Finite Group Databasebeta

← C127×#15310 #44578983

Subgroups — C127×#15310 #44578983

Order 32512.

3562 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#127×C127C211yesmaximal, characteristic, complemented
2C22×#121×C127C211yesmaximal, characteristic, complemented
3C2×#394×C127C211yesmaximal, characteristic, complemented
4C2×#392×C127C212yesmaximal, complemented
5C2×#392×C127C212yesmaximal, complemented
6C2×#392×C127C211yesmaximal, characteristic, complemented
7C2×#386×C127C212yesmaximal, complemented
8C127×#1438C212yesmaximal, complemented
9C127×#1438C211yesmaximal, characteristic, complemented
10C127×#1437C211yesmaximal, characteristic, complemented
11C127×#1436C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C23×D4×C127C2211yescharacteristic
15C23×D4×C127C2212yes—
16C23×D4×C127C2212yes—
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2212yes—
19C24×C4×C127C2211yescharacteristic
20C2×#127×C127—24no—
21C2×#127×C127—28no—
22C2×#121×C127—24no—
23C2×#121×C127—24no—
24C2×#121×C127—24no—
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2212yes—
30C22×C22⋊C4×C127C2212yes—
31C22×C22⋊C4×C127C2212yes—
32C22×C22⋊C4×C127C2211yescharacteristic
33C22×C22⋊C4×C127C2212yes—
34C22×C42×C127C2211yescharacteristic
35#394×C127—24no—
36#392×C127—28no—
37#392×C127—24no—
38#392×C127—28no—
39#386×C127—28no—
40C2×#95×C127C2212yes—
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
43C2×#95×C127C2212yes—
44C2×#95×C127C2212yes—
45C25×C127C2312yes—
46C25×C127C2311yescharacteristic
47C25×C127C2311yescharacteristic
48C25×C127C2311yescharacteristic
49C22×D4×C127—22no—
50C22×D4×C127—22no—
51C22×D4×C127—22no—
52C22×D4×C127—22no—
53C22×D4×C127—24no—
54C22×D4×C127—24no—
55C22×D4×C127—24no—
56C22×D4×C127—24no—
57C22×D4×C127—24no—
58C22×D4×C127—24no—
59C22×D4×C127—24no—
60C22×D4×C127—24no—
61C22×D4×C127—24no—
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—22no—
71C22×D4×C127—24no—
72C22×D4×C127—24no—
73C22×D4×C127—22no—
74C22×D4×C127—24no—
75C22×D4×C127—24no—
76C22×D4×C127—42no—
77C22×D4×C127—42no—
78C22×D4×C127—42no—
79C22×D4×C127—42no—
80C22×D4×C127—42no—
81C22×D4×C127—42no—
82C22×D4×C127—42no—
83C22×D4×C127—42no—
84C22×D4×C127—42no—
85C22×D4×C127—42no—
86C22×D4×C127—42no—
87C22×D4×C127—42no—
88C22×D4×C127D414yescomplemented
89C22×D4×C127D418yescomplemented
90C23×C4×C127—22no—
91C23×C4×C127—22no—
92C23×C4×C127—22no—
93C23×C4×C127—24no—
94C23×C4×C127—42no—
95C23×C4×C127C2312yes—
96C23×C4×C127C2311yescharacteristic
97C23×C4×C127C2311yescharacteristic
98C23×C4×C127C2312yes—
99C23×C4×C127C2311yescharacteristic
100C23×C4×C127C2311yescharacteristic
101C23×C4×C127C2312yes—
102#127×C127—232no—
103#121×C127—232no—
104C2×C4⋊C4×C127—22no—
105C2×C4⋊C4×C127—22no—
106C2×C4⋊C4×C127D414yescomplemented
107C2×C22⋊C4×C127—22no—
108C2×C22⋊C4×C127—22no—
109C2×C22⋊C4×C127—22no—
110C2×C22⋊C4×C127—22no—
111C2×C22⋊C4×C127—22no—
112C2×C22⋊C4×C127—24no—
113C2×C22⋊C4×C127—24no—
114C2×C22⋊C4×C127—24no—
115C2×C22⋊C4×C127—24no—
116C2×C22⋊C4×C127—24no—
117C2×C22⋊C4×C127—24no—
118C2×C22⋊C4×C127—24no—
119C2×C22⋊C4×C127—24no—
120C2×C22⋊C4×C127—24no—
121C2×C22⋊C4×C127—24no—
122C2×C22⋊C4×C127—24no—
123C2×C22⋊C4×C127—24no—
124C2×C22⋊C4×C127—24no—
125C2×C22⋊C4×C127—42no—
126C2×C22⋊C4×C127—42no—
127C2×C22⋊C4×C127—42no—
128C2×C22⋊C4×C127—42no—
129C2×C22⋊C4×C127—42no—
130C2×C22⋊C4×C127D414yescomplemented
131C2×C42×C127—22no—
132C2×C42×C127—24no—
133#95×C127—24no—
134#95×C127—22no—
135#95×C127—24no—
136#95×C127—22no—
137#95×C127D418yescomplemented
138C24×C127—22no—
139C24×C127—21no—
140C24×C127—21no—
141C24×C127—22no—
142C24×C127—22no—
143C24×C127—22no—
144C24×C127—22no—
145C24×C127—22no—
146C24×C127—22no—
147C24×C127—21no—
148C24×C127—21no—
149C24×C127—21no—
150C24×C127—21no—
151C24×C127—22no—
152C24×C127—22no—
153C24×C127—22no—
154C24×C127—22no—
155C24×C127—22no—
156C24×C127—22no—
157C24×C127—22no—
158C24×C127—22no—
159C24×C127—22no—
160C24×C127—22no—
161C24×C127—22no—
162C24×C127—22no—
163C24×C127—22no—
164C24×C127—22no—
165C24×C127—22no—
166C24×C127—22no—
167C24×C127—22no—
168C24×C127—22no—
169C24×C127—22no—
170C24×C127—22no—
171C24×C127—22no—
172C24×C127—22no—
173C24×C127—22no—
174C24×C127—22no—
175C24×C127C2×D412yes—
176C24×C127C2×D414yes—
177C24×C127C2×D412yes—
178C24×C127C2×D414yes—
179C24×C127C2×D412yes—
180C24×C127C2411yescharacteristic
181C2×D4×C127—28no—
182C2×D4×C127—28no—
183C2×D4×C127—28no—
184C2×D4×C127—216no—
185C2×D4×C127—28no—
186C2×D4×C127—216no—
187C2×D4×C127—28no—
188C2×D4×C127—216no—
189C2×D4×C127—44no—
190C2×D4×C127—48no—
191C2×D4×C127—48no—
192C2×D4×C127—48no—
193C2×D4×C127—48no—
194C2×D4×C127—48no—
195C2×D4×C127—48no—
196C2×D4×C127—48no—
197C2×D4×C127—48no—
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—48no—
205C2×D4×C127—48no—
206C2×D4×C127—48no—
207C2×D4×C127—48no—
208C2×D4×C127—44no—
209C2×D4×C127—48no—
210C2×D4×C127—44no—
211C2×D4×C127—48no—
212C2×D4×C127—48no—
213C2×D4×C127—48no—
214C2×D4×C127—44no—
215C2×D4×C127—48no—
216C2×D4×C127—48no—
217C2×D4×C127—48no—
218C2×D4×C127—44no—
219C2×D4×C127—44no—
220C2×D4×C127—48no—
221C2×D4×C127—44no—
222C22×C4×C127—22no—
223C22×C4×C127—22no—
224C22×C4×C127—22no—
225C22×C4×C127—21no—
226C22×C4×C127—21no—
227C22×C4×C127—22no—
228C22×C4×C127—22no—
229C22×C4×C127—22no—
230C22×C4×C127—22no—
231C22×C4×C127—28no—
232C22×C4×C127—22no—
233C22×C4×C127—22no—
234C22×C4×C127—22no—
235C22×C4×C127—22no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—22no—
241C22×C4×C127—22no—
242C22×C4×C127—22no—
243C22×C4×C127—22no—
244C22×C4×C127—22no—
245C22×C4×C127—22no—
246C22×C4×C127—22no—
247C22×C4×C127—22no—
248C22×C4×C127—22no—
249C22×C4×C127—22no—
250C22×C4×C127—22no—
251C22×C4×C127—22no—
252C22×C4×C127—22no—
253C22×C4×C127—48no—
254C22×C4×C127—48no—
255C22×C4×C127—44no—
256C22×C4×C127—44no—
257C22×C4×C127C2×D414yes—
258C22×C4×C127C2×D412yes—
259C22×C4×C127C2×D412yes—
260C22×C4×C127C2×D412yes—
261C22×C4×C127C2×D412yes—
262C22×C4×C127C2×D412yes—
263C22×C4×C127C2×D414yes—
264C22×C4×C127C2×D414yes—
265C22×C4×C127C2×D414yes—
266C22×C4×C127C2×D412yes—
267C22×C4×C127#4114yes—
268C4⋊C4×C127—28no—
269C22⋊C4×C127—28no—
270C22⋊C4×C127—28no—
271C22⋊C4×C127—48no—
272C22⋊C4×C127—48no—
273C22⋊C4×C127—48no—
274C22⋊C4×C127—48no—
275C22⋊C4×C127—48no—
276C22⋊C4×C127—48no—
277C42×C127—28no—
278C23×C127—22no—
279C23×C127—24no—
280C23×C127—22no—
281C23×C127—24no—
282C23×C127—24no—
283C23×C127—24no—
284C23×C127—24no—
285C23×C127—24no—
286C23×C127—24no—
287C23×C127—24no—
288C23×C127—22no—
289C23×C127—22no—
290C23×C127—22no—
291C23×C127—24no—
292C23×C127—24no—
293C23×C127—22no—
294C23×C127—24no—
295C23×C127—22no—
296C23×C127—22no—
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—41no—
306C23×C127—41no—
307C23×C127—41no—
308C23×C127—41no—
309C23×C127—42no—
310C23×C127—42no—
311C23×C127—42no—
312C23×C127—42no—
313C23×C127—42no—
314C23×C127—42no—
315C23×C127—41no—
316C23×C127—42no—
317C23×C127—42no—
318C23×C127—42no—
319C23×C127—42no—
320C23×C127—42no—
321C23×C127—41no—
322C23×C127—41no—
323C23×C127—42no—
324C23×C127—41no—
325C23×C127—42no—
326C23×C127—41no—
327C23×C127—42no—
328C23×C127—42no—
329C23×C127—42no—
330C23×C127—42no—
331C23×C127—42no—
332C23×C127—42no—
333C23×C127—42no—
334C23×C127—41no—
335C23×C127—41no—
336C23×C127—42no—
337C23×C127—41no—
338C23×C127—42no—
339C23×C127—42no—
340C23×C127—42no—
341C23×C127—42no—
342C23×C127—42no—
343C23×C127—42no—
344C23×C127—42no—
345C23×C127—42no—
346C23×C127—42no—
347C23×C127—42no—
348C23×C127—42no—
349C23×C127—42no—
350C23×C127—42no—
351C23×C127—42no—
352C23×C127—42no—
353C23×C127—42no—
354C23×C127—42no—
355C23×C127—42no—
356C23×C127—42no—
357C23×C127—42no—
358C23×C127—42no—
359C23×C127—42no—
360C23×C127—42no—
361C23×C127—42no—
362C23×C127—42no—
363C23×C127—42no—
364C23×C127—42no—
365C23×C127—42no—
366C23×C127—42no—
367C23×C127—42no—
368C23×C127—42no—
369C23×C127—42no—
370C23×C127—42no—
371C23×C127—42no—
372C23×C127—42no—
373C23×C127—42no—
374C23×C127—42no—
375C23×C127#12014yes—
376C23×C127C22×D411yescharacteristic
377C23×C127C22×D412yes—
378C23×C127C22×D411yescharacteristic
379C23×C127C22×D411yescharacteristic
380C23×C127C22×D412yes—
381C23×C127C2×#4112yes—
382C23×C127H(5,𝔽2)12yes—
383C23×C127H(5,𝔽2)12yes—
384C23×C127H(5,𝔽2)12yes—
385D4×C127—416no—
386D4×C127—432no—
387D4×C127—416no—
388D4×C127—432no—
389D4×C127—416no—
390D4×C127—416no—
391D4×C127—432no—
392C2×C4×C127—22no—
393C2×C4×C127—24no—
394C2×C4×C127—22no—
395C2×C4×C127—22no—
396C2×C4×C127—24no—
397C2×C4×C127—22no—
398C2×C4×C127—24no—
399C2×C4×C127—24no—
400C2×C4×C127—24no—
401C2×C4×C127—24no—
402C2×C4×C127—24no—
403C2×C4×C127—24no—
404C2×C4×C127—24no—
405C2×C4×C127—24no—
406C2×C4×C127—22no—
407C2×C4×C127—22no—
408C2×C4×C127—24no—
409C2×C4×C127—24no—
410C2×C4×C127—24no—
411C2×C4×C127—24no—
412C2×C4×C127—24no—
413C2×C4×C127—416no—
414C2×C4×C127—41no—
415C2×C4×C127—41no—
416C2×C4×C127—41no—
417C2×C4×C127—42no—
418C2×C4×C127—41no—
419C2×C4×C127—42no—
420C2×C4×C127—42no—
421C2×C4×C127—42no—
422C2×C4×C127—42no—
423C2×C4×C127—42no—
424C2×C4×C127—42no—
425C2×C4×C127—42no—
426C2×C4×C127—42no—
427C2×C4×C127—42no—
428C2×C4×C127—42no—
429C2×C4×C127—42no—
430C2×C4×C127—42no—
431C2×C4×C127#12014yes—
432C2×C4×C127#12118yescomplemented
433C2×C4×C127#12714yescomplemented
434C22×C127—24no—
435C22×C127—28no—
436C22×C127—44no—
437C22×C127—44no—
438C22×C127—44no—
439C22×C127—44no—
440C22×C127—42no—
441C22×C127—42no—
442C22×C127—44no—
443C22×C127—42no—
444C22×C127—44no—
445C22×C127—42no—
446C22×C127—44no—
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—42no—
456C22×C127—42no—
457C22×C127—42no—
458C22×C127—42no—
459C22×C127—44no—
460C22×C127—82no—
461C22×C127—82no—
462C22×C127—82no—
463C22×C127—82no—
464C22×C127—82no—
465C22×C127—82no—
466C22×C127—82no—
467C22×C127—82no—
468C22×C127—82no—
469C22×C127—82no—
470C22×C127—82no—
471C22×C127—82no—
472C22×C127—82no—
473C22×C127—82no—
474C22×C127—82no—
475C22×C127—82no—
476C22×C127C2×#12011yescharacteristic
477C22×C127C2×#12011yescharacteristic
478C22×C127C2×#12112yes—
479C22×C127C2×#12711yescharacteristic
480C22×C127#53211yescharacteristic
481C22×C127#53411yescharacteristic
482C22×C127#53412yes—
483C22×C127#53511yescharacteristic
484C22×C127#53512yes—
485C22×C127#53511yescharacteristic
486C22×C127#54012yes—
487C22×C127D4212yes—
488C22×C127D4212yes—
489C22×C127D4212yes—
490C22×C127D4212yes—
491C22×C127D4212yes—
492C22×C127#54612yes—
493C22×C127#54612yes—
494C22×C127#55012yes—
495C22×C127#55012yes—
496C22×C127#56012yes—
497C4×C127—24no—
498C4×C127—28no—
499C4×C127—24no—
500C4×C127—42no—
501C4×C127—44no—
502C4×C127—42no—
503C4×C127—82no—
504#15310C12711yesmaximal, characteristic, direct product factor, Sylow
505C2×C127—44no—
506C2×C127—84no—
507C2×C127—82no—
508C2×C127—82no—
509C2×C127#240311yescharacteristic
510C2×C127#241012yes—
511C2×C127#242812yes—
512C2×C127#243111yescharacteristic
513C2×C127#243311yescharacteristic
514C2×C127#254112yes—
515C2×C127#266912yes—
516C2×C127#267312yes—
517C2×C127#267312yes—
518C22×#127C2×C12711yescharacteristic, complemented
519C22×#121C2×C12711yescharacteristic, complemented
520C2×#394C2×C12711yescharacteristic, complemented
521C2×#392C2×C12712yescomplemented
522C2×#392C2×C12712yescomplemented
523C2×#392C2×C12711yescharacteristic, complemented
524C2×#386C2×C12712yescomplemented
525#1438C2×C12712yescomplemented
526#1438C2×C12711yescharacteristic, complemented
527#1437C2×C12711yescharacteristic, complemented
528#1436C2×C12711yescharacteristic, complemented
529C127#1531011yescharacteristic, direct product factor, Sylow
530C23×D4C22×C12711yescharacteristic
531C23×D4C22×C12711yescharacteristic
532C23×D4C22×C12711yescharacteristic
533C23×D4C22×C12712yes—
534C23×D4C22×C12712yes—
535C23×D4C22×C12711yescharacteristic
536C23×D4C22×C12712yes—
537C24×C4C22×C12711yescharacteristic
538C2×#127—24no—
539C2×#127—28no—
540C2×#121—24no—
541C2×#121—24no—
542C2×#121—24no—
543C22×C4⋊C4C22×C12711yescharacteristic
544C22×C22⋊C4C22×C12712yes—
545C22×C22⋊C4C22×C12712yes—
546C22×C22⋊C4C22×C12711yescharacteristic
547C22×C22⋊C4C22×C12712yes—
548C22×C22⋊C4C22×C12712yes—
549C22×C22⋊C4C22×C12712yes—
550C22×C22⋊C4C22×C12711yescharacteristic
551C22×C22⋊C4C22×C12712yes—
552C22×C42C22×C12711yescharacteristic
553#394—24no—
554#392—28no—
555#392—24no—
556#392—28no—
557#386—28no—
558C2×#95C22×C12712yes—
559C2×#95C22×C12711yescharacteristic
560C2×#95C22×C12711yescharacteristic
561C2×#95C22×C12712yes—
562C2×#95C22×C12712yes—
563C25C23×C12712yes—
564C25C23×C12711yescharacteristic
565C25C23×C12711yescharacteristic
566C25C23×C12711yescharacteristic
567C22×D4—22no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—24no—
572C22×D4—24no—
573C22×D4—24no—
574C22×D4—24no—
575C22×D4—24no—
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—24no—
579C22×D4—24no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—24no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—22no—
592C22×D4—24no—
593C22×D4—24no—
594C22×D4—42no—
595C22×D4—42no—
596C22×D4—42no—
597C22×D4—42no—
598C22×D4—42no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4—42no—
602C22×D4—42no—
603C22×D4—42no—
604C22×D4—42no—
605C22×D4—42no—
606C22×D4D4×C12714yescomplemented
607C22×D4D4×C12718yescomplemented
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—24no—
612C23×C4—42no—
613C23×C4C23×C12712yes—
614C23×C4C23×C12711yescharacteristic
615C23×C4C23×C12711yescharacteristic
616C23×C4C23×C12712yes—
617C23×C4C23×C12711yescharacteristic
618C23×C4C23×C12711yescharacteristic
619C23×C4C23×C12712yes—
620#127—232no—
621#121—232no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4D4×C12714yescomplemented
625C2×C22⋊C4—22no—
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—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—42no—
644C2×C22⋊C4—42no—
645C2×C22⋊C4—42no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4—42no—
648C2×C22⋊C4D4×C12714yescomplemented
649C2×C42—22no—
650C2×C42—24no—
651#95—24no—
652#95—22no—
653#95—24no—
654#95—22no—
655#95D4×C12718yescomplemented
656C24—22no—
657C24—21no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24C2×D4×C12712yes—
694C24C2×D4×C12714yes—
695C24C2×D4×C12712yes—
696C24C2×D4×C12714yes—
697C24C2×D4×C12712yes—
698C24C24×C12711yescharacteristic
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—216no—
705C2×D4—28no—
706C2×D4—216no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—44no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—44no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—44no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4C2×D4×C12714yes—
776C22×C4C2×D4×C12712yes—
777C22×C4C2×D4×C12712yes—
778C22×C4C2×D4×C12712yes—
779C22×C4C2×D4×C12712yes—
780C22×C4C2×D4×C12712yes—
781C22×C4C2×D4×C12714yes—
782C22×C4C2×D4×C12714yes—
783C22×C4C2×D4×C12714yes—
784C22×C4C2×D4×C12712yes—
785C22×C4#41×C12714yes—
786C4⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C42—28no—
796C23—22no—
797C23—24no—
798C23—22no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—24no—
810C23—24no—
811C23—22no—
812C23—24no—
813C23—22no—
814C23—22no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—41no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—41no—
840C23—41no—
841C23—42no—
842C23—41no—
843C23—42no—
844C23—41no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23#120×C12714yes—
894C23C22×D4×C12711yescharacteristic
895C23C22×D4×C12712yes—
896C23C22×D4×C12711yescharacteristic
897C23C22×D4×C12711yescharacteristic
898C23C22×D4×C12712yes—
899C23C2×#41×C12712yes—
900C23H(5,𝔽2)×C12712yes—
901C23H(5,𝔽2)×C12712yes—
902C23H(5,𝔽2)×C12712yes—
903D4—416no—
904D4—432no—
905D4—416no—
906D4—432no—
907D4—416no—
908D4—416no—
909D4—432no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C12714yes—
950C2×C4#121×C12718yescomplemented
951C2×C4#127×C12714yescomplemented
952C22—24no—
953C22—28no—
954C22—44no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—42no—
959C22—42no—
960C22—44no—
961C22—42no—
962C22—44no—
963C22—42no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—44no—
978C22—82no—
979C22—82no—
980C22—82no—
981C22—82no—
982C22—82no—
983C22—82no—
984C22—82no—
985C22—82no—
986C22—82no—
987C22—82no—
988C22—82no—
989C22—82no—
990C22—82no—
991C22—82no—
992C22—82no—
993C22—82no—
994C22C2×#120×C12711yescharacteristic
995C22C2×#120×C12711yescharacteristic
996C22C2×#121×C12712yes—
997C22C2×#127×C12711yescharacteristic
998C22#532×C12711yescharacteristic
999C22#534×C12711yescharacteristic
1000C22#534×C12712yes—
1001C22#535×C12711yescharacteristic
1002C22#535×C12712yes—
1003C22#535×C12711yescharacteristic
1004C22#540×C12712yes—
1005C22D42×C12712yes—
1006C22D42×C12712yes—
1007C22D42×C12712yes—
1008C22D42×C12712yes—
1009C22D42×C12712yes—
1010C22#546×C12712yes—
1011C22#546×C12712yes—
1012C22#550×C12712yes—
1013C22#550×C12712yes—
1014C22#560×C12712yes—
1015C4—24no—
1016C4—28no—
1017C4—24no—
1018C4—42no—
1019C4—44no—
1020C4—42no—
1021C4—82no—
1022C2—44no—
1023C2—84no—
1024C2—82no—
1025C2—82no—
1026C2C127×#240311yescharacteristic
1027C2C127×#241012yes—
1028C2C127×#242812yes—
1029C2C127×#243111yescharacteristic
1030C2C127×#243311yescharacteristic
1031C2C127×#254112yes—
1032C2C127×#266912yes—
1033C2C127×#267312yes—
1034C2C127×#267312yes—
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×#127×C127C2semidirect
2. C22×#121×C127C2semidirect
3. C2×#394×C127C2semidirect
4. C2×#392×C127C2semidirect
5. C2×#392×C127C2semidirect
6. C2×#392×C127C2semidirect
7. C2×#386×C127C2semidirect
8. C127×#1438C2semidirect
9. C127×#1438C2semidirect
10. C127×#1437C2semidirect
11. C127×#1436C2semidirect
88. C22×D4×C127D4semidirect
89. C22×D4×C127D4semidirect
106. C2×C4⋊C4×C127D4semidirect
130. C2×C22⋊C4×C127D4semidirect
137. #95×C127D4semidirect
432. C2×C4×C127#121semidirect
433. C2×C4×C127#127semidirect
504. #15310C127direct (N × H)
518. C22×#127C2×C127semidirect
519. C22×#121C2×C127semidirect
520. C2×#394C2×C127semidirect
521. C2×#392C2×C127semidirect
522. C2×#392C2×C127semidirect
523. C2×#392C2×C127semidirect
524. C2×#386C2×C127semidirect
525. #1438C2×C127semidirect
526. #1438C2×C127semidirect
527. #1437C2×C127semidirect
528. #1436C2×C127semidirect
529. C127#15310direct (N × H)
606. C22×D4D4×C127semidirect
607. C22×D4D4×C127semidirect
624. C2×C4⋊C4D4×C127semidirect
648. C2×C22⋊C4D4×C127semidirect
655. #95D4×C127semidirect
950. C2×C4#121×C127semidirect
951. C2×C4#127×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#127×C1272
C22×#121×C1272
C2×#394×C1272
C2×#392×C1272
C2×#386×C1272
C127×#14382
C127×#14372
C127×#14362
#15310127