Finite Group Databasebeta

← C127×#14762 #44578435

Subgroups — C127×#14762 #44578435

Order 32512.

2970 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic, complemented
2C2×#394×C127C212yesmaximal, complemented
3C2×#392×C127C211yesmaximal, characteristic, complemented
4C2×#392×C127C212yesmaximal, complemented
5C2×#390×C127C212yesmaximal, complemented
6C2×#386×C127C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
8C127×#1444C211yesmaximal, characteristic, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1438C211yesmaximal, characteristic, complemented
11C127×#1437C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C23×D4×C127C2212yes—
14C23×D4×C127C2212yes—
15C23×D4×C127C2211yescharacteristic
16C24×C4×C127C2211yescharacteristic
17C2×#121×C127—24no—
18C2×#121×C127—28no—
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2212yes—
29C22×C22⋊C4×C127C2212yes—
30C22×C42×C127C2212yes—
31#394×C127—28no—
32#392×C127—28no—
33#392×C127—24no—
34#390×C127—28no—
35#386×C127—24no—
36C4×C22⋊C4×C127—24no—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
43C25×C127C2312yes—
44C25×C127C2311yescharacteristic
45C25×C127C2311yescharacteristic
46C22×D4×C127—24no—
47C22×D4×C127—24no—
48C22×D4×C127—24no—
49C22×D4×C127—22no—
50C22×D4×C127—24no—
51C22×D4×C127—24no—
52C22×D4×C127—22no—
53C22×D4×C127—24no—
54C22×D4×C127—24no—
55C22×D4×C127—24no—
56C22×D4×C127—24no—
57C22×D4×C127—22no—
58C22×D4×C127—22no—
59C22×D4×C127—24no—
60C22×D4×C127—24no—
61C22×D4×C127—22no—
62C22×D4×C127—24no—
63C22×D4×C127—22no—
64C22×D4×C127—42no—
65C22×D4×C127—42no—
66C22×D4×C127—42no—
67C22×D4×C127—42no—
68C22×D4×C127—42no—
69C22×D4×C127—42no—
70C23×C4×C127—24no—
71C23×C4×C127—22no—
72C23×C4×C127—22no—
73C23×C4×C127—42no—
74C23×C4×C127D414yescomplemented
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2312yes—
78C23×C4×C127C2312yes—
79C23×C4×C127C2311yescharacteristic
80C23×C4×C127C2311yescharacteristic
81C23×C4×C127C2312yes—
82C23×C4×C127C2311yescharacteristic
83#121×C127—232no—
84C2×C4⋊C4×C127—24no—
85C2×C4⋊C4×C127—22no—
86C2×C4⋊C4×C127—24no—
87C2×C4⋊C4×C127—24no—
88C2×C4⋊C4×C127—42no—
89C2×C22⋊C4×C127—24no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—24no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127—24no—
95C2×C22⋊C4×C127—24no—
96C2×C22⋊C4×C127—22no—
97C2×C22⋊C4×C127—22no—
98C2×C22⋊C4×C127—24no—
99C2×C22⋊C4×C127—24no—
100C2×C22⋊C4×C127—24no—
101C2×C22⋊C4×C127—24no—
102C2×C22⋊C4×C127—22no—
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—42no—
110C2×C22⋊C4×C127—42no—
111C2×C22⋊C4×C127—42no—
112C2×C22⋊C4×C127D418yescomplemented
113C2×C22⋊C4×C127D418yescomplemented
114C2×C42×C127—24no—
115C2×C42×C127—24no—
116C2×C42×C127—42no—
117#95×C127—22no—
118#95×C127—22no—
119#95×C127—22no—
120#95×C127—24no—
121#95×C127—24no—
122#95×C127D414yescomplemented
123C24×C127—21no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—21no—
127C24×C127—21no—
128C24×C127—21no—
129C24×C127—22no—
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—21no—
140C24×C127—22no—
141C24×C127—22no—
142C24×C127—22no—
143C24×C127—21no—
144C24×C127—22no—
145C24×C127—22no—
146C24×C127—22no—
147C24×C127—21no—
148C24×C127—22no—
149C24×C127—21no—
150C24×C127—22no—
151C24×C127—22no—
152C24×C127—22no—
153C24×C127—22no—
154C24×C127—22no—
155C24×C127—21no—
156C24×C127C2×D414yes—
157C24×C127C2×D414yes—
158C24×C127C2×D412yes—
159C24×C127#4112yes—
160C24×C127C2411yescharacteristic
161C2×D4×C127—28no—
162C2×D4×C127—216no—
163C2×D4×C127—216no—
164C2×D4×C127—28no—
165C2×D4×C127—48no—
166C2×D4×C127—48no—
167C2×D4×C127—48no—
168C2×D4×C127—48no—
169C2×D4×C127—48no—
170C2×D4×C127—48no—
171C2×D4×C127—48no—
172C2×D4×C127—48no—
173C2×D4×C127—48no—
174C2×D4×C127—44no—
175C2×D4×C127—48no—
176C2×D4×C127—48no—
177C2×D4×C127—48no—
178C2×D4×C127—48no—
179C2×D4×C127—44no—
180C2×D4×C127—48no—
181C2×D4×C127—48no—
182C2×D4×C127—44no—
183C2×D4×C127—44no—
184C2×D4×C127—48no—
185C22×C4×C127—21no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
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—22no—
203C22×C4×C127—22no—
204C22×C4×C127—21no—
205C22×C4×C127—22no—
206C22×C4×C127—22no—
207C22×C4×C127—22no—
208C22×C4×C127—22no—
209C22×C4×C127—22no—
210C22×C4×C127—28no—
211C22×C4×C127—28no—
212C22×C4×C127—21no—
213C22×C4×C127—21no—
214C22×C4×C127—22no—
215C22×C4×C127—21no—
216C22×C4×C127—22no—
217C22×C4×C127—22no—
218C22×C4×C127—22no—
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—44no—
223C22×C4×C127—48no—
224C22×C4×C127—48no—
225C22×C4×C127C2×D414yes—
226C22×C4×C127C2×D414yes—
227C22×C4×C127C2×D412yes—
228C22×C4×C127C2×D414yes—
229C22×C4×C127C2×D412yes—
230C22×C4×C127C2×D412yes—
231C22×C4×C127C2×D414yes—
232C22×C4×C127C2×D414yes—
233C22×C4×C127#4112yes—
234C22×C4×C127#4112yes—
235C22×C4×C127#4114yes—
236C4⋊C4×C127—28no—
237C4⋊C4×C127—48no—
238C22⋊C4×C127—216no—
239C22⋊C4×C127—216no—
240C22⋊C4×C127—48no—
241C22⋊C4×C127—48no—
242C22⋊C4×C127—48no—
243C22⋊C4×C127—44no—
244C22⋊C4×C127—44no—
245C22⋊C4×C127—44no—
246C22⋊C4×C127—48no—
247C42×C127—48no—
248C23×C127—22no—
249C23×C127—24no—
250C23×C127—22no—
251C23×C127—22no—
252C23×C127—22no—
253C23×C127—24no—
254C23×C127—22no—
255C23×C127—22no—
256C23×C127—24no—
257C23×C127—24no—
258C23×C127—24no—
259C23×C127—24no—
260C23×C127—24no—
261C23×C127—24no—
262C23×C127—22no—
263C23×C127—24no—
264C23×C127—24no—
265C23×C127—24no—
266C23×C127—24no—
267C23×C127—24no—
268C23×C127—22no—
269C23×C127—24no—
270C23×C127—24no—
271C23×C127—22no—
272C23×C127—42no—
273C23×C127—42no—
274C23×C127—42no—
275C23×C127—42no—
276C23×C127—42no—
277C23×C127—42no—
278C23×C127—41no—
279C23×C127—41no—
280C23×C127—41no—
281C23×C127—41no—
282C23×C127—41no—
283C23×C127—41no—
284C23×C127—42no—
285C23×C127—42no—
286C23×C127—42no—
287C23×C127—42no—
288C23×C127—42no—
289C23×C127—42no—
290C23×C127—42no—
291C23×C127—41no—
292C23×C127—41no—
293C23×C127—42no—
294C23×C127—42no—
295C23×C127—42no—
296C23×C127—42no—
297C23×C127—42no—
298C23×C127—42no—
299C23×C127—42no—
300C23×C127—41no—
301C23×C127—42no—
302C23×C127—41no—
303C23×C127—42no—
304C23×C127—42no—
305C23×C127—42no—
306C23×C127—42no—
307C23×C127—42no—
308C23×C127—42no—
309C23×C127—42no—
310C23×C127—42no—
311C23×C127—42no—
312C23×C127—42no—
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—41no—
324C23×C127—42no—
325C23×C127—42no—
326C23×C127—41no—
327C23×C127—42no—
328C23×C127#12714yes—
329C23×C127C22×D411yescharacteristic
330C23×C127C22×D412yes—
331C23×C127C22×D411yescharacteristic
332C23×C127C22×D412yes—
333C23×C127C2×#4112yes—
334C23×C127C2×#4111yescharacteristic
335C23×C127C2×#4111yescharacteristic
336C23×C127C2×#4111yescharacteristic
337C23×C127H(5,𝔽2)12yes—
338C23×C127H(5,𝔽2)11yescharacteristic
339C23×C127H(5,𝔽2)11yescharacteristic
340D4×C127—416no—
341D4×C127—432no—
342D4×C127—432no—
343D4×C127—416no—
344C2×C4×C127—22no—
345C2×C4×C127—22no—
346C2×C4×C127—24no—
347C2×C4×C127—22no—
348C2×C4×C127—22no—
349C2×C4×C127—24no—
350C2×C4×C127—24no—
351C2×C4×C127—24no—
352C2×C4×C127—24no—
353C2×C4×C127—24no—
354C2×C4×C127—24no—
355C2×C4×C127—24no—
356C2×C4×C127—24no—
357C2×C4×C127—24no—
358C2×C4×C127—24no—
359C2×C4×C127—24no—
360C2×C4×C127—22no—
361C2×C4×C127—24no—
362C2×C4×C127—24no—
363C2×C4×C127—24no—
364C2×C4×C127—24no—
365C2×C4×C127—24no—
366C2×C4×C127—416no—
367C2×C4×C127—42no—
368C2×C4×C127—41no—
369C2×C4×C127—42no—
370C2×C4×C127—41no—
371C2×C4×C127—42no—
372C2×C4×C127—42no—
373C2×C4×C127—42no—
374C2×C4×C127—42no—
375C2×C4×C127—42no—
376C2×C4×C127—42no—
377C2×C4×C127—42no—
378C2×C4×C127—41no—
379C2×C4×C127—41no—
380C2×C4×C127—42no—
381C2×C4×C127—41no—
382C2×C4×C127—41no—
383C2×C4×C127—41no—
384C2×C4×C127—42no—
385C2×C4×C127—41no—
386C2×C4×C127—42no—
387C2×C4×C127—42no—
388C2×C4×C127#12014yes—
389C2×C4×C127#12114yes—
390C2×C4×C127#12118yescomplemented
391C22×C127—24no—
392C22×C127—24no—
393C22×C127—24no—
394C22×C127—42no—
395C22×C127—42no—
396C22×C127—42no—
397C22×C127—42no—
398C22×C127—44no—
399C22×C127—44no—
400C22×C127—44no—
401C22×C127—44no—
402C22×C127—44no—
403C22×C127—42no—
404C22×C127—44no—
405C22×C127—42no—
406C22×C127—44no—
407C22×C127—44no—
408C22×C127—44no—
409C22×C127—44no—
410C22×C127—44no—
411C22×C127—44no—
412C22×C127—42no—
413C22×C127—44no—
414C22×C127—82no—
415C22×C127—81no—
416C22×C127—82no—
417C22×C127—81no—
418C22×C127—81no—
419C22×C127—82no—
420C22×C127—82no—
421C22×C127—82no—
422C22×C127—82no—
423C22×C127—81no—
424C22×C127—82no—
425C22×C127—82no—
426C22×C127—82no—
427C22×C127—82no—
428C22×C127C2×#12011yescharacteristic
429C22×C127C2×#12111yescharacteristic
430C22×C127C2×#12112yes—
431C22×C127#52511yescharacteristic
432C22×C127#52512yes—
433C22×C127C2×#12711yescharacteristic
434C22×C127#53211yescharacteristic
435C22×C127#53212yes—
436C22×C127#53212yes—
437C22×C127#53411yescharacteristic
438C22×C127#53511yescharacteristic
439C22×C127#53812yes—
440C22×C127#54012yes—
441C22×C127D4212yes—
442C22×C127D4212yes—
443C22×C127D4212yes—
444C22×C127#54612yes—
445C22×C127#54611yescharacteristic
446C22×C127#54612yes—
447C22×C127#54612yes—
448C22×C127#55011yescharacteristic
449C22×C127#55311yescharacteristic
450C22×C127#55511yescharacteristic
451C4×C127—24no—
452C4×C127—24no—
453C4×C127—28no—
454C4×C127—44no—
455C4×C127—44no—
456C4×C127—42no—
457C4×C127—81no—
458C4×C127—81no—
459#14762C12711yesmaximal, characteristic, direct product factor, Sylow
460C2×C127—44no—
461C2×C127—84no—
462C2×C127—82no—
463C2×C127#238811yescharacteristic
464C2×C127#241011yescharacteristic
465C2×C127#241411yescharacteristic
466C2×C127#242412yes—
467C2×C127#242812yes—
468C2×C127#243311yescharacteristic
469C2×C127#246412yes—
470C2×C127#253911yescharacteristic
471C2×C127#255512yes—
472C2×C127#266111yescharacteristic
473C2×C127#285611yescharacteristic
474C22×#121C2×C12711yescharacteristic, complemented
475C2×#394C2×C12712yescomplemented
476C2×#392C2×C12711yescharacteristic, complemented
477C2×#392C2×C12712yescomplemented
478C2×#390C2×C12712yescomplemented
479C2×#386C2×C12711yescharacteristic, complemented
480C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
481#1444C2×C12711yescharacteristic, complemented
482#1439C2×C12711yescharacteristic, complemented
483#1438C2×C12711yescharacteristic, complemented
484#1437C2×C12712yescomplemented
485C127#1476211yescharacteristic, direct product factor, Sylow
486C23×D4C22×C12711yescharacteristic
487C23×D4C22×C12712yes—
488C23×D4C22×C12712yes—
489C23×D4C22×C12711yescharacteristic
490C24×C4C22×C12711yescharacteristic
491C2×#121—24no—
492C2×#121—28no—
493C22×C4⋊C4C22×C12711yescharacteristic
494C22×C4⋊C4C22×C12712yes—
495C22×C22⋊C4C22×C12712yes—
496C22×C22⋊C4C22×C12711yescharacteristic
497C22×C22⋊C4C22×C12711yescharacteristic
498C22×C22⋊C4C22×C12711yescharacteristic
499C22×C22⋊C4C22×C12712yes—
500C22×C22⋊C4C22×C12712yes—
501C22×C22⋊C4C22×C12712yes—
502C22×C22⋊C4C22×C12712yes—
503C22×C22⋊C4C22×C12712yes—
504C22×C42C22×C12712yes—
505#394—28no—
506#392—28no—
507#392—24no—
508#390—28no—
509#386—24no—
510C4×C22⋊C4—24no—
511C2×#95C22×C12712yes—
512C2×#95C22×C12712yes—
513C2×#95C22×C12711yescharacteristic
514C2×#95C22×C12711yescharacteristic
515C2×#95C22×C12711yescharacteristic
516C2×#95C22×C12711yescharacteristic
517C25C23×C12712yes—
518C25C23×C12711yescharacteristic
519C25C23×C12711yescharacteristic
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—24no—
523C22×D4—22no—
524C22×D4—24no—
525C22×D4—24no—
526C22×D4—22no—
527C22×D4—24no—
528C22×D4—24no—
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—22no—
532C22×D4—22no—
533C22×D4—24no—
534C22×D4—24no—
535C22×D4—22no—
536C22×D4—24no—
537C22×D4—22no—
538C22×D4—42no—
539C22×D4—42no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4—42no—
543C22×D4—42no—
544C23×C4—24no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—42no—
548C23×C4D4×C12714yescomplemented
549C23×C4C23×C12711yescharacteristic
550C23×C4C23×C12711yescharacteristic
551C23×C4C23×C12712yes—
552C23×C4C23×C12712yes—
553C23×C4C23×C12711yescharacteristic
554C23×C4C23×C12711yescharacteristic
555C23×C4C23×C12712yes—
556C23×C4C23×C12711yescharacteristic
557#121—232no—
558C2×C4⋊C4—24no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—24no—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—42no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—24no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4D4×C12718yescomplemented
587C2×C22⋊C4D4×C12718yescomplemented
588C2×C42—24no—
589C2×C42—24no—
590C2×C42—42no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—24no—
595#95—24no—
596#95D4×C12714yescomplemented
597C24—21no—
598C24—22no—
599C24—22no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—22no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—21no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—21no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—21no—
622C24—22no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24C2×D4×C12714yes—
631C24C2×D4×C12714yes—
632C24C2×D4×C12712yes—
633C24#41×C12712yes—
634C24C24×C12711yescharacteristic
635C2×D4—28no—
636C2×D4—216no—
637C2×D4—216no—
638C2×D4—28no—
639C2×D4—48no—
640C2×D4—48no—
641C2×D4—48no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—48no—
646C2×D4—48no—
647C2×D4—48no—
648C2×D4—44no—
649C2×D4—48no—
650C2×D4—48no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—44no—
654C2×D4—48no—
655C2×D4—48no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—48no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—21no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—44no—
697C22×C4—48no—
698C22×C4—48no—
699C22×C4C2×D4×C12714yes—
700C22×C4C2×D4×C12714yes—
701C22×C4C2×D4×C12712yes—
702C22×C4C2×D4×C12714yes—
703C22×C4C2×D4×C12712yes—
704C22×C4C2×D4×C12712yes—
705C22×C4C2×D4×C12714yes—
706C22×C4C2×D4×C12714yes—
707C22×C4#41×C12712yes—
708C22×C4#41×C12712yes—
709C22×C4#41×C12714yes—
710C4⋊C4—28no—
711C4⋊C4—48no—
712C22⋊C4—216no—
713C22⋊C4—216no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—44no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—48no—
721C42—48no—
722C23—22no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—22no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—22no—
743C23—24no—
744C23—24no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—41no—
766C23—41no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—41no—
775C23—42no—
776C23—41no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—41no—
798C23—42no—
799C23—42no—
800C23—41no—
801C23—42no—
802C23#127×C12714yes—
803C23C22×D4×C12711yescharacteristic
804C23C22×D4×C12712yes—
805C23C22×D4×C12711yescharacteristic
806C23C22×D4×C12712yes—
807C23C2×#41×C12712yes—
808C23C2×#41×C12711yescharacteristic
809C23C2×#41×C12711yescharacteristic
810C23C2×#41×C12711yescharacteristic
811C23H(5,𝔽2)×C12712yes—
812C23H(5,𝔽2)×C12711yescharacteristic
813C23H(5,𝔽2)×C12711yescharacteristic
814D4—416no—
815D4—432no—
816D4—432no—
817D4—416no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—416no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—42no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4#120×C12714yes—
863C2×C4#121×C12714yes—
864C2×C4#121×C12718yescomplemented
865C22—24no—
866C22—24no—
867C22—24no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—44no—
879C22—42no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—42no—
887C22—44no—
888C22—82no—
889C22—81no—
890C22—82no—
891C22—81no—
892C22—81no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—81no—
898C22—82no—
899C22—82no—
900C22—82no—
901C22—82no—
902C22C2×#120×C12711yescharacteristic
903C22C2×#121×C12711yescharacteristic
904C22C2×#121×C12712yes—
905C22#525×C12711yescharacteristic
906C22#525×C12712yes—
907C22C2×#127×C12711yescharacteristic
908C22#532×C12711yescharacteristic
909C22#532×C12712yes—
910C22#532×C12712yes—
911C22#534×C12711yescharacteristic
912C22#535×C12711yescharacteristic
913C22#538×C12712yes—
914C22#540×C12712yes—
915C22D42×C12712yes—
916C22D42×C12712yes—
917C22D42×C12712yes—
918C22#546×C12712yes—
919C22#546×C12711yescharacteristic
920C22#546×C12712yes—
921C22#546×C12712yes—
922C22#550×C12711yescharacteristic
923C22#553×C12711yescharacteristic
924C22#555×C12711yescharacteristic
925C4—24no—
926C4—24no—
927C4—28no—
928C4—44no—
929C4—44no—
930C4—42no—
931C4—81no—
932C4—81no—
933C2—44no—
934C2—84no—
935C2—82no—
936C2C127×#238811yescharacteristic
937C2C127×#241011yescharacteristic
938C2C127×#241411yescharacteristic
939C2C127×#242412yes—
940C2C127×#242812yes—
941C2C127×#243311yescharacteristic
942C2C127×#246412yes—
943C2C127×#253911yescharacteristic
944C2C127×#255512yes—
945C2C127×#266111yescharacteristic
946C2C127×#285611yescharacteristic
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×#392×C127C2semidirect
5. C2×#390×C127C2semidirect
6. C2×#386×C127C2semidirect
7. C2×C4×C22⋊C4×C127C2semidirect
8. C127×#1444C2semidirect
9. C127×#1439C2semidirect
10. C127×#1438C2semidirect
11. C127×#1437C2semidirect
74. C23×C4×C127D4semidirect
112. C2×C22⋊C4×C127D4semidirect
113. C2×C22⋊C4×C127D4semidirect
122. #95×C127D4semidirect
390. C2×C4×C127#121semidirect
459. #14762C127direct (N × H)
474. C22×#121C2×C127semidirect
475. C2×#394C2×C127semidirect
476. C2×#392C2×C127semidirect
477. C2×#392C2×C127semidirect
478. C2×#390C2×C127semidirect
479. C2×#386C2×C127semidirect
480. C2×C4×C22⋊C4C2×C127semidirect
481. #1444C2×C127semidirect
482. #1439C2×C127semidirect
483. #1438C2×C127semidirect
484. #1437C2×C127semidirect
485. C127#14762direct (N × H)
548. C23×C4D4×C127semidirect
586. C2×C22⋊C4D4×C127semidirect
587. C2×C22⋊C4D4×C127semidirect
596. #95D4×C127semidirect
864. 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×#390×C1272
C2×#386×C1272
C2×C4×C22⋊C4×C1272
C127×#14442
C127×#14392
C127×#14382
C127×#14372
#14762127