Finite Group Databasebeta

← C127×#14695 #44578368

Subgroups — C127×#14695 #44578368

Order 32512.

2430 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C42×C127C211yesmaximal, characteristic
2C2×#387×C127C212yesmaximal, complemented
3C2×#385×C127C211yesmaximal, characteristic
4C2×#385×C127C211yesmaximal, characteristic
5C127×#1436C212yesmaximal, complemented
6C127×#1436C212yesmaximal, complemented
7C127×#1434C212yesmaximal, complemented
8C127×C22⋊#95C211yesmaximal, characteristic
9C127×C22⋊#95C211yesmaximal, characteristic
10C127×C22⋊#95C211yesmaximal, characteristic
11C127×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C42×C127—24no—
23C22×C42×C127—28no—
24C22×C42×C127C2212yes—
25C22×C42×C127C2212yes—
26#387×C127—28no—
27#385×C127—24no—
28#385×C127C418yescomplemented
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2212yes—
40C25×C127C2311yescharacteristic
41C23×C4×C127—22no—
42C23×C4×C127—22no—
43C23×C4×C127—22no—
44C23×C4×C127—22no—
45C23×C4×C127—22no—
46C23×C4×C127—22no—
47C23×C4×C127—24no—
48C23×C4×C127—24no—
49C23×C4×C127—24no—
50C23×C4×C127—24no—
51C23×C4×C127—24no—
52C23×C4×C127—24no—
53C23×C4×C127C2×C414yes—
54C23×C4×C127D414yes—
55C23×C4×C127Q814yes—
56C23×C4×C127C2311yescharacteristic
57C23×C4×C127C2312yes—
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2312yes—
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2312yes—
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2312yes—
65C23×C4×C127C2311yescharacteristic
66C2×C4⋊C4×C127—24no—
67C2×C4⋊C4×C127—24no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—24no—
71C2×C4⋊C4×C127—24no—
72C2×C4⋊C4×C127C2×C418yescomplemented
73C2×C22⋊C4×C127—22no—
74C2×C22⋊C4×C127—22no—
75C2×C22⋊C4×C127—22no—
76C2×C22⋊C4×C127—22no—
77C2×C22⋊C4×C127—22no—
78C2×C22⋊C4×C127—22no—
79C2×C22⋊C4×C127—22no—
80C2×C22⋊C4×C127—22no—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127C2×C414yes—
84C2×C22⋊C4×C127C2×C414yes—
85C2×C42×C127—232no—
86C2×C42×C127—24no—
87C2×C42×C127—24no—
88C2×C42×C127—24no—
89C2×C42×C127—24no—
90C2×C42×C127—24no—
91C2×C42×C127D418yes—
92#95×C127—22no—
93#95×C127—22no—
94#95×C127—24no—
95#95×C127—24no—
96#95×C127—24no—
97#95×C127—24no—
98#95×C127—24no—
99#95×C127—24no—
100#95×C127—24no—
101#95×C127—24no—
102#95×C127C2×C418yescomplemented
103C24×C127—22no—
104C24×C127—22no—
105C24×C127—22no—
106C24×C127—22no—
107C24×C127C22×C412yes—
108C24×C127C2×D412yes—
109C24×C127C2×Q812yes—
110C24×C127#4112yes—
111C24×C127#4112yes—
112C24×C127#4112yes—
113C24×C127#4112yes—
114C24×C127C2411yescharacteristic
115C22×C4×C127—28no—
116C22×C4×C127—28no—
117C22×C4×C127—216no—
118C22×C4×C127—216no—
119C22×C4×C127—216no—
120C22×C4×C127—216no—
121C22×C4×C127—28no—
122C22×C4×C127—28no—
123C22×C4×C127—28no—
124C22×C4×C127—28no—
125C22×C4×C127—28no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
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—22no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—216no—
141C22×C4×C127—28no—
142C22×C4×C127—216no—
143C22×C4×C127—28no—
144C22×C4×C127—22no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
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—21no—
154C22×C4×C127—21no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—22no—
158C22×C4×C127—22no—
159C22×C4×C127—21no—
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—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—22no—
172C22×C4×C127—22no—
173C22×C4×C127—22no—
174C22×C4×C127—22no—
175C22×C4×C127C22×C412yes—
176C22×C4×C127C22×C414yes—
177C22×C4×C127C22×C412yes—
178C22×C4×C127C22×C414yes—
179C22×C4×C127C2×D414yes—
180C22×C4×C127C2×D412yes—
181C22×C4×C127C2×D414yes—
182C22×C4×C127C2×D414yes—
183C22×C4×C127C2×D412yes—
184C22×C4×C127C2×Q814yes—
185C22×C4×C127#4114yes—
186C22×C4×C127#4114yes—
187C22×C4×C127#4114yes—
188C4⋊C4×C127—216no—
189C4⋊C4×C127—44no—
190C4⋊C4×C127—44no—
191C22⋊C4×C127—28no—
192C22⋊C4×C127—28no—
193C22⋊C4×C127—44no—
194C22⋊C4×C127—44no—
195C42×C127—216no—
196C42×C127—216no—
197C23×C127—24no—
198C23×C127—24no—
199C23×C127—22no—
200C23×C127—24no—
201C23×C127—22no—
202C23×C127—22no—
203C23×C127—22no—
204C23×C127—24no—
205C23×C127—24no—
206C23×C127—24no—
207C23×C127—24no—
208C23×C127—24no—
209C23×C127—24no—
210C23×C127—24no—
211C23×C127—24no—
212C23×C127—24no—
213C23×C127#11714yes—
214C23×C127C4×D414yes—
215C23×C127C4×Q814yes—
216C23×C127C22⋊Q814yes—
217C23×C127#12314yes—
218C23×C127#12514yes—
219C23×C127#12614yes—
220C23×C127C23×C411yescharacteristic
221C23×C127C22×D411yescharacteristic
222C23×C127C22×D412yes—
223C23×C127C22×Q811yescharacteristic
224C23×C127C2×#4111yescharacteristic
225C23×C127C2×#4111yescharacteristic
226C23×C127C2×#4111yescharacteristic
227C23×C127C2×#4112yes—
228C23×C127C2×#4111yescharacteristic
229C23×C127C2×#4112yes—
230C23×C127C2×#4112yes—
231C2×C4×C127—232no—
232C2×C4×C127—232no—
233C2×C4×C127—232no—
234C2×C4×C127—24no—
235C2×C4×C127—24no—
236C2×C4×C127—24no—
237C2×C4×C127—22no—
238C2×C4×C127—24no—
239C2×C4×C127—24no—
240C2×C4×C127—24no—
241C2×C4×C127—22no—
242C2×C4×C127—22no—
243C2×C4×C127—22no—
244C2×C4×C127—24no—
245C2×C4×C127—24no—
246C2×C4×C127—24no—
247C2×C4×C127—24no—
248C2×C4×C127—24no—
249C2×C4×C127—24no—
250C2×C4×C127—24no—
251C2×C4×C127—24no—
252C2×C4×C127—24no—
253C2×C4×C127—24no—
254C2×C4×C127—24no—
255C2×C4×C127—22no—
256C2×C4×C127—22no—
257C2×C4×C127—24no—
258C2×C4×C127—24no—
259C2×C4×C127—24no—
260C2×C4×C127—24no—
261C2×C4×C127—41no—
262C2×C4×C127—41no—
263C2×C4×C127—42no—
264C2×C4×C127—42no—
265C2×C4×C127—42no—
266C2×C4×C127—41no—
267C2×C4×C127—41no—
268C2×C4×C127—42no—
269C2×C4×C127—42no—
270C2×C4×C127—42no—
271C2×C4×C127—41no—
272C2×C4×C127—41no—
273C2×C4×C127—41no—
274C2×C4×C127—41no—
275C2×C4×C127—42no—
276C2×C4×C127—42no—
277C2×C4×C127—42no—
278C2×C4×C127—42no—
279C2×C4×C127—42no—
280C2×C4×C127—41no—
281C2×C4×C127—41no—
282C2×C4×C127—42no—
283C2×C4×C127—42no—
284C2×C4×C127—42no—
285C2×C4×C127—42no—
286C2×C4×C127—42no—
287C2×C4×C127—42no—
288C2×C4×C127C4×D418yes—
289C2×C4×C127#12014yes—
290C2×C4×C127C22⋊Q818yes—
291C2×C4×C127#12314yes—
292C22×C127—24no—
293C22×C127—24no—
294C22×C127—28no—
295C22×C127—28no—
296C22×C127—24no—
297C22×C127—24no—
298C22×C127—28no—
299C22×C127—24no—
300C22×C127—24no—
301C22×C127—28no—
302C22×C127#38718yescomplemented
303C22×C127C2×#11711yescharacteristic
304C22×C127C2×C4×D411yescharacteristic
305C22×C127C2×C4×D412yes—
306C22×C127C2×C4×Q811yescharacteristic
307C22×C127C4×#4112yes—
308C22×C127C2×#12011yescharacteristic
309C22×C127C2×C22⋊Q812yes—
310C22×C127C2×C22⋊Q811yescharacteristic
311C22×C127C2×#12311yescharacteristic
312C22×C127C2×#12311yescharacteristic
313C22×C127#52512yes—
314C22×C127#52511yescharacteristic
315C22×C127#52512yes—
316C22×C127#52512yes—
317C22×C127#52512yes—
318C22×C127#52511yescharacteristic
319C22×C127C2×#12511yescharacteristic
320C22×C127C2×#12611yescharacteristic
321C22×C127#52912yes—
322C22×C127#52912yes—
323C22×C127#52912yes—
324C22×C127#52912yes—
325C22×C127#53312yes—
326C4×C127—28no—
327C4×C127—24no—
328C4×C127—24no—
329C4×C127—28no—
330C4×C127—44no—
331C4×C127—42no—
332C4×C127—42no—
333C4×C127—81no—
334C4×C127—82no—
335C4×C127—81no—
336#14695C12711yesmaximal, characteristic, direct product factor, Sylow
337C2×C127—28no—
338C2×C127C2×#38711yescharacteristic
339C2×C127#229012yes—
340C2×C127C4×#12011yescharacteristic
341C2×C127C4×#12311yescharacteristic
342C2×C127C4×C22⋊Q812yes—
343C2×C127#284811yescharacteristic
344C2×C127#284911yescharacteristic
345C2×C127#285112yes—
346C2×C127#285212yes—
347C2×C127#285311yescharacteristic
348C2×C127#285511yescharacteristic
349C23×C42C2×C12711yescharacteristic
350C2×#387C2×C12712yescomplemented
351C2×#385C2×C12711yescharacteristic
352C2×#385C2×C12711yescharacteristic
353#1436C2×C12712yescomplemented
354#1436C2×C12712yescomplemented
355#1434C2×C12712yescomplemented
356C22⋊#95C2×C12711yescharacteristic
357C22⋊#95C2×C12711yescharacteristic
358C22⋊#95C2×C12711yescharacteristic
359C22⋊#95C2×C12711yescharacteristic
360C127#1469511yescharacteristic, direct product factor, Sylow
361C24×C4C22×C12711yescharacteristic
362C24×C4C22×C12711yescharacteristic
363C24×C4C22×C12711yescharacteristic
364C22×C4⋊C4C22×C12711yescharacteristic
365C22×C4⋊C4C22×C12711yescharacteristic
366C22×C4⋊C4C22×C12712yes—
367C22×C22⋊C4C22×C12711yescharacteristic
368C22×C22⋊C4C22×C12711yescharacteristic
369C22×C22⋊C4C22×C12711yescharacteristic
370C22×C22⋊C4C22×C12711yescharacteristic
371C22×C42—24no—
372C22×C42—28no—
373C22×C42C22×C12712yes—
374C22×C42C22×C12712yes—
375#387—28no—
376#385—24no—
377#385C4×C12718yescomplemented
378C2×#95C22×C12712yes—
379C2×#95C22×C12712yes—
380C2×#95C22×C12712yes—
381C2×#95C22×C12712yes—
382C2×#95C22×C12712yes—
383C2×#95C22×C12712yes—
384C2×#95C22×C12712yes—
385C2×#95C22×C12712yes—
386C2×#95C22×C12711yescharacteristic
387C2×#95C22×C12711yescharacteristic
388C2×#95C22×C12712yes—
389C25C23×C12711yescharacteristic
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4C2×C4×C12714yes—
403C23×C4D4×C12714yes—
404C23×C4Q8×C12714yes—
405C23×C4C23×C12711yescharacteristic
406C23×C4C23×C12712yes—
407C23×C4C23×C12711yescharacteristic
408C23×C4C23×C12711yescharacteristic
409C23×C4C23×C12712yes—
410C23×C4C23×C12711yescharacteristic
411C23×C4C23×C12712yes—
412C23×C4C23×C12711yescharacteristic
413C23×C4C23×C12712yes—
414C23×C4C23×C12711yescharacteristic
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4C2×C4×C12718yescomplemented
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4C2×C4×C12714yes—
433C2×C22⋊C4C2×C4×C12714yes—
434C2×C42—232no—
435C2×C42—24no—
436C2×C42—24no—
437C2×C42—24no—
438C2×C42—24no—
439C2×C42—24no—
440C2×C42D4×C12718yes—
441#95—22no—
442#95—22no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95C2×C4×C12718yescomplemented
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24C22×C4×C12712yes—
457C24C2×D4×C12712yes—
458C24C2×Q8×C12712yes—
459C24#41×C12712yes—
460C24#41×C12712yes—
461C24#41×C12712yes—
462C24#41×C12712yes—
463C24C24×C12711yescharacteristic
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—216no—
467C22×C4—216no—
468C22×C4—216no—
469C22×C4—216no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—216no—
490C22×C4—28no—
491C22×C4—216no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4C22×C4×C12712yes—
525C22×C4C22×C4×C12714yes—
526C22×C4C22×C4×C12712yes—
527C22×C4C22×C4×C12714yes—
528C22×C4C2×D4×C12714yes—
529C22×C4C2×D4×C12712yes—
530C22×C4C2×D4×C12714yes—
531C22×C4C2×D4×C12714yes—
532C22×C4C2×D4×C12712yes—
533C22×C4C2×Q8×C12714yes—
534C22×C4#41×C12714yes—
535C22×C4#41×C12714yes—
536C22×C4#41×C12714yes—
537C4⋊C4—216no—
538C4⋊C4—44no—
539C4⋊C4—44no—
540C22⋊C4—28no—
541C22⋊C4—28no—
542C22⋊C4—44no—
543C22⋊C4—44no—
544C42—216no—
545C42—216no—
546C23—24no—
547C23—24no—
548C23—22no—
549C23—24no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23#117×C12714yes—
563C23C4×D4×C12714yes—
564C23C4×Q8×C12714yes—
565C23C22⋊Q8×C12714yes—
566C23#123×C12714yes—
567C23#125×C12714yes—
568C23#126×C12714yes—
569C23C23×C4×C12711yescharacteristic
570C23C22×D4×C12711yescharacteristic
571C23C22×D4×C12712yes—
572C23C22×Q8×C12711yescharacteristic
573C23C2×#41×C12711yescharacteristic
574C23C2×#41×C12711yescharacteristic
575C23C2×#41×C12711yescharacteristic
576C23C2×#41×C12712yes—
577C23C2×#41×C12711yescharacteristic
578C23C2×#41×C12712yes—
579C23C2×#41×C12712yes—
580C2×C4—232no—
581C2×C4—232no—
582C2×C4—232no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4C4×D4×C12718yes—
638C2×C4#120×C12714yes—
639C2×C4C22⋊Q8×C12718yes—
640C2×C4#123×C12714yes—
641C22—24no—
642C22—24no—
643C22—28no—
644C22—28no—
645C22—24no—
646C22—24no—
647C22—28no—
648C22—24no—
649C22—24no—
650C22—28no—
651C22#387×C12718yescomplemented
652C22C2×#117×C12711yescharacteristic
653C22C2×C4×D4×C12711yescharacteristic
654C22C2×C4×D4×C12712yes—
655C22C2×C4×Q8×C12711yescharacteristic
656C22C4×#41×C12712yes—
657C22C2×#120×C12711yescharacteristic
658C22C2×C22⋊Q8×C12712yes—
659C22C2×C22⋊Q8×C12711yescharacteristic
660C22C2×#123×C12711yescharacteristic
661C22C2×#123×C12711yescharacteristic
662C22#525×C12712yes—
663C22#525×C12711yescharacteristic
664C22#525×C12712yes—
665C22#525×C12712yes—
666C22#525×C12712yes—
667C22#525×C12711yescharacteristic
668C22C2×#125×C12711yescharacteristic
669C22C2×#126×C12711yescharacteristic
670C22#529×C12712yes—
671C22#529×C12712yes—
672C22#529×C12712yes—
673C22#529×C12712yes—
674C22#533×C12712yes—
675C4—28no—
676C4—24no—
677C4—24no—
678C4—28no—
679C4—44no—
680C4—42no—
681C4—42no—
682C4—81no—
683C4—82no—
684C4—81no—
685C2—28no—
686C2C2×#387×C12711yescharacteristic
687C2C127×#229012yes—
688C2C4×#120×C12711yescharacteristic
689C2C4×#123×C12711yescharacteristic
690C2C4×C22⋊Q8×C12712yes—
691C2C127×#284811yescharacteristic
692C2C127×#284911yescharacteristic
693C2C127×#285112yes—
694C2C127×#285212yes—
695C2C127×#285311yescharacteristic
696C2C127×#285511yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#387×C127C2semidirect
5. C127×#1436C2semidirect
6. C127×#1436C2semidirect
7. C127×#1434C2semidirect
28. #385×C127C4semidirect
72. C2×C4⋊C4×C127C2×C4semidirect
102. #95×C127C2×C4semidirect
302. C22×C127#387semidirect
336. #14695C127direct (N × H)
350. C2×#387C2×C127semidirect
353. #1436C2×C127semidirect
354. #1436C2×C127semidirect
355. #1434C2×C127semidirect
360. C127#14695direct (N × H)
377. #385C4×C127semidirect
421. C2×C4⋊C4C2×C4×C127semidirect
451. #95C2×C4×C127semidirect
651. C22#387×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C42×C1272
C2×#387×C1272
C2×#385×C1272
C127×#14362
C127×#14342
C127×C22⋊#952
#14695127