Finite Group Databasebeta

← C127×#13082 #44576755

Subgroups — C127×#13082 #44576755

Order 32512.

1088 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C127C211yesmaximal, characteristic, complemented
2C127×#2403C211yesmaximal, characteristic
3C2×AΣL(1,𝔽16)×C127C212yesmaximal, complemented
4C127×#1781C211yesmaximal, characteristic, complemented
5C127×#1390C212yesmaximal, complemented
6C23×D4×C127C411yescharacteristic, complemented
7C23×D4×C127C2211yescharacteristic
8C22×M16×C127—21no—
9C2×#120×C127—21no—
10C2×#120×C127C411yescharacteristic, complemented
11C2×#120×C127C2211yescharacteristic
12C2×#100×C127—21no—
13C2×#100×C127—24no—
14C2×#100×C127C2212yes—
15C2×#99×C127—21no—
16C2×#99×C127C2212yes—
17#392×C127—21no—
18#392×C127—21no—
19#386×C127—21no—
20#386×C127C411yescharacteristic, complemented
21#386×C127C2211yescharacteristic
22#379×C127—21no—
23#379×C127C411yescharacteristic, complemented
24AΣL(1,𝔽16)×C127—24no—
25C25×C127C2×C411yescharacteristic
26C25×C127C2×C411yescharacteristic
27C25×C127D411yescharacteristic
28C22×D4×C127—21no—
29C22×D4×C127—22no—
30C22×D4×C127—22no—
31C22×D4×C127—21no—
32C22×D4×C127—21no—
33C22×D4×C127—21no—
34C22×D4×C127—42no—
35C22×D4×C127—41no—
36C22×D4×C127—41no—
37C22×D4×C127—44no—
38C22×D4×C127—41no—
39C22×D4×C127—41no—
40C22×D4×C127C2×C411yescharacteristic
41C22×D4×C127D411yescharacteristic
42C22×D4×C127D411yescharacteristic
43C22×D4×C127C2311yescharacteristic
44C23×C4×C127C2×C411yescharacteristic
45C23×C4×C127D411yescharacteristic
46C2×M16×C127—24no—
47C2×M16×C127—22no—
48C2×M16×C127—41no—
49C2×M16×C127—42no—
50C22×C8×C127—41no—
51#120×C127—22no—
52#120×C127—22no—
53#120×C127—44no—
54#120×C127—42no—
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—22no—
61C2×C22⋊C4×C127—21no—
62C2×C22⋊C4×C127—41no—
63C2×C22⋊C4×C127—41no—
64C2×C22⋊C4×C127C2×C411yescharacteristic
65C2×C22⋊C4×C127C2×C411yescharacteristic
66#100×C127—24no—
67#100×C127—22no—
68#100×C127D414yescomplemented
69#99×C127—22no—
70#99×C127—22no—
71#99×C127—42no—
72#95×C127—21no—
73#95×C127—21no—
74C24×C127—21no—
75C24×C127—21no—
76C24×C127—21no—
77C24×C127—21no—
78C24×C127—21no—
79C24×C127—22no—
80C24×C127—22no—
81C24×C127—22no—
82C24×C127—41no—
83C24×C127—41no—
84C24×C127—42no—
85C24×C127—41no—
86C24×C127—42no—
87C24×C127—42no—
88C24×C127—41no—
89C24×C127—81no—
90C24×C127—81no—
91C24×C127—81no—
92C24×C127C22⋊C411yescharacteristic
93C24×C127C22⋊C411yescharacteristic
94C24×C127C22⋊C411yescharacteristic
95C24×C127C22×C411yescharacteristic
96C24×C127C2×D411yescharacteristic
97C2×D4×C127—24no—
98C2×D4×C127—22no—
99C2×D4×C127—22no—
100C2×D4×C127—22no—
101C2×D4×C127—22no—
102C2×D4×C127—21no—
103C2×D4×C127—21no—
104C2×D4×C127—41no—
105C2×D4×C127—41no—
106C2×D4×C127—41no—
107C2×D4×C127—41no—
108C2×D4×C127—41no—
109C2×D4×C127—41no—
110C2×D4×C127—44no—
111C2×D4×C127—44no—
112C2×D4×C127—44no—
113C2×D4×C127—44no—
114C2×D4×C127—42no—
115C2×D4×C127—42no—
116C2×D4×C127—42no—
117C2×D4×C127—42no—
118C2×D4×C127—44no—
119C2×D4×C127—44no—
120C2×D4×C127—44no—
121C2×D4×C127—41no—
122C2×D4×C127—41no—
123C2×D4×C127—44no—
124C2×D4×C127—42no—
125C2×D4×C127—42no—
126C2×D4×C127—42no—
127C2×D4×C127—42no—
128C2×D4×C127—81no—
129C2×D4×C127—81no—
130C2×D4×C127C2×D412yes—
131C2×D4×C127#4112yes—
132C22×C4×C127—21no—
133C22×C4×C127—21no—
134C22×C4×C127—22no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—42no—
141C22×C4×C127—41no—
142C22×C4×C127—42no—
143C22×C4×C127C22⋊C411yescharacteristic
144C22×C4×C127C2×D411yescharacteristic
145M16×C127—24no—
146M16×C127—44no—
147M16×C127—42no—
148C2×C8×C127—44no—
149C2×C8×C127—42no—
150C22⋊C4×C127—22no—
151C22⋊C4×C127—42no—
152C22⋊C4×C127—42no—
153C22⋊C4×C127—42no—
154C22⋊C4×C127—42no—
155C22⋊C4×C127—41no—
156C22⋊C4×C127—41no—
157C22⋊C4×C127—41no—
158C22⋊C4×C127—42no—
159C22⋊C4×C127—42no—
160C22⋊C4×C127—81no—
161C22⋊C4×C127—82no—
162C22⋊C4×C127—82no—
163C23×C127—22no—
164C23×C127—21no—
165C23×C127—21no—
166C23×C127—21no—
167C23×C127—21no—
168C23×C127—21no—
169C23×C127—21no—
170C23×C127—22no—
171C23×C127—21no—
172C23×C127—21no—
173C23×C127—21no—
174C23×C127—21no—
175C23×C127—21no—
176C23×C127—21no—
177C23×C127—41no—
178C23×C127—42no—
179C23×C127—42no—
180C23×C127—42no—
181C23×C127—42no—
182C23×C127—41no—
183C23×C127—41no—
184C23×C127—41no—
185C23×C127—41no—
186C23×C127—41no—
187C23×C127—41no—
188C23×C127—42no—
189C23×C127—41no—
190C23×C127—42no—
191C23×C127—41no—
192C23×C127—41no—
193C23×C127—41no—
194C23×C127—41no—
195C23×C127—42no—
196C23×C127—42no—
197C23×C127—42no—
198C23×C127—42no—
199C23×C127—41no—
200C23×C127—41no—
201C23×C127—41no—
202C23×C127—81no—
203C23×C127—81no—
204C23×C127—81no—
205C23×C127—81no—
206C23×C127—82no—
207C23×C127—84no—
208C23×C127—84no—
209C23×C127—84no—
210C23×C127—84no—
211C23×C127—84no—
212C23×C127—84no—
213C23×C127—82no—
214C23×C127#9911yescharacteristic
215C23×C127#9911yescharacteristic
216C23×C127C2×C22⋊C411yescharacteristic
217C23×C127C4×D412yes—
218C23×C127#12112yes—
219D4×C127—42no—
220D4×C127—42no—
221D4×C127—44no—
222D4×C127—44no—
223D4×C127—42no—
224D4×C127—42no—
225D4×C127—44no—
226D4×C127—48no—
227D4×C127—44no—
228D4×C127—84no—
229D4×C127—84no—
230C2×C4×C127—22no—
231C2×C4×C127—22no—
232C2×C4×C127—22no—
233C2×C4×C127—22no—
234C2×C4×C127—21no—
235C2×C4×C127—21no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—22no—
239C2×C4×C127—41no—
240C2×C4×C127—42no—
241C2×C4×C127—41no—
242C2×C4×C127—42no—
243C2×C4×C127—41no—
244C2×C4×C127—41no—
245C2×C4×C127—41no—
246C2×C4×C127—41no—
247C2×C4×C127—41no—
248C2×C4×C127—41no—
249C2×C4×C127—82no—
250C2×C4×C127—82no—
251C2×C4×C127—82no—
252C2×C4×C127#9912yes—
253C2×C4×C127#12011yescharacteristic
254C2×C4×C127#12311yescharacteristic
255C8×C127—44no—
256C22×C127—21no—
257C22×C127—21no—
258C22×C127—21no—
259C22×C127—21no—
260C22×C127—21no—
261C22×C127—21no—
262C22×C127—21no—
263C22×C127—22no—
264C22×C127—22no—
265C22×C127—42no—
266C22×C127—42no—
267C22×C127—42no—
268C22×C127—42no—
269C22×C127—42no—
270C22×C127—42no—
271C22×C127—42no—
272C22×C127—42no—
273C22×C127—41no—
274C22×C127—41no—
275C22×C127—41no—
276C22×C127—41no—
277C22×C127—42no—
278C22×C127—41no—
279C22×C127—41no—
280C22×C127—41no—
281C22×C127—41no—
282C22×C127—41no—
283C22×C127—41no—
284C22×C127—81no—
285C22×C127—84no—
286C22×C127—84no—
287C22×C127—81no—
288C22×C127—81no—
289C22×C127—81no—
290C22×C127—81no—
291C22×C127—81no—
292C22×C127—84no—
293C22×C127—84no—
294C22×C127—84no—
295C22×C127—84no—
296C22×C127—81no—
297C22×C127—81no—
298C22×C127AΣL(1,𝔽16)12yescomplemented
299C22×C127#38611yescharacteristic
300C22×C127C2×#9911yescharacteristic
301C22×C127C2×#9911yescharacteristic
302C4×C127—21no—
303C4×C127—22no—
304C4×C127—21no—
305C4×C127—42no—
306C4×C127—81no—
307C4×C127—81no—
308C4×C127—162no—
309#13082C12711yesmaximal, characteristic, direct product factor, Sylow
310C2×C127—21no—
311C2×C127—21no—
312C2×C127—22no—
313C2×C127—42no—
314C2×C127—41no—
315C2×C127—42no—
316C2×C127—81no—
317C2×C127—82no—
318C2×C127—81no—
319C2×C127#189811yescharacteristic
320C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
321C2×C127#212111yescharacteristic
322C22×#100C2×C12711yescharacteristic, complemented
323#2403C2×C12711yescharacteristic
324C2×AΣL(1,𝔽16)C2×C12712yescomplemented
325#1781C2×C12711yescharacteristic, complemented
326#1390C2×C12712yescomplemented
327C127#1308211yescharacteristic, direct product factor, Sylow
328C23×D4C4×C12711yescharacteristic, complemented
329C23×D4C22×C12711yescharacteristic
330C22×M16—21no—
331C2×#120—21no—
332C2×#120C4×C12711yescharacteristic, complemented
333C2×#120C22×C12711yescharacteristic
334C2×#100—21no—
335C2×#100—24no—
336C2×#100C22×C12712yes—
337C2×#99—21no—
338C2×#99C22×C12712yes—
339#392—21no—
340#392—21no—
341#386—21no—
342#386C4×C12711yescharacteristic, complemented
343#386C22×C12711yescharacteristic
344#379—21no—
345#379C4×C12711yescharacteristic, complemented
346AΣL(1,𝔽16)—24no—
347C25C2×C4×C12711yescharacteristic
348C25C2×C4×C12711yescharacteristic
349C25D4×C12711yescharacteristic
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—42no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—44no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4C2×C4×C12711yescharacteristic
363C22×D4D4×C12711yescharacteristic
364C22×D4D4×C12711yescharacteristic
365C22×D4C23×C12711yescharacteristic
366C23×C4C2×C4×C12711yescharacteristic
367C23×C4D4×C12711yescharacteristic
368C2×M16—24no—
369C2×M16—22no—
370C2×M16—41no—
371C2×M16—42no—
372C22×C8—41no—
373#120—22no—
374#120—22no—
375#120—44no—
376#120—42no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4C2×C4×C12711yescharacteristic
387C2×C22⋊C4C2×C4×C12711yescharacteristic
388#100—24no—
389#100—22no—
390#100D4×C12714yescomplemented
391#99—22no—
392#99—22no—
393#99—42no—
394#95—21no—
395#95—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—41no—
405C24—41no—
406C24—42no—
407C24—41no—
408C24—42no—
409C24—42no—
410C24—41no—
411C24—81no—
412C24—81no—
413C24—81no—
414C24C22⋊C4×C12711yescharacteristic
415C24C22⋊C4×C12711yescharacteristic
416C24C22⋊C4×C12711yescharacteristic
417C24C22×C4×C12711yescharacteristic
418C24C2×D4×C12711yescharacteristic
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—44no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—81no—
452C2×D4C2×D4×C12712yes—
453C2×D4#41×C12712yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—41no—
464C22×C4—42no—
465C22×C4C22⋊C4×C12711yescharacteristic
466C22×C4C2×D4×C12711yescharacteristic
467M16—24no—
468M16—44no—
469M16—42no—
470C2×C8—44no—
471C2×C8—42no—
472C22⋊C4—22no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—42no—
476C22⋊C4—42no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—82no—
484C22⋊C4—82no—
485C23—22no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—42no—
511C23—41no—
512C23—42no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—81no—
528C23—82no—
529C23—84no—
530C23—84no—
531C23—84no—
532C23—84no—
533C23—84no—
534C23—84no—
535C23—82no—
536C23#99×C12711yescharacteristic
537C23#99×C12711yescharacteristic
538C23C2×C22⋊C4×C12711yescharacteristic
539C23C4×D4×C12712yes—
540C23#121×C12712yes—
541D4—42no—
542D4—42no—
543D4—44no—
544D4—44no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—48no—
549D4—44no—
550D4—84no—
551D4—84no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#99×C12712yes—
575C2×C4#120×C12711yescharacteristic
576C2×C4#123×C12711yescharacteristic
577C8—44no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—42no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—81no—
607C22—84no—
608C22—84no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—84no—
615C22—84no—
616C22—84no—
617C22—84no—
618C22—81no—
619C22—81no—
620C22AΣL(1,𝔽16)×C12712yescomplemented
621C22#386×C12711yescharacteristic
622C22C2×#99×C12711yescharacteristic
623C22C2×#99×C12711yescharacteristic
624C4—21no—
625C4—22no—
626C4—21no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—162no—
631C2—21no—
632C2—21no—
633C2—22no—
634C2—42no—
635C2—41no—
636C2—42no—
637C2—81no—
638C2—82no—
639C2—81no—
640C2C127×#189811yescharacteristic
641C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
642C2C127×#212111yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC24C22×C4×C127
Frattini, cosocleC22×D4C23×C127
prime radicalC127×#2403C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C23×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#100×C127C2semidirect
3. C2×AΣL(1,𝔽16)×C127C2semidirect
4. C127×#1781C2semidirect
5. C127×#1390C2semidirect
6. C23×D4×C127C4semidirect
10. C2×#120×C127C4semidirect
20. #386×C127C4semidirect
23. #379×C127C4semidirect
68. #100×C127D4semidirect
298. C22×C127AΣL(1,𝔽16)semidirect
309. #13082C127direct (N × H)
322. C22×#100C2×C127semidirect
324. C2×AΣL(1,𝔽16)C2×C127semidirect
325. #1781C2×C127semidirect
326. #1390C2×C127semidirect
327. C127#13082direct (N × H)
328. C23×D4C4×C127semidirect
332. C2×#120C4×C127semidirect
342. #386C4×C127semidirect
345. #379C4×C127semidirect
390. #100D4×C127semidirect
620. C22AΣL(1,𝔽16)×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1272
C127×#24032
C2×AΣL(1,𝔽16)×C1272
C127×#17812
C127×#13902
#13082127