Finite Group Databasebeta

← C127×#15278 #44578951

Subgroups — C127×#15278 #44578951

Order 32512.

3134 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C212yesmaximal, complemented
2C2×#394×C127C212yesmaximal, complemented
3C2×#392×C127C212yesmaximal, complemented
4C2×#386×C127C212yesmaximal, complemented
5C127×#1444C211yesmaximal, characteristic, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1438C211yesmaximal, characteristic, complemented
8C127×#1438C211yesmaximal, characteristic, complemented
9C127×C22⋊#95C212yesmaximal, complemented
10C23×D4×C127C2212yes—
11C23×D4×C127C2212yes—
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C24×C4×C127C2212yes—
15C2×#121×C127—28no—
16C2×#121×C127—28no—
17C2×#121×C127—28no—
18C22×C4⋊C4×C127C2212yes—
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27#394×C127—28no—
28#392×C127—28no—
29#386×C127—28no—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2211yescharacteristic
37C25×C127C2312yes—
38C25×C127C2312yes—
39C22×D4×C127—24no—
40C22×D4×C127—24no—
41C22×D4×C127—24no—
42C22×D4×C127—24no—
43C22×D4×C127—24no—
44C22×D4×C127—24no—
45C22×D4×C127—24no—
46C22×D4×C127—24no—
47C22×D4×C127—24no—
48C22×D4×C127—24no—
49C22×D4×C127—24no—
50C22×D4×C127—24no—
51C22×D4×C127—22no—
52C22×D4×C127—42no—
53C22×D4×C127—42no—
54C22×D4×C127—41no—
55C22×D4×C127—41no—
56C22×D4×C127—41no—
57C22×D4×C127—41no—
58C22×D4×C127—42no—
59C22×D4×C127—42no—
60C22×D4×C127—42no—
61C22×D4×C127D414yescomplemented
62C22×D4×C127D418yescomplemented
63C23×C4×C127—24no—
64C23×C4×C127—24no—
65C23×C4×C127—24no—
66C23×C4×C127—24no—
67C23×C4×C127—24no—
68C23×C4×C127—42no—
69C23×C4×C127—42no—
70C23×C4×C127C2312yes—
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2312yes—
73C23×C4×C127C2312yes—
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2312yes—
77#121×C127—264no—
78C2×C4⋊C4×C127—24no—
79C2×C4⋊C4×C127—24no—
80C2×C4⋊C4×C127—24no—
81C2×C4⋊C4×C127—24no—
82C2×C4⋊C4×C127—41no—
83C2×C22⋊C4×C127—24no—
84C2×C22⋊C4×C127—24no—
85C2×C22⋊C4×C127—24no—
86C2×C22⋊C4×C127—24no—
87C2×C22⋊C4×C127—24no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—24no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—24no—
93C2×C22⋊C4×C127—24no—
94C2×C22⋊C4×C127—24no—
95C2×C22⋊C4×C127—24no—
96C2×C22⋊C4×C127—24no—
97C2×C22⋊C4×C127—24no—
98C2×C22⋊C4×C127—24no—
99C2×C22⋊C4×C127—42no—
100C2×C22⋊C4×C127—42no—
101C2×C22⋊C4×C127—42no—
102C2×C22⋊C4×C127—42no—
103C2×C22⋊C4×C127D418yescomplemented
104#95×C127—24no—
105#95×C127—24no—
106#95×C127—24no—
107#95×C127—41no—
108#95×C127—41no—
109#95×C127—41no—
110#95×C127D414yescomplemented
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—22no—
121C24×C127—22no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127—22no—
130C24×C127—22no—
131C24×C127—22no—
132C24×C127—22no—
133C24×C127—22no—
134C24×C127—22no—
135C24×C127—22no—
136C24×C127—22no—
137C24×C127C2×D414yes—
138C24×C127C2×D414yes—
139C24×C127C2×D414yes—
140C24×C127C2×D414yes—
141C24×C127C2411yescharacteristic
142C2×D4×C127—216no—
143C2×D4×C127—216no—
144C2×D4×C127—216no—
145C2×D4×C127—216no—
146C2×D4×C127—48no—
147C2×D4×C127—44no—
148C2×D4×C127—48no—
149C2×D4×C127—48no—
150C2×D4×C127—48no—
151C2×D4×C127—48no—
152C2×D4×C127—48no—
153C2×D4×C127—48no—
154C2×D4×C127—48no—
155C2×D4×C127—44no—
156C2×D4×C127—44no—
157C2×D4×C127—48no—
158C2×D4×C127—44no—
159C2×D4×C127—48no—
160C2×D4×C127—48no—
161C2×D4×C127—44no—
162C2×D4×C127—48no—
163C2×D4×C127—48no—
164C2×D4×C127—44no—
165C2×D4×C127—48no—
166C22×C4×C127—22no—
167C22×C4×C127—22no—
168C22×C4×C127—22no—
169C22×C4×C127—22no—
170C22×C4×C127—216no—
171C22×C4×C127—22no—
172C22×C4×C127—22no—
173C22×C4×C127—22no—
174C22×C4×C127—22no—
175C22×C4×C127—22no—
176C22×C4×C127—22no—
177C22×C4×C127—22no—
178C22×C4×C127—22no—
179C22×C4×C127—22no—
180C22×C4×C127—22no—
181C22×C4×C127—22no—
182C22×C4×C127—22no—
183C22×C4×C127—21no—
184C22×C4×C127—22no—
185C22×C4×C127—21no—
186C22×C4×C127—21no—
187C22×C4×C127—21no—
188C22×C4×C127—21no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127—22no—
192C22×C4×C127—22no—
193C22×C4×C127—22no—
194C22×C4×C127—21no—
195C22×C4×C127—22no—
196C22×C4×C127—22no—
197C22×C4×C127—22no—
198C22×C4×C127—22no—
199C22×C4×C127—22no—
200C22×C4×C127—22no—
201C22×C4×C127—22no—
202C22×C4×C127—48no—
203C22×C4×C127—48no—
204C22×C4×C127—48no—
205C22×C4×C127—48no—
206C22×C4×C127—48no—
207C22×C4×C127—48no—
208C22×C4×C127C2×D414yes—
209C22×C4×C127C2×D412yes—
210C22×C4×C127C2×D412yes—
211C22×C4×C127C2×D414yes—
212C22×C4×C127C2×D414yes—
213C22×C4×C127C2×D414yes—
214C22×C4×C127#4112yes—
215C22×C4×C127#4114yes—
216C4⋊C4×C127—216no—
217C4⋊C4×C127—44no—
218C22⋊C4×C127—216no—
219C22⋊C4×C127—216no—
220C22⋊C4×C127—48no—
221C22⋊C4×C127—48no—
222C22⋊C4×C127—48no—
223C22⋊C4×C127—48no—
224C22⋊C4×C127—48no—
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—24no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—24no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—24no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—24no—
246C23×C127—24no—
247C23×C127—24no—
248C23×C127—24no—
249C23×C127—24no—
250C23×C127—42no—
251C23×C127—42no—
252C23×C127—42no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127—42no—
256C23×C127—42no—
257C23×C127—42no—
258C23×C127—42no—
259C23×C127—42no—
260C23×C127—42no—
261C23×C127—42no—
262C23×C127—42no—
263C23×C127—42no—
264C23×C127—42no—
265C23×C127—42no—
266C23×C127—42no—
267C23×C127—42no—
268C23×C127—42no—
269C23×C127—42no—
270C23×C127—42no—
271C23×C127—42no—
272C23×C127—42no—
273C23×C127—42no—
274C23×C127—42no—
275C23×C127—42no—
276C23×C127—42no—
277C23×C127—42no—
278C23×C127—42no—
279C23×C127—42no—
280C23×C127—42no—
281C23×C127—42no—
282C23×C127—42no—
283C23×C127—42no—
284C23×C127—42no—
285C23×C127—42no—
286C23×C127—42no—
287C23×C127—42no—
288C23×C127—42no—
289C23×C127—42no—
290C23×C127—42no—
291C23×C127—42no—
292C23×C127—42no—
293C23×C127—42no—
294C23×C127#12018yes—
295C23×C127C22×D411yescharacteristic
296C23×C127C22×D412yes—
297C23×C127C22×D412yes—
298C23×C127C22×D411yescharacteristic
299C23×C127C2×#4112yes—
300C23×C127C2×#4111yescharacteristic
301C23×C127H(5,𝔽2)11yescharacteristic
302C23×C127H(5,𝔽2)11yescharacteristic
303C23×C127H(5,𝔽2)12yes—
304C23×C127H(5,𝔽2)11yescharacteristic
305C23×C1272−1+411yescharacteristic
306D4×C127—432no—
307D4×C127—416no—
308D4×C127—432no—
309D4×C127—416no—
310C2×C4×C127—24no—
311C2×C4×C127—24no—
312C2×C4×C127—24no—
313C2×C4×C127—24no—
314C2×C4×C127—24no—
315C2×C4×C127—24no—
316C2×C4×C127—24no—
317C2×C4×C127—24no—
318C2×C4×C127—24no—
319C2×C4×C127—22no—
320C2×C4×C127—22no—
321C2×C4×C127—22no—
322C2×C4×C127—24no—
323C2×C4×C127—24no—
324C2×C4×C127—24no—
325C2×C4×C127—24no—
326C2×C4×C127—24no—
327C2×C4×C127—24no—
328C2×C4×C127—432no—
329C2×C4×C127—42no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127—42no—
334C2×C4×C127—42no—
335C2×C4×C127—41no—
336C2×C4×C127—42no—
337C2×C4×C127—42no—
338C2×C4×C127—41no—
339C2×C4×C127—42no—
340C2×C4×C127—42no—
341C2×C4×C127—41no—
342C2×C4×C127—41no—
343C2×C4×C127—42no—
344C2×C4×C127—41no—
345C2×C4×C127—41no—
346C2×C4×C127—42no—
347C2×C4×C127—42no—
348C2×C4×C127—42no—
349C2×C4×C127—42no—
350C2×C4×C127—42no—
351C2×C4×C127—42no—
352C2×C4×C127—42no—
353C2×C4×C127#12118yescomplemented
354C22×C127—28no—
355C22×C127—28no—
356C22×C127—28no—
357C22×C127—44no—
358C22×C127—44no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—44no—
362C22×C127—44no—
363C22×C127—44no—
364C22×C127—44no—
365C22×C127—44no—
366C22×C127—44no—
367C22×C127—44no—
368C22×C127—44no—
369C22×C127—44no—
370C22×C127—44no—
371C22×C127—44no—
372C22×C127—44no—
373C22×C127—44no—
374C22×C127—44no—
375C22×C127—44no—
376C22×C127—82no—
377C22×C127—82no—
378C22×C127—82no—
379C22×C127—82no—
380C22×C127—82no—
381C22×C127—82no—
382C22×C127—82no—
383C22×C127—82no—
384C22×C127C2×#12012yes—
385C22×C127C2×#12112yes—
386C22×C127#53212yes—
387C22×C127#53411yescharacteristic
388C22×C127#53412yes—
389C22×C127#53712yes—
390C22×C127#53711yescharacteristic
391C22×C127#53811yescharacteristic
392C22×C127#54012yes—
393C22×C127D4211yescharacteristic
394C22×C127D4212yes—
395C22×C127D4211yescharacteristic
396C22×C127D4211yescharacteristic
397C22×C127D4212yes—
398C22×C127#54612yes—
399C22×C127#54612yes—
400C22×C127#54612yes—
401C22×C127#54712yes—
402C22×C127#54711yescharacteristic
403C22×C127#55011yescharacteristic
404C22×C127#55511yescharacteristic
405C22×C127#56011yescharacteristic
406C22×C127#56211yescharacteristic
407C4×C127—28no—
408C4×C127—42no—
409C4×C127—44no—
410C4×C127—44no—
411C4×C127—42no—
412C4×C127—42no—
413C4×C127—82no—
414#15278C12711yesmaximal, characteristic, direct product factor, Sylow
415C2×C127—48no—
416C2×C127—84no—
417C2×C127#240311yescharacteristic
418C2×C127#241012yes—
419C2×C127#242812yes—
420C2×C127#243012yes—
421C2×C127#253711yescharacteristic
422C2×C127#255511yescharacteristic
423C2×C127#266811yescharacteristic
424C2×C127#267112yes—
425C2×C127#267511yescharacteristic
426C2×C127#268211yescharacteristic
427C2×C127#269911yescharacteristic
428C22×#121C2×C12712yescomplemented
429C2×#394C2×C12712yescomplemented
430C2×#392C2×C12712yescomplemented
431C2×#386C2×C12712yescomplemented
432#1444C2×C12711yescharacteristic, complemented
433#1439C2×C12712yescomplemented
434#1438C2×C12711yescharacteristic, complemented
435#1438C2×C12711yescharacteristic, complemented
436C22⋊#95C2×C12712yescomplemented
437C127#1527811yescharacteristic, direct product factor, Sylow
438C23×D4C22×C12712yes—
439C23×D4C22×C12712yes—
440C23×D4C22×C12711yescharacteristic
441C23×D4C22×C12711yescharacteristic
442C24×C4C22×C12712yes—
443C2×#121—28no—
444C2×#121—28no—
445C2×#121—28no—
446C22×C4⋊C4C22×C12712yes—
447C22×C4⋊C4C22×C12711yescharacteristic
448C22×C22⋊C4C22×C12712yes—
449C22×C22⋊C4C22×C12712yes—
450C22×C22⋊C4C22×C12712yes—
451C22×C22⋊C4C22×C12712yes—
452C22×C22⋊C4C22×C12712yes—
453C22×C22⋊C4C22×C12712yes—
454C22×C22⋊C4C22×C12712yes—
455#394—28no—
456#392—28no—
457#386—28no—
458C2×#95C22×C12712yes—
459C2×#95C22×C12712yes—
460C2×#95C22×C12712yes—
461C2×#95C22×C12711yescharacteristic
462C2×#95C22×C12711yescharacteristic
463C2×#95C22×C12711yescharacteristic
464C2×#95C22×C12711yescharacteristic
465C25C23×C12712yes—
466C25C23×C12712yes—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—24no—
472C22×D4—24no—
473C22×D4—24no—
474C22×D4—24no—
475C22×D4—24no—
476C22×D4—24no—
477C22×D4—24no—
478C22×D4—24no—
479C22×D4—22no—
480C22×D4—42no—
481C22×D4—42no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4—41no—
486C22×D4—42no—
487C22×D4—42no—
488C22×D4—42no—
489C22×D4D4×C12714yescomplemented
490C22×D4D4×C12718yescomplemented
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—24no—
495C23×C4—24no—
496C23×C4—42no—
497C23×C4—42no—
498C23×C4C23×C12712yes—
499C23×C4C23×C12711yescharacteristic
500C23×C4C23×C12712yes—
501C23×C4C23×C12712yes—
502C23×C4C23×C12711yescharacteristic
503C23×C4C23×C12711yescharacteristic
504C23×C4C23×C12712yes—
505#121—264no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—41no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4D4×C12718yescomplemented
532#95—24no—
533#95—24no—
534#95—24no—
535#95—41no—
536#95—41no—
537#95—41no—
538#95D4×C12714yescomplemented
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24C2×D4×C12714yes—
566C24C2×D4×C12714yes—
567C24C2×D4×C12714yes—
568C24C2×D4×C12714yes—
569C24C24×C12711yescharacteristic
570C2×D4—216no—
571C2×D4—216no—
572C2×D4—216no—
573C2×D4—216no—
574C2×D4—48no—
575C2×D4—44no—
576C2×D4—48no—
577C2×D4—48no—
578C2×D4—48no—
579C2×D4—48no—
580C2×D4—48no—
581C2×D4—48no—
582C2×D4—48no—
583C2×D4—44no—
584C2×D4—44no—
585C2×D4—48no—
586C2×D4—44no—
587C2×D4—48no—
588C2×D4—48no—
589C2×D4—44no—
590C2×D4—48no—
591C2×D4—48no—
592C2×D4—44no—
593C2×D4—48no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—216no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4C2×D4×C12714yes—
637C22×C4C2×D4×C12712yes—
638C22×C4C2×D4×C12712yes—
639C22×C4C2×D4×C12714yes—
640C22×C4C2×D4×C12714yes—
641C22×C4C2×D4×C12714yes—
642C22×C4#41×C12712yes—
643C22×C4#41×C12714yes—
644C4⋊C4—216no—
645C4⋊C4—44no—
646C22⋊C4—216no—
647C22⋊C4—216no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23#120×C12718yes—
723C23C22×D4×C12711yescharacteristic
724C23C22×D4×C12712yes—
725C23C22×D4×C12712yes—
726C23C22×D4×C12711yescharacteristic
727C23C2×#41×C12712yes—
728C23C2×#41×C12711yescharacteristic
729C23H(5,𝔽2)×C12711yescharacteristic
730C23H(5,𝔽2)×C12711yescharacteristic
731C23H(5,𝔽2)×C12712yes—
732C23H(5,𝔽2)×C12711yescharacteristic
733C232−1+4×C12711yescharacteristic
734D4—432no—
735D4—416no—
736D4—432no—
737D4—416no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—432no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4#121×C12718yescomplemented
782C22—28no—
783C22—28no—
784C22—28no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—44no—
803C22—44no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22C2×#120×C12712yes—
813C22C2×#121×C12712yes—
814C22#532×C12712yes—
815C22#534×C12711yescharacteristic
816C22#534×C12712yes—
817C22#537×C12712yes—
818C22#537×C12711yescharacteristic
819C22#538×C12711yescharacteristic
820C22#540×C12712yes—
821C22D42×C12711yescharacteristic
822C22D42×C12712yes—
823C22D42×C12711yescharacteristic
824C22D42×C12711yescharacteristic
825C22D42×C12712yes—
826C22#546×C12712yes—
827C22#546×C12712yes—
828C22#546×C12712yes—
829C22#547×C12712yes—
830C22#547×C12711yescharacteristic
831C22#550×C12711yescharacteristic
832C22#555×C12711yescharacteristic
833C22#560×C12711yescharacteristic
834C22#562×C12711yescharacteristic
835C4—28no—
836C4—42no—
837C4—44no—
838C4—44no—
839C4—42no—
840C4—42no—
841C4—82no—
842C2—48no—
843C2—84no—
844C2C127×#240311yescharacteristic
845C2C127×#241012yes—
846C2C127×#242812yes—
847C2C127×#243012yes—
848C2C127×#253711yescharacteristic
849C2C127×#255511yescharacteristic
850C2C127×#266811yescharacteristic
851C2C127×#267112yes—
852C2C127×#267511yescharacteristic
853C2C127×#268211yescharacteristic
854C2C127×#269911yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C127C2semidirect
2. C2×#394×C127C2semidirect
3. C2×#392×C127C2semidirect
4. C2×#386×C127C2semidirect
5. C127×#1444C2semidirect
6. C127×#1439C2semidirect
7. C127×#1438C2semidirect
8. C127×#1438C2semidirect
9. C127×C22⋊#95C2semidirect
61. C22×D4×C127D4semidirect
62. C22×D4×C127D4semidirect
103. C2×C22⋊C4×C127D4semidirect
110. #95×C127D4semidirect
353. C2×C4×C127#121semidirect
414. #15278C127direct (N × H)
428. C22×#121C2×C127semidirect
429. C2×#394C2×C127semidirect
430. C2×#392C2×C127semidirect
431. C2×#386C2×C127semidirect
432. #1444C2×C127semidirect
433. #1439C2×C127semidirect
434. #1438C2×C127semidirect
435. #1438C2×C127semidirect
436. C22⋊#95C2×C127semidirect
437. C127#15278direct (N × H)
489. C22×D4D4×C127semidirect
490. C22×D4D4×C127semidirect
531. C2×C22⋊C4D4×C127semidirect
538. #95D4×C127semidirect
781. C2×C4#121×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1272
C2×#394×C1272
C2×#392×C1272
C2×#386×C1272
C127×#14442
C127×#14392
C127×#14382
C127×C22⋊#952
#15278127