—
263C22×C127—21no—
264C22×C127—21no—
265C22×C127—21no—
266C22×C127—21no—
267C22×C127—21no—
268C22×C127—41no—
269C22×C127—41no—
270C22×C127—41no—
271C22×C127—41no—
272C22×C127—42no—
273C22×C127—42no—
274C22×C127—41no—
275C22×C127—41no—
276C22×C127—41no—
277C22×C127—41no—
278C22×C127—44no—
279C22×C127—42no—
280C22×C127—42no—
281C22×C127—81no—
282C22×C127—81no—
283C22×C127—81no—
284C22×C127—81no—
285C22×C127—82no—
286C22×C127—82no—
287C22×C127—82no—
288C22×C127—82no—
289C22×C127—82no—
290C22×C127—81no—
291C22×C127—81no—
292C22×C127—81no—
293C22×C127—81no—
294C22×C127—161no—
295C22×C127—161no—
296C22×C127#38611yescharacteristic
297C22×C127B(4,𝔽2)11yescharacteristic
298C22×C127B(4,𝔽2)11yescharacteristic
299C4×C127—21no—
300C4×C127—21no—
301C4×C127—42no—
302C4×C127—42no—
303C4×C127—81no—
304C4×C127—81no—
305C4×C127—82no—
306C4×C127—81no—
307C4×C127—81no—
308C4×C127—161no—
309#13043C12711yesmaximal, characteristic, direct product factor, Sylow
310C2×C127—21no—
311C2×C127—21no—
312C2×C127—41no—
313C2×C127—41no—
314C2×C127—41no—
315C2×C127—41no—
316C2×C127—82no—
317C2×C127—82no—
318C2×C127#188911yescharacteristic
319C2×C127#219911yescharacteristic
320C2×C127#220011yescharacteristic
321C2×B(4,𝔽2)C2×C12711yescharacteristic
322#2375C2×C12711yescharacteristic, complemented
323C2×AΣL(1,𝔽16)C2×C12711yescharacteristic, complemented
324#1792C2×C12711yescharacteristic, complemented
325#1790C2×C12711yescharacteristic, complemented
326#1393C2×C12711yescharacteristic, complemented
327#1390C2×C12711yescharacteristic, complemented
328C127#1304311yescharacteristic, direct product factor, Sylow
329C2×H(5,𝔽2)C22×C12711yescharacteristic
330C2×#120—21no—
331C2×#120C22×C12711yescharacteristic
332B(4,𝔽2)—22no—
333B(4,𝔽2)C4×C12714yescomplemented
334C2×#104—21no—
335#417—21no—
336C2×#100C22×C12711yescharacteristic
337C2×#99—21no—
338C2×#99—21no—
339C2×#99C22×C12711yescharacteristic
340C2×#99C22×C12711yescharacteristic
341#390—21no—
342#390C22×C12711yescharacteristic
343#388—21no—
344#388—21no—
345#388—21no—
346#386—21no—
347#386—21no—
348#386C22×C12711yescharacteristic
349#379—21no—
350AΣL(1,𝔽16)—22no—
351C25D4×C12711yescharacteristic
352H(5,𝔽2)—21no—
353H(5,𝔽2)—21no—
354H(5,𝔽2)—21no—
355H(5,𝔽2)—42no—
356H(5,𝔽2)C2×C4×C12712yes—
357C2×#41—21no—
358C2×#41—41no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4C23×C12711yescharacteristic
365C23×C4D4×C12711yescharacteristic, complemented
366C2×M16—21no—
367#120—21no—
368#120—21no—
369#120—24no—
370#120—42no—
371#120C2×C4×C12712yes—
372#120D4×C12712yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C12711yescharacteristic, complemented
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4D4×C12711yescharacteristic
388C2×C22⋊C4D4×C12711yescharacteristic, complemented
389C2×C42—21no—
390C2×C42D4×C12711yescharacteristic, complemented
391#104—42no—
392#103—41no—
393#102—41no—
394#100—21no—
395#100—21no—
396#99—21no—
397#99—24no—
398#99—21no—
399#99—21no—
400#99—42no—
401#99C2×C4×C12712yes—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—41no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—41no—
411C24—41no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C12712yescomplemented
415C24C2×D4×C12711yescharacteristic
416C24C2×D4×C12711yescharacteristic
417#41—22no—
418#41—22no—
419#41—42no—
420#41—41no—
421#41—42no—
422#41—42no—
423#41—42no—
424#41—41no—
425C2×Q8—21no—
426C2×D4—21no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—44no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—82no—
450C2×D4—82no—
451C2×D4C22×C4×C12711yescharacteristic
452C2×D4C2×D4×C12711yescharacteristic
453C2×D4#41×C12711yescharacteristic
454C2×D4#41×C12711yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—81no—
467C22×C4C2×D4×C12711yescharacteristic
468M16—41no—
469M16—41no—
470C2×C8—41no—
471C4⋊C4—41no—
472C4⋊C4—81no—
473C22⋊C4—21no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—44no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—82no—
490C22⋊C4C22⋊C4×C12712yescomplemented
491C42—41no—
492C42—81no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—42no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—81no—
517C23—82no—
518C23—82no—
519C23—81no—
520C23—81no—
521C23—84no—
522C23—81no—
523C23—81no—
524C23—81no—
525C23—81no—
526C23C2×C22⋊C4×C12711yescharacteristic
527C23C4×D4×C12711yescharacteristic
528C23#120×C12711yescharacteristic
529C23#121×C12711yescharacteristic
530C23#123×C12711yescharacteristic
531Q8—22no—
532Q8—41no—
533D4—22no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—82no—
546D4—82no—
547D4—88no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4C4×D4×C12711yescharacteristic
581C2×C4#121×C12711yescharacteristic
582C8—81no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—44no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22—82no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—161no—
616C22—161no—
617C22#386×C12711yescharacteristic
618C22B(4,𝔽2)×C12711yescharacteristic
619C22B(4,𝔽2)×C12711yescharacteristic
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—82no—
627C4—81no—
628C4—81no—
629C4—161no—
630C2—21no—
631C2—21no—
632C2—41no—
633C2—41no—
634C2—41no—
635C2—41no—
636C2—82no—
637C2—82no—
638C2C127×#188911yescharacteristic
639C2C127×#219911yescharacteristic
640C2C127×#220011yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutatorC2×D4C22×C4×C127
Frattini, cosocleC22×D4C23×C127
prime radicalC2×B(4,𝔽2)×C127C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2375C2semidirect
3. C2×AΣL(1,𝔽16)×C127C2semidirect
4. C127×#1792C2semidirect
5. C127×#1790C2semidirect
6. C127×#1393C2semidirect
7. C127×#1390C2semidirect
12. B(4,𝔽2)×C127C4semidirect
44. C23×C4×C127D4semidirect
53. C2×C4⋊C4×C127D4semidirect
67. C2×C22⋊C4×C127D4semidirect
69. C2×C42×C127D4semidirect
93. C24×C127C22⋊C4semidirect
169. C22⋊C4×C127C22⋊C4semidirect
309. #13043C127direct (N × H)
322. #2375C2×C127semidirect
323. C2×AΣL(1,𝔽16)C2×C127semidirect
324. #1792C2×C127semidirect
325. #1790C2×C127semidirect
326. #1393C2×C127semidirect
327. #1390C2×C127semidirect
328. C127#13043direct (N × H)
333. B(4,𝔽2)C4×C127semidirect
365. C23×C4D4×C127semidirect
374. C2×C4⋊C4D4×C127semidirect
388. C2×C22⋊C4D4×C127semidirect
390. C2×C42D4×C127semidirect
414. C24C22⋊C4×C127semidirect
490. C22⋊C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×B(4,𝔽2)×C1272
C127×#23752
C2×AΣL(1,𝔽16)×C1272
C127×#17922
C127×#17902
C127×#13932
C127×#13902
#13043127