Finite Group Databasebeta

← C127×#11023 #44574696

Subgroups — C127×#11023 #44574696

Order 32512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×SD16×C127C211yesmaximal, characteristic
2C22×#103×C127C211yesmaximal, characteristic, complemented
3C22×#102×C127C211yesmaximal, characteristic
4C2×#391×C127C211yesmaximal, characteristic, complemented
5C2×#390×C127C211yesmaximal, characteristic
6C2×#340×C127C211yesmaximal, characteristic, complemented
7C2×#336×C127C211yesmaximal, characteristic, complemented
8C23×Q8×C127C2211yescharacteristic
9C23×D4×C127C2211yescharacteristic
10C22×SD16×C127—22no—
11C22×SD16×C127—22no—
12C22×SD16×C127—22no—
13C22×SD16×C127—22no—
14C22×SD16×C127—22no—
15C22×SD16×C127—22no—
16C22×SD16×C127C414yescomplemented
17C23×C8×C127C2211yescharacteristic
18C23×C8×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127—22no—
22C22×C42×C127C2211yescharacteristic
23C2×#103×C127—22no—
24C2×#103×C127—22no—
25C2×#103×C127—22no—
26C2×#102×C127—22no—
27C2×#102×C127—22no—
28C2×#102×C127—22no—
29#391×C127—22no—
30#391×C127—22no—
31#390×C127—22no—
32#390×C127—22no—
33C2×#95×C127—22no—
34#340×C127—22no—
35#336×C127—22no—
36C25×C127—21no—
37C22×Q8×C127—21no—
38C22×Q8×C127—21no—
39C22×Q8×C127—21no—
40C22×Q8×C127—21no—
41C22×Q8×C127—21no—
42C22×Q8×C127—21no—
43C22×Q8×C127—21no—
44C22×Q8×C127—21no—
45C22×Q8×C127—21no—
46C22×Q8×C127—21no—
47C22×Q8×C127—21no—
48C22×Q8×C127C2×C412yes—
49C22×Q8×C127D412yes—
50C22×Q8×C127D412yes—
51C22×D4×C127—21no—
52C22×D4×C127—21no—
53C22×D4×C127—21no—
54C22×D4×C127—21no—
55C22×D4×C127—21no—
56C22×D4×C127—21no—
57C22×D4×C127—21no—
58C22×D4×C127—21no—
59C22×D4×C127—21no—
60C22×D4×C127—21no—
61C22×D4×C127—21no—
62C22×D4×C127C2×C412yes—
63C22×D4×C127D412yes—
64C22×D4×C127D412yes—
65C23×C4×C127—21no—
66C23×C4×C127—21no—
67C23×C4×C127—21no—
68C23×C4×C127D412yes—
69C23×C4×C127C2311yescharacteristic
70C2×SD16×C127—28no—
71C2×SD16×C127—28no—
72C2×SD16×C127—28no—
73C2×SD16×C127—28no—
74C2×SD16×C127—28no—
75C2×SD16×C127—28no—
76C2×SD16×C127—28no—
77C22×C8×C127—21no—
78C22×C8×C127—21no—
79C22×C8×C127—21no—
80C22×C8×C127—21no—
81C22×C8×C127—21no—
82C22×C8×C127—21no—
83C22×C8×C127—21no—
84C22×C8×C127—21no—
85C22×C8×C127—21no—
86C22×C8×C127—21no—
87C22×C8×C127C2×C412yes—
88C22×C8×C127D412yes—
89C22×C8×C127D412yes—
90C22×C8×C127D412yes—
91C2×C4⋊C4×C127—21no—
92C2×C4⋊C4×C127—21no—
93C2×C4⋊C4×C127—21no—
94C2×C4⋊C4×C127—21no—
95C2×C4⋊C4×C127—21no—
96C2×C4⋊C4×C127—21no—
97C2×C4⋊C4×C127—21no—
98C2×C4⋊C4×C127—21no—
99C2×C4⋊C4×C127—21no—
100C2×C4⋊C4×C127—21no—
101C2×C4⋊C4×C127D412yes—
102C2×C4⋊C4×C127D412yes—
103C2×C22⋊C4×C127—28no—
104C2×C22⋊C4×C127—44no—
105C2×C22⋊C4×C127—44no—
106C2×C42×C127—21no—
107C2×C42×C127—21no—
108C2×C42×C127—21no—
109C2×C42×C127—21no—
110C2×C42×C127—21no—
111C2×C42×C127—21no—
112#103×C127—28no—
113#102×C127—28no—
114#95×C127—28no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—22no—
118C24×C127—41no—
119C24×C127—41no—
120C24×C127—41no—
121C24×C127—41no—
122C24×C127—42no—
123C24×C127—42no—
124C24×C127—42no—
125C24×C127—42no—
126C24×C127C2×D411yescharacteristic
127C2×Q8×C127—22no—
128C2×Q8×C127—22no—
129C2×Q8×C127—22no—
130C2×Q8×C127—22no—
131C2×Q8×C127—22no—
132C2×Q8×C127—22no—
133C2×Q8×C127—22no—
134C2×Q8×C127—22no—
135C2×Q8×C127—22no—
136C2×Q8×C127—22no—
137C2×Q8×C127—22no—
138C2×Q8×C127—22no—
139C2×Q8×C127—22no—
140C2×Q8×C127—22no—
141C2×Q8×C127—22no—
142C2×Q8×C127—41no—
143C2×Q8×C127—41no—
144C2×Q8×C127—41no—
145C2×Q8×C127—41no—
146C2×Q8×C127—41no—
147C2×Q8×C127—41no—
148C2×Q8×C127—41no—
149C2×Q8×C127—41no—
150C2×Q8×C127—41no—
151C2×Q8×C127—41no—
152C2×Q8×C127—41no—
153C2×Q8×C127—41no—
154C2×Q8×C127C22⋊C414yescomplemented
155C2×D4×C127—22no—
156C2×D4×C127—22no—
157C2×D4×C127—22no—
158C2×D4×C127—22no—
159C2×D4×C127—22no—
160C2×D4×C127—22no—
161C2×D4×C127—22no—
162C2×D4×C127—22no—
163C2×D4×C127—22no—
164C2×D4×C127—22no—
165C2×D4×C127—22no—
166C2×D4×C127—22no—
167C2×D4×C127—22no—
168C2×D4×C127—22no—
169C2×D4×C127—22no—
170C2×D4×C127—41no—
171C2×D4×C127—41no—
172C2×D4×C127—41no—
173C2×D4×C127—41no—
174C2×D4×C127—41no—
175C2×D4×C127—41no—
176C2×D4×C127—41no—
177C2×D4×C127—41no—
178C2×D4×C127—41no—
179C2×D4×C127—41no—
180C2×D4×C127—41no—
181C2×D4×C127—41no—
182C2×D4×C127C22⋊C414yes—
183C22×C4×C127—22no—
184C22×C4×C127—22no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
188C22×C4×C127—22no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127—22no—
192C22×C4×C127—22no—
193C22×C4×C127—22no—
194C22×C4×C127—41no—
195C22×C4×C127—41no—
196C22×C4×C127—41no—
197C22×C4×C127—41no—
198C22×C4×C127—41no—
199C22×C4×C127—41no—
200C22×C4×C127—41no—
201C22×C4×C127—41no—
202C22×C4×C127—42no—
203C22×C4×C127—42no—
204C22×C4×C127—42no—
205C22×C4×C127—42no—
206C22×C4×C127SD1614yescomplemented
207C22×C4×C127C22×C411yescharacteristic
208C22×C4×C127C2×D411yescharacteristic
209C22×C4×C127C2×D411yescharacteristic
210C22×C4×C127C2×D411yescharacteristic
211C22×C4×C127C2×D411yescharacteristic
212C22×C4×C127C2×D411yescharacteristic
213C22×C4×C127C2×D411yescharacteristic
214C22×C4×C127C2×D411yescharacteristic
215C22×C4×C127C2×D411yescharacteristic
216C22×C4×C127C2×D411yescharacteristic
217C22×C4×C127#4111yescharacteristic
218C22×C4×C127#4111yescharacteristic
219C22×C4×C127#4111yescharacteristic
220C22×C4×C127#4111yescharacteristic
221SD16×C127—232no—
222C2×C8×C127—22no—
223C2×C8×C127—22no—
224C2×C8×C127—22no—
225C2×C8×C127—22no—
226C2×C8×C127—22no—
227C2×C8×C127—22no—
228C2×C8×C127—22no—
229C2×C8×C127—22no—
230C2×C8×C127—22no—
231C2×C8×C127—41no—
232C2×C8×C127—41no—
233C2×C8×C127—41no—
234C2×C8×C127—41no—
235C2×C8×C127C22⋊C414yescomplemented
236C4⋊C4×C127—22no—
237C4⋊C4×C127—22no—
238C4⋊C4×C127—22no—
239C4⋊C4×C127—22no—
240C4⋊C4×C127—41no—
241C4⋊C4×C127—41no—
242C4⋊C4×C127—41no—
243C4⋊C4×C127—41no—
244C22⋊C4×C127—416no—
245C42×C127—41no—
246C42×C127—41no—
247C42×C127—41no—
248C42×C127—41no—
249C23×C127—24no—
250C23×C127—42no—
251C23×C127—42no—
252C23×C127—42no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127—42no—
256C23×C127—44no—
257C23×C127—44no—
258C23×C127—44no—
259C23×C127—44no—
260C23×C127—44no—
261C23×C127—44no—
262C23×C127—82no—
263C23×C127—82no—
264C23×C127—82no—
265C23×C127—82no—
266C23×C127—82no—
267C23×C127—82no—
268C23×C127—81no—
269C23×C127—81no—
270C23×C127—81no—
271C23×C127—81no—
272C23×C127C4×D411yescharacteristic
273C23×C127#12011yescharacteristic
274C23×C127#12011yescharacteristic
275C23×C127#12111yescharacteristic
276C23×C127#12111yescharacteristic
277C23×C127#12111yescharacteristic
278C23×C127#12711yescharacteristic
279C23×C127C2×SD1612yes—
280C23×C127#13512yes—
281C23×C127AGL(1,ℤ/8)12yes—
282C23×C127#13712yes—
283Q8×C127—24no—
284Q8×C127—24no—
285Q8×C127—42no—
286Q8×C127—42no—
287Q8×C127—42no—
288Q8×C127—42no—
289Q8×C127—42no—
290Q8×C127—42no—
291D4×C127—24no—
292D4×C127—24no—
293D4×C127—42no—
294D4×C127—42no—
295D4×C127—42no—
296D4×C127—42no—
297D4×C127—42no—
298D4×C127—42no—
299C2×C4×C127—24no—
300C2×C4×C127—24no—
301C2×C4×C127—24no—
302C2×C4×C127—24no—
303C2×C4×C127—42no—
304C2×C4×C127—42no—
305C2×C4×C127—42no—
306C2×C4×C127—42no—
307C2×C4×C127—42no—
308C2×C4×C127—42no—
309C2×C4×C127—42no—
310C2×C4×C127—42no—
311C2×C4×C127—42no—
312C2×C4×C127—42no—
313C2×C4×C127—42no—
314C2×C4×C127—42no—
315C2×C4×C127—44no—
316C2×C4×C127—44no—
317C2×C4×C127—82no—
318C2×C4×C127—82no—
319C2×C4×C127—81no—
320C2×C4×C127—81no—
321C2×C4×C127—81no—
322C2×C4×C127—81no—
323C2×C4×C127C2×C22⋊C411yescharacteristic
324C2×C4×C127C2×C22⋊C411yescharacteristic
325C2×C4×C127C2×C22⋊C411yescharacteristic
326C2×C4×C127C4×D411yescharacteristic
327C2×C4×C127C4×D411yescharacteristic
328C2×C4×C127C4×D411yescharacteristic
329C2×C4×C127#12011yescharacteristic
330C2×C4×C127#12011yescharacteristic
331C2×C4×C127#12011yescharacteristic
332C2×C4×C127#12011yescharacteristic
333C2×C4×C127#12011yescharacteristic
334C2×C4×C127#12011yescharacteristic
335C2×C4×C127#12111yescharacteristic
336C2×C4×C127#12111yescharacteristic
337C2×C4×C127#12111yescharacteristic
338C2×C4×C127#12111yescharacteristic
339C2×C4×C127#12111yescharacteristic
340C2×C4×C127#12111yescharacteristic
341C2×C4×C127#12111yescharacteristic
342C2×C4×C127#12111yescharacteristic
343C2×C4×C127#12111yescharacteristic
344C2×C4×C127#12311yescharacteristic
345C2×C4×C127#12311yescharacteristic
346C2×C4×C127#12311yescharacteristic
347C2×C4×C127#12311yescharacteristic
348C2×C4×C127#12411yescharacteristic
349C2×C4×C127#12411yescharacteristic
350C2×C4×C127#12711yescharacteristic
351C8×C127—24no—
352C8×C127—42no—
353C22×C127—48no—
354C22×C127—44no—
355C22×C127—84no—
356C22×C127—84no—
357C22×C127—82no—
358C22×C127—82no—
359C22×C127—84no—
360C22×C127—82no—
361C22×C127—82no—
362C22×C127—82no—
363C22×C127—82no—
364C22×C127#38611yescharacteristic
365C22×C127#38611yescharacteristic
366C22×C127#39011yescharacteristic
367C22×C127#39211yescharacteristic
368C22×C127#39211yescharacteristic
369C22×C127#39211yescharacteristic
370C22×C127#39411yescharacteristic
371C22×C127C4×SD1612yes—
372C22×C127#44012yes—
373C22×C127#44812yes—
374C22×C127#44912yes—
375C22×C127#45012yes—
376C22×C127#45212yes—
377C22×C127#46012yes—
378C22×C127#46112yes—
379C22×C127#46312yes—
380C22×C127#46412yes—
381C22×C127#46512yes—
382C22×C127#46812yes—
383C22×C127#49211yescharacteristic
384C22×C127#49511yescharacteristic
385C22×C127#49611yescharacteristic
386C22×C127#49711yescharacteristic
387C4×C127—44no—
388C4×C127—44no—
389C4×C127—82no—
390C4×C127—82no—
391C4×C127#37911yescharacteristic
392C4×C127#38611yescharacteristic
393C4×C127#38611yescharacteristic
394C4×C127#39011yescharacteristic
395C4×C127#39211yescharacteristic
396C4×C127#39411yescharacteristic
397C4×C127#39411yescharacteristic
398C4×C127#39411yescharacteristic
399#11023C12711yesmaximal, characteristic, direct product factor, Sylow
400C2×C127—84no—
401C2×C127#143811yescharacteristic
402C2×C127#187712yes—
403C2×C127#188012yes—
404C2×C127#196811yescharacteristic
405C2×C127#197311yescharacteristic
406C2×C127#200012yes—
407C2×C127#201211yescharacteristic
408C2×C127#201311yescharacteristic
409C2×C127#201411yescharacteristic
410C2×C127#201511yescharacteristic
411C2×C127#205512yes—
412C23×SD16C2×C12711yescharacteristic
413C22×#103C2×C12711yescharacteristic, complemented
414C22×#102C2×C12711yescharacteristic
415C2×#391C2×C12711yescharacteristic, complemented
416C2×#390C2×C12711yescharacteristic
417C2×#340C2×C12711yescharacteristic, complemented
418C2×#336C2×C12711yescharacteristic, complemented
419C127#1102311yescharacteristic, direct product factor, Sylow
420C23×Q8C22×C12711yescharacteristic
421C23×D4C22×C12711yescharacteristic
422C22×SD16—22no—
423C22×SD16—22no—
424C22×SD16—22no—
425C22×SD16—22no—
426C22×SD16—22no—
427C22×SD16—22no—
428C22×SD16C4×C12714yescomplemented
429C23×C8C22×C12711yescharacteristic
430C23×C8C22×C12711yescharacteristic
431C22×C4⋊C4C22×C12711yescharacteristic
432C22×C4⋊C4C22×C12711yescharacteristic
433C22×C22⋊C4—22no—
434C22×C42C22×C12711yescharacteristic
435C2×#103—22no—
436C2×#103—22no—
437C2×#103—22no—
438C2×#102—22no—
439C2×#102—22no—
440C2×#102—22no—
441#391—22no—
442#391—22no—
443#390—22no—
444#390—22no—
445C2×#95—22no—
446#340—22no—
447#336—22no—
448C25—21no—
449C22×Q8—21no—
450C22×Q8—21no—
451C22×Q8—21no—
452C22×Q8—21no—
453C22×Q8—21no—
454C22×Q8—21no—
455C22×Q8—21no—
456C22×Q8—21no—
457C22×Q8—21no—
458C22×Q8—21no—
459C22×Q8—21no—
460C22×Q8C2×C4×C12712yes—
461C22×Q8D4×C12712yes—
462C22×Q8D4×C12712yes—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4C2×C4×C12712yes—
475C22×D4D4×C12712yes—
476C22×D4D4×C12712yes—
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4D4×C12712yes—
481C23×C4C23×C12711yescharacteristic
482C2×SD16—28no—
483C2×SD16—28no—
484C2×SD16—28no—
485C2×SD16—28no—
486C2×SD16—28no—
487C2×SD16—28no—
488C2×SD16—28no—
489C22×C8—21no—
490C22×C8—21no—
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—21no—
498C22×C8—21no—
499C22×C8C2×C4×C12712yes—
500C22×C8D4×C12712yes—
501C22×C8D4×C12712yes—
502C22×C8D4×C12712yes—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4D4×C12712yes—
514C2×C4⋊C4D4×C12712yes—
515C2×C22⋊C4—28no—
516C2×C22⋊C4—44no—
517C2×C22⋊C4—44no—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524#103—28no—
525#102—28no—
526#95—28no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24—41no—
534C24—42no—
535C24—42no—
536C24—42no—
537C24—42no—
538C24C2×D4×C12711yescharacteristic
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×Q8—41no—
563C2×Q8—41no—
564C2×Q8—41no—
565C2×Q8—41no—
566C2×Q8C22⋊C4×C12714yescomplemented
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4C22⋊C4×C12714yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4SD16×C12714yescomplemented
619C22×C4C22×C4×C12711yescharacteristic
620C22×C4C2×D4×C12711yescharacteristic
621C22×C4C2×D4×C12711yescharacteristic
622C22×C4C2×D4×C12711yescharacteristic
623C22×C4C2×D4×C12711yescharacteristic
624C22×C4C2×D4×C12711yescharacteristic
625C22×C4C2×D4×C12711yescharacteristic
626C22×C4C2×D4×C12711yescharacteristic
627C22×C4C2×D4×C12711yescharacteristic
628C22×C4C2×D4×C12711yescharacteristic
629C22×C4#41×C12711yescharacteristic
630C22×C4#41×C12711yescharacteristic
631C22×C4#41×C12711yescharacteristic
632C22×C4#41×C12711yescharacteristic
633SD16—232no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8C22⋊C4×C12714yescomplemented
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C22⋊C4—416no—
657C42—41no—
658C42—41no—
659C42—41no—
660C42—41no—
661C23—24no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—81no—
675C23—81no—
676C23—82no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23—82no—
681C23—82no—
682C23—81no—
683C23—81no—
684C23C4×D4×C12711yescharacteristic
685C23#120×C12711yescharacteristic
686C23#120×C12711yescharacteristic
687C23#121×C12711yescharacteristic
688C23#121×C12711yescharacteristic
689C23#121×C12711yescharacteristic
690C23#127×C12711yescharacteristic
691C23C2×SD16×C12712yes—
692C23#135×C12712yes—
693C23AGL(1,ℤ/8)×C12712yes—
694C23#137×C12712yes—
695Q8—24no—
696Q8—24no—
697Q8—42no—
698Q8—42no—
699Q8—42no—
700Q8—42no—
701Q8—42no—
702Q8—42no—
703D4—24no—
704D4—24no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4C2×C22⋊C4×C12711yescharacteristic
736C2×C4C2×C22⋊C4×C12711yescharacteristic
737C2×C4C2×C22⋊C4×C12711yescharacteristic
738C2×C4C4×D4×C12711yescharacteristic
739C2×C4C4×D4×C12711yescharacteristic
740C2×C4C4×D4×C12711yescharacteristic
741C2×C4#120×C12711yescharacteristic
742C2×C4#120×C12711yescharacteristic
743C2×C4#120×C12711yescharacteristic
744C2×C4#120×C12711yescharacteristic
745C2×C4#120×C12711yescharacteristic
746C2×C4#120×C12711yescharacteristic
747C2×C4#121×C12711yescharacteristic
748C2×C4#121×C12711yescharacteristic
749C2×C4#121×C12711yescharacteristic
750C2×C4#121×C12711yescharacteristic
751C2×C4#121×C12711yescharacteristic
752C2×C4#121×C12711yescharacteristic
753C2×C4#121×C12711yescharacteristic
754C2×C4#121×C12711yescharacteristic
755C2×C4#121×C12711yescharacteristic
756C2×C4#123×C12711yescharacteristic
757C2×C4#123×C12711yescharacteristic
758C2×C4#123×C12711yescharacteristic
759C2×C4#123×C12711yescharacteristic
760C2×C4#124×C12711yescharacteristic
761C2×C4#124×C12711yescharacteristic
762C2×C4#127×C12711yescharacteristic
763C8—24no—
764C8—42no—
765C22—48no—
766C22—44no—
767C22—84no—
768C22—82no—
769C22—82no—
770C22—84no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—84no—
776C22#386×C12711yescharacteristic
777C22#386×C12711yescharacteristic
778C22#390×C12711yescharacteristic
779C22#392×C12711yescharacteristic
780C22#392×C12711yescharacteristic
781C22#392×C12711yescharacteristic
782C22#394×C12711yescharacteristic
783C22C4×SD16×C12712yes—
784C22#440×C12712yes—
785C22#448×C12712yes—
786C22#449×C12712yes—
787C22#450×C12712yes—
788C22#452×C12712yes—
789C22#460×C12712yes—
790C22#461×C12712yes—
791C22#463×C12712yes—
792C22#464×C12712yes—
793C22#465×C12712yes—
794C22#468×C12712yes—
795C22#492×C12711yescharacteristic
796C22#495×C12711yescharacteristic
797C22#496×C12711yescharacteristic
798C22#497×C12711yescharacteristic
799C4—44no—
800C4—44no—
801C4—82no—
802C4—82no—
803C4#379×C12711yescharacteristic
804C4#386×C12711yescharacteristic
805C4#386×C12711yescharacteristic
806C4#390×C12711yescharacteristic
807C4#392×C12711yescharacteristic
808C4#394×C12711yescharacteristic
809C4#394×C12711yescharacteristic
810C4#394×C12711yescharacteristic
811C2—84no—
812C2C127×#143811yescharacteristic
813C2C127×#187712yes—
814C2C127×#188012yes—
815C2C127×#196811yescharacteristic
816C2C127×#197311yescharacteristic
817C2C127×#200012yes—
818C2C127×#201211yescharacteristic
819C2C127×#201311yescharacteristic
820C2C127×#201411yescharacteristic
821C2C127×#201511yescharacteristic
822C2C127×#205512yes—
subgroupG/H
center, socleC24×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC23×D4×C127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#103×C127C2semidirect
4. C2×#391×C127C2semidirect
6. C2×#340×C127C2semidirect
7. C2×#336×C127C2semidirect
16. C22×SD16×C127C4semidirect
154. C2×Q8×C127C22⋊C4semidirect
206. C22×C4×C127SD16semidirect
235. C2×C8×C127C22⋊C4semidirect
399. #11023C127direct (N × H)
413. C22×#103C2×C127semidirect
415. C2×#391C2×C127semidirect
417. C2×#340C2×C127semidirect
418. C2×#336C2×C127semidirect
419. C127#11023direct (N × H)
428. C22×SD16C4×C127semidirect
566. C2×Q8C22⋊C4×C127semidirect
618. C22×C4SD16×C127semidirect
647. C2×C8C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×SD16×C1272
C22×#103×C1272
C22×#102×C1272
C2×#391×C1272
C2×#390×C1272
C2×#340×C1272
C2×#336×C1272
#11023127