Finite Group Databasebeta

← C127×#16807 #44580480

Subgroups — C127×#16807 #44580480

Order 32512.

1790 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C127C212yesmaximal, complemented
2C2×#394×C127C212yesmaximal
3C2×#386×C127C211yesmaximal, characteristic
4C2×#380×C127C211yesmaximal, characteristic, complemented
5C127×#1445C212yesmaximal, complemented
6C127×#1444C211yesmaximal, characteristic, complemented
7C127×#1444C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1439C212yesmaximal, complemented
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25#397×C127—28no—
26#394×C127—28no—
27#386×C127—24no—
28#380×C127—24no—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2212yes—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2212yes—
39C25×C127C2311yescharacteristic
40C25×C127C2311yescharacteristic
41C22×D4×C127—22no—
42C22×D4×C127—22no—
43C22×D4×C127—24no—
44C22×D4×C127—22no—
45C22×D4×C127—42no—
46C23×C4×C127—22no—
47C23×C4×C127—22no—
48C23×C4×C127—42no—
49C23×C4×C127—42no—
50C23×C4×C127D414yes—
51C23×C4×C127C2312yes—
52C23×C4×C127C2312yes—
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C23×C4×C127C2312yes—
56C23×C4×C127C2312yes—
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—24no—
63C2×C4⋊C4×C127—24no—
64C2×C4⋊C4×C127—24no—
65C2×C4⋊C4×C127—42no—
66C2×C4⋊C4×C127—42no—
67C2×C4⋊C4×C127—42no—
68C2×C4⋊C4×C127—42no—
69C2×C4⋊C4×C127—42no—
70C2×C22⋊C4×C127—24no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—24no—
73C2×C22⋊C4×C127—24no—
74C2×C22⋊C4×C127—24no—
75C2×C22⋊C4×C127—24no—
76C2×C22⋊C4×C127—22no—
77C2×C22⋊C4×C127—22no—
78C2×C22⋊C4×C127—24no—
79C2×C22⋊C4×C127—24no—
80C2×C22⋊C4×C127—22no—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127—42no—
83C2×C22⋊C4×C127—42no—
84C2×C22⋊C4×C127—42no—
85C2×C22⋊C4×C127—42no—
86C2×C22⋊C4×C127—42no—
87C2×C22⋊C4×C127—42no—
88C2×C22⋊C4×C127D418yes—
89#95×C127—24no—
90#95×C127—22no—
91#95×C127—22no—
92#95×C127—24no—
93#95×C127—24no—
94#95×C127—24no—
95#95×C127—24no—
96#95×C127—22no—
97#95×C127—22no—
98#95×C127—42no—
99C24×C127—21no—
100C24×C127—21no—
101C24×C127—21no—
102C24×C127—21no—
103C24×C127—21no—
104C24×C127—22no—
105C24×C127—22no—
106C24×C127—22no—
107C24×C127—21no—
108C24×C127—21no—
109C24×C127—22no—
110C24×C127—21no—
111C24×C127—21no—
112C24×C127—21no—
113C24×C127—22no—
114C24×C127—21no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—21no—
118C24×C127C2×D414yes—
119C24×C127C2×D412yes—
120C24×C127#4112yes—
121C24×C127C2411yescharacteristic
122C2×D4×C127—28no—
123C2×D4×C127—48no—
124C2×D4×C127—48no—
125C2×D4×C127—44no—
126C2×D4×C127—44no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—21no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—28no—
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—21no—
153C22×C4×C127—21no—
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—21no—
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—21no—
170C22×C4×C127—22no—
171C22×C4×C127—22no—
172C22×C4×C127—22no—
173C22×C4×C127—21no—
174C22×C4×C127—44no—
175C22×C4×C127—44no—
176C22×C4×C127—48no—
177C22×C4×C127—48no—
178C22×C4×C127C2×D412yes—
179C22×C4×C127C2×D414yes—
180C22×C4×C127C2×D414yes—
181C22×C4×C127C2×D412yes—
182C22×C4×C127#4112yes—
183C22×C4×C127#4112yes—
184C22×C4×C127#4112yes—
185C4⋊C4×C127—48no—
186C4⋊C4×C127—44no—
187C4⋊C4×C127—44no—
188C4⋊C4×C127—48no—
189C22⋊C4×C127—48no—
190C22⋊C4×C127—48no—
191C22⋊C4×C127—48no—
192C22⋊C4×C127—44no—
193C22⋊C4×C127—48no—
194C22⋊C4×C127—44no—
195C22⋊C4×C127—44no—
196C23×C127—22no—
197C23×C127—22no—
198C23×C127—24no—
199C23×C127—22no—
200C23×C127—22no—
201C23×C127—22no—
202C23×C127—24no—
203C23×C127—22no—
204C23×C127—24no—
205C23×C127—24no—
206C23×C127—24no—
207C23×C127—24no—
208C23×C127—22no—
209C23×C127—24no—
210C23×C127—24no—
211C23×C127—22no—
212C23×C127—22no—
213C23×C127—42no—
214C23×C127—42no—
215C23×C127—42no—
216C23×C127—42no—
217C23×C127—41no—
218C23×C127—41no—
219C23×C127—41no—
220C23×C127—41no—
221C23×C127—42no—
222C23×C127—42no—
223C23×C127—41no—
224C23×C127—41no—
225C23×C127—41no—
226C23×C127—42no—
227C23×C127—41no—
228C23×C127—41no—
229C23×C127—42no—
230C23×C127—41no—
231C23×C127—42no—
232C23×C127—42no—
233C23×C127—42no—
234C23×C127—42no—
235C23×C127—42no—
236C23×C127—42no—
237C23×C127—41no—
238C23×C127—41no—
239C23×C127—42no—
240C23×C127—42no—
241C23×C127#12714yes—
242C23×C127C22×D411yescharacteristic
243C23×C127C22×D412yes—
244C23×C127C2×#4111yescharacteristic
245C23×C127C2×#4111yescharacteristic
246C23×C127C2×#4111yescharacteristic
247C23×C127C2×#4111yescharacteristic
248C23×C127H(5,𝔽2)12yes—
249C23×C127H(5,𝔽2)11yescharacteristic
250C23×C127H(5,𝔽2)12yes—
251C23×C1272−1+412yes—
252C23×C1272−1+411yescharacteristic
253D4×C127—416no—
254C2×C4×C127—22no—
255C2×C4×C127—22no—
256C2×C4×C127—24no—
257C2×C4×C127—24no—
258C2×C4×C127—22no—
259C2×C4×C127—22no—
260C2×C4×C127—24no—
261C2×C4×C127—24no—
262C2×C4×C127—22no—
263C2×C4×C127—22no—
264C2×C4×C127—24no—
265C2×C4×C127—24no—
266C2×C4×C127—24no—
267C2×C4×C127—24no—
268C2×C4×C127—24no—
269C2×C4×C127—416no—
270C2×C4×C127—41no—
271C2×C4×C127—41no—
272C2×C4×C127—42no—
273C2×C4×C127—42no—
274C2×C4×C127—42no—
275C2×C4×C127—42no—
276C2×C4×C127—42no—
277C2×C4×C127—42no—
278C2×C4×C127—42no—
279C2×C4×C127—42no—
280C2×C4×C127—42no—
281C2×C4×C127—42no—
282C2×C4×C127—42no—
283C2×C4×C127—41no—
284C2×C4×C127—42no—
285C2×C4×C127—42no—
286C2×C4×C127—41no—
287C2×C4×C127—41no—
288C2×C4×C127—42no—
289C2×C4×C127—41no—
290C2×C4×C127—42no—
291C2×C4×C127—42no—
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—41no—
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#12314yes—
308C22×C127—24no—
309C22×C127—24no—
310C22×C127—24no—
311C22×C127—42no—
312C22×C127—42no—
313C22×C127—44no—
314C22×C127—44no—
315C22×C127—44no—
316C22×C127—44no—
317C22×C127—42no—
318C22×C127—42no—
319C22×C127—42no—
320C22×C127—44no—
321C22×C127—44no—
322C22×C127—42no—
323C22×C127—42no—
324C22×C127—81no—
325C22×C127—81no—
326C22×C127—82no—
327C22×C127—82no—
328C22×C127—81no—
329C22×C127—81no—
330C22×C127C2×#12311yescharacteristic
331C22×C127#52511yescharacteristic
332C22×C127C2×#12711yescharacteristic
333C22×C127#53411yescharacteristic
334C22×C127#53411yescharacteristic
335C22×C127#53412yes—
336C22×C127#53611yescharacteristic
337C22×C127#53712yes—
338C22×C127#53711yescharacteristic
339C22×C127#53812yes—
340C22×C127#53812yes—
341C22×C127#53912yes—
342C22×C127#54212yes—
343C22×C127#54612yes—
344C22×C127#54612yes—
345C22×C127#54712yes—
346C22×C127#54712yes—
347C22×C127#55211yescharacteristic
348C22×C127#55311yescharacteristic
349C22×C127#55511yescharacteristic
350C22×C127#55611yescharacteristic
351C22×C127#56212yes—
352C22×C127#56312yes—
353C4×C127—24no—
354C4×C127—42no—
355C4×C127—44no—
356C4×C127—44no—
357C4×C127—42no—
358C4×C127—81no—
359C4×C127—82no—
360C4×C127—81no—
361C4×C127—82no—
362#16807C12711yesmaximal, characteristic, direct product factor, Sylow
363C2×C127—44no—
364C2×C127—82no—
365C2×C127#248511yescharacteristic
366C2×C127#250111yescharacteristic
367C2×C127#253911yescharacteristic
368C2×C127#262211yescharacteristic
369C2×C127#263811yescharacteristic
370C2×C127#265611yescharacteristic
371C2×C127#268612yes—
372C2×C127#269512yes—
373C2×C127#270812yes—
374C2×C127#271512yes—
375C2×C127#281411yescharacteristic
376C2×#397C2×C12712yescomplemented
377C2×#394C2×C12712yes—
378C2×#386C2×C12711yescharacteristic
379C2×#380C2×C12711yescharacteristic, complemented
380#1445C2×C12712yescomplemented
381#1444C2×C12711yescharacteristic, complemented
382#1444C2×C12711yescharacteristic, complemented
383#1439C2×C12711yescharacteristic, complemented
384#1439C2×C12711yescharacteristic, complemented
385#1439C2×C12712yescomplemented
386C22⋊#95C2×C12711yescharacteristic, complemented
387C127#1680711yescharacteristic, direct product factor, Sylow
388C23×D4C22×C12711yescharacteristic
389C24×C4C22×C12711yescharacteristic
390C22×C4⋊C4C22×C12712yes—
391C22×C4⋊C4C22×C12712yes—
392C22×C4⋊C4C22×C12711yescharacteristic
393C22×C4⋊C4C22×C12711yescharacteristic
394C22×C22⋊C4C22×C12712yes—
395C22×C22⋊C4C22×C12711yescharacteristic
396C22×C22⋊C4C22×C12711yescharacteristic
397C22×C22⋊C4C22×C12712yes—
398C22×C22⋊C4C22×C12712yes—
399C22×C22⋊C4C22×C12711yescharacteristic
400C22×C22⋊C4C22×C12712yes—
401#397—28no—
402#394—28no—
403#386—24no—
404#380—24no—
405C2×#95C22×C12712yes—
406C2×#95C22×C12712yes—
407C2×#95C22×C12712yes—
408C2×#95C22×C12712yes—
409C2×#95C22×C12711yescharacteristic
410C2×#95C22×C12711yescharacteristic
411C2×#95C22×C12712yes—
412C2×#95C22×C12711yescharacteristic
413C2×#95C22×C12711yescharacteristic
414C2×#95C22×C12712yes—
415C25C23×C12711yescharacteristic
416C25C23×C12711yescharacteristic
417C22×D4—22no—
418C22×D4—22no—
419C22×D4—24no—
420C22×D4—22no—
421C22×D4—42no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4D4×C12714yes—
427C23×C4C23×C12712yes—
428C23×C4C23×C12712yes—
429C23×C4C23×C12711yescharacteristic
430C23×C4C23×C12711yescharacteristic
431C23×C4C23×C12712yes—
432C23×C4C23×C12712yes—
433C23×C4C23×C12711yescharacteristic
434C23×C4C23×C12711yescharacteristic
435C23×C4C23×C12711yescharacteristic
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4D4×C12718yes—
465#95—24no—
466#95—22no—
467#95—22no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—24no—
472#95—22no—
473#95—22no—
474#95—42no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—22no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24C2×D4×C12714yes—
495C24C2×D4×C12712yes—
496C24#41×C12712yes—
497C24C24×C12711yescharacteristic
498C2×D4—28no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—44no—
502C2×D4—44no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—28no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4C2×D4×C12712yes—
555C22×C4C2×D4×C12714yes—
556C22×C4C2×D4×C12714yes—
557C22×C4C2×D4×C12712yes—
558C22×C4#41×C12712yes—
559C22×C4#41×C12712yes—
560C22×C4#41×C12712yes—
561C4⋊C4—48no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—48no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—44no—
569C22⋊C4—48no—
570C22⋊C4—44no—
571C22⋊C4—44no—
572C23—22no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—22no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—42no—
598C23—42no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—42no—
603C23—41no—
604C23—41no—
605C23—42no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23#127×C12714yes—
618C23C22×D4×C12711yescharacteristic
619C23C22×D4×C12712yes—
620C23C2×#41×C12711yescharacteristic
621C23C2×#41×C12711yescharacteristic
622C23C2×#41×C12711yescharacteristic
623C23C2×#41×C12711yescharacteristic
624C23H(5,𝔽2)×C12712yes—
625C23H(5,𝔽2)×C12711yescharacteristic
626C23H(5,𝔽2)×C12712yes—
627C232−1+4×C12712yes—
628C232−1+4×C12711yescharacteristic
629D4—416no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—416no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4#123×C12714yes—
684C22—24no—
685C22—24no—
686C22—24no—
687C22—42no—
688C22—42no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—44no—
697C22—44no—
698C22—42no—
699C22—42no—
700C22—81no—
701C22—81no—
702C22—82no—
703C22—82no—
704C22—81no—
705C22—81no—
706C22C2×#123×C12711yescharacteristic
707C22#525×C12711yescharacteristic
708C22C2×#127×C12711yescharacteristic
709C22#534×C12711yescharacteristic
710C22#534×C12711yescharacteristic
711C22#534×C12712yes—
712C22#536×C12711yescharacteristic
713C22#537×C12712yes—
714C22#537×C12711yescharacteristic
715C22#538×C12712yes—
716C22#538×C12712yes—
717C22#539×C12712yes—
718C22#542×C12712yes—
719C22#546×C12712yes—
720C22#546×C12712yes—
721C22#547×C12712yes—
722C22#547×C12712yes—
723C22#552×C12711yescharacteristic
724C22#553×C12711yescharacteristic
725C22#555×C12711yescharacteristic
726C22#556×C12711yescharacteristic
727C22#562×C12712yes—
728C22#563×C12712yes—
729C4—24no—
730C4—42no—
731C4—44no—
732C4—44no—
733C4—42no—
734C4—81no—
735C4—82no—
736C4—81no—
737C4—82no—
738C2—44no—
739C2—82no—
740C2C127×#248511yescharacteristic
741C2C127×#250111yescharacteristic
742C2C127×#253911yescharacteristic
743C2C127×#262211yescharacteristic
744C2C127×#263811yescharacteristic
745C2C127×#265611yescharacteristic
746C2C127×#268612yes—
747C2C127×#269512yes—
748C2C127×#270812yes—
749C2C127×#271512yes—
750C2C127×#281411yescharacteristic
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. C2×#397×C127C2semidirect
4. C2×#380×C127C2semidirect
5. C127×#1445C2semidirect
6. C127×#1444C2semidirect
7. C127×#1444C2semidirect
8. C127×#1439C2semidirect
9. C127×#1439C2semidirect
10. C127×#1439C2semidirect
11. C127×C22⋊#95C2semidirect
362. #16807C127direct (N × H)
376. C2×#397C2×C127semidirect
379. C2×#380C2×C127semidirect
380. #1445C2×C127semidirect
381. #1444C2×C127semidirect
382. #1444C2×C127semidirect
383. #1439C2×C127semidirect
384. #1439C2×C127semidirect
385. #1439C2×C127semidirect
386. C22⋊#95C2×C127semidirect
387. C127#16807direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#397×C1272
C2×#394×C1272
C2×#386×C1272
C2×#380×C1272
C127×#14452
C127×#14442
C127×#14392
C127×C22⋊#952
#16807127