Finite Group Databasebeta

← C127×#14725 #44578398

Subgroups — C127×#14725 #44578398

Order 32512.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C127C211yesmaximal, characteristic
2C23×C22⋊C4×C127C211yesmaximal, characteristic, complemented
3C2×#394×C127C212yesmaximal, complemented
4C2×#386×C127C211yesmaximal, characteristic, complemented
5C2×#386×C127C211yesmaximal, characteristic, complemented
6C2×#380×C127C211yesmaximal, characteristic, complemented
7C2×#379×C127C211yesmaximal, characteristic, complemented
8C127×#1440C212yesmaximal, complemented
9C127×#1439C212yesmaximal, complemented
10C127×#1438C212yesmaximal, complemented
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C23×D4×C127C2212yes—
15C24×C4×C127C2211yescharacteristic
16C24×C4×C127C2211yescharacteristic
17C2×#120×C127—24no—
18C2×#120×C127—24no—
19C2×#120×C127—24no—
20C22×C4⋊C4×C127C2212yescomplemented
21C22×C22⋊C4×C127—24no—
22C22×C22⋊C4×C127—28no—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2212yes—
30C22×C22⋊C4×C127C2212yes—
31C22×C22⋊C4×C127C2211yescharacteristic, complemented
32C22×C22⋊C4×C127C2212yescomplemented
33C22×C22⋊C4×C127C2211yescharacteristic, complemented
34#394×C127—28no—
35#386×C127—24no—
36#386×C127—24no—
37#380×C127—24no—
38#379×C127—24no—
39C2×#95×C127C2212yescomplemented
40C2×#95×C127C2212yescomplemented
41C2×#95×C127C2211yescharacteristic, complemented
42C2×#95×C127C2212yescomplemented
43C2×#95×C127C2211yescharacteristic, complemented
44C2×#95×C127C2212yescomplemented
45C25×C127—24no—
46C25×C127—22no—
47C25×C127—24no—
48C25×C127—22no—
49C25×C127—22no—
50C25×C127—22no—
51C25×C127—22no—
52C25×C127—22no—
53C25×C127—42no—
54C25×C127—42no—
55C25×C127D414yes—
56C25×C127C2311yescharacteristic
57C25×C127C2312yes—
58C25×C127C2311yescharacteristic
59C22×D4×C127—24no—
60C22×D4×C127—24no—
61C22×D4×C127—22no—
62C22×D4×C127—22no—
63C22×D4×C127—22no—
64C22×D4×C127—22no—
65C22×D4×C127—22no—
66C22×D4×C127—22no—
67C22×D4×C127—24no—
68C22×D4×C127—24no—
69C22×D4×C127—24no—
70C22×D4×C127—42no—
71C22×D4×C127—42no—
72C22×D4×C127D414yes—
73C23×C4×C127—22no—
74C23×C4×C127—22no—
75C23×C4×C127—22no—
76C23×C4×C127—24no—
77C23×C4×C127—24no—
78C23×C4×C127—22no—
79C23×C4×C127—22no—
80C23×C4×C127—42no—
81C23×C4×C127—42no—
82C23×C4×C127D414yescomplemented
83C23×C4×C127C2312yes—
84C23×C4×C127C2311yescharacteristic
85C23×C4×C127C2311yescharacteristic
86C23×C4×C127C2311yescharacteristic
87C23×C4×C127C2312yes—
88C23×C4×C127C2312yes—
89C23×C4×C127C2311yescharacteristic
90C23×C4×C127C2311yescharacteristic
91#120×C127—232no—
92C2×C4⋊C4×C127—24no—
93C2×C4⋊C4×C127—24no—
94C2×C4⋊C4×C127—42no—
95C2×C22⋊C4×C127—232no—
96C2×C22⋊C4×C127—24no—
97C2×C22⋊C4×C127—24no—
98C2×C22⋊C4×C127—22no—
99C2×C22⋊C4×C127—22no—
100C2×C22⋊C4×C127—24no—
101C2×C22⋊C4×C127—24no—
102C2×C22⋊C4×C127—24no—
103C2×C22⋊C4×C127—24no—
104C2×C22⋊C4×C127—24no—
105C2×C22⋊C4×C127—24no—
106C2×C22⋊C4×C127—24no—
107C2×C22⋊C4×C127—22no—
108C2×C22⋊C4×C127—24no—
109C2×C22⋊C4×C127—22no—
110C2×C22⋊C4×C127—22no—
111C2×C22⋊C4×C127—22no—
112C2×C22⋊C4×C127—22no—
113C2×C22⋊C4×C127—24no—
114C2×C22⋊C4×C127—24no—
115C2×C22⋊C4×C127—24no—
116C2×C22⋊C4×C127—22no—
117C2×C22⋊C4×C127—22no—
118C2×C22⋊C4×C127—22no—
119C2×C22⋊C4×C127—24no—
120C2×C22⋊C4×C127—24no—
121C2×C22⋊C4×C127—42no—
122C2×C22⋊C4×C127—42no—
123C2×C22⋊C4×C127—42no—
124C2×C22⋊C4×C127—42no—
125C2×C22⋊C4×C127D414yes—
126C2×C22⋊C4×C127D418yescomplemented
127#95×C127—24no—
128#95×C127—22no—
129#95×C127—22no—
130#95×C127—24no—
131#95×C127—24no—
132#95×C127—42no—
133C24×C127—22no—
134C24×C127—22no—
135C24×C127—22no—
136C24×C127—22no—
137C24×C127—28no—
138C24×C127—28no—
139C24×C127—216no—
140C24×C127—216no—
141C24×C127—28no—
142C24×C127—22no—
143C24×C127—22no—
144C24×C127—22no—
145C24×C127—22no—
146C24×C127—22no—
147C24×C127—22no—
148C24×C127—22no—
149C24×C127—22no—
150C24×C127—22no—
151C24×C127—22no—
152C24×C127—22no—
153C24×C127—22no—
154C24×C127—28no—
155C24×C127—28no—
156C24×C127—21no—
157C24×C127—22no—
158C24×C127—21no—
159C24×C127—21no—
160C24×C127—21no—
161C24×C127—21no—
162C24×C127—21no—
163C24×C127—22no—
164C24×C127—22no—
165C24×C127—22no—
166C24×C127—48no—
167C24×C127—48no—
168C24×C127—48no—
169C24×C127—48no—
170C24×C127—48no—
171C24×C127—48no—
172C24×C127—48no—
173C24×C127—48no—
174C24×C127—48no—
175C24×C127—44no—
176C24×C127—44no—
177C24×C127—48no—
178C24×C127—44no—
179C24×C127—44no—
180C24×C127—44no—
181C24×C127—44no—
182C24×C127C2×D412yes—
183C24×C127C2×D414yes—
184C24×C127C2×D414yes—
185C24×C127C2×D412yes—
186C24×C127C2×D412yes—
187C24×C127C2×D412yes—
188C24×C127C2×D412yes—
189C24×C127#4114yes—
190C24×C127#4112yes—
191C24×C127#4112yes—
192C24×C127#4112yes—
193C24×C127C2411yescharacteristic
194C2×D4×C127—216no—
195C2×D4×C127—28no—
196C2×D4×C127—28no—
197C2×D4×C127—28no—
198C2×D4×C127—48no—
199C2×D4×C127—48no—
200C2×D4×C127—48no—
201C2×D4×C127—48no—
202C2×D4×C127—48no—
203C2×D4×C127—48no—
204C2×D4×C127—44no—
205C2×D4×C127—44no—
206C2×D4×C127—44no—
207C2×D4×C127—44no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—22no—
211C22×C4×C127—28no—
212C22×C4×C127—28no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—22no—
216C22×C4×C127—22no—
217C22×C4×C127—22no—
218C22×C4×C127—22no—
219C22×C4×C127—22no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—22no—
223C22×C4×C127—22no—
224C22×C4×C127—21no—
225C22×C4×C127—22no—
226C22×C4×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—22no—
230C22×C4×C127—22no—
231C22×C4×C127—22no—
232C22×C4×C127—22no—
233C22×C4×C127—22no—
234C22×C4×C127—22no—
235C22×C4×C127—28no—
236C22×C4×C127—21no—
237C22×C4×C127—22no—
238C22×C4×C127—22no—
239C22×C4×C127—21no—
240C22×C4×C127—22no—
241C22×C4×C127—22no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—22no—
245C22×C4×C127—21no—
246C22×C4×C127—22no—
247C22×C4×C127—21no—
248C22×C4×C127—22no—
249C22×C4×C127—22no—
250C22×C4×C127—22no—
251C22×C4×C127—22no—
252C22×C4×C127—22no—
253C22×C4×C127—44no—
254C22×C4×C127—48no—
255C22×C4×C127—48no—
256C22×C4×C127—48no—
257C22×C4×C127—48no—
258C22×C4×C127—44no—
259C22×C4×C127—44no—
260C22×C4×C127C2×D412yes—
261C22×C4×C127C2×D412yes—
262C22×C4×C127C2×D414yes—
263C22×C4×C127C2×D414yes—
264C22×C4×C127C2×D412yes—
265C22×C4×C127C2×D414yes—
266C4⋊C4×C127—48no—
267C22⋊C4×C127—216no—
268C22⋊C4×C127—216no—
269C22⋊C4×C127—28no—
270C22⋊C4×C127—216no—
271C22⋊C4×C127—48no—
272C22⋊C4×C127—44no—
273C22⋊C4×C127—48no—
274C22⋊C4×C127—44no—
275C22⋊C4×C127—48no—
276C22⋊C4×C127—44no—
277C22⋊C4×C127—44no—
278C23×C127—22no—
279C23×C127—24no—
280C23×C127—22no—
281C23×C127—24no—
282C23×C127—22no—
283C23×C127—24no—
284C23×C127—22no—
285C23×C127—24no—
286C23×C127—24no—
287C23×C127—24no—
288C23×C127—24no—
289C23×C127—24no—
290C23×C127—24no—
291C23×C127—24no—
292C23×C127—24no—
293C23×C127—24no—
294C23×C127—232no—
295C23×C127—24no—
296C23×C127—24no—
297C23×C127—24no—
298C23×C127—24no—
299C23×C127—24no—
300C23×C127—24no—
301C23×C127—24no—
302C23×C127—24no—
303C23×C127—24no—
304C23×C127—24no—
305C23×C127—24no—
306C23×C127—24no—
307C23×C127—24no—
308C23×C127—24no—
309C23×C127—24no—
310C23×C127—24no—
311C23×C127—24no—
312C23×C127—24no—
313C23×C127—22no—
314C23×C127—22no—
315C23×C127—22no—
316C23×C127—24no—
317C23×C127—24no—
318C23×C127—432no—
319C23×C127—432no—
320C23×C127—416no—
321C23×C127—416no—
322C23×C127—416no—
323C23×C127—416no—
324C23×C127—432no—
325C23×C127—432no—
326C23×C127—416no—
327C23×C127—42no—
328C23×C127—42no—
329C23×C127—42no—
330C23×C127—42no—
331C23×C127—42no—
332C23×C127—42no—
333C23×C127—42no—
334C23×C127—42no—
335C23×C127—42no—
336C23×C127—42no—
337C23×C127—42no—
338C23×C127—42no—
339C23×C127—42no—
340C23×C127—42no—
341C23×C127—42no—
342C23×C127—42no—
343C23×C127—416no—
344C23×C127—41no—
345C23×C127—41no—
346C23×C127—41no—
347C23×C127—42no—
348C23×C127—41no—
349C23×C127—42no—
350C23×C127—41no—
351C23×C127—41no—
352C23×C127—41no—
353C23×C127—42no—
354C23×C127—41no—
355C23×C127—42no—
356C23×C127—42no—
357C23×C127—42no—
358C23×C127—42no—
359C23×C127—42no—
360C23×C127—42no—
361C23×C127—42no—
362C23×C127#12014yes—
363C23×C127#12118yes—
364C23×C127#12114yes—
365C23×C127#12114yes—
366C23×C127#12114yes—
367C23×C127#12314yes—
368C23×C127#12314yes—
369C23×C127#12414yes—
370C23×C127C22×D411yescharacteristic
371C23×C127C22×D411yescharacteristic
372C23×C127C22×D411yescharacteristic
373C23×C127C22×D412yes—
374C23×C127C22×D411yescharacteristic
375C23×C127C2×#4111yescharacteristic
376C23×C127C2×#4111yescharacteristic
377C23×C127C2×#4111yescharacteristic
378C23×C127C2×#4112yes—
379C23×C127H(5,𝔽2)12yes—
380C23×C127H(5,𝔽2)12yes—
381D4×C127—432no—
382D4×C127—416no—
383C2×C4×C127—22no—
384C2×C4×C127—22no—
385C2×C4×C127—24no—
386C2×C4×C127—24no—
387C2×C4×C127—24no—
388C2×C4×C127—22no—
389C2×C4×C127—22no—
390C2×C4×C127—24no—
391C2×C4×C127—22no—
392C2×C4×C127—22no—
393C2×C4×C127—22no—
394C2×C4×C127—22no—
395C2×C4×C127—24no—
396C2×C4×C127—24no—
397C2×C4×C127—24no—
398C2×C4×C127—24no—
399C2×C4×C127—416no—
400C2×C4×C127—416no—
401C2×C4×C127—42no—
402C2×C4×C127—41no—
403C2×C4×C127—41no—
404C2×C4×C127—42no—
405C2×C4×C127—41no—
406C2×C4×C127—41no—
407C2×C4×C127—42no—
408C2×C4×C127—42no—
409C2×C4×C127—42no—
410C2×C4×C127—42no—
411C2×C4×C127—42no—
412C2×C4×C127—42no—
413C2×C4×C127—42no—
414C2×C4×C127—42no—
415C2×C4×C127—41no—
416C2×C4×C127—42no—
417C2×C4×C127—41no—
418C2×C4×C127—42no—
419C2×C4×C127—41no—
420C2×C4×C127—42no—
421C2×C4×C127—41no—
422C2×C4×C127—42no—
423C2×C4×C127—42no—
424C2×C4×C127—41no—
425C2×C4×C127—42no—
426C2×C4×C127—41no—
427C2×C4×C127—42no—
428C2×C4×C127—42no—
429C2×C4×C127—42no—
430C2×C4×C127—42no—
431C2×C4×C127—42no—
432C2×C4×C127#12014yescomplemented
433C22×C127—24no—
434C22×C127—24no—
435C22×C127—24no—
436C22×C127—24no—
437C22×C127—28no—
438C22×C127—24no—
439C22×C127—28no—
440C22×C127—28no—
441C22×C127—28no—
442C22×C127—24no—
443C22×C127—28no—
444C22×C127—28no—
445C22×C127—28no—
446C22×C127—464no—
447C22×C127—44no—
448C22×C127—44no—
449C22×C127—44no—
450C22×C127—44no—
451C22×C127—44no—
452C22×C127—44no—
453C22×C127—44no—
454C22×C127—44no—
455C22×C127—44no—
456C22×C127—44no—
457C22×C127—44no—
458C22×C127—44no—
459C22×C127—42no—
460C22×C127—42no—
461C22×C127—44no—
462C22×C127—44no—
463C22×C127—42no—
464C22×C127—81no—
465C22×C127—81no—
466C22×C127—81no—
467C22×C127—81no—
468C22×C127—82no—
469C22×C127—82no—
470C22×C127#39418yescomplemented
471C22×C127C2×#12011yescharacteristic
472C22×C127C2×#12011yescharacteristic
473C22×C127C2×#12111yescharacteristic
474C22×C127C2×#12112yes—
475C22×C127C2×#12111yescharacteristic
476C22×C127C2×#12111yescharacteristic
477C22×C127C2×#12311yescharacteristic
478C22×C127C2×#12311yescharacteristic
479C22×C127#52511yescharacteristic
480C22×C127#52512yes—
481C22×C127C2×#12411yescharacteristic
482C22×C127#53412yes—
483C22×C127#53411yescharacteristic
484C22×C127#53511yescharacteristic
485C22×C127#53812yes—
486C22×C127D4212yes—
487C22×C127D4212yes—
488C22×C127#54612yes—
489C22×C127#54612yes—
490C22×C127#54612yes—
491C22×C127#54612yes—
492C22×C127#55112yes—
493C22×C127#55112yes—
494C4×C127—24no—
495C4×C127—42no—
496C4×C127—44no—
497C4×C127—42no—
498C4×C127—44no—
499C4×C127—81no—
500C4×C127—81no—
501C4×C127—82no—
502#14725C12711yesmaximal, characteristic, direct product factor, Sylow
503C2×C127—28no—
504C2×C127—48no—
505C2×C127—82no—
506C2×C127C2×#39411yescharacteristic
507C2×C127#240811yescharacteristic
508C2×C127#241011yescharacteristic
509C2×C127#241012yes—
510C2×C127#241111yescharacteristic
511C2×C127#241212yes—
512C2×C127#241812yes—
513C2×C127#247212yes—
514C2×C127#253411yescharacteristic
515C2×C127#261711yescharacteristic
516C2×C127#284711yescharacteristic
517C22×#120C2×C12711yescharacteristic
518C23×C22⋊C4C2×C12711yescharacteristic, complemented
519C2×#394C2×C12712yescomplemented
520C2×#386C2×C12711yescharacteristic, complemented
521C2×#386C2×C12711yescharacteristic, complemented
522C2×#380C2×C12711yescharacteristic, complemented
523C2×#379C2×C12711yescharacteristic, complemented
524#1440C2×C12712yescomplemented
525#1439C2×C12712yescomplemented
526#1438C2×C12712yescomplemented
527C22⋊#95C2×C12711yescharacteristic, complemented
528C127#1472511yescharacteristic, direct product factor, Sylow
529C26C22×C12711yescharacteristic
530C23×D4C22×C12711yescharacteristic
531C23×D4C22×C12712yes—
532C24×C4C22×C12711yescharacteristic
533C24×C4C22×C12711yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C12712yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C12712yes—
541C22×C22⋊C4C22×C12712yes—
542C22×C22⋊C4C22×C12712yes—
543C22×C22⋊C4C22×C12711yescharacteristic
544C22×C22⋊C4C22×C12711yescharacteristic
545C22×C22⋊C4C22×C12711yescharacteristic
546C22×C22⋊C4C22×C12712yes—
547C22×C22⋊C4C22×C12712yes—
548C22×C22⋊C4C22×C12711yescharacteristic, complemented
549C22×C22⋊C4C22×C12712yescomplemented
550C22×C22⋊C4C22×C12711yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C12712yescomplemented
557C2×#95C22×C12712yescomplemented
558C2×#95C22×C12711yescharacteristic, complemented
559C2×#95C22×C12712yescomplemented
560C2×#95C22×C12711yescharacteristic, complemented
561C2×#95C22×C12712yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C12714yes—
573C25C23×C12711yescharacteristic
574C25C23×C12712yes—
575C25C23×C12711yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C12714yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C12714yescomplemented
600C23×C4C23×C12712yes—
601C23×C4C23×C12711yescharacteristic
602C23×C4C23×C12711yescharacteristic
603C23×C4C23×C12711yescharacteristic
604C23×C4C23×C12712yes—
605C23×C4C23×C12712yes—
606C23×C4C23×C12711yescharacteristic
607C23×C4C23×C12711yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C12714yes—
643C2×C22⋊C4D4×C12718yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C12712yes—
700C24C2×D4×C12714yes—
701C24C2×D4×C12714yes—
702C24C2×D4×C12712yes—
703C24C2×D4×C12712yes—
704C24C2×D4×C12712yes—
705C24C2×D4×C12712yes—
706C24#41×C12714yes—
707C24#41×C12712yes—
708C24#41×C12712yes—
709C24#41×C12712yes—
710C24C24×C12711yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C12712yes—
778C22×C4C2×D4×C12712yes—
779C22×C4C2×D4×C12714yes—
780C22×C4C2×D4×C12714yes—
781C22×C4C2×D4×C12712yes—
782C22×C4C2×D4×C12714yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—432no—
842C23—432no—
843C23—416no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—416no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—42no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C12714yes—
880C23#121×C12718yes—
881C23#121×C12714yes—
882C23#121×C12714yes—
883C23#121×C12714yes—
884C23#123×C12714yes—
885C23#123×C12714yes—
886C23#124×C12714yes—
887C23C22×D4×C12711yescharacteristic
888C23C22×D4×C12711yescharacteristic
889C23C22×D4×C12711yescharacteristic
890C23C22×D4×C12712yes—
891C23C22×D4×C12711yescharacteristic
892C23C2×#41×C12711yescharacteristic
893C23C2×#41×C12711yescharacteristic
894C23C2×#41×C12711yescharacteristic
895C23C2×#41×C12712yes—
896C23H(5,𝔽2)×C12712yes—
897C23H(5,𝔽2)×C12712yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—41no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C12714yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—28no—
955C22—24no—
956C22—28no—
957C22—28no—
958C22—28no—
959C22—24no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—44no—
979C22—44no—
980C22—42no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22#394×C12718yescomplemented
988C22C2×#120×C12711yescharacteristic
989C22C2×#120×C12711yescharacteristic
990C22C2×#121×C12711yescharacteristic
991C22C2×#121×C12712yes—
992C22C2×#121×C12711yescharacteristic
993C22C2×#121×C12711yescharacteristic
994C22C2×#123×C12711yescharacteristic
995C22C2×#123×C12711yescharacteristic
996C22#525×C12711yescharacteristic
997C22#525×C12712yes—
998C22C2×#124×C12711yescharacteristic
999C22#534×C12712yes—
1000C22#534×C12711yescharacteristic
1001C22#535×C12711yescharacteristic
1002C22#538×C12712yes—
1003C22D42×C12712yes—
1004C22D42×C12712yes—
1005C22#546×C12712yes—
1006C22#546×C12712yes—
1007C22#546×C12712yes—
1008C22#546×C12712yes—
1009C22#551×C12712yes—
1010C22#551×C12712yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C12711yescharacteristic
1023C2C127×#240811yescharacteristic
1024C2C127×#241011yescharacteristic
1025C2C127×#241012yes—
1026C2C127×#241111yescharacteristic
1027C2C127×#241212yes—
1028C2C127×#241812yes—
1029C2C127×#247212yes—
1030C2C127×#253411yescharacteristic
1031C2C127×#261711yescharacteristic
1032C2C127×#284711yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC22×#120×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C127C2semidirect
3. C2×#394×C127C2semidirect
4. C2×#386×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#380×C127C2semidirect
7. C2×#379×C127C2semidirect
8. C127×#1440C2semidirect
9. C127×#1439C2semidirect
10. C127×#1438C2semidirect
11. C127×C22⋊#95C2semidirect
20. C22×C4⋊C4×C127C22semidirect
31. C22×C22⋊C4×C127C22semidirect
32. C22×C22⋊C4×C127C22semidirect
33. C22×C22⋊C4×C127C22semidirect
39. C2×#95×C127C22semidirect
40. C2×#95×C127C22semidirect
41. C2×#95×C127C22semidirect
42. C2×#95×C127C22semidirect
43. C2×#95×C127C22semidirect
44. C2×#95×C127C22semidirect
82. C23×C4×C127D4semidirect
126. C2×C22⋊C4×C127D4semidirect
432. C2×C4×C127#120semidirect
470. C22×C127#394semidirect
502. #14725C127direct (N × H)
518. C23×C22⋊C4C2×C127semidirect
519. C2×#394C2×C127semidirect
520. C2×#386C2×C127semidirect
521. C2×#386C2×C127semidirect
522. C2×#380C2×C127semidirect
523. C2×#379C2×C127semidirect
524. #1440C2×C127semidirect
525. #1439C2×C127semidirect
526. #1438C2×C127semidirect
527. C22⋊#95C2×C127semidirect
528. C127#14725direct (N × H)
537. C22×C4⋊C4C22×C127semidirect
548. C22×C22⋊C4C22×C127semidirect
549. C22×C22⋊C4C22×C127semidirect
550. C22×C22⋊C4C22×C127semidirect
556. C2×#95C22×C127semidirect
557. C2×#95C22×C127semidirect
558. C2×#95C22×C127semidirect
559. C2×#95C22×C127semidirect
560. C2×#95C22×C127semidirect
561. C2×#95C22×C127semidirect
599. C23×C4D4×C127semidirect
643. C2×C22⋊C4D4×C127semidirect
949. C2×C4#120×C127semidirect
987. C22#394×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1272
C23×C22⋊C4×C1272
C2×#394×C1272
C2×#386×C1272
C2×#380×C1272
C2×#379×C1272
C127×#14402
C127×#14392
C127×#14382
C127×C22⋊#952
#14725127