Finite Group Databasebeta

← C127×#18228 #44581901

Subgroups — C127×#18228 #44581901

Order 32512.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3537C211yesmaximal, characteristic, complemented
2C127×#3006C211yesmaximal, characteristic, complemented
3C127×#3002C211yesmaximal, characteristic, complemented
4C127×#2615C211yesmaximal, characteristic, complemented
5C127×#1606C212yesmaximal, complemented
6C127×#1601C212yesmaximal, complemented
7C127×#1600C212yesmaximal, complemented
8C127×#1595C212yesmaximal, complemented
9C127×#1519C211yesmaximal, characteristic, complemented
10C127×#1513C211yesmaximal, characteristic, complemented
11C127×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C127C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C127—21no—
14C2×#135×C127—21no—
15#560×C127—22no—
16#553×C127—21no—
17#553×C127—21no—
18D42×C127—22no—
19D42×C127—21no—
20D42×C127—21no—
21#540×C127—21no—
22#538×C127—21no—
23#538×C127C2212yes—
24#535×C127—21no—
25#534×C127—21no—
26#534×C127C2212yes—
27#525×C127C2211yescharacteristic
28C2×#121×C127—21no—
29C2×#121×C127C2211yescharacteristic
30C2×#121×C127C2211yescharacteristic
31#452×C127—21no—
32#451×C127C2211yescharacteristic, complemented
33#450×C127C2211yescharacteristic, complemented
34#449×C127—21no—
35#449×C127—22no—
36#448×C127C2211yescharacteristic, complemented
37#448×C127C2212yescomplemented
38#447×C127C2211yescharacteristic, complemented
39#447×C127C2212yescomplemented
40#417×C127—21no—
41#416×C127—21no—
42#407×C127C2211yescharacteristic, complemented
43C2×C22⋊C8×C127C2211yescharacteristic, complemented
44#393×C127C2212yescomplemented
45#392×C127—22no—
46#392×C127C2212yescomplemented
47#380×C127—21no—
48#380×C127C2211yescharacteristic, complemented
49#328×C127C2212yescomplemented
50#327×C127C2212yescomplemented
51#327×C127C2212yescomplemented
52#327×C127C2212yescomplemented
53#323×C127C2212yescomplemented
54#323×C127C2212yescomplemented
55C2×#41×C127—21no—
56C2×#41×C127—21no—
57C2×#41×C127—21no—
58C2×#41×C127—21no—
59C2×#41×C127—44no—
60C2×#41×C127D411yescharacteristic, complemented
61C22×Q8×C127C2311yescharacteristic
62C22×D4×C127—22no—
63C22×D4×C127—21no—
64C22×D4×C127—21no—
65C22×D4×C127—22no—
66C22×D4×C127—21no—
67C22×D4×C127—22no—
68C22×D4×C127D411yescharacteristic
69C22×D4×C127D412yes—
70C22×D4×C127D411yescharacteristic, complemented
71C22×D4×C127C2311yescharacteristic
72C23×C4×C127—21no—
73C23×C4×C127C2311yescharacteristic
74AGL(1,ℤ/8)×C127—44no—
75#135×C127—44no—
76C2×Q16×C127—21no—
77C2×SD16×C127—21no—
78C2×SD16×C127—21no—
79C2×SD16×C127—22no—
80C2×D8×C127—21no—
81C2×D8×C127—22no—
82C2×M16×C127—21no—
83C22×C8×C127—21no—
84#127×C127—22no—
85#127×C127—21no—
86#126×C127—22no—
87#126×C127—22no—
88#125×C127—21no—
89#124×C127—22no—
90#123×C127—22no—
91#123×C127—21no—
92#123×C127—22no—
93#123×C127—22no—
94#123×C127—22no—
95C22⋊Q8×C127D411yescharacteristic, complemented
96C22⋊Q8×C127C2311yescharacteristic
97#121×C127—22no—
98#121×C127—21no—
99#121×C127—21no—
100#121×C127—22no—
101#121×C127—22no—
102#121×C127—22no—
103#121×C127—22no—
104#121×C127—21no—
105#121×C127—21no—
106#121×C127—21no—
107#121×C127—21no—
108#121×C127—21no—
109#121×C127—21no—
110#121×C127—22no—
111#121×C127—44no—
112#121×C127D412yescomplemented
113#121×C127D411yescharacteristic, complemented
114#121×C127C2312yes—
115#121×C127C2311yescharacteristic
116#120×C127—22no—
117#120×C127—22no—
118#120×C127—22no—
119#120×C127—21no—
120#120×C127—22no—
121#120×C127—22no—
122#120×C127—22no—
123C4×D4×C127—22no—
124C4×D4×C127—21no—
125C4×D4×C127—21no—
126C4×D4×C127—21no—
127C4×D4×C127—21no—
128C4×D4×C127—22no—
129#117×C127—21no—
130#117×C127D411yescharacteristic, complemented
131C2×C4⋊C4×C127—21no—
132C2×C4⋊C4×C127D411yescharacteristic
133C2×C4⋊C4×C127D411yescharacteristic, complemented
134C2×C22⋊C4×C127—21no—
135C2×C22⋊C4×C127—22no—
136C2×C22⋊C4×C127—21no—
137C2×C22⋊C4×C127—22no—
138C2×C22⋊C4×C127C2312yes—
139#103×C127—21no—
140#103×C127—21no—
141#103×C127—22no—
142#102×C127—21no—
143#102×C127—21no—
144#102×C127—22no—
145C22⋊C8×C127—21no—
146C22⋊C8×C127—21no—
147C22⋊C8×C127C2311yescharacteristic
148C22⋊C8×C127C2311yescharacteristic
149C22⋊C8×C127C2312yes—
150#95×C127—22no—
151#95×C127C2312yes—
152C24×C127—22no—
153C24×C127—21no—
154C24×C127—21no—
155C24×C127C2×D412yes—
156C24×C127C2×D411yescharacteristic
157#41×C127—24no—
158#41×C127—24no—
159#41×C127—42no—
160#41×C127—42no—
161#41×C127—42no—
162#41×C127—42no—
163#41×C127—42no—
164#41×C127—42no—
165#41×C127—42no—
166C2×Q8×C127—21no—
167C2×Q8×C127—21no—
168C2×Q8×C127—42no—
169C2×Q8×C127C2×D411yescharacteristic
170C2×D4×C127—22no—
171C2×D4×C127—21no—
172C2×D4×C127—21no—
173C2×D4×C127—22no—
174C2×D4×C127—22no—
175C2×D4×C127—22no—
176C2×D4×C127—22no—
177C2×D4×C127—22no—
178C2×D4×C127—22no—
179C2×D4×C127—21no—
180C2×D4×C127—22no—
181C2×D4×C127—22no—
182C2×D4×C127—21no—
183C2×D4×C127—21no—
184C2×D4×C127—21no—
185C2×D4×C127—21no—
186C2×D4×C127—21no—
187C2×D4×C127—42no—
188C2×D4×C127—42no—
189C2×D4×C127—42no—
190C2×D4×C127—42no—
191C2×D4×C127—42no—
192C2×D4×C127—41no—
193C2×D4×C127—41no—
194C2×D4×C127—44no—
195C2×D4×C127—82no—
196C2×D4×C127—82no—
197C2×D4×C127—82no—
198C2×D4×C127—82no—
199C2×D4×C127—81no—
200C2×D4×C127—81no—
201C2×D4×C127—82no—
202C2×D4×C127—82no—
203C2×D4×C127—84no—
204C2×D4×C127C2×D411yescharacteristic
205C2×D4×C127C2×D412yes—
206C22×C4×C127—24no—
207C22×C4×C127—21no—
208C22×C4×C127—22no—
209C22×C4×C127—22no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—22no—
213C22×C4×C127—42no—
214C22×C4×C127—42no—
215C22×C4×C127—41no—
216C22×C4×C127—41no—
217C22×C4×C127C2×D411yescharacteristic
218C22×C4×C127C2×D411yescharacteristic
219C22×C4×C127C2×D411yescharacteristic
220C22×C4×C127C2×D412yes—
221C22×C4×C127C2×D411yescharacteristic
222C22×C4×C127C2×D411yescharacteristic
223C22×C4×C127C2411yescharacteristic
224Q16×C127—42no—
225SD16×C127—42no—
226SD16×C127—42no—
227SD16×C127—44no—
228D8×C127—42no—
229D8×C127—44no—
230M16×C127—42no—
231C2×C8×C127—21no—
232C2×C8×C127—21no—
233C2×C8×C127—22no—
234C2×C8×C127—42no—
235C4⋊C4×C127—22no—
236C4⋊C4×C127—22no—
237C4⋊C4×C127—21no—
238C4⋊C4×C127—21no—
239C4⋊C4×C127—21no—
240C4⋊C4×C127—21no—
241C4⋊C4×C127—21no—
242C4⋊C4×C127—42no—
243C4⋊C4×C127C2×D412yes—
244C4⋊C4×C127C2×D411yescharacteristic
245C4⋊C4×C127C2×D411yescharacteristic
246C22⋊C4×C127—22no—
247C22⋊C4×C127—22no—
248C22⋊C4×C127—22no—
249C22⋊C4×C127—22no—
250C22⋊C4×C127—22no—
251C22⋊C4×C127—21no—
252C22⋊C4×C127—21no—
253C22⋊C4×C127—21no—
254C22⋊C4×C127—22no—
255C22⋊C4×C127—21no—
256C22⋊C4×C127—22no—
257C22⋊C4×C127—22no—
258C22⋊C4×C127—22no—
259C22⋊C4×C127—21no—
260C22⋊C4×C127—44no—
261C22⋊C4×C127—81no—
262C22⋊C4×C127—82no—
263C42×C127—22no—
264C42×C127—21no—
265C23×C127—21no—
266C23×C127—21no—
267C23×C127—22no—
268C23×C127—22no—
269C23×C127—22no—
270C23×C127—21no—
271C23×C127—22no—
272C23×C127—22no—
273C23×C127—41no—
274C23×C127—41no—
275C23×C127—41no—
276C23×C127—41no—
277C23×C127—41no—
278C23×C127—42no—
279C23×C127—42no—
280C23×C127—42no—
281C23×C127—41no—
282C23×C127—41no—
283C23×C127—41no—
284C23×C127—81no—
285C23×C127—81no—
286C23×C127—82no—
287C23×C127—82no—
288C23×C127—82no—
289C23×C127#12011yescharacteristic
290C23×C127#12011yescharacteristic
291C23×C127C22×D411yescharacteristic
292Q8×C127—22no—
293Q8×C127—22no—
294Q8×C127—41no—
295Q8×C127—41no—
296Q8×C127—41no—
297D4×C127—22no—
298D4×C127—22no—
299D4×C127—42no—
300D4×C127—41no—
301D4×C127—41no—
302D4×C127—41no—
303D4×C127—44no—
304D4×C127—42no—
305D4×C127—44no—
306D4×C127—44no—
307D4×C127—42no—
308D4×C127—41no—
309D4×C127—42no—
310D4×C127—41no—
311D4×C127—42no—
312D4×C127—42no—
313D4×C127—81no—
314D4×C127—82no—
315D4×C127—82no—
316D4×C127—81no—
317D4×C127—82no—
318D4×C127—82no—
319D4×C127—82no—
320D4×C127—82no—
321D4×C127—82no—
322D4×C127—88no—
323C2×C4×C127—22no—
324C2×C4×C127—22no—
325C2×C4×C127—22no—
326C2×C4×C127—22no—
327C2×C4×C127—21no—
328C2×C4×C127—22no—
329C2×C4×C127—22no—
330C2×C4×C127—21no—
331C2×C4×C127—21no—
332C2×C4×C127—41no—
333C2×C4×C127—41no—
334C2×C4×C127—41no—
335C2×C4×C127—44no—
336C2×C4×C127—41no—
337C2×C4×C127—41no—
338C2×C4×C127—44no—
339C2×C4×C127—42no—
340C2×C4×C127—42no—
341C2×C4×C127—42no—
342C2×C4×C127—42no—
343C2×C4×C127—42no—
344C2×C4×C127—81no—
345C2×C4×C127—82no—
346C2×C4×C127—82no—
347C2×C4×C127#12011yescharacteristic
348C2×C4×C127#12011yescharacteristic
349C2×C4×C127C22×D411yescharacteristic
350C2×C4×C127C22×D411yescharacteristic
351C8×C127—41no—
352C8×C127—41no—
353C8×C127—42no—
354C22×C127—21no—
355C22×C127—21no—
356C22×C127—21no—
357C22×C127—21no—
358C22×C127—21no—
359C22×C127—21no—
360C22×C127—21no—
361C22×C127—21no—
362C22×C127—42no—
363C22×C127—42no—
364C22×C127—42no—
365C22×C127—42no—
366C22×C127—41no—
367C22×C127—42no—
368C22×C127—42no—
369C22×C127—41no—
370C22×C127—42no—
371C22×C127—41no—
372C22×C127—42no—
373C22×C127—42no—
374C22×C127—81no—
375C22×C127—81no—
376C22×C127—82no—
377C22×C127—82no—
378C22×C127—81no—
379C22×C127—81no—
380C22×C127—81no—
381C22×C127—81no—
382C22×C127—162no—
383C22×C127—164no—
384C22×C127C2×#12011yescharacteristic
385C22×C127#57611yescharacteristic
386C22×C127#57711yescharacteristic
387C4×C127—21no—
388C4×C127—21no—
389C4×C127—21no—
390C4×C127—42no—
391C4×C127—41no—
392C4×C127—42no—
393C4×C127—41no—
394C4×C127—42no—
395C4×C127—41no—
396C4×C127—82no—
397C4×C127B(4,𝔽2)12yes—
398#18228C12711yesmaximal, characteristic, direct product factor, Sylow
399C2×C127—21no—
400C2×C127—21no—
401C2×C127—41no—
402C2×C127—41no—
403C2×C127—82no—
404C2×C127—82no—
405C2×C127—82no—
406C2×C127—81no—
407C2×C127#301211yescharacteristic
408C2×C127#301911yescharacteristic
409C2×C127C2×B(4,𝔽2)11yescharacteristic
410#3537C2×C12711yescharacteristic, complemented
411#3006C2×C12711yescharacteristic, complemented
412#3002C2×C12711yescharacteristic, complemented
413#2615C2×C12711yescharacteristic, complemented
414#1606C2×C12712yescomplemented
415#1601C2×C12712yescomplemented
416#1600C2×C12712yescomplemented
417#1595C2×C12712yescomplemented
418#1519C2×C12711yescharacteristic, complemented
419#1513C2×C12711yescharacteristic, complemented
420#1471C2×C12711yescharacteristic, complemented
421C127#1822811yescharacteristic, direct product factor, Sylow
422C22×#41C22×C12711yescharacteristic, complemented
423C2×AGL(1,ℤ/8)—21no—
424C2×#135—21no—
425#560—22no—
426#553—21no—
427#553—21no—
428D42—22no—
429D42—21no—
430D42—21no—
431#540—21no—
432#538—21no—
433#538C22×C12712yes—
434#535—21no—
435#534—21no—
436#534C22×C12712yes—
437#525C22×C12711yescharacteristic
438C2×#121—21no—
439C2×#121C22×C12711yescharacteristic
440C2×#121C22×C12711yescharacteristic
441#452—21no—
442#451C22×C12711yescharacteristic, complemented
443#450C22×C12711yescharacteristic, complemented
444#449—21no—
445#449—22no—
446#448C22×C12711yescharacteristic, complemented
447#448C22×C12712yescomplemented
448#447C22×C12711yescharacteristic, complemented
449#447C22×C12712yescomplemented
450#417—21no—
451#416—21no—
452#407C22×C12711yescharacteristic, complemented
453C2×C22⋊C8C22×C12711yescharacteristic, complemented
454#393C22×C12712yescomplemented
455#392—22no—
456#392C22×C12712yescomplemented
457#380—21no—
458#380C22×C12711yescharacteristic, complemented
459#328C22×C12712yescomplemented
460#327C22×C12712yescomplemented
461#327C22×C12712yescomplemented
462#327C22×C12712yescomplemented
463#323C22×C12712yescomplemented
464#323C22×C12712yescomplemented
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—44no—
470C2×#41D4×C12711yescharacteristic, complemented
471C22×Q8C23×C12711yescharacteristic
472C22×D4—22no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—22no—
476C22×D4—21no—
477C22×D4—22no—
478C22×D4D4×C12711yescharacteristic
479C22×D4D4×C12712yes—
480C22×D4D4×C12711yescharacteristic, complemented
481C22×D4C23×C12711yescharacteristic
482C23×C4—21no—
483C23×C4C23×C12711yescharacteristic
484AGL(1,ℤ/8)—44no—
485#135—44no—
486C2×Q16—21no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×D8—21no—
491C2×D8—22no—
492C2×M16—21no—
493C22×C8—21no—
494#127—22no—
495#127—21no—
496#126—22no—
497#126—22no—
498#125—21no—
499#124—22no—
500#123—22no—
501#123—21no—
502#123—22no—
503#123—22no—
504#123—22no—
505C22⋊Q8D4×C12711yescharacteristic, complemented
506C22⋊Q8C23×C12711yescharacteristic
507#121—22no—
508#121—21no—
509#121—21no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—22no—
521#121—44no—
522#121D4×C12712yescomplemented
523#121D4×C12711yescharacteristic, complemented
524#121C23×C12712yes—
525#121C23×C12711yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529#120—21no—
530#120—22no—
531#120—22no—
532#120—22no—
533C4×D4—22no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—22no—
539#117—21no—
540#117D4×C12711yescharacteristic, complemented
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C12711yescharacteristic
543C2×C4⋊C4D4×C12711yescharacteristic, complemented
544C2×C22⋊C4—21no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4C23×C12712yes—
549#103—21no—
550#103—21no—
551#103—22no—
552#102—21no—
553#102—21no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C12711yescharacteristic
558C22⋊C8C23×C12711yescharacteristic
559C22⋊C8C23×C12712yes—
560#95—22no—
561#95C23×C12712yes—
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C12712yes—
566C24C2×D4×C12711yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C12711yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C12711yescharacteristic
615C2×D4C2×D4×C12712yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C12711yescharacteristic
628C22×C4C2×D4×C12711yescharacteristic
629C22×C4C2×D4×C12711yescharacteristic
630C22×C4C2×D4×C12712yes—
631C22×C4C2×D4×C12711yescharacteristic
632C22×C4C2×D4×C12711yescharacteristic
633C22×C4C24×C12711yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C12712yes—
654C4⋊C4C2×D4×C12711yescharacteristic
655C4⋊C4C2×D4×C12711yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23#120×C12711yescharacteristic
700C23#120×C12711yescharacteristic
701C23C22×D4×C12711yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4#120×C12711yescharacteristic
758C2×C4#120×C12711yescharacteristic
759C2×C4C22×D4×C12711yescharacteristic
760C2×C4C22×D4×C12711yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×#120×C12711yescharacteristic
795C22#576×C12711yescharacteristic
796C22#577×C12711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4B(4,𝔽2)×C12712yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C127×#301211yescharacteristic
817C2C127×#301911yescharacteristic
818C2C2×B(4,𝔽2)×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
LCSG ▷ C22×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×#3537C2semidirect
2. C127×#3006C2semidirect
3. C127×#3002C2semidirect
4. C127×#2615C2semidirect
5. C127×#1606C2semidirect
6. C127×#1601C2semidirect
7. C127×#1600C2semidirect
8. C127×#1595C2semidirect
9. C127×#1519C2semidirect
10. C127×#1513C2semidirect
11. C127×#1471C2semidirect
12. C22×#41×C127C22semidirect
32. #451×C127C22semidirect
33. #450×C127C22semidirect
36. #448×C127C22semidirect
37. #448×C127C22semidirect
38. #447×C127C22semidirect
39. #447×C127C22semidirect
42. #407×C127C22semidirect
43. C2×C22⋊C8×C127C22semidirect
44. #393×C127C22semidirect
46. #392×C127C22semidirect
48. #380×C127C22semidirect
49. #328×C127C22semidirect
50. #327×C127C22semidirect
51. #327×C127C22semidirect
52. #327×C127C22semidirect
53. #323×C127C22semidirect
54. #323×C127C22semidirect
60. C2×#41×C127D4semidirect
70. C22×D4×C127D4semidirect
95. C22⋊Q8×C127D4semidirect
112. #121×C127D4semidirect
113. #121×C127D4semidirect
130. #117×C127D4semidirect
133. C2×C4⋊C4×C127D4semidirect
398. #18228C127direct (N × H)
410. #3537C2×C127semidirect
411. #3006C2×C127semidirect
412. #3002C2×C127semidirect
413. #2615C2×C127semidirect
414. #1606C2×C127semidirect
415. #1601C2×C127semidirect
416. #1600C2×C127semidirect
417. #1595C2×C127semidirect
418. #1519C2×C127semidirect
419. #1513C2×C127semidirect
420. #1471C2×C127semidirect
421. C127#18228direct (N × H)
422. C22×#41C22×C127semidirect
442. #451C22×C127semidirect
443. #450C22×C127semidirect
446. #448C22×C127semidirect
447. #448C22×C127semidirect
448. #447C22×C127semidirect
449. #447C22×C127semidirect
452. #407C22×C127semidirect
453. C2×C22⋊C8C22×C127semidirect
454. #393C22×C127semidirect
456. #392C22×C127semidirect
458. #380C22×C127semidirect
459. #328C22×C127semidirect
460. #327C22×C127semidirect
461. #327C22×C127semidirect
462. #327C22×C127semidirect
463. #323C22×C127semidirect
464. #323C22×C127semidirect
470. C2×#41D4×C127semidirect
480. C22×D4D4×C127semidirect
505. C22⋊Q8D4×C127semidirect
522. #121D4×C127semidirect
523. #121D4×C127semidirect
540. #117D4×C127semidirect
543. C2×C4⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35372
C127×#30062
C127×#30022
C127×#26152
C127×#16062
C127×#16012
C127×#16002
C127×#15952
C127×#15192
C127×#15132
C127×#14712
#18228127