Finite Group Databasebeta

← C127×#14765 #44578438

Subgroups — C127×#14765 #44578438

Order 32512.

2154 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
2C2×#393×C127C211yesmaximal, characteristic, complemented
3C2×#388×C127C212yesmaximal, complemented
4C2×#386×C127C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
6C127×#1446C211yesmaximal, characteristic, complemented
7C127×#1442C211yesmaximal, characteristic, complemented
8C127×#1440C212yesmaximal, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1438C212yesmaximal
11C127×#1436C212yesmaximal, complemented
12C23×Q8×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C2×C22⋊Q8×C127—24no—
16C2×C22⋊Q8×C127—28no—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2212yes—
26C22×C42×C127C2212yes—
27#393×C127—24no—
28#388×C127—28no—
29#386×C127—24no—
30C4×C22⋊C4×C127—24no—
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2212yes—
40C2×#95×C127C2211yescharacteristic
41C25×C127C2311yescharacteristic
42C25×C127C2311yescharacteristic
43C22×Q8×C127—24no—
44C22×Q8×C127—22no—
45C22×Q8×C127—22no—
46C22×Q8×C127—22no—
47C22×Q8×C127—42no—
48C22×D4×C127—22no—
49C22×D4×C127—22no—
50C22×D4×C127—24no—
51C22×D4×C127—22no—
52C22×D4×C127—42no—
53C23×C4×C127—24no—
54C23×C4×C127—22no—
55C23×C4×C127—22no—
56C23×C4×C127—42no—
57C23×C4×C127D414yes—
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2312yes—
61C23×C4×C127C2312yes—
62C23×C4×C127C2312yes—
63C23×C4×C127C2312yes—
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C22⋊Q8×C127—232no—
68C2×C4⋊C4×C127—24no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—24no—
71C2×C4⋊C4×C127—24no—
72C2×C4⋊C4×C127D418yescomplemented
73C2×C22⋊C4×C127—24no—
74C2×C22⋊C4×C127—24no—
75C2×C22⋊C4×C127—24no—
76C2×C22⋊C4×C127—24no—
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127—24no—
79C2×C22⋊C4×C127—24no—
80C2×C22⋊C4×C127—24no—
81C2×C22⋊C4×C127—24no—
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127—24no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—24no—
87C2×C22⋊C4×C127—24no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—42no—
92C2×C42×C127—24no—
93C2×C42×C127—24no—
94C2×C42×C127—42no—
95#95×C127—22no—
96#95×C127—22no—
97#95×C127—22no—
98#95×C127—24no—
99#95×C127—24no—
100#95×C127—24no—
101#95×C127—24no—
102#95×C127—24no—
103#95×C127—42no—
104#95×C127D414yescomplemented
105C24×C127—22no—
106C24×C127—21no—
107C24×C127—22no—
108C24×C127—21no—
109C24×C127—21no—
110C24×C127—21no—
111C24×C127—22no—
112C24×C127—21no—
113C24×C127—21no—
114C24×C127—22no—
115C24×C127—21no—
116C24×C127—21no—
117C24×C127—22no—
118C24×C127—21no—
119C24×C127—21no—
120C24×C127—22no—
121C24×C127—22no—
122C24×C127—21no—
123C24×C127—21no—
124C24×C127C2×D412yes—
125C24×C127#4112yes—
126C24×C127#4114yes—
127C24×C127C2411yescharacteristic
128C2×Q8×C127—28no—
129C2×Q8×C127—48no—
130C2×Q8×C127—48no—
131C2×Q8×C127—44no—
132C2×Q8×C127—44no—
133C2×D4×C127—28no—
134C2×D4×C127—48no—
135C2×D4×C127—48no—
136C2×D4×C127—44no—
137C2×D4×C127—44no—
138C22×C4×C127—21no—
139C22×C4×C127—22no—
140C22×C4×C127—21no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—21no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—22no—
158C22×C4×C127—22no—
159C22×C4×C127—22no—
160C22×C4×C127—22no—
161C22×C4×C127—21no—
162C22×C4×C127—22no—
163C22×C4×C127—22no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—22no—
167C22×C4×C127—22no—
168C22×C4×C127—22no—
169C22×C4×C127—22no—
170C22×C4×C127—22no—
171C22×C4×C127—28no—
172C22×C4×C127—28no—
173C22×C4×C127—22no—
174C22×C4×C127—21no—
175C22×C4×C127—21no—
176C22×C4×C127—21no—
177C22×C4×C127—22no—
178C22×C4×C127—21no—
179C22×C4×C127—22no—
180C22×C4×C127—22no—
181C22×C4×C127—21no—
182C22×C4×C127—21no—
183C22×C4×C127—44no—
184C22×C4×C127—48no—
185C22×C4×C127—48no—
186C22×C4×C127C2×D414yes—
187C22×C4×C127C2×D414yes—
188C22×C4×C127C2×D414yes—
189C22×C4×C127C2×D412yes—
190C22×C4×C127C2×D414yes—
191C22×C4×C127C2×D412yes—
192C22×C4×C127C2×D412yes—
193C22×C4×C127#4112yes—
194C22×C4×C127#4114yes—
195C22×C4×C127#4112yes—
196C4⋊C4×C127—28no—
197C4⋊C4×C127—216no—
198C22⋊C4×C127—216no—
199C22⋊C4×C127—216no—
200C22⋊C4×C127—216no—
201C22⋊C4×C127—48no—
202C22⋊C4×C127—44no—
203C22⋊C4×C127—44no—
204C22⋊C4×C127—44no—
205C42×C127—48no—
206C23×C127—22no—
207C23×C127—22no—
208C23×C127—24no—
209C23×C127—22no—
210C23×C127—24no—
211C23×C127—22no—
212C23×C127—22no—
213C23×C127—22no—
214C23×C127—24no—
215C23×C127—24no—
216C23×C127—24no—
217C23×C127—24no—
218C23×C127—24no—
219C23×C127—22no—
220C23×C127—22no—
221C23×C127—24no—
222C23×C127—22no—
223C23×C127—42no—
224C23×C127—42no—
225C23×C127—42no—
226C23×C127—42no—
227C23×C127—42no—
228C23×C127—42no—
229C23×C127—41no—
230C23×C127—41no—
231C23×C127—41no—
232C23×C127—41no—
233C23×C127—41no—
234C23×C127—41no—
235C23×C127—42no—
236C23×C127—41no—
237C23×C127—42no—
238C23×C127—42no—
239C23×C127—41no—
240C23×C127—41no—
241C23×C127—41no—
242C23×C127—42no—
243C23×C127—42no—
244C23×C127—42no—
245C23×C127—42no—
246C23×C127—41no—
247C23×C127—42no—
248C23×C127—42no—
249C23×C127—42no—
250C23×C127—41no—
251C23×C127#12414yes—
252C23×C127C22×D411yescharacteristic
253C23×C127C22×D412yes—
254C23×C127C22×D411yescharacteristic
255C23×C127C2×#4111yescharacteristic
256C23×C127C2×#4111yescharacteristic
257C23×C127C2×#4112yes—
258C23×C127C2×#4112yes—
259C23×C127C2×#4111yescharacteristic
260C23×C127H(5,𝔽2)12yes—
261C23×C1272−1+411yescharacteristic
262C23×C1272−1+411yescharacteristic
263Q8×C127—416no—
264D4×C127—416no—
265C2×C4×C127—22no—
266C2×C4×C127—22no—
267C2×C4×C127—22no—
268C2×C4×C127—22no—
269C2×C4×C127—24no—
270C2×C4×C127—24no—
271C2×C4×C127—24no—
272C2×C4×C127—24no—
273C2×C4×C127—24no—
274C2×C4×C127—24no—
275C2×C4×C127—24no—
276C2×C4×C127—24no—
277C2×C4×C127—24no—
278C2×C4×C127—24no—
279C2×C4×C127—22no—
280C2×C4×C127—24no—
281C2×C4×C127—24no—
282C2×C4×C127—24no—
283C2×C4×C127—24no—
284C2×C4×C127—24no—
285C2×C4×C127—24no—
286C2×C4×C127—24no—
287C2×C4×C127—416no—
288C2×C4×C127—42no—
289C2×C4×C127—42no—
290C2×C4×C127—42no—
291C2×C4×C127—41no—
292C2×C4×C127—42no—
293C2×C4×C127—42no—
294C2×C4×C127—42no—
295C2×C4×C127—41no—
296C2×C4×C127—42no—
297C2×C4×C127—42no—
298C2×C4×C127—42no—
299C2×C4×C127—42no—
300C2×C4×C127—42no—
301C2×C4×C127—42no—
302C2×C4×C127—42no—
303C2×C4×C127—42no—
304C2×C4×C127—42no—
305C2×C4×C127—42no—
306C2×C4×C127—42no—
307C2×C4×C127—41no—
308C2×C4×C127—41no—
309C2×C4×C127—42no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—42no—
313C2×C4×C127—41no—
314C2×C4×C127—41no—
315C2×C4×C127—42no—
316C2×C4×C127—42no—
317C2×C4×C127#12014yes—
318C2×C4×C127#12114yes—
319C22×C127—24no—
320C22×C127—24no—
321C22×C127—24no—
322C22×C127—44no—
323C22×C127—42no—
324C22×C127—42no—
325C22×C127—42no—
326C22×C127—42no—
327C22×C127—44no—
328C22×C127—44no—
329C22×C127—44no—
330C22×C127—42no—
331C22×C127—42no—
332C22×C127—42no—
333C22×C127—44no—
334C22×C127—44no—
335C22×C127—82no—
336C22×C127—81no—
337C22×C127—81no—
338C22×C127—81no—
339C22×C127—81no—
340C22×C127—82no—
341C22×C127C2×#12011yescharacteristic
342C22×C127C2×#12111yescharacteristic
343C22×C127#52511yescharacteristic
344C22×C127#52512yes—
345C22×C127#52512yes—
346C22×C127C2×#12411yescharacteristic
347C22×C127#52912yes—
348C22×C127#53212yes—
349C22×C127#53211yescharacteristic
350C22×C127#53411yescharacteristic
351C22×C127#53611yescharacteristic
352C22×C127#53912yes—
353C22×C127#54212yes—
354C22×C127D4212yes—
355C22×C127#54612yes—
356C22×C127#54711yescharacteristic
357C22×C127#54812yes—
358C22×C127#54811yescharacteristic
359C22×C127#54812yes—
360C22×C127#55112yes—
361C22×C127#55112yes—
362C22×C127#55211yescharacteristic
363C22×C127#55611yescharacteristic
364C4×C127—24no—
365C4×C127—24no—
366C4×C127—42no—
367C4×C127—44no—
368C4×C127—44no—
369C4×C127—44no—
370C4×C127—44no—
371C4×C127—81no—
372C4×C127—81no—
373#14765C12711yesmaximal, characteristic, direct product factor, Sylow
374C2×C127—44no—
375C2×C127—82no—
376C2×C127#238811yescharacteristic
377C2×C127#241011yescharacteristic
378C2×C127#241511yescharacteristic
379C2×C127#243611yescharacteristic
380C2×C127#246112yes—
381C2×C127#246312yes—
382C2×C127#247712yes—
383C2×C127#256012yes—
384C2×C127#256111yescharacteristic
385C2×C127#266311yescharacteristic
386C2×C127#285011yescharacteristic
387C22×C22⋊Q8C2×C12711yescharacteristic, complemented
388C2×#393C2×C12711yescharacteristic, complemented
389C2×#388C2×C12712yescomplemented
390C2×#386C2×C12711yescharacteristic
391C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
392#1446C2×C12711yescharacteristic, complemented
393#1442C2×C12711yescharacteristic, complemented
394#1440C2×C12712yescomplemented
395#1439C2×C12711yescharacteristic, complemented
396#1438C2×C12712yes—
397#1436C2×C12712yescomplemented
398C127#1476511yescharacteristic, direct product factor, Sylow
399C23×Q8C22×C12711yescharacteristic
400C23×D4C22×C12711yescharacteristic
401C24×C4C22×C12711yescharacteristic
402C2×C22⋊Q8—24no—
403C2×C22⋊Q8—28no—
404C22×C4⋊C4C22×C12711yescharacteristic
405C22×C4⋊C4C22×C12712yes—
406C22×C22⋊C4C22×C12711yescharacteristic
407C22×C22⋊C4C22×C12712yes—
408C22×C22⋊C4C22×C12712yes—
409C22×C22⋊C4C22×C12712yes—
410C22×C22⋊C4C22×C12711yescharacteristic
411C22×C22⋊C4C22×C12711yescharacteristic
412C22×C22⋊C4C22×C12712yes—
413C22×C42C22×C12712yes—
414#393—24no—
415#388—28no—
416#386—24no—
417C4×C22⋊C4—24no—
418C2×#95C22×C12712yes—
419C2×#95C22×C12711yescharacteristic
420C2×#95C22×C12712yes—
421C2×#95C22×C12712yes—
422C2×#95C22×C12711yescharacteristic
423C2×#95C22×C12712yes—
424C2×#95C22×C12712yes—
425C2×#95C22×C12711yescharacteristic
426C2×#95C22×C12712yes—
427C2×#95C22×C12711yescharacteristic
428C25C23×C12711yescharacteristic
429C25C23×C12711yescharacteristic
430C22×Q8—24no—
431C22×Q8—22no—
432C22×Q8—22no—
433C22×Q8—22no—
434C22×Q8—42no—
435C22×D4—22no—
436C22×D4—22no—
437C22×D4—24no—
438C22×D4—22no—
439C22×D4—42no—
440C23×C4—24no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—42no—
444C23×C4D4×C12714yes—
445C23×C4C23×C12711yescharacteristic
446C23×C4C23×C12711yescharacteristic
447C23×C4C23×C12712yes—
448C23×C4C23×C12712yes—
449C23×C4C23×C12712yes—
450C23×C4C23×C12712yes—
451C23×C4C23×C12711yescharacteristic
452C23×C4C23×C12711yescharacteristic
453C23×C4C23×C12711yescharacteristic
454C22⋊Q8—232no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4D4×C12718yescomplemented
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—42no—
479C2×C42—24no—
480C2×C42—24no—
481C2×C42—42no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—24no—
486#95—24no—
487#95—24no—
488#95—24no—
489#95—24no—
490#95—42no—
491#95D4×C12714yescomplemented
492C24—22no—
493C24—21no—
494C24—22no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—22no—
502C24—21no—
503C24—21no—
504C24—22no—
505C24—21no—
506C24—21no—
507C24—22no—
508C24—22no—
509C24—21no—
510C24—21no—
511C24C2×D4×C12712yes—
512C24#41×C12712yes—
513C24#41×C12714yes—
514C24C24×C12711yescharacteristic
515C2×Q8—28no—
516C2×Q8—48no—
517C2×Q8—48no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×D4—28no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—44no—
524C2×D4—44no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—44no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4C2×D4×C12714yes—
574C22×C4C2×D4×C12714yes—
575C22×C4C2×D4×C12714yes—
576C22×C4C2×D4×C12712yes—
577C22×C4C2×D4×C12714yes—
578C22×C4C2×D4×C12712yes—
579C22×C4C2×D4×C12712yes—
580C22×C4#41×C12712yes—
581C22×C4#41×C12714yes—
582C22×C4#41×C12712yes—
583C4⋊C4—28no—
584C4⋊C4—216no—
585C22⋊C4—216no—
586C22⋊C4—216no—
587C22⋊C4—216no—
588C22⋊C4—48no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C42—48no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—22no—
597C23—24no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—24no—
609C23—22no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—41no—
624C23—42no—
625C23—41no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23#124×C12714yes—
639C23C22×D4×C12711yescharacteristic
640C23C22×D4×C12712yes—
641C23C22×D4×C12711yescharacteristic
642C23C2×#41×C12711yescharacteristic
643C23C2×#41×C12711yescharacteristic
644C23C2×#41×C12712yes—
645C23C2×#41×C12712yes—
646C23C2×#41×C12711yescharacteristic
647C23H(5,𝔽2)×C12712yes—
648C232−1+4×C12711yescharacteristic
649C232−1+4×C12711yescharacteristic
650Q8—416no—
651D4—416no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—416no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4#120×C12714yes—
705C2×C4#121×C12714yes—
706C22—24no—
707C22—24no—
708C22—24no—
709C22—42no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—44no—
714C22—44no—
715C22—44no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—44no—
720C22—44no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—82no—
727C22—82no—
728C22C2×#120×C12711yescharacteristic
729C22C2×#121×C12711yescharacteristic
730C22#525×C12712yes—
731C22#525×C12711yescharacteristic
732C22#525×C12712yes—
733C22C2×#124×C12711yescharacteristic
734C22#529×C12712yes—
735C22#532×C12711yescharacteristic
736C22#532×C12712yes—
737C22#534×C12711yescharacteristic
738C22#536×C12711yescharacteristic
739C22#539×C12712yes—
740C22#542×C12712yes—
741C22D42×C12712yes—
742C22#546×C12712yes—
743C22#547×C12711yescharacteristic
744C22#548×C12711yescharacteristic
745C22#548×C12712yes—
746C22#548×C12712yes—
747C22#551×C12712yes—
748C22#551×C12712yes—
749C22#552×C12711yescharacteristic
750C22#556×C12711yescharacteristic
751C4—24no—
752C4—24no—
753C4—44no—
754C4—44no—
755C4—44no—
756C4—44no—
757C4—42no—
758C4—81no—
759C4—81no—
760C2—44no—
761C2—82no—
762C2C127×#238811yescharacteristic
763C2C127×#241011yescharacteristic
764C2C127×#241511yescharacteristic
765C2C127×#243611yescharacteristic
766C2C127×#246112yes—
767C2C127×#246312yes—
768C2C127×#247712yes—
769C2C127×#256012yes—
770C2C127×#256111yescharacteristic
771C2C127×#266311yescharacteristic
772C2C127×#285011yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊Q8×C127C2semidirect
2. C2×#393×C127C2semidirect
3. C2×#388×C127C2semidirect
5. C2×C4×C22⋊C4×C127C2semidirect
6. C127×#1446C2semidirect
7. C127×#1442C2semidirect
8. C127×#1440C2semidirect
9. C127×#1439C2semidirect
11. C127×#1436C2semidirect
72. C2×C4⋊C4×C127D4semidirect
104. #95×C127D4semidirect
373. #14765C127direct (N × H)
387. C22×C22⋊Q8C2×C127semidirect
388. C2×#393C2×C127semidirect
389. C2×#388C2×C127semidirect
391. C2×C4×C22⋊C4C2×C127semidirect
392. #1446C2×C127semidirect
393. #1442C2×C127semidirect
394. #1440C2×C127semidirect
395. #1439C2×C127semidirect
397. #1436C2×C127semidirect
398. C127#14765direct (N × H)
459. C2×C4⋊C4D4×C127semidirect
491. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C2×#393×C1272
C2×#388×C1272
C2×#386×C1272
C2×C4×C22⋊C4×C1272
C127×#14462
C127×#14422
C127×#14402
C127×#14392
C127×#14382
C127×#14362
#14765127