Finite Group Databasebeta

← C127×#14299 #44577972

Subgroups — C127×#14299 #44577972

Order 32512.

2566 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic, complemented
2C2×#392×C127C211yesmaximal, characteristic
3C2×#388×C127C211yesmaximal, characteristic, complemented
4C2×#386×C127C212yesmaximal, complemented
5C127×#1442C211yesmaximal, characteristic, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1439C211yesmaximal, characteristic, complemented
8C127×#1438C212yesmaximal, complemented
9C127×#1438C211yesmaximal, characteristic, complemented
10C127×#1434C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2212yes—
14C24×C4×C127C2212yes—
15C2×C4×D4×C127—28no—
16C2×C4×D4×C127—24no—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27C22×C42×C127C2211yescharacteristic
28#392×C127C418yescomplemented
29#388×C127—24no—
30#386×C127—28no—
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2211yescharacteristic
40C25×C127C2311yescharacteristic
41C25×C127C2312yes—
42C22×D4×C127—24no—
43C22×D4×C127—24no—
44C22×D4×C127—24no—
45C22×D4×C127—24no—
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127—42no—
49C22×D4×C127—42no—
50C22×D4×C127—42no—
51C22×D4×C127—42no—
52C22×D4×C127C2×C414yes—
53C22×D4×C127C2×C418yescomplemented
54C23×C4×C127—24no—
55C23×C4×C127—24no—
56C23×C4×C127—42no—
57C23×C4×C127—42no—
58C23×C4×C127—42no—
59C23×C4×C127—42no—
60C23×C4×C127D418yescomplemented
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2312yes—
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2312yes—
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2312yes—
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C4×D4×C127—232no—
71C2×C4⋊C4×C127—24no—
72C2×C4⋊C4×C127—22no—
73C2×C4⋊C4×C127—22no—
74C2×C4⋊C4×C127—42no—
75C2×C22⋊C4×C127—24no—
76C2×C22⋊C4×C127—24no—
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127—22no—
79C2×C22⋊C4×C127—22no—
80C2×C22⋊C4×C127—24no—
81C2×C22⋊C4×C127—24no—
82C2×C22⋊C4×C127—24no—
83C2×C22⋊C4×C127—24no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—42no—
87C2×C22⋊C4×C127—42no—
88C2×C22⋊C4×C127—42no—
89C2×C22⋊C4×C127—42no—
90C2×C22⋊C4×C127—42no—
91C2×C22⋊C4×C127—42no—
92C2×C22⋊C4×C127—42no—
93C2×C22⋊C4×C127—42no—
94C2×C22⋊C4×C127—42no—
95C2×C22⋊C4×C127C2×C414yescomplemented
96C2×C22⋊C4×C127C2×C418yescomplemented
97C2×C42×C127—24no—
98C2×C42×C127D414yescomplemented
99#95×C127—24no—
100#95×C127—24no—
101#95×C127—22no—
102#95×C127—22no—
103#95×C127—22no—
104#95×C127—42no—
105#95×C127—42no—
106#95×C127—42no—
107#95×C127C2×C414yescomplemented
108C24×C127—22no—
109C24×C127—22no—
110C24×C127—22no—
111C24×C127—22no—
112C24×C127—22no—
113C24×C127—22no—
114C24×C127—22no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—22no—
118C24×C127—22no—
119C24×C127—22no—
120C24×C127—21no—
121C24×C127—22no—
122C24×C127—21no—
123C24×C127—22no—
124C24×C127—21no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—21no—
128C24×C127—21no—
129C24×C127—21no—
130C24×C127C22×C412yes—
131C24×C127C22×C414yes—
132C24×C127C2×D414yes—
133C24×C127#4114yes—
134C24×C127C2411yescharacteristic
135C2×D4×C127—28no—
136C2×D4×C127—28no—
137C2×D4×C127—216no—
138C2×D4×C127—216no—
139C2×D4×C127—216no—
140C2×D4×C127—28no—
141C2×D4×C127—48no—
142C2×D4×C127—48no—
143C2×D4×C127—48no—
144C2×D4×C127—48no—
145C2×D4×C127—48no—
146C2×D4×C127—48no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—21no—
150C22×C4×C127—22no—
151C22×C4×C127—21no—
152C22×C4×C127—22no—
153C22×C4×C127—21no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
156C22×C4×C127—22no—
157C22×C4×C127—21no—
158C22×C4×C127—22no—
159C22×C4×C127—21no—
160C22×C4×C127—22no—
161C22×C4×C127—22no—
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—21no—
172C22×C4×C127—216no—
173C22×C4×C127—21no—
174C22×C4×C127—22no—
175C22×C4×C127—22no—
176C22×C4×C127—21no—
177C22×C4×C127—22no—
178C22×C4×C127—22no—
179C22×C4×C127—22no—
180C22×C4×C127—21no—
181C22×C4×C127—22no—
182C22×C4×C127—22no—
183C22×C4×C127—22no—
184C22×C4×C127—21no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—21no—
188C22×C4×C127—22no—
189C22×C4×C127—21no—
190C22×C4×C127—48no—
191C22×C4×C127—48no—
192C22×C4×C127—48no—
193C22×C4×C127—48no—
194C22×C4×C127—48no—
195C22×C4×C127—48no—
196C22×C4×C127C22×C414yes—
197C22×C4×C127C22×C412yes—
198C22×C4×C127C22×C412yes—
199C22×C4×C127C2×D414yes—
200C22×C4×C127C2×D412yes—
201C22×C4×C127C2×D412yes—
202C22×C4×C127C2×D414yes—
203C22×C4×C127C2×D412yes—
204C22×C4×C127#4112yes—
205C4⋊C4×C127—28no—
206C4⋊C4×C127—44no—
207C22⋊C4×C127—216no—
208C22⋊C4×C127—28no—
209C22⋊C4×C127—48no—
210C22⋊C4×C127—48no—
211C22⋊C4×C127—44no—
212C22⋊C4×C127—48no—
213C22⋊C4×C127—48no—
214C22⋊C4×C127—44no—
215C42×C127—28no—
216C23×C127—24no—
217C23×C127—24no—
218C23×C127—24no—
219C23×C127—24no—
220C23×C127—24no—
221C23×C127—24no—
222C23×C127—24no—
223C23×C127—24no—
224C23×C127—24no—
225C23×C127—24no—
226C23×C127—24no—
227C23×C127—24no—
228C23×C127—24no—
229C23×C127—24no—
230C23×C127—24no—
231C23×C127—24no—
232C23×C127—24no—
233C23×C127—24no—
234C23×C127—22no—
235C23×C127—24no—
236C23×C127—22no—
237C23×C127—24no—
238C23×C127—22no—
239C23×C127—42no—
240C23×C127—42no—
241C23×C127—42no—
242C23×C127—42no—
243C23×C127—42no—
244C23×C127—42no—
245C23×C127—42no—
246C23×C127—42no—
247C23×C127—42no—
248C23×C127—42no—
249C23×C127—42no—
250C23×C127—42no—
251C23×C127—42no—
252C23×C127—42no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127—41no—
256C23×C127—42no—
257C23×C127—41no—
258C23×C127—42no—
259C23×C127—42no—
260C23×C127—41no—
261C23×C127—42no—
262C23×C127—41no—
263C23×C127—41no—
264C23×C127—41no—
265C23×C127—42no—
266C23×C127—42no—
267C23×C127—42no—
268C23×C127—42no—
269C23×C127—42no—
270C23×C127—41no—
271C23×C127—42no—
272C23×C127—41no—
273C23×C127C4×D418yes—
274C23×C127C23×C411yescharacteristic
275C23×C127C22×D412yes—
276C23×C127C22×D411yescharacteristic
277C23×C127C2×#4112yes—
278C23×C127C2×#4111yescharacteristic
279C23×C127H(5,𝔽2)11yescharacteristic
280C23×C127H(5,𝔽2)12yes—
281C23×C127H(5,𝔽2)11yescharacteristic
282C23×C127H(5,𝔽2)12yes—
283C23×C127H(5,𝔽2)11yescharacteristic
284C23×C1272−1+411yescharacteristic
285D4×C127—232no—
286D4×C127—432no—
287C2×C4×C127—24no—
288C2×C4×C127—22no—
289C2×C4×C127—22no—
290C2×C4×C127—24no—
291C2×C4×C127—24no—
292C2×C4×C127—24no—
293C2×C4×C127—22no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—24no—
297C2×C4×C127—24no—
298C2×C4×C127—24no—
299C2×C4×C127—24no—
300C2×C4×C127—22no—
301C2×C4×C127—24no—
302C2×C4×C127—24no—
303C2×C4×C127—24no—
304C2×C4×C127—22no—
305C2×C4×C127—22no—
306C2×C4×C127—432no—
307C2×C4×C127—42no—
308C2×C4×C127—42no—
309C2×C4×C127—42no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—42no—
313C2×C4×C127—42no—
314C2×C4×C127—42no—
315C2×C4×C127—42no—
316C2×C4×C127—42no—
317C2×C4×C127—42no—
318C2×C4×C127—42no—
319C2×C4×C127—42no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—42no—
323C2×C4×C127—42no—
324C2×C4×C127—42no—
325C2×C4×C127—41no—
326C2×C4×C127—42no—
327C2×C4×C127—41no—
328C2×C4×C127—41no—
329C2×C4×C127—41no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127—42no—
334C2×C4×C127—42no—
335C2×C4×C127—42no—
336C2×C4×C127—42no—
337C2×C4×C127C4×D414yes—
338C2×C4×C127#12014yes—
339C22×C127—28no—
340C22×C127—28no—
341C22×C127—28no—
342C22×C127—44no—
343C22×C127—44no—
344C22×C127—44no—
345C22×C127—44no—
346C22×C127—44no—
347C22×C127—44no—
348C22×C127—44no—
349C22×C127—44no—
350C22×C127—44no—
351C22×C127—44no—
352C22×C127—44no—
353C22×C127—44no—
354C22×C127—44no—
355C22×C127—42no—
356C22×C127—44no—
357C22×C127—42no—
358C22×C127—42no—
359C22×C127—81no—
360C22×C127—81no—
361C22×C127—82no—
362C22×C127—81no—
363C22×C127—82no—
364C22×C127—81no—
365C22×C127C2×C4×D412yes—
366C22×C127C2×C4×D411yescharacteristic
367C22×C127#51811yescharacteristic
368C22×C127#51812yes—
369C22×C127#52011yescharacteristic
370C22×C127C2×#12011yescharacteristic
371C22×C127#52512yes—
372C22×C127#52511yescharacteristic
373C22×C127#53412yes—
374C22×C127#53412yes—
375C22×C127#53512yes—
376C22×C127#53511yescharacteristic
377C22×C127#53511yescharacteristic
378C22×C127#53511yescharacteristic
379C22×C127#53711yescharacteristic
380C22×C127#53712yes—
381C22×C127#53812yes—
382C22×C127#53812yes—
383C22×C127#53812yes—
384C22×C127#53912yes—
385C22×C127#54011yescharacteristic
386C22×C127#54012yes—
387C22×C127#54211yescharacteristic
388C4×C127—24no—
389C4×C127—24no—
390C4×C127—44no—
391C4×C127—42no—
392C4×C127—44no—
393C4×C127—42no—
394C4×C127—81no—
395C4×C127—81no—
396C4×C127—82no—
397#14299C12711yesmaximal, characteristic, direct product factor, Sylow
398C2×C127—48no—
399C2×C127—82no—
400C2×C127C4×#12011yescharacteristic
401C2×C127#232112yes—
402C2×C127#232411yescharacteristic
403C2×C127#232512yes—
404C2×C127#232811yescharacteristic
405C2×C127#261311yescharacteristic
406C2×C127#261511yescharacteristic
407C2×C127#263012yes—
408C2×C127#263111yescharacteristic
409C2×C127#263512yes—
410C2×C127#263611yescharacteristic
411C22×C4×D4C2×C12711yescharacteristic, complemented
412C2×#392C2×C12711yescharacteristic
413C2×#388C2×C12711yescharacteristic, complemented
414C2×#386C2×C12712yescomplemented
415#1442C2×C12711yescharacteristic, complemented
416#1439C2×C12712yescomplemented
417#1439C2×C12711yescharacteristic, complemented
418#1438C2×C12712yescomplemented
419#1438C2×C12711yescharacteristic, complemented
420#1434C2×C12711yescharacteristic, complemented
421C22⋊#95C2×C12712yescomplemented
422C127#1429911yescharacteristic, direct product factor, Sylow
423C23×D4C22×C12711yescharacteristic
424C23×D4C22×C12712yes—
425C24×C4C22×C12712yes—
426C2×C4×D4—28no—
427C2×C4×D4—24no—
428C22×C4⋊C4C22×C12711yescharacteristic
429C22×C4⋊C4C22×C12711yescharacteristic
430C22×C22⋊C4C22×C12712yes—
431C22×C22⋊C4C22×C12711yescharacteristic
432C22×C22⋊C4C22×C12711yescharacteristic
433C22×C22⋊C4C22×C12712yes—
434C22×C22⋊C4C22×C12711yescharacteristic
435C22×C22⋊C4C22×C12712yes—
436C22×C22⋊C4C22×C12712yes—
437C22×C22⋊C4C22×C12712yes—
438C22×C42C22×C12711yescharacteristic
439#392C4×C12718yescomplemented
440#388—24no—
441#386—28no—
442C2×#95C22×C12711yescharacteristic
443C2×#95C22×C12712yes—
444C2×#95C22×C12711yescharacteristic
445C2×#95C22×C12711yescharacteristic
446C2×#95C22×C12712yes—
447C2×#95C22×C12712yes—
448C2×#95C22×C12712yes—
449C2×#95C22×C12712yes—
450C2×#95C22×C12711yescharacteristic
451C25C23×C12711yescharacteristic
452C25C23×C12712yes—
453C22×D4—24no—
454C22×D4—24no—
455C22×D4—24no—
456C22×D4—24no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—42no—
460C22×D4—42no—
461C22×D4—42no—
462C22×D4—42no—
463C22×D4C2×C4×C12714yes—
464C22×D4C2×C4×C12718yescomplemented
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—42no—
468C23×C4—42no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4D4×C12718yescomplemented
472C23×C4C23×C12711yescharacteristic
473C23×C4C23×C12711yescharacteristic
474C23×C4C23×C12712yes—
475C23×C4C23×C12711yescharacteristic
476C23×C4C23×C12712yes—
477C23×C4C23×C12711yescharacteristic
478C23×C4C23×C12712yes—
479C23×C4C23×C12711yescharacteristic
480C23×C4C23×C12711yescharacteristic
481C4×D4—232no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—42no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4C2×C4×C12714yescomplemented
507C2×C22⋊C4C2×C4×C12718yescomplemented
508C2×C42—24no—
509C2×C42D4×C12714yescomplemented
510#95—24no—
511#95—24no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—42no—
516#95—42no—
517#95—42no—
518#95C2×C4×C12714yescomplemented
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—21no—
532C24—22no—
533C24—21no—
534C24—22no—
535C24—21no—
536C24—22no—
537C24—22no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24C22×C4×C12712yes—
542C24C22×C4×C12714yes—
543C24C2×D4×C12714yes—
544C24#41×C12714yes—
545C24C24×C12711yescharacteristic
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—216no—
549C2×D4—216no—
550C2×D4—216no—
551C2×D4—28no—
552C2×D4—48no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C2×D4—48no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—216no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4C22×C4×C12714yes—
608C22×C4C22×C4×C12712yes—
609C22×C4C22×C4×C12712yes—
610C22×C4C2×D4×C12714yes—
611C22×C4C2×D4×C12712yes—
612C22×C4C2×D4×C12712yes—
613C22×C4C2×D4×C12714yes—
614C22×C4C2×D4×C12712yes—
615C22×C4#41×C12712yes—
616C4⋊C4—28no—
617C4⋊C4—44no—
618C22⋊C4—216no—
619C22⋊C4—28no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—44no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—44no—
626C42—28no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23C4×D4×C12718yes—
685C23C23×C4×C12711yescharacteristic
686C23C22×D4×C12712yes—
687C23C22×D4×C12711yescharacteristic
688C23C2×#41×C12712yes—
689C23C2×#41×C12711yescharacteristic
690C23H(5,𝔽2)×C12711yescharacteristic
691C23H(5,𝔽2)×C12712yes—
692C23H(5,𝔽2)×C12711yescharacteristic
693C23H(5,𝔽2)×C12712yes—
694C23H(5,𝔽2)×C12711yescharacteristic
695C232−1+4×C12711yescharacteristic
696D4—232no—
697D4—432no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—432no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4C4×D4×C12714yes—
749C2×C4#120×C12714yes—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—42no—
767C22—44no—
768C22—42no—
769C22—42no—
770C22—81no—
771C22—81no—
772C22—82no—
773C22—81no—
774C22—82no—
775C22—81no—
776C22C2×C4×D4×C12712yes—
777C22C2×C4×D4×C12711yescharacteristic
778C22#518×C12711yescharacteristic
779C22#518×C12712yes—
780C22#520×C12711yescharacteristic
781C22C2×#120×C12711yescharacteristic
782C22#525×C12712yes—
783C22#525×C12711yescharacteristic
784C22#534×C12712yes—
785C22#534×C12712yes—
786C22#535×C12712yes—
787C22#535×C12711yescharacteristic
788C22#535×C12711yescharacteristic
789C22#535×C12711yescharacteristic
790C22#537×C12711yescharacteristic
791C22#537×C12712yes—
792C22#538×C12712yes—
793C22#538×C12712yes—
794C22#538×C12712yes—
795C22#539×C12712yes—
796C22#540×C12711yescharacteristic
797C22#540×C12712yes—
798C22#542×C12711yescharacteristic
799C4—24no—
800C4—24no—
801C4—44no—
802C4—42no—
803C4—44no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4—82no—
808C2—48no—
809C2—82no—
810C2C4×#120×C12711yescharacteristic
811C2C127×#232112yes—
812C2C127×#232411yescharacteristic
813C2C127×#232512yes—
814C2C127×#232811yescharacteristic
815C2C127×#261311yescharacteristic
816C2C127×#261511yescharacteristic
817C2C127×#263012yes—
818C2C127×#263111yescharacteristic
819C2C127×#263512yes—
820C2C127×#263611yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C127C2semidirect
3. C2×#388×C127C2semidirect
4. C2×#386×C127C2semidirect
5. C127×#1442C2semidirect
6. C127×#1439C2semidirect
7. C127×#1439C2semidirect
8. C127×#1438C2semidirect
9. C127×#1438C2semidirect
10. C127×#1434C2semidirect
11. C127×C22⋊#95C2semidirect
28. #392×C127C4semidirect
53. C22×D4×C127C2×C4semidirect
60. C23×C4×C127D4semidirect
95. C2×C22⋊C4×C127C2×C4semidirect
96. C2×C22⋊C4×C127C2×C4semidirect
98. C2×C42×C127D4semidirect
107. #95×C127C2×C4semidirect
397. #14299C127direct (N × H)
411. C22×C4×D4C2×C127semidirect
413. C2×#388C2×C127semidirect
414. C2×#386C2×C127semidirect
415. #1442C2×C127semidirect
416. #1439C2×C127semidirect
417. #1439C2×C127semidirect
418. #1438C2×C127semidirect
419. #1438C2×C127semidirect
420. #1434C2×C127semidirect
421. C22⋊#95C2×C127semidirect
422. C127#14299direct (N × H)
439. #392C4×C127semidirect
464. C22×D4C2×C4×C127semidirect
471. C23×C4D4×C127semidirect
506. C2×C22⋊C4C2×C4×C127semidirect
507. C2×C22⋊C4C2×C4×C127semidirect
509. C2×C42D4×C127semidirect
518. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C2×#392×C1272
C2×#388×C1272
C2×#386×C1272
C127×#14422
C127×#14392
C127×#14382
C127×#14342
C127×C22⋊#952
#14299127