Finite Group Databasebeta

← C127×#15283 #44578956

Subgroups — C127×#15283 #44578956

Order 32512.

3494 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C127C211yesmaximal, characteristic
2C2×#399×C127C211yesmaximal, characteristic, complemented
3C2×#397×C127C211yesmaximal, characteristic, complemented
4C2×#394×C127C212yesmaximal, complemented
5C2×#390×C127C211yesmaximal, characteristic, complemented
6C2×#379×C127C212yesmaximal, complemented
7C127×#1439C212yesmaximal, complemented
8C127×#1438C212yesmaximal, complemented
9C127×#1438C211yesmaximal, characteristic, complemented
10C127×#1437C211yesmaximal, characteristic, complemented
11C127×#1437C211yesmaximal, characteristic, complemented
12C26×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C23×D4×C127C2211yescharacteristic
15C23×D4×C127C2211yescharacteristic
16C2×#120×C127—24no—
17C2×#120×C127—24no—
18C2×#120×C127—24no—
19C22×C4⋊C4×C127C2211yescharacteristic, complemented
20C22×C4⋊C4×C127C2212yescomplemented
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2212yes—
30C22×C22⋊C4×C127C2212yescomplemented
31C22×C22⋊C4×C127C2212yescomplemented
32C22×C42×C127C2211yescharacteristic, complemented
33#399×C127—24no—
34#397×C127—24no—
35#394×C127—28no—
36#390×C127—24no—
37#379×C127—28no—
38C2×#95×C127C2212yescomplemented
39C2×#95×C127C2211yescharacteristic, complemented
40C2×#95×C127C2212yescomplemented
41C2×#95×C127C2211yescharacteristic, complemented
42C2×#95×C127C2212yescomplemented
43C25×C127—22no—
44C25×C127—22no—
45C25×C127—22no—
46C25×C127—24no—
47C25×C127—24no—
48C25×C127—24no—
49C25×C127—42no—
50C25×C127—42no—
51C25×C127—42no—
52C25×C127C2311yescharacteristic
53C25×C127C2311yescharacteristic
54C25×C127C2311yescharacteristic
55C25×C127C2311yescharacteristic
56C22×D4×C127—22no—
57C22×D4×C127—22no—
58C22×D4×C127—22no—
59C22×D4×C127—22no—
60C22×D4×C127—24no—
61C22×D4×C127—24no—
62C22×D4×C127—24no—
63C22×D4×C127—22no—
64C22×D4×C127—22no—
65C22×D4×C127—22no—
66C22×D4×C127—22no—
67C22×D4×C127—42no—
68C22×D4×C127—42no—
69C22×D4×C127—42no—
70C22×D4×C127D414yes—
71C23×C4×C127C2312yes—
72C23×C4×C127C2312yes—
73C23×C4×C127C2312yes—
74C23×C4×C127C2312yes—
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2311yescharacteristic
78#120×C127—232no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—24no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—24no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—42no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—22no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—22no—
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—24no—
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—42no—
107C2×C22⋊C4×C127—42no—
108C2×C22⋊C4×C127—42no—
109C2×C22⋊C4×C127—42no—
110C2×C22⋊C4×C127—42no—
111C2×C22⋊C4×C127—42no—
112C2×C22⋊C4×C127—42no—
113C2×C22⋊C4×C127—42no—
114C2×C22⋊C4×C127—42no—
115C2×C22⋊C4×C127D414yes—
116C2×C22⋊C4×C127D414yes—
117C2×C22⋊C4×C127D418yescomplemented
118C2×C42×C127—22no—
119C2×C42×C127—42no—
120#95×C127—24no—
121#95×C127—22no—
122#95×C127—24no—
123#95×C127—22no—
124#95×C127—42no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—21no—
128C24×C127—21no—
129C24×C127—21no—
130C24×C127—21no—
131C24×C127—21no—
132C24×C127—21no—
133C24×C127—22no—
134C24×C127—22no—
135C24×C127—22no—
136C24×C127—22no—
137C24×C127—22no—
138C24×C127—22no—
139C24×C127—22no—
140C24×C127—22no—
141C24×C127—22no—
142C24×C127—22no—
143C24×C127—22no—
144C24×C127—22no—
145C24×C127—22no—
146C24×C127—28no—
147C24×C127—216no—
148C24×C127—22no—
149C24×C127—21no—
150C24×C127—21no—
151C24×C127—22no—
152C24×C127—22no—
153C24×C127—22no—
154C24×C127—22no—
155C24×C127—22no—
156C24×C127—48no—
157C24×C127—48no—
158C24×C127—48no—
159C24×C127—48no—
160C24×C127—48no—
161C24×C127—48no—
162C24×C127—48no—
163C24×C127—48no—
164C24×C127—48no—
165C24×C127—48no—
166C24×C127—44no—
167C24×C127—44no—
168C24×C127—44no—
169C24×C127—48no—
170C24×C127—48no—
171C24×C127—48no—
172C24×C127—44no—
173C24×C127—44no—
174C24×C127—44no—
175C24×C127C2×D412yes—
176C24×C127C2×D412yes—
177C24×C127C2×D412yes—
178C24×C127C2×D412yes—
179C24×C127C2×D414yes—
180C24×C127#4114yes—
181C24×C127#4114yes—
182C24×C127C2411yescharacteristic
183C2×D4×C127—28no—
184C2×D4×C127—28no—
185C2×D4×C127—28no—
186C2×D4×C127—28no—
187C2×D4×C127—44no—
188C2×D4×C127—48no—
189C2×D4×C127—48no—
190C2×D4×C127—48no—
191C2×D4×C127—48no—
192C2×D4×C127—48no—
193C2×D4×C127—48no—
194C2×D4×C127—44no—
195C2×D4×C127—44no—
196C2×D4×C127—44no—
197C2×D4×C127—44no—
198C22×C4×C127—22no—
199C22×C4×C127—22no—
200C22×C4×C127—22no—
201C22×C4×C127—22no—
202C22×C4×C127—22no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—22no—
208C22×C4×C127—22no—
209C22×C4×C127—22no—
210C22×C4×C127—22no—
211C22×C4×C127—22no—
212C22×C4×C127—22no—
213C22×C4×C127—22no—
214C22×C4×C127—22no—
215C22×C4×C127—22no—
216C22×C4×C127—22no—
217C22×C4×C127—22no—
218C22×C4×C127—22no—
219C22×C4×C127—22no—
220C22×C4×C127—22no—
221C22×C4×C127—22no—
222C22×C4×C127—22no—
223C22×C4×C127—22no—
224C22×C4×C127—22no—
225C22×C4×C127—22no—
226C22×C4×C127—22no—
227C22×C4×C127—22no—
228C22×C4×C127—22no—
229C22×C4×C127—22no—
230C22×C4×C127—22no—
231C22×C4×C127—22no—
232C22×C4×C127—22no—
233C22×C4×C127—22no—
234C22×C4×C127C2×D412yes—
235C22×C4×C127C2×D414yes—
236C22×C4×C127C2×D414yes—
237C22×C4×C127C2×D412yes—
238C22×C4×C127C2×D412yes—
239C22×C4×C127C2×D412yes—
240C22×C4×C127C2×D412yes—
241C4⋊C4×C127—48no—
242C4⋊C4×C127—44no—
243C22⋊C4×C127—28no—
244C22⋊C4×C127—28no—
245C22⋊C4×C127—28no—
246C22⋊C4×C127—48no—
247C22⋊C4×C127—48no—
248C22⋊C4×C127—48no—
249C22⋊C4×C127—48no—
250C22⋊C4×C127—48no—
251C22⋊C4×C127—48no—
252C22⋊C4×C127—48no—
253C22⋊C4×C127—48no—
254C42×C127—44no—
255C23×C127—22no—
256C23×C127—22no—
257C23×C127—22no—
258C23×C127—24no—
259C23×C127—24no—
260C23×C127—24no—
261C23×C127—24no—
262C23×C127—22no—
263C23×C127—22no—
264C23×C127—22no—
265C23×C127—24no—
266C23×C127—24no—
267C23×C127—24no—
268C23×C127—24no—
269C23×C127—24no—
270C23×C127—24no—
271C23×C127—24no—
272C23×C127—24no—
273C23×C127—24no—
274C23×C127—24no—
275C23×C127—24no—
276C23×C127—24no—
277C23×C127—24no—
278C23×C127—24no—
279C23×C127—24no—
280C23×C127—24no—
281C23×C127—24no—
282C23×C127—24no—
283C23×C127—24no—
284C23×C127—24no—
285C23×C127—22no—
286C23×C127—22no—
287C23×C127—22no—
288C23×C127—24no—
289C23×C127—24no—
290C23×C127—416no—
291C23×C127—432no—
292C23×C127—416no—
293C23×C127—416no—
294C23×C127—432no—
295C23×C127—432no—
296C23×C127—432no—
297C23×C127—432no—
298C23×C127—432no—
299C23×C127—41no—
300C23×C127—41no—
301C23×C127—41no—
302C23×C127—41no—
303C23×C127—41no—
304C23×C127—41no—
305C23×C127—41no—
306C23×C127—41no—
307C23×C127—42no—
308C23×C127—42no—
309C23×C127—41no—
310C23×C127—41no—
311C23×C127—41no—
312C23×C127—41no—
313C23×C127—42no—
314C23×C127—42no—
315C23×C127—42no—
316C23×C127—42no—
317C23×C127—42no—
318C23×C127—42no—
319C23×C127—42no—
320C23×C127—42no—
321C23×C127—42no—
322C23×C127—42no—
323C23×C127—42no—
324C23×C127—42no—
325C23×C127—42no—
326C23×C127—42no—
327C23×C127—42no—
328C23×C127—42no—
329C23×C127—42no—
330C23×C127—41no—
331C23×C127—41no—
332C23×C127—42no—
333C23×C127—41no—
334C23×C127—41no—
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—42no—
344C23×C127—42no—
345C23×C127#12314yes—
346C23×C127#12414yes—
347C23×C127#12714yes—
348C23×C127C22×D411yescharacteristic
349C23×C127C22×D411yescharacteristic
350C23×C127C22×D411yescharacteristic
351C23×C127C22×D412yes—
352C23×C127C2×#4112yes—
353C23×C127C2×#4112yes—
354C23×C127H(5,𝔽2)12yes—
355C23×C127H(5,𝔽2)12yes—
356C23×C127H(5,𝔽2)12yes—
357D4×C127—416no—
358D4×C127—416no—
359D4×C127—416no—
360C2×C4×C127—22no—
361C2×C4×C127—22no—
362C2×C4×C127—24no—
363C2×C4×C127—24no—
364C2×C4×C127—22no—
365C2×C4×C127—22no—
366C2×C4×C127—24no—
367C2×C4×C127—24no—
368C2×C4×C127—24no—
369C2×C4×C127—24no—
370C2×C4×C127—24no—
371C2×C4×C127—24no—
372C2×C4×C127—24no—
373C2×C4×C127—24no—
374C2×C4×C127—41no—
375C2×C4×C127—41no—
376C2×C4×C127—42no—
377C2×C4×C127—42no—
378C2×C4×C127—41no—
379C2×C4×C127—41no—
380C2×C4×C127—42no—
381C2×C4×C127—42no—
382C2×C4×C127—42no—
383C2×C4×C127—42no—
384C2×C4×C127—42no—
385C2×C4×C127—42no—
386C2×C4×C127—42no—
387C2×C4×C127—42no—
388C2×C4×C127—42no—
389C2×C4×C127—42no—
390C2×C4×C127—42no—
391C2×C4×C127—42no—
392C2×C4×C127—42no—
393C2×C4×C127—42no—
394C2×C4×C127—42no—
395C2×C4×C127—42no—
396C2×C4×C127—42no—
397C2×C4×C127—42no—
398C2×C4×C127—42no—
399C2×C4×C127—42no—
400C2×C4×C127—42no—
401C2×C4×C127—42no—
402C2×C4×C127#12014yes—
403C22×C127—24no—
404C22×C127—28no—
405C22×C127—24no—
406C22×C127—24no—
407C22×C127—28no—
408C22×C127—28no—
409C22×C127—464no—
410C22×C127—42no—
411C22×C127—42no—
412C22×C127—44no—
413C22×C127—44no—
414C22×C127—44no—
415C22×C127—44no—
416C22×C127—44no—
417C22×C127—44no—
418C22×C127—44no—
419C22×C127—44no—
420C22×C127—44no—
421C22×C127—44no—
422C22×C127—44no—
423C22×C127—42no—
424C22×C127—42no—
425C22×C127—42no—
426C22×C127—42no—
427C22×C127—44no—
428C22×C127—44no—
429C22×C127—44no—
430C22×C127—44no—
431C22×C127—42no—
432C22×C127—44no—
433C22×C127—44no—
434C22×C127—42no—
435C22×C127—42no—
436C22×C127—82no—
437C22×C127—82no—
438C22×C127—82no—
439C22×C127—82no—
440C22×C127C2×#12011yescharacteristic
441C22×C127C2×#12311yescharacteristic
442C22×C127#52512yes—
443C22×C127C2×#12411yescharacteristic
444C22×C127C2×#12711yescharacteristic
445C22×C127#53411yescharacteristic
446C22×C127#53412yes—
447C22×C127#53511yescharacteristic
448C22×C127#53511yescharacteristic
449C22×C127#53812yes—
450C22×C127#53812yes—
451C22×C127D4212yes—
452C22×C127D4212yes—
453C22×C127#54612yes—
454C22×C127#54612yes—
455C22×C127#54612yes—
456C22×C127#54612yes—
457C22×C127#54612yes—
458C22×C127#54612yes—
459C22×C127#55112yes—
460C22×C127#56012yes—
461C4×C127—24no—
462C4×C127—44no—
463C4×C127—44no—
464C4×C127—42no—
465C4×C127—42no—
466C4×C127—82no—
467C4×C127—82no—
468#15283C12711yesmaximal, characteristic, direct product factor, Sylow
469C2×C127—44no—
470C2×C127—44no—
471C2×C127—44no—
472C2×C127—82no—
473C2×C127#240511yescharacteristic
474C2×C127#241812yes—
475C2×C127#243311yescharacteristic
476C2×C127#243511yescharacteristic
477C2×C127#247212yes—
478C2×C127#253912yes—
479C2×C127#266812yes—
480C2×C127#267812yes—
481C2×C127#268512yes—
482C22×#120C2×C12711yescharacteristic
483C2×#399C2×C12711yescharacteristic, complemented
484C2×#397C2×C12711yescharacteristic, complemented
485C2×#394C2×C12712yescomplemented
486C2×#390C2×C12711yescharacteristic, complemented
487C2×#379C2×C12712yescomplemented
488#1439C2×C12712yescomplemented
489#1438C2×C12712yescomplemented
490#1438C2×C12711yescharacteristic, complemented
491#1437C2×C12711yescharacteristic, complemented
492#1437C2×C12711yescharacteristic, complemented
493C127#1528311yescharacteristic, direct product factor, Sylow
494C26C22×C12711yescharacteristic
495C23×D4C22×C12711yescharacteristic
496C23×D4C22×C12711yescharacteristic
497C23×D4C22×C12711yescharacteristic
498C2×#120—24no—
499C2×#120—24no—
500C2×#120—24no—
501C22×C4⋊C4C22×C12711yescharacteristic, complemented
502C22×C4⋊C4C22×C12712yescomplemented
503C22×C22⋊C4C22×C12712yes—
504C22×C22⋊C4C22×C12711yescharacteristic
505C22×C22⋊C4C22×C12712yes—
506C22×C22⋊C4C22×C12712yes—
507C22×C22⋊C4C22×C12712yes—
508C22×C22⋊C4C22×C12712yes—
509C22×C22⋊C4C22×C12711yescharacteristic
510C22×C22⋊C4C22×C12711yescharacteristic
511C22×C22⋊C4C22×C12712yes—
512C22×C22⋊C4C22×C12712yescomplemented
513C22×C22⋊C4C22×C12712yescomplemented
514C22×C42C22×C12711yescharacteristic, complemented
515#399—24no—
516#397—24no—
517#394—28no—
518#390—24no—
519#379—28no—
520C2×#95C22×C12712yescomplemented
521C2×#95C22×C12711yescharacteristic, complemented
522C2×#95C22×C12712yescomplemented
523C2×#95C22×C12711yescharacteristic, complemented
524C2×#95C22×C12712yescomplemented
525C25—22no—
526C25—22no—
527C25—22no—
528C25—24no—
529C25—24no—
530C25—24no—
531C25—42no—
532C25—42no—
533C25—42no—
534C25C23×C12711yescharacteristic
535C25C23×C12711yescharacteristic
536C25C23×C12711yescharacteristic
537C25C23×C12711yescharacteristic
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—24no—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—42no—
550C22×D4—42no—
551C22×D4—42no—
552C22×D4D4×C12714yes—
553C23×C4C23×C12712yes—
554C23×C4C23×C12712yes—
555C23×C4C23×C12712yes—
556C23×C4C23×C12712yes—
557C23×C4C23×C12711yescharacteristic
558C23×C4C23×C12711yescharacteristic
559C23×C4C23×C12711yescharacteristic
560#120—232no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—24no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—24no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—42no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4D4×C12714yes—
598C2×C22⋊C4D4×C12714yes—
599C2×C22⋊C4D4×C12718yescomplemented
600C2×C42—22no—
601C2×C42—42no—
602#95—24no—
603#95—22no—
604#95—24no—
605#95—22no—
606#95—42no—
607C24—22no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—28no—
629C24—216no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—48no—
639C24—48no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—44no—
649C24—44no—
650C24—44no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—44no—
655C24—44no—
656C24—44no—
657C24C2×D4×C12712yes—
658C24C2×D4×C12712yes—
659C24C2×D4×C12712yes—
660C24C2×D4×C12712yes—
661C24C2×D4×C12714yes—
662C24#41×C12714yes—
663C24#41×C12714yes—
664C24C24×C12711yescharacteristic
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—44no—
670C2×D4—48no—
671C2×D4—48no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4C2×D4×C12712yes—
717C22×C4C2×D4×C12714yes—
718C22×C4C2×D4×C12714yes—
719C22×C4C2×D4×C12712yes—
720C22×C4C2×D4×C12712yes—
721C22×C4C2×D4×C12712yes—
722C22×C4C2×D4×C12712yes—
723C4⋊C4—48no—
724C4⋊C4—44no—
725C22⋊C4—28no—
726C22⋊C4—28no—
727C22⋊C4—28no—
728C22⋊C4—48no—
729C22⋊C4—48no—
730C22⋊C4—48no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—48no—
734C22⋊C4—48no—
735C22⋊C4—48no—
736C42—44no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—24no—
772C23—416no—
773C23—432no—
774C23—416no—
775C23—416no—
776C23—432no—
777C23—432no—
778C23—432no—
779C23—432no—
780C23—432no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—42no—
790C23—42no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—41no—
816C23—41no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23#123×C12714yes—
828C23#124×C12714yes—
829C23#127×C12714yes—
830C23C22×D4×C12711yescharacteristic
831C23C22×D4×C12711yescharacteristic
832C23C22×D4×C12711yescharacteristic
833C23C22×D4×C12712yes—
834C23C2×#41×C12712yes—
835C23C2×#41×C12712yes—
836C23H(5,𝔽2)×C12712yes—
837C23H(5,𝔽2)×C12712yes—
838C23H(5,𝔽2)×C12712yes—
839D4—416no—
840D4—416no—
841D4—416no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4#120×C12714yes—
885C22—24no—
886C22—28no—
887C22—24no—
888C22—24no—
889C22—28no—
890C22—28no—
891C22—464no—
892C22—42no—
893C22—42no—
894C22—44no—
895C22—44no—
896C22—44no—
897C22—44no—
898C22—44no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—44no—
910C22—44no—
911C22—44no—
912C22—44no—
913C22—42no—
914C22—44no—
915C22—44no—
916C22—42no—
917C22—42no—
918C22—82no—
919C22—82no—
920C22—82no—
921C22—82no—
922C22C2×#120×C12711yescharacteristic
923C22C2×#123×C12711yescharacteristic
924C22#525×C12712yes—
925C22C2×#124×C12711yescharacteristic
926C22C2×#127×C12711yescharacteristic
927C22#534×C12711yescharacteristic
928C22#534×C12712yes—
929C22#535×C12711yescharacteristic
930C22#535×C12711yescharacteristic
931C22#538×C12712yes—
932C22#538×C12712yes—
933C22D42×C12712yes—
934C22D42×C12712yes—
935C22#546×C12712yes—
936C22#546×C12712yes—
937C22#546×C12712yes—
938C22#546×C12712yes—
939C22#546×C12712yes—
940C22#546×C12712yes—
941C22#551×C12712yes—
942C22#560×C12712yes—
943C4—24no—
944C4—44no—
945C4—44no—
946C4—42no—
947C4—42no—
948C4—82no—
949C4—82no—
950C2—44no—
951C2—44no—
952C2—44no—
953C2—82no—
954C2C127×#240511yescharacteristic
955C2C127×#241812yes—
956C2C127×#243311yescharacteristic
957C2C127×#243511yescharacteristic
958C2C127×#247212yes—
959C2C127×#253912yes—
960C2C127×#266812yes—
961C2C127×#267812yes—
962C2C127×#268512yes—
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. C2×#399×C127C2semidirect
3. C2×#397×C127C2semidirect
4. C2×#394×C127C2semidirect
5. C2×#390×C127C2semidirect
6. C2×#379×C127C2semidirect
7. C127×#1439C2semidirect
8. C127×#1438C2semidirect
9. C127×#1438C2semidirect
10. C127×#1437C2semidirect
11. C127×#1437C2semidirect
19. C22×C4⋊C4×C127C22semidirect
20. C22×C4⋊C4×C127C22semidirect
30. C22×C22⋊C4×C127C22semidirect
31. C22×C22⋊C4×C127C22semidirect
32. C22×C42×C127C22semidirect
38. C2×#95×C127C22semidirect
39. C2×#95×C127C22semidirect
40. C2×#95×C127C22semidirect
41. C2×#95×C127C22semidirect
42. C2×#95×C127C22semidirect
117. C2×C22⋊C4×C127D4semidirect
468. #15283C127direct (N × H)
483. C2×#399C2×C127semidirect
484. C2×#397C2×C127semidirect
485. C2×#394C2×C127semidirect
486. C2×#390C2×C127semidirect
487. C2×#379C2×C127semidirect
488. #1439C2×C127semidirect
489. #1438C2×C127semidirect
490. #1438C2×C127semidirect
491. #1437C2×C127semidirect
492. #1437C2×C127semidirect
493. C127#15283direct (N × H)
501. C22×C4⋊C4C22×C127semidirect
502. C22×C4⋊C4C22×C127semidirect
512. C22×C22⋊C4C22×C127semidirect
513. C22×C22⋊C4C22×C127semidirect
514. C22×C42C22×C127semidirect
520. C2×#95C22×C127semidirect
521. C2×#95C22×C127semidirect
522. C2×#95C22×C127semidirect
523. C2×#95C22×C127semidirect
524. C2×#95C22×C127semidirect
599. C2×C22⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1272
C2×#399×C1272
C2×#397×C1272
C2×#394×C1272
C2×#390×C1272
C2×#379×C1272
C127×#14392
C127×#14382
C127×#14372
#15283127