Finite Group Databasebeta

← C127×#18523 #44582196

Subgroups — C127×#18523 #44582196

Order 32512.

946 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3475C211yesmaximal, characteristic
2C127×#3170C211yesmaximal, characteristic, complemented
3C127×#3101C211yesmaximal, characteristic, complemented
4C127×#3076C211yesmaximal, characteristic, complemented
5C127×#1650C211yesmaximal, characteristic, complemented
6C127×#1647C211yesmaximal, characteristic, complemented
7C127×#1646C211yesmaximal, characteristic, complemented
8C127×#1643C211yesmaximal, characteristic, complemented
9C127×#1638C211yesmaximal, characteristic, complemented
10C127×#1635C211yesmaximal, characteristic, complemented
11C127×#1634C211yesmaximal, characteristic, complemented
12C127×#1632C211yesmaximal, characteristic, complemented
13C127×#1542C211yesmaximal, characteristic, complemented
14C127×#1476C211yesmaximal, characteristic, complemented
15C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
16#556×C127C2211yescharacteristic
17#555×C127C2211yescharacteristic
18#554×C127C2211yescharacteristic
19#553×C127—21no—
20#552×C127—21no—
21#552×C127—21no—
22#551×C127—22no—
23#547×C127C2211yescharacteristic
24#546×C127—21no—
25#533×C127C2211yescharacteristic
26#533×C127C2211yescharacteristic
27#529×C127—22no—
28#529×C127—21no—
29#525×C127—21no—
30C4×#41×C127—21no—
31C4×#41×C127C2211yescharacteristic
32C2×C4×D4×C127C2211yescharacteristic
33C2×#117×C127—21no—
34#500×C127C2211yescharacteristic, complemented
35#494×C127C2211yescharacteristic, complemented
36#487×C127C2211yescharacteristic, complemented
37#487×C127C2211yescharacteristic, complemented
38#483×C127—21no—
39#479×C127—21no—
40#478×C127—21no—
41#477×C127C2211yescharacteristic, complemented
42#476×C127C2211yescharacteristic
43#476×C127C2211yescharacteristic
44#476×C127C2211yescharacteristic, complemented
45#475×C127C2211yescharacteristic, complemented
46#474×C127C2211yescharacteristic, complemented
47#467×C127—22no—
48#461×C127C2211yescharacteristic
49#461×C127C2211yescharacteristic
50#450×C127—21no—
51C4×Q16×C127—22no—
52C4×SD16×C127—21no—
53C4×SD16×C127—21no—
54#431×C127C2211yescharacteristic
55#427×C127—21no—
56C2×C4⋊C8×C127C2211yescharacteristic
57#416×C127—21no—
58C2×C4×C8×C127C2211yescharacteristic
59#333×C127C2211yescharacteristic, complemented
60#333×C127C2211yescharacteristic, complemented
61#332×C127C2211yescharacteristic, complemented
62#332×C127C2211yescharacteristic, complemented
63Q8⋊C8×C127C2211yescharacteristic, complemented
64Q8⋊C8×C127C2211yescharacteristic, complemented
65D4⋊C8×C127C2211yescharacteristic
66D4⋊C8×C127C2211yescharacteristic
67D4⋊C8×C127C2211yescharacteristic
68D4⋊C8×C127C2211yescharacteristic
69D4⋊C8×C127C2211yescharacteristic, complemented
70D4⋊C8×C127C2211yescharacteristic, complemented
71C2×#41×C127—21no—
72C2×#41×C127D411yescharacteristic
73C22×D4×C127D411yescharacteristic
74C23×C4×C127—21no—
75C2×Q16×C127—22no—
76C2×SD16×C127—21no—
77C2×SD16×C127—21no—
78C22×C8×C127—21no—
79C22×C8×C127—21no—
80C4⋊Q8×C127C2311yescharacteristic
81C4⋊Q8×C127C2311yescharacteristic
82C4⋊Q8×C127C2311yescharacteristic
83C4⋊Q8×C127C2311yescharacteristic
84#126×C127—22no—
85#126×C127—22no—
86#126×C127—22no—
87#125×C127—22no—
88#125×C127—21no—
89#125×C127—21no—
90#125×C127—21no—
91#124×C127—22no—
92#124×C127—21no—
93#123×C127—22no—
94#123×C127—22no—
95#123×C127—22no—
96#123×C127—22no—
97C22⋊Q8×C127—21no—
98C22⋊Q8×C127—21no—
99C22⋊Q8×C127—22no—
100C22⋊Q8×C127—21no—
101C22⋊Q8×C127—21no—
102C22⋊Q8×C127—21no—
103C22⋊Q8×C127—21no—
104C22⋊Q8×C127D412yes—
105#121×C127—22no—
106#121×C127—21no—
107#121×C127—21no—
108#121×C127—21no—
109#120×C127—22no—
110C4×Q8×C127—21no—
111C4×Q8×C127—21no—
112C4×Q8×C127—21no—
113C4×Q8×C127—21no—
114C4×Q8×C127D411yescharacteristic
115C4×Q8×C127D412yes—
116C4×Q8×C127C2311yescharacteristic
117C4×D4×C127—22no—
118C4×D4×C127—22no—
119C4×D4×C127—22no—
120C4×D4×C127—21no—
121C4×D4×C127—21no—
122C4×D4×C127—21no—
123C4×D4×C127—21no—
124C4×D4×C127—21no—
125C4×D4×C127D411yescharacteristic
126C4×D4×C127D411yescharacteristic
127C4×D4×C127D411yescharacteristic
128C4×D4×C127C2311yescharacteristic
129C4×D4×C127C2311yescharacteristic
130C4×D4×C127C2311yescharacteristic
131#117×C127—22no—
132#117×C127—22no—
133#117×C127—22no—
134#117×C127—21no—
135#117×C127—21no—
136#117×C127—21no—
137#117×C127—21no—
138#117×C127—21no—
139#117×C127—21no—
140#117×C127D411yescharacteristic
141C2×C4⋊C4×C127—21no—
142C2×C4⋊C4×C127—21no—
143C2×C4⋊C4×C127D411yescharacteristic
144C2×C22⋊C4×C127—22no—
145C2×C22⋊C4×C127—21no—
146C2×C42×C127—22no—
147C2×C42×C127—21no—
148C2×C42×C127C2311yescharacteristic
149#107×C127—22no—
150#107×C127—21no—
151#107×C127—21no—
152#106×C127—21no—
153#106×C127—21no—
154#106×C127—21no—
155#106×C127—21no—
156C4⋊C8×C127—21no—
157C4⋊C8×C127C2311yescharacteristic
158C4⋊C8×C127C2311yescharacteristic
159C4⋊C8×C127C2311yescharacteristic
160C4⋊C8×C127C2311yescharacteristic
161#103×C127—21no—
162#103×C127—21no—
163#103×C127—22no—
164#103×C127—21no—
165#103×C127—21no—
166#103×C127—22no—
167#102×C127—21no—
168#102×C127—21no—
169#102×C127—21no—
170#102×C127—21no—
171C22⋊C8×C127—21no—
172C4×C8×C127—21no—
173C4×C8×C127—21no—
174C4×C8×C127C2311yescharacteristic
175C4×C8×C127C2311yescharacteristic
176C24×C127—21no—
177#41×C127—22no—
178#41×C127—22no—
179#41×C127—42no—
180#41×C127—42no—
181C2×Q8×C127—21no—
182C2×Q8×C127—21no—
183C2×Q8×C127—21no—
184C2×Q8×C127C2×D411yescharacteristic
185C2×Q8×C127C2×D412yes—
186C2×D4×C127—22no—
187C2×D4×C127—22no—
188C2×D4×C127—21no—
189C2×D4×C127—22no—
190C2×D4×C127—21no—
191C2×D4×C127—41no—
192C2×D4×C127C2×D411yescharacteristic
193C2×D4×C127C2×D411yescharacteristic
194C2×D4×C127C2×D411yescharacteristic
195C22×C4×C127—22no—
196C22×C4×C127—21no—
197C22×C4×C127—22no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—42no—
206C22×C4×C127—42no—
207C22×C4×C127C2×D411yescharacteristic
208C22×C4×C127C2×D411yescharacteristic
209C22×C4×C127C2×D411yescharacteristic
210Q16×C127—44no—
211SD16×C127—42no—
212SD16×C127—42no—
213C2×C8×C127—21no—
214C2×C8×C127—21no—
215C2×C8×C127—21no—
216C2×C8×C127—21no—
217C2×C8×C127—21no—
218C2×C8×C127—21no—
219C2×C8×C127—42no—
220C2×C8×C127—42no—
221C4⋊C4×C127—22no—
222C4⋊C4×C127—22no—
223C4⋊C4×C127—22no—
224C4⋊C4×C127—22no—
225C4⋊C4×C127—21no—
226C4⋊C4×C127—22no—
227C4⋊C4×C127—21no—
228C4⋊C4×C127—22no—
229C4⋊C4×C127—21no—
230C4⋊C4×C127—21no—
231C4⋊C4×C127—21no—
232C4⋊C4×C127—21no—
233C4⋊C4×C127—21no—
234C4⋊C4×C127—21no—
235C4⋊C4×C127—21no—
236C4⋊C4×C127—21no—
237C4⋊C4×C127—41no—
238C4⋊C4×C127—41no—
239C4⋊C4×C127C2×D411yescharacteristic
240C4⋊C4×C127C2×D411yescharacteristic
241C4⋊C4×C127C2×D412yes—
242C4⋊C4×C127C2×D411yescharacteristic
243C4⋊C4×C127C2×D411yescharacteristic
244C22⋊C4×C127—22no—
245C22⋊C4×C127—22no—
246C22⋊C4×C127—22no—
247C22⋊C4×C127—22no—
248C22⋊C4×C127—22no—
249C22⋊C4×C127—22no—
250C22⋊C4×C127—21no—
251C22⋊C4×C127—22no—
252C22⋊C4×C127—21no—
253C22⋊C4×C127—21no—
254C22⋊C4×C127—21no—
255C22⋊C4×C127—21no—
256C22⋊C4×C127—21no—
257C22⋊C4×C127—21no—
258C22⋊C4×C127—41no—
259C42×C127—22no—
260C42×C127—22no—
261C42×C127—21no—
262C42×C127—21no—
263C42×C127—22no—
264C42×C127—21no—
265C42×C127—41no—
266C42×C127C2×D411yescharacteristic
267C42×C127C2×D411yescharacteristic
268C42×C127C2×D411yescharacteristic
269C42×C127C2411yescharacteristic
270C23×C127—21no—
271C23×C127—21no—
272C23×C127—21no—
273C23×C127—42no—
274C23×C127—42no—
275C23×C127—81no—
276C23×C127#12011yescharacteristic
277Q8×C127—21no—
278Q8×C127—21no—
279Q8×C127—42no—
280Q8×C127—42no—
281Q8×C127—41no—
282Q8×C127—41no—
283Q8×C127—41no—
284Q8×C127—41no—
285D4×C127—21no—
286D4×C127—21no—
287D4×C127—21no—
288D4×C127—21no—
289D4×C127—21no—
290D4×C127—42no—
291D4×C127—44no—
292D4×C127—42no—
293D4×C127—82no—
294D4×C127#13512yes—
295C2×C4×C127—21no—
296C2×C4×C127—21no—
297C2×C4×C127—21no—
298C2×C4×C127—21no—
299C2×C4×C127—21no—
300C2×C4×C127—21no—
301C2×C4×C127—22no—
302C2×C4×C127—22no—
303C2×C4×C127—21no—
304C2×C4×C127—41no—
305C2×C4×C127—44no—
306C2×C4×C127—42no—
307C2×C4×C127—41no—
308C2×C4×C127—41no—
309C2×C4×C127—41no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—41no—
313C2×C4×C127—42no—
314C2×C4×C127—42no—
315C2×C4×C127—42no—
316C2×C4×C127—41no—
317C2×C4×C127—41no—
318C2×C4×C127—81no—
319C2×C4×C127—82no—
320C2×C4×C127#12011yescharacteristic
321C2×C4×C127#12011yescharacteristic
322C2×C4×C127#12011yescharacteristic
323C2×C4×C127#13512yes—
324C2×C4×C127#13712yes—
325C2×C4×C127C22×D411yescharacteristic
326C2×C4×C127C22×D411yescharacteristic
327C2×C4×C127C22×D411yescharacteristic
328C8×C127—22no—
329C8×C127—41no—
330C8×C127—41no—
331C8×C127—41no—
332C8×C127—41no—
333C8×C127—41no—
334C22×C127—21no—
335C22×C127—21no—
336C22×C127—22no—
337C22×C127—41no—
338C22×C127—41no—
339C22×C127—41no—
340C22×C127—41no—
341C22×C127—41no—
342C22×C127—41no—
343C22×C127—41no—
344C22×C127—41no—
345C22×C127—84no—
346C22×C127#45212yes—
347C22×C127C2×#12011yescharacteristic
348C4×C127—21no—
349C4×C127—21no—
350C4×C127—21no—
351C4×C127—41no—
352C4×C127—41no—
353C4×C127—41no—
354C4×C127—41no—
355C4×C127—42no—
356C4×C127—41no—
357C4×C127—42no—
358C4×C127—81no—
359C4×C127—81no—
360C4×C127#45212yes—
361C4×C127C2×#13511yescharacteristic
362C4×C127C2×#13511yescharacteristic
363C4×C127C2×#13711yescharacteristic
364C4×C127#57511yescharacteristic
365#18523C12711yesmaximal, characteristic, direct product factor, Sylow
366C2×C127—22no—
367C2×C127—42no—
368C2×C127—81no—
369C2×C127—81no—
370C2×C127C2×#45211yescharacteristic
371C2×C127#300211yescharacteristic
372C2×C127#301811yescharacteristic
373#3475C2×C12711yescharacteristic
374#3170C2×C12711yescharacteristic, complemented
375#3101C2×C12711yescharacteristic, complemented
376#3076C2×C12711yescharacteristic, complemented
377#1650C2×C12711yescharacteristic, complemented
378#1647C2×C12711yescharacteristic, complemented
379#1646C2×C12711yescharacteristic, complemented
380#1643C2×C12711yescharacteristic, complemented
381#1638C2×C12711yescharacteristic, complemented
382#1635C2×C12711yescharacteristic, complemented
383#1634C2×C12711yescharacteristic, complemented
384#1632C2×C12711yescharacteristic, complemented
385#1542C2×C12711yescharacteristic, complemented
386#1476C2×C12711yescharacteristic, complemented
387C2×D4⋊C8C2×C12711yescharacteristic, complemented
388C127#1852311yescharacteristic, direct product factor, Sylow
389#556C22×C12711yescharacteristic
390#555C22×C12711yescharacteristic
391#554C22×C12711yescharacteristic
392#553—21no—
393#552—21no—
394#552—21no—
395#551—22no—
396#547C22×C12711yescharacteristic
397#546—21no—
398#533C22×C12711yescharacteristic
399#533C22×C12711yescharacteristic
400#529—22no—
401#529—21no—
402#525—21no—
403C4×#41—21no—
404C4×#41C22×C12711yescharacteristic
405C2×C4×D4C22×C12711yescharacteristic
406C2×#117—21no—
407#500C22×C12711yescharacteristic, complemented
408#494C22×C12711yescharacteristic, complemented
409#487C22×C12711yescharacteristic, complemented
410#487C22×C12711yescharacteristic, complemented
411#483—21no—
412#479—21no—
413#478—21no—
414#477C22×C12711yescharacteristic, complemented
415#476C22×C12711yescharacteristic
416#476C22×C12711yescharacteristic
417#476C22×C12711yescharacteristic, complemented
418#475C22×C12711yescharacteristic, complemented
419#474C22×C12711yescharacteristic, complemented
420#467—22no—
421#461C22×C12711yescharacteristic
422#461C22×C12711yescharacteristic
423#450—21no—
424C4×Q16—22no—
425C4×SD16—21no—
426C4×SD16—21no—
427#431C22×C12711yescharacteristic
428#427—21no—
429C2×C4⋊C8C22×C12711yescharacteristic
430#416—21no—
431C2×C4×C8C22×C12711yescharacteristic
432#333C22×C12711yescharacteristic, complemented
433#333C22×C12711yescharacteristic, complemented
434#332C22×C12711yescharacteristic, complemented
435#332C22×C12711yescharacteristic, complemented
436Q8⋊C8C22×C12711yescharacteristic, complemented
437Q8⋊C8C22×C12711yescharacteristic, complemented
438D4⋊C8C22×C12711yescharacteristic
439D4⋊C8C22×C12711yescharacteristic
440D4⋊C8C22×C12711yescharacteristic
441D4⋊C8C22×C12711yescharacteristic
442D4⋊C8C22×C12711yescharacteristic, complemented
443D4⋊C8C22×C12711yescharacteristic, complemented
444C2×#41—21no—
445C2×#41D4×C12711yescharacteristic
446C22×D4D4×C12711yescharacteristic
447C23×C4—21no—
448C2×Q16—22no—
449C2×SD16—21no—
450C2×SD16—21no—
451C22×C8—21no—
452C22×C8—21no—
453C4⋊Q8C23×C12711yescharacteristic
454C4⋊Q8C23×C12711yescharacteristic
455C4⋊Q8C23×C12711yescharacteristic
456C4⋊Q8C23×C12711yescharacteristic
457#126—22no—
458#126—22no—
459#126—22no—
460#125—22no—
461#125—21no—
462#125—21no—
463#125—21no—
464#124—22no—
465#124—21no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—22no—
473C22⋊Q8—21no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8D4×C12712yes—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#120—22no—
483C4×Q8—21no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8D4×C12711yescharacteristic
488C4×Q8D4×C12712yes—
489C4×Q8C23×C12711yescharacteristic
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4D4×C12711yescharacteristic
499C4×D4D4×C12711yescharacteristic
500C4×D4D4×C12711yescharacteristic
501C4×D4C23×C12711yescharacteristic
502C4×D4C23×C12711yescharacteristic
503C4×D4C23×C12711yescharacteristic
504#117—22no—
505#117—22no—
506#117—22no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117D4×C12711yescharacteristic
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4D4×C12711yescharacteristic
517C2×C22⋊C4—22no—
518C2×C22⋊C4—21no—
519C2×C42—22no—
520C2×C42—21no—
521C2×C42C23×C12711yescharacteristic
522#107—21no—
523#107—21no—
524#107—22no—
525#106—21no—
526#106—21no—
527#106—21no—
528#106—21no—
529C4⋊C8—21no—
530C4⋊C8C23×C12711yescharacteristic
531C4⋊C8C23×C12711yescharacteristic
532C4⋊C8C23×C12711yescharacteristic
533C4⋊C8C23×C12711yescharacteristic
534#103—21no—
535#103—21no—
536#103—22no—
537#103—21no—
538#103—21no—
539#103—22no—
540#102—21no—
541#102—21no—
542#102—21no—
543#102—21no—
544C22⋊C8—21no—
545C4×C8—21no—
546C4×C8—21no—
547C4×C8C23×C12711yescharacteristic
548C4×C8C23×C12711yescharacteristic
549C24—21no—
550#41—22no—
551#41—22no—
552#41—42no—
553#41—42no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C2×D4×C12711yescharacteristic
558C2×Q8C2×D4×C12712yes—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—41no—
565C2×D4C2×D4×C12711yescharacteristic
566C2×D4C2×D4×C12711yescharacteristic
567C2×D4C2×D4×C12711yescharacteristic
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4C2×D4×C12711yescharacteristic
581C22×C4C2×D4×C12711yescharacteristic
582C22×C4C2×D4×C12711yescharacteristic
583Q16—44no—
584SD16—42no—
585SD16—42no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—42no—
593C2×C8—42no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4C2×D4×C12711yescharacteristic
613C4⋊C4C2×D4×C12711yescharacteristic
614C4⋊C4C2×D4×C12712yes—
615C4⋊C4C2×D4×C12711yescharacteristic
616C4⋊C4C2×D4×C12711yescharacteristic
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—21no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—41no—
632C42—22no—
633C42—22no—
634C42—21no—
635C42—22no—
636C42—21no—
637C42—21no—
638C42—41no—
639C42C2×D4×C12711yescharacteristic
640C42C2×D4×C12711yescharacteristic
641C42C2×D4×C12711yescharacteristic
642C42C24×C12711yescharacteristic
643C23—21no—
644C23—21no—
645C23—21no—
646C23—42no—
647C23—42no—
648C23—81no—
649C23#120×C12711yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—42no—
653Q8—42no—
654Q8—41no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—42no—
664D4—44no—
665D4—42no—
666D4—82no—
667D4#135×C12712yes—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—81no—
692C2×C4—82no—
693C2×C4#120×C12711yescharacteristic
694C2×C4#120×C12711yescharacteristic
695C2×C4#120×C12711yescharacteristic
696C2×C4#135×C12712yes—
697C2×C4#137×C12712yes—
698C2×C4C22×D4×C12711yescharacteristic
699C2×C4C22×D4×C12711yescharacteristic
700C2×C4C22×D4×C12711yescharacteristic
701C8—22no—
702C8—41no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—41no—
707C22—21no—
708C22—21no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—84no—
719C22#452×C12712yes—
720C22C2×#120×C12711yescharacteristic
721C4—21no—
722C4—21no—
723C4—21no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4#452×C12712yes—
734C4C2×#135×C12711yescharacteristic
735C4C2×#135×C12711yescharacteristic
736C4C2×#137×C12711yescharacteristic
737C4#575×C12711yescharacteristic
738C2—22no—
739C2—42no—
740C2—81no—
741C2—81no—
742C2C2×#452×C12711yescharacteristic
743C2C127×#300211yescharacteristic
744C2C127×#301811yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutator, Frattini, cosocleC42C24×C127
socleC22×C127C2×#120
prime radicalC127×#3475C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3170C2semidirect
3. C127×#3101C2semidirect
4. C127×#3076C2semidirect
5. C127×#1650C2semidirect
6. C127×#1647C2semidirect
7. C127×#1646C2semidirect
8. C127×#1643C2semidirect
9. C127×#1638C2semidirect
10. C127×#1635C2semidirect
11. C127×#1634C2semidirect
12. C127×#1632C2semidirect
13. C127×#1542C2semidirect
14. C127×#1476C2semidirect
15. C2×D4⋊C8×C127C2semidirect
34. #500×C127C22semidirect
35. #494×C127C22semidirect
36. #487×C127C22semidirect
37. #487×C127C22semidirect
41. #477×C127C22semidirect
44. #476×C127C22semidirect
45. #475×C127C22semidirect
46. #474×C127C22semidirect
59. #333×C127C22semidirect
60. #333×C127C22semidirect
61. #332×C127C22semidirect
62. #332×C127C22semidirect
63. Q8⋊C8×C127C22semidirect
64. Q8⋊C8×C127C22semidirect
69. D4⋊C8×C127C22semidirect
70. D4⋊C8×C127C22semidirect
365. #18523C127direct (N × H)
374. #3170C2×C127semidirect
375. #3101C2×C127semidirect
376. #3076C2×C127semidirect
377. #1650C2×C127semidirect
378. #1647C2×C127semidirect
379. #1646C2×C127semidirect
380. #1643C2×C127semidirect
381. #1638C2×C127semidirect
382. #1635C2×C127semidirect
383. #1634C2×C127semidirect
384. #1632C2×C127semidirect
385. #1542C2×C127semidirect
386. #1476C2×C127semidirect
387. C2×D4⋊C8C2×C127semidirect
388. C127#18523direct (N × H)
407. #500C22×C127semidirect
408. #494C22×C127semidirect
409. #487C22×C127semidirect
410. #487C22×C127semidirect
414. #477C22×C127semidirect
417. #476C22×C127semidirect
418. #475C22×C127semidirect
419. #474C22×C127semidirect
432. #333C22×C127semidirect
433. #333C22×C127semidirect
434. #332C22×C127semidirect
435. #332C22×C127semidirect
436. Q8⋊C8C22×C127semidirect
437. Q8⋊C8C22×C127semidirect
442. D4⋊C8C22×C127semidirect
443. D4⋊C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34752
C127×#31702
C127×#31012
C127×#30762
C127×#16502
C127×#16472
C127×#16462
C127×#16432
C127×#16382
C127×#16352
C127×#16342
C127×#16322
C127×#15422
C127×#14762
C2×D4⋊C8×C1272
#18523127