Finite Group Databasebeta

← C127×#21000 #44584673

Subgroups — C127×#21000 #44584673

Order 32512.

1704 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C127C211yesmaximal, characteristic
2C127×#3428C211yesmaximal, characteristic, complemented
3C2×#421×C127C211yesmaximal, characteristic, complemented
4C2×#421×C127C211yesmaximal, characteristic, complemented
5C2×#410×C127C211yesmaximal, characteristic, complemented
6C127×#1906C218yesmaximal, complemented
7C2×#344×C127C211yesmaximal, characteristic, complemented
8C127×#1733C211yesmaximal, characteristic, complemented
9C22×#41×C127C2211yescharacteristic
10C22×#41×C127C2211yescharacteristic
11#575×C127—22no—
12#575×C127—22no—
13#575×C127C414yescomplemented
14#575×C127C2214yes—
15C2×#137×C127—21no—
16C2×#137×C127C412yescomplemented
17C2×AGL(1,ℤ/8)×C127—21no—
18C2×AGL(1,ℤ/8)×C127C412yescomplemented
19C2×#135×C127—22no—
20C22×M16×C127C2211yescharacteristic
21C22×M16×C127C2211yescharacteristic
22#520×C127—22no—
23#520×C127—22no—
24#519×C127—21no—
25#518×C127—21no—
26#518×C127—22no—
27C4×#41×C127—22no—
28C4×#41×C127C2214yescomplemented
29C2×#117×C127—22no—
30C2×#117×C127C2211yescharacteristic
31C2×#117×C127C2211yescharacteristic
32C2×#117×C127C2211yescharacteristic
33#421×C127—22no—
34#421×C127—22no—
35#421×C127—22no—
36#421×C127C2214yescomplemented
37C2×#104×C127—22no—
38C2×#104×C127C2214yescomplemented
39#410×C127—22no—
40#410×C127C2214yescomplemented
41C2×#99×C127—22no—
42#344×C127C2214yescomplemented
43#339×C127C2214yescomplemented
44C2×#41×C127—21no—
45C2×#41×C127—21no—
46C2×#41×C127—21no—
47C2×#41×C127—21no—
48C2×#41×C127—21no—
49C2×#41×C127—21no—
50C2×#41×C127—21no—
51C2×#41×C127—21no—
52C2×#41×C127—21no—
53C2×#41×C127—21no—
54C2×#41×C127—21no—
55C2×#41×C127—21no—
56C2×#41×C127—21no—
57C2×#41×C127—21no—
58C2×#41×C127—21no—
59C2×#41×C127—21no—
60C2×#41×C127C2×C412yes—
61C2×#41×C127C2×C412yes—
62C2×#41×C127C2×C412yescomplemented
63C2×#41×C127D412yes—
64C2×#41×C127D412yes—
65C2×#41×C127D412yes—
66C2×#41×C127C2312yes—
67C2×#41×C127C2312yes—
68C22×Q8×C127C2×C411yescharacteristic, complemented
69C22×Q8×C127D411yescharacteristic
70C22×D4×C127—21no—
71C22×D4×C127—21no—
72C22×D4×C127C2×C411yescharacteristic, complemented
73C22×D4×C127D411yescharacteristic
74C23×C4×C127—21no—
75C23×C4×C127—21no—
76C23×C4×C127C2311yescharacteristic
77#137×C127—24no—
78#137×C127—24no—
79#137×C127—24no—
80#137×C127C2×C418yescomplemented
81AGL(1,ℤ/8)×C127—24no—
82AGL(1,ℤ/8)×C127—24no—
83AGL(1,ℤ/8)×C127—24no—
84AGL(1,ℤ/8)×C127C2×C418yescomplemented
85#135×C127—28no—
86#135×C127—28no—
87C2×Q16×C127—22no—
88C2×SD16×C127—22no—
89C2×SD16×C127—22no—
90C2×D8×C127—22no—
91C2×M16×C127—21no—
92C2×M16×C127—21no—
93C2×M16×C127—21no—
94C2×M16×C127—21no—
95C2×M16×C127—21no—
96C2×M16×C127—21no—
97C2×M16×C127—21no—
98C2×M16×C127—21no—
99C2×M16×C127C2×C412yescomplemented
100C2×M16×C127C2×C412yescomplemented
101C2×M16×C127C2312yes—
102C2×M16×C127C2312yes—
103C22×C8×C127—21no—
104C22×C8×C127—21no—
105C4×Q8×C127—24no—
106C4×Q8×C127—24no—
107C4×D4×C127—28no—
108C4×D4×C127—24no—
109C4×D4×C127—24no—
110C4×D4×C127—28no—
111#117×C127—24no—
112#117×C127—24no—
113#117×C127—21no—
114#117×C127—21no—
115#117×C127—21no—
116#117×C127—21no—
117#117×C127—21no—
118#117×C127—24no—
119#117×C127—21no—
120#117×C127—21no—
121#117×C127D412yes—
122#117×C127D412yes—
123#117×C127D412yes—
124#117×C127C2312yes—
125#117×C127C2312yes—
126C2×C4⋊C4×C127—24no—
127C2×C4⋊C4×C127—21no—
128C2×C4⋊C4×C127—21no—
129C2×C4⋊C4×C127—21no—
130C2×C22⋊C4×C127—24no—
131C2×C22⋊C4×C127—21no—
132C2×C22⋊C4×C127—21no—
133C2×C22⋊C4×C127D412yes—
134C2×C42×C127—21no—
135C2×C42×C127—24no—
136C2×C42×C127—21no—
137C2×C42×C127C2312yes—
138#104×C127—28no—
139#104×C127—28no—
140#99×C127—28no—
141C24×C127—21no—
142C24×C127—21no—
143C24×C127C2×D411yescharacteristic
144#41×C127—22no—
145#41×C127—22no—
146#41×C127—22no—
147#41×C127—22no—
148#41×C127—22no—
149#41×C127—22no—
150#41×C127—22no—
151#41×C127—22no—
152#41×C127—22no—
153#41×C127—22no—
154#41×C127—22no—
155#41×C127—22no—
156#41×C127—22no—
157#41×C127—22no—
158#41×C127—22no—
159#41×C127—22no—
160#41×C127—22no—
161#41×C127—22no—
162#41×C127—22no—
163#41×C127—22no—
164#41×C127—41no—
165#41×C127—41no—
166#41×C127—41no—
167#41×C127—41no—
168#41×C127—41no—
169#41×C127—41no—
170#41×C127—41no—
171#41×C127—41no—
172#41×C127C22⋊C414yes—
173#41×C127C22⋊C414yes—
174#41×C127C22×C414yes—
175#41×C127C2×D414yes—
176C2×Q8×C127—21no—
177C2×Q8×C127—21no—
178C2×Q8×C127—21no—
179C2×Q8×C127—21no—
180C2×Q8×C127—21no—
181C2×Q8×C127—21no—
182C2×Q8×C127—21no—
183C2×Q8×C127—21no—
184C2×Q8×C127C22⋊C412yes—
185C2×Q8×C127C22⋊C412yes—
186C2×Q8×C127C22×C412yes—
187C2×Q8×C127C2×D412yes—
188C2×D4×C127—22no—
189C2×D4×C127—22no—
190C2×D4×C127—22no—
191C2×D4×C127—22no—
192C2×D4×C127—22no—
193C2×D4×C127—22no—
194C2×D4×C127—22no—
195C2×D4×C127—22no—
196C2×D4×C127—21no—
197C2×D4×C127—21no—
198C2×D4×C127—21no—
199C2×D4×C127—21no—
200C2×D4×C127—21no—
201C2×D4×C127—21no—
202C2×D4×C127—21no—
203C2×D4×C127—21no—
204C2×D4×C127—41no—
205C2×D4×C127—41no—
206C2×D4×C127—41no—
207C2×D4×C127—41no—
208C2×D4×C127C22⋊C412yes—
209C2×D4×C127C22⋊C412yes—
210C2×D4×C127C22×C412yes—
211C2×D4×C127C2×D412yes—
212C22×C4×C127—21no—
213C22×C4×C127—22no—
214C22×C4×C127—22no—
215C22×C4×C127—22no—
216C22×C4×C127—22no—
217C22×C4×C127—22no—
218C22×C4×C127—22no—
219C22×C4×C127—21no—
220C22×C4×C127—28no—
221C22×C4×C127—22no—
222C22×C4×C127—22no—
223C22×C4×C127—22no—
224C22×C4×C127—22no—
225C22×C4×C127—41no—
226C22×C4×C127—41no—
227C22×C4×C127—41no—
228C22×C4×C127—41no—
229C22×C4×C127—41no—
230C22×C4×C127C22×C411yescharacteristic
231C22×C4×C127C22×C411yescharacteristic
232C22×C4×C127C2×D411yescharacteristic
233C22×C4×C127C2×D411yescharacteristic
234C22×C4×C127C2×D411yescharacteristic
235C22×C4×C127C2×D411yescharacteristic
236C22×C4×C127C2×D411yescharacteristic
237C22×C4×C127C2×D411yescharacteristic
238C22×C4×C127C2×D411yescharacteristic
239C22×C4×C127#4111yescharacteristic
240C22×C4×C127#4111yescharacteristic
241C22×C4×C127#4111yescharacteristic
242C22×C4×C127#4111yescharacteristic
243C22×C4×C127C2411yescharacteristic
244Q16×C127—28no—
245SD16×C127—28no—
246SD16×C127—28no—
247D8×C127—28no—
248M16×C127—22no—
249M16×C127—22no—
250M16×C127—22no—
251M16×C127—22no—
252M16×C127—22no—
253M16×C127—41no—
254M16×C127—41no—
255M16×C127C22×C414yes—
256C2×C8×C127—22no—
257C2×C8×C127—22no—
258C2×C8×C127—22no—
259C2×C8×C127—22no—
260C2×C8×C127—41no—
261C2×C8×C127—41no—
262C4⋊C4×C127—28no—
263C4⋊C4×C127—22no—
264C4⋊C4×C127—22no—
265C4⋊C4×C127—22no—
266C4⋊C4×C127—22no—
267C4⋊C4×C127—22no—
268C4⋊C4×C127—41no—
269C22⋊C4×C127—28no—
270C22⋊C4×C127—22no—
271C22⋊C4×C127—22no—
272C22⋊C4×C127—22no—
273C22⋊C4×C127—22no—
274C22⋊C4×C127—41no—
275C22⋊C4×C127C2×D414yes—
276C42×C127—28no—
277C42×C127—22no—
278C42×C127—22no—
279C42×C127—22no—
280C42×C127—22no—
281C42×C127—41no—
282C42×C127C2×D414yes—
283C23×C127—22no—
284C23×C127—22no—
285C23×C127—22no—
286C23×C127—22no—
287C23×C127—41no—
288C23×C127—41no—
289C23×C127—81no—
290C23×C127—82no—
291C23×C127—82no—
292C23×C127C4×D411yescharacteristic
293C23×C127C4×D411yescharacteristic
294C23×C127#12011yescharacteristic
295C23×C127#12011yescharacteristic
296C23×C127#12111yescharacteristic
297C23×C127#12111yescharacteristic
298C23×C127C22×D411yescharacteristic
299Q8×C127—22no—
300Q8×C127—22no—
301Q8×C127—22no—
302Q8×C127—22no—
303Q8×C127—22no—
304Q8×C127—41no—
305Q8×C127—41no—
306Q8×C127C2×C22⋊C414yes—
307D4×C127—24no—
308D4×C127—24no—
309D4×C127—24no—
310D4×C127—24no—
311D4×C127—22no—
312D4×C127—22no—
313D4×C127—22no—
314D4×C127—22no—
315D4×C127—22no—
316D4×C127—42no—
317D4×C127—42no—
318D4×C127—42no—
319D4×C127—42no—
320D4×C127—41no—
321D4×C127—41no—
322D4×C127C2×C22⋊C414yes—
323C2×C4×C127—22no—
324C2×C4×C127—22no—
325C2×C4×C127—22no—
326C2×C4×C127—24no—
327C2×C4×C127—24no—
328C2×C4×C127—24no—
329C2×C4×C127—24no—
330C2×C4×C127—22no—
331C2×C4×C127—24no—
332C2×C4×C127—24no—
333C2×C4×C127—41no—
334C2×C4×C127—41no—
335C2×C4×C127—42no—
336C2×C4×C127—42no—
337C2×C4×C127—42no—
338C2×C4×C127—42no—
339C2×C4×C127—42no—
340C2×C4×C127—82no—
341C2×C4×C127—82no—
342C2×C4×C127—88no—
343C2×C4×C127—82no—
344C2×C4×C127C2×C22⋊C411yescharacteristic
345C2×C4×C127C2×C22⋊C411yescharacteristic
346C2×C4×C127C2×C22⋊C411yescharacteristic
347C2×C4×C127C2×C22⋊C411yescharacteristic
348C2×C4×C127C4×D411yescharacteristic
349C2×C4×C127C4×D411yescharacteristic
350C2×C4×C127C4×D411yescharacteristic
351C2×C4×C127C4×D411yescharacteristic
352C2×C4×C127C4×D411yescharacteristic
353C2×C4×C127C4×D411yescharacteristic
354C2×C4×C127#12011yescharacteristic
355C2×C4×C127#12011yescharacteristic
356C2×C4×C127#12111yescharacteristic
357C2×C4×C127#12111yescharacteristic
358C2×C4×C127#12111yescharacteristic
359C2×C4×C127#12111yescharacteristic
360C2×C4×C127#12111yescharacteristic
361C2×C4×C127#12111yescharacteristic
362C2×C4×C127#12311yescharacteristic
363C2×C4×C127#12311yescharacteristic
364C2×C4×C127#12311yescharacteristic
365C2×C4×C127#12311yescharacteristic
366C2×C4×C127C23×C411yescharacteristic
367C2×C4×C127C22×D411yescharacteristic
368C2×C4×C127C22×D411yescharacteristic
369C2×C4×C127C22×D411yescharacteristic
370C2×C4×C127C2×#4111yescharacteristic
371C2×C4×C127C2×#4111yescharacteristic
372C8×C127—24no—
373C8×C127—42no—
374C22×C127—24no—
375C22×C127—41no—
376C22×C127—41no—
377C22×C127—41no—
378C22×C127—41no—
379C22×C127—41no—
380C22×C127—41no—
381C22×C127—41no—
382C22×C127—44no—
383C22×C127—42no—
384C22×C127—82no—
385C22×C127—82no—
386C22×C127—82no—
387C22×C127—82no—
388C22×C127—82no—
389C22×C127#38611yescharacteristic
390C22×C127#38611yescharacteristic
391C22×C127#38611yescharacteristic
392C22×C127#38611yescharacteristic
393C22×C127C2×C4×D411yescharacteristic
394C22×C127C2×#12011yescharacteristic
395C22×C127C2×#12111yescharacteristic
396C4×C127—24no—
397C4×C127—44no—
398C4×C127—44no—
399C4×C127—42no—
400C4×C127—82no—
401C4×C127#38611yescharacteristic
402C4×C127#38611yescharacteristic
403C4×C127#38611yescharacteristic
404C4×C127#38611yescharacteristic
405C4×C127C22×C22⋊C411yescharacteristic
406C4×C127C2×C4×D411yescharacteristic
407C4×C127C2×#12111yescharacteristic
408C4×C127C2×#12311yescharacteristic
409#21000C12711yesmaximal, characteristic, direct product factor, Sylow
410C2×C127—21no—
411C2×C127—21no—
412C2×C127—21no—
413C2×C127—21no—
414C2×C127—21no—
415C2×C127—21no—
416C2×C127—21no—
417C2×C127—44no—
418C2×C127—82no—
419C2×C127C2×#38611yescharacteristic
420C2×#575C2×C12711yescharacteristic
421#3428C2×C12711yescharacteristic, complemented
422C2×#421C2×C12711yescharacteristic, complemented
423C2×#421C2×C12711yescharacteristic, complemented
424C2×#410C2×C12711yescharacteristic, complemented
425#1906C2×C12718yescomplemented
426C2×#344C2×C12711yescharacteristic, complemented
427#1733C2×C12711yescharacteristic, complemented
428C127#2100011yescharacteristic, direct product factor, Sylow
429C22×#41C22×C12711yescharacteristic
430C22×#41C22×C12711yescharacteristic
431#575—22no—
432#575—22no—
433#575C4×C12714yescomplemented
434#575C22×C12714yes—
435C2×#137—21no—
436C2×#137C4×C12712yescomplemented
437C2×AGL(1,ℤ/8)—21no—
438C2×AGL(1,ℤ/8)C4×C12712yescomplemented
439C2×#135—22no—
440C22×M16C22×C12711yescharacteristic
441C22×M16C22×C12711yescharacteristic
442#520—22no—
443#520—22no—
444#519—21no—
445#518—21no—
446#518—22no—
447C4×#41—22no—
448C4×#41C22×C12714yescomplemented
449C2×#117—22no—
450C2×#117C22×C12711yescharacteristic
451C2×#117C22×C12711yescharacteristic
452C2×#117C22×C12711yescharacteristic
453#421—22no—
454#421—22no—
455#421—22no—
456#421C22×C12714yescomplemented
457C2×#104—22no—
458C2×#104C22×C12714yescomplemented
459#410—22no—
460#410C22×C12714yescomplemented
461C2×#99—22no—
462#344C22×C12714yescomplemented
463#339C22×C12714yescomplemented
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41C2×C4×C12712yes—
481C2×#41C2×C4×C12712yes—
482C2×#41C2×C4×C12712yescomplemented
483C2×#41D4×C12712yes—
484C2×#41D4×C12712yes—
485C2×#41D4×C12712yes—
486C2×#41C23×C12712yes—
487C2×#41C23×C12712yes—
488C22×Q8C2×C4×C12711yescharacteristic, complemented
489C22×Q8D4×C12711yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2×C4×C12711yescharacteristic, complemented
493C22×D4D4×C12711yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C12711yescharacteristic
497#137—24no—
498#137—24no—
499#137—24no—
500#137C2×C4×C12718yescomplemented
501AGL(1,ℤ/8)—24no—
502AGL(1,ℤ/8)—24no—
503AGL(1,ℤ/8)—24no—
504AGL(1,ℤ/8)C2×C4×C12718yescomplemented
505#135—28no—
506#135—28no—
507C2×Q16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×D8—22no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16C2×C4×C12712yescomplemented
520C2×M16C2×C4×C12712yescomplemented
521C2×M16C23×C12712yes—
522C2×M16C23×C12712yes—
523C22×C8—21no—
524C22×C8—21no—
525C4×Q8—24no—
526C4×Q8—24no—
527C4×D4—28no—
528C4×D4—24no—
529C4×D4—24no—
530C4×D4—28no—
531#117—24no—
532#117—24no—
533#117—21no—
534#117—21no—
535#117—21no—
536#117—21no—
537#117—21no—
538#117—24no—
539#117—21no—
540#117—21no—
541#117D4×C12712yes—
542#117D4×C12712yes—
543#117D4×C12712yes—
544#117C23×C12712yes—
545#117C23×C12712yes—
546C2×C4⋊C4—24no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4D4×C12712yes—
554C2×C42—21no—
555C2×C42—24no—
556C2×C42—21no—
557C2×C42C23×C12712yes—
558#104—28no—
559#104—28no—
560#99—28no—
561C24—21no—
562C24—21no—
563C24C2×D4×C12711yescharacteristic
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—22no—
569#41—22no—
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—22no—
579#41—22no—
580#41—22no—
581#41—22no—
582#41—22no—
583#41—22no—
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41C22⋊C4×C12714yes—
593#41C22⋊C4×C12714yes—
594#41C22×C4×C12714yes—
595#41C2×D4×C12714yes—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8C22⋊C4×C12712yes—
605C2×Q8C22⋊C4×C12712yes—
606C2×Q8C22×C4×C12712yes—
607C2×Q8C2×D4×C12712yes—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—41no—
628C2×D4C22⋊C4×C12712yes—
629C2×D4C22⋊C4×C12712yes—
630C2×D4C22×C4×C12712yes—
631C2×D4C2×D4×C12712yes—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—28no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4C22×C4×C12711yescharacteristic
651C22×C4C22×C4×C12711yescharacteristic
652C22×C4C2×D4×C12711yescharacteristic
653C22×C4C2×D4×C12711yescharacteristic
654C22×C4C2×D4×C12711yescharacteristic
655C22×C4C2×D4×C12711yescharacteristic
656C22×C4C2×D4×C12711yescharacteristic
657C22×C4C2×D4×C12711yescharacteristic
658C22×C4C2×D4×C12711yescharacteristic
659C22×C4#41×C12711yescharacteristic
660C22×C4#41×C12711yescharacteristic
661C22×C4#41×C12711yescharacteristic
662C22×C4#41×C12711yescharacteristic
663C22×C4C24×C12711yescharacteristic
664Q16—28no—
665SD16—28no—
666SD16—28no—
667D8—28no—
668M16—22no—
669M16—22no—
670M16—22no—
671M16—22no—
672M16—22no—
673M16—41no—
674M16—41no—
675M16C22×C4×C12714yes—
676C2×C8—22no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—41no—
681C2×C8—41no—
682C4⋊C4—28no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—41no—
689C22⋊C4—28no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—41no—
695C22⋊C4C2×D4×C12714yes—
696C42—28no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—41no—
702C42C2×D4×C12714yes—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—81no—
710C23—82no—
711C23—82no—
712C23C4×D4×C12711yescharacteristic
713C23C4×D4×C12711yescharacteristic
714C23#120×C12711yescharacteristic
715C23#120×C12711yescharacteristic
716C23#121×C12711yescharacteristic
717C23#121×C12711yescharacteristic
718C23C22×D4×C12711yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—41no—
725Q8—41no—
726Q8C2×C22⋊C4×C12714yes—
727D4—24no—
728D4—24no—
729D4—24no—
730D4—24no—
731D4—22no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—41no—
741D4—41no—
742D4C2×C22⋊C4×C12714yes—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4—88no—
763C2×C4—82no—
764C2×C4C2×C22⋊C4×C12711yescharacteristic
765C2×C4C2×C22⋊C4×C12711yescharacteristic
766C2×C4C2×C22⋊C4×C12711yescharacteristic
767C2×C4C2×C22⋊C4×C12711yescharacteristic
768C2×C4C4×D4×C12711yescharacteristic
769C2×C4C4×D4×C12711yescharacteristic
770C2×C4C4×D4×C12711yescharacteristic
771C2×C4C4×D4×C12711yescharacteristic
772C2×C4C4×D4×C12711yescharacteristic
773C2×C4C4×D4×C12711yescharacteristic
774C2×C4#120×C12711yescharacteristic
775C2×C4#120×C12711yescharacteristic
776C2×C4#121×C12711yescharacteristic
777C2×C4#121×C12711yescharacteristic
778C2×C4#121×C12711yescharacteristic
779C2×C4#121×C12711yescharacteristic
780C2×C4#121×C12711yescharacteristic
781C2×C4#121×C12711yescharacteristic
782C2×C4#123×C12711yescharacteristic
783C2×C4#123×C12711yescharacteristic
784C2×C4#123×C12711yescharacteristic
785C2×C4#123×C12711yescharacteristic
786C2×C4C23×C4×C12711yescharacteristic
787C2×C4C22×D4×C12711yescharacteristic
788C2×C4C22×D4×C12711yescharacteristic
789C2×C4C22×D4×C12711yescharacteristic
790C2×C4C2×#41×C12711yescharacteristic
791C2×C4C2×#41×C12711yescharacteristic
792C8—24no—
793C8—42no—
794C22—24no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—44no—
803C22—42no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22#386×C12711yescharacteristic
810C22#386×C12711yescharacteristic
811C22#386×C12711yescharacteristic
812C22#386×C12711yescharacteristic
813C22C2×C4×D4×C12711yescharacteristic
814C22C2×#120×C12711yescharacteristic
815C22C2×#121×C12711yescharacteristic
816C4—24no—
817C4—44no—
818C4—44no—
819C4—42no—
820C4—82no—
821C4#386×C12711yescharacteristic
822C4#386×C12711yescharacteristic
823C4#386×C12711yescharacteristic
824C4#386×C12711yescharacteristic
825C4C22×C22⋊C4×C12711yescharacteristic
826C4C2×C4×D4×C12711yescharacteristic
827C4C2×#121×C12711yescharacteristic
828C4C2×#123×C12711yescharacteristic
829C2—21no—
830C2—21no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—21no—
835C2—21no—
836C2—44no—
837C2—82no—
838C2C2×#386×C12711yescharacteristic
subgroupG/H
centerC4×C127C2×#121
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC2×C127C2×#386
prime radicalC2×#575×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3428C2semidirect
3. C2×#421×C127C2semidirect
4. C2×#421×C127C2semidirect
5. C2×#410×C127C2semidirect
6. C127×#1906C2semidirect
7. C2×#344×C127C2semidirect
8. C127×#1733C2semidirect
13. #575×C127C4semidirect
16. C2×#137×C127C4semidirect
18. C2×AGL(1,ℤ/8)×C127C4semidirect
28. C4×#41×C127C22semidirect
36. #421×C127C22semidirect
38. C2×#104×C127C22semidirect
40. #410×C127C22semidirect
42. #344×C127C22semidirect
43. #339×C127C22semidirect
62. C2×#41×C127C2×C4semidirect
68. C22×Q8×C127C2×C4semidirect
72. C22×D4×C127C2×C4semidirect
80. #137×C127C2×C4semidirect
84. AGL(1,ℤ/8)×C127C2×C4semidirect
99. C2×M16×C127C2×C4semidirect
100. C2×M16×C127C2×C4semidirect
409. #21000C127direct (N × H)
421. #3428C2×C127semidirect
422. C2×#421C2×C127semidirect
423. C2×#421C2×C127semidirect
424. C2×#410C2×C127semidirect
425. #1906C2×C127semidirect
426. C2×#344C2×C127semidirect
427. #1733C2×C127semidirect
428. C127#21000direct (N × H)
433. #575C4×C127semidirect
436. C2×#137C4×C127semidirect
438. C2×AGL(1,ℤ/8)C4×C127semidirect
448. C4×#41C22×C127semidirect
456. #421C22×C127semidirect
458. C2×#104C22×C127semidirect
460. #410C22×C127semidirect
462. #344C22×C127semidirect
463. #339C22×C127semidirect
482. C2×#41C2×C4×C127semidirect
488. C22×Q8C2×C4×C127semidirect
492. C22×D4C2×C4×C127semidirect
500. #137C2×C4×C127semidirect
504. AGL(1,ℤ/8)C2×C4×C127semidirect
519. C2×M16C2×C4×C127semidirect
520. C2×M16C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C1272
C127×#34282
C2×#421×C1272
C2×#410×C1272
C127×#19062
C2×#344×C1272
C127×#17332
#21000127