Finite Group Databasebeta

← C127×#15257 #44578930

Subgroups — C127×#15257 #44578930

Order 32512.

4462 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic, complemented
2C22×#120×C127C211yesmaximal, characteristic, complemented
3C22×#120×C127C211yesmaximal, characteristic, complemented
4C2×#392×C127C212yesmaximal, complemented
5C2×#386×C127C212yesmaximal, complemented
6C2×#379×C127C211yesmaximal, characteristic, complemented
7C127×#1440C211yesmaximal, characteristic, complemented
8C127×#1439C212yesmaximal, complemented
9C127×#1438C212yesmaximal, complemented
10C127×#1438C211yesmaximal, characteristic, complemented
11C127×#1438C211yesmaximal, characteristic, complemented
12C26×C127C2211yescharacteristic
13C23×D4×C127C2212yes—
14C23×D4×C127C2212yes—
15C23×D4×C127C2211yescharacteristic
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic, complemented
18C24×C4×C127C2211yescharacteristic, complemented
19C2×#121×C127—24no—
20C2×#121×C127—24no—
21C2×#121×C127—24no—
22C2×#120×C127—24no—
23C2×#120×C127—24no—
24C2×#120×C127—28no—
25C2×#120×C127—28no—
26C22×C4⋊C4×C127C2211yescharacteristic, complemented
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2212yes—
31C22×C22⋊C4×C127C2212yes—
32C22×C22⋊C4×C127C2212yes—
33C22×C22⋊C4×C127C2211yescharacteristic
34C22×C22⋊C4×C127C2211yescharacteristic
35C22×C22⋊C4×C127C2211yescharacteristic, complemented
36C22×C22⋊C4×C127C2212yescomplemented
37C22×C22⋊C4×C127C2212yescomplemented
38#392×C127—28no—
39#386×C127—28no—
40#379×C127—24no—
41C2×#95×C127C2212yescomplemented
42C2×#95×C127C2212yescomplemented
43C2×#95×C127C2212yescomplemented
44C2×#95×C127C2212yescomplemented
45C25×C127—22no—
46C25×C127—22no—
47C25×C127—24no—
48C25×C127—24no—
49C25×C127—22no—
50C25×C127—24no—
51C25×C127—42no—
52C25×C127—42no—
53C25×C127—42no—
54C25×C127C2311yescharacteristic
55C25×C127C2311yescharacteristic
56C25×C127C2311yescharacteristic
57C25×C127C2312yes—
58C22×D4×C127—24no—
59C22×D4×C127—24no—
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—22no—
68C22×D4×C127—22no—
69C22×D4×C127—24no—
70C22×D4×C127—24no—
71C22×D4×C127—24no—
72C22×D4×C127—24no—
73C22×D4×C127—24no—
74C22×D4×C127—24no—
75C22×D4×C127—24no—
76C22×D4×C127—22no—
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×C127D414yescomplemented
85C22×D4×C127D414yescomplemented
86C22×D4×C127D418yescomplemented
87C23×C4×C127—22no—
88C23×C4×C127—22no—
89C23×C4×C127—22no—
90C23×C4×C127—24no—
91C23×C4×C127—42no—
92C23×C4×C127C2312yes—
93C23×C4×C127C2311yescharacteristic
94C23×C4×C127C2311yescharacteristic
95C23×C4×C127C2311yescharacteristic
96C23×C4×C127C2312yes—
97C23×C4×C127C2312yes—
98C23×C4×C127C2311yescharacteristic
99#121×C127—232no—
100#120×C127—232no—
101#120×C127—232no—
102C2×C4⋊C4×C127—22no—
103C2×C4⋊C4×C127—22no—
104C2×C4⋊C4×C127—22no—
105C2×C22⋊C4×C127—22no—
106C2×C22⋊C4×C127—22no—
107C2×C22⋊C4×C127—24no—
108C2×C22⋊C4×C127—22no—
109C2×C22⋊C4×C127—22no—
110C2×C22⋊C4×C127—22no—
111C2×C22⋊C4×C127—24no—
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—22no—
118C2×C22⋊C4×C127—22no—
119C2×C22⋊C4×C127—22no—
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—24no—
126C2×C22⋊C4×C127—24no—
127C2×C22⋊C4×C127—42no—
128C2×C22⋊C4×C127—42no—
129C2×C22⋊C4×C127—42no—
130C2×C22⋊C4×C127—42no—
131C2×C22⋊C4×C127—42no—
132C2×C22⋊C4×C127—42no—
133C2×C22⋊C4×C127D418yescomplemented
134C2×C22⋊C4×C127D414yescomplemented
135#95×C127—24no—
136#95×C127—24no—
137#95×C127—24no—
138#95×C127—42no—
139C24×C127—22no—
140C24×C127—22no—
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—22no—
150C24×C127—22no—
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—28no—
165C24×C127—28no—
166C24×C127—28no—
167C24×C127—21no—
168C24×C127—21no—
169C24×C127—22no—
170C24×C127—22no—
171C24×C127—22no—
172C24×C127—22no—
173C24×C127—22no—
174C24×C127—22no—
175C24×C127—48no—
176C24×C127—48no—
177C24×C127—48no—
178C24×C127—48no—
179C24×C127—48no—
180C24×C127—48no—
181C24×C127—48no—
182C24×C127—48no—
183C24×C127—48no—
184C24×C127—44no—
185C24×C127—44no—
186C24×C127—48no—
187C24×C127—44no—
188C24×C127—48no—
189C24×C127—48no—
190C24×C127—48no—
191C24×C127—44no—
192C24×C127—48no—
193C24×C127C2×D412yes—
194C24×C127C2×D412yes—
195C24×C127C2×D412yes—
196C24×C127C2×D412yes—
197C24×C127C2×D414yes—
198C24×C127C2×D412yes—
199C24×C127C2×D414yes—
200C24×C127C2×D414yes—
201C24×C127#4114yes—
202C24×C127C2411yescharacteristic
203C2×D4×C127—216no—
204C2×D4×C127—28no—
205C2×D4×C127—28no—
206C2×D4×C127—28no—
207C2×D4×C127—28no—
208C2×D4×C127—216no—
209C2×D4×C127—216no—
210C2×D4×C127—28no—
211C2×D4×C127—44no—
212C2×D4×C127—48no—
213C2×D4×C127—44no—
214C2×D4×C127—48no—
215C2×D4×C127—48no—
216C2×D4×C127—48no—
217C2×D4×C127—48no—
218C2×D4×C127—48no—
219C2×D4×C127—48no—
220C2×D4×C127—48no—
221C2×D4×C127—48no—
222C2×D4×C127—48no—
223C2×D4×C127—48no—
224C2×D4×C127—48no—
225C2×D4×C127—48no—
226C2×D4×C127—48no—
227C2×D4×C127—48no—
228C2×D4×C127—44no—
229C2×D4×C127—48no—
230C2×D4×C127—44no—
231C2×D4×C127—48no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—22no—
235C22×C4×C127—28no—
236C22×C4×C127—22no—
237C22×C4×C127—22no—
238C22×C4×C127—22no—
239C22×C4×C127—22no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—22no—
243C22×C4×C127—22no—
244C22×C4×C127—22no—
245C22×C4×C127—22no—
246C22×C4×C127—22no—
247C22×C4×C127—21no—
248C22×C4×C127—21no—
249C22×C4×C127—21no—
250C22×C4×C127—21no—
251C22×C4×C127—22no—
252C22×C4×C127—22no—
253C22×C4×C127—22no—
254C22×C4×C127—22no—
255C22×C4×C127—22no—
256C22×C4×C127—22no—
257C22×C4×C127—22no—
258C22×C4×C127—22no—
259C22×C4×C127—22no—
260C22×C4×C127—22no—
261C22×C4×C127—22no—
262C22×C4×C127—22no—
263C22×C4×C127—22no—
264C22×C4×C127—22no—
265C22×C4×C127—22no—
266C22×C4×C127—22no—
267C22×C4×C127—48no—
268C22×C4×C127—48no—
269C22×C4×C127—44no—
270C22×C4×C127—44no—
271C22×C4×C127C2×D414yes—
272C22×C4×C127C2×D414yes—
273C22×C4×C127C2×D412yes—
274C22×C4×C127C2×D412yes—
275C22×C4×C127C2×D412yes—
276C22×C4×C127C2×D414yes—
277C22×C4×C127C2×D412yes—
278C4⋊C4×C127—28no—
279C22⋊C4×C127—216no—
280C22⋊C4×C127—28no—
281C22⋊C4×C127—28no—
282C22⋊C4×C127—28no—
283C22⋊C4×C127—28no—
284C22⋊C4×C127—216no—
285C22⋊C4×C127—48no—
286C22⋊C4×C127—48no—
287C22⋊C4×C127—48no—
288C22⋊C4×C127—48no—
289C22⋊C4×C127—44no—
290C23×C127—22no—
291C23×C127—22no—
292C23×C127—24no—
293C23×C127—24no—
294C23×C127—22no—
295C23×C127—24no—
296C23×C127—22no—
297C23×C127—24no—
298C23×C127—22no—
299C23×C127—22no—
300C23×C127—22no—
301C23×C127—24no—
302C23×C127—24no—
303C23×C127—22no—
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—24no—
314C23×C127—24no—
315C23×C127—24no—
316C23×C127—24no—
317C23×C127—24no—
318C23×C127—24no—
319C23×C127—24no—
320C23×C127—24no—
321C23×C127—24no—
322C23×C127—24no—
323C23×C127—24no—
324C23×C127—24no—
325C23×C127—24no—
326C23×C127—24no—
327C23×C127—24no—
328C23×C127—24no—
329C23×C127—24no—
330C23×C127—22no—
331C23×C127—22no—
332C23×C127—22no—
333C23×C127—24no—
334C23×C127—24no—
335C23×C127—416no—
336C23×C127—416no—
337C23×C127—416no—
338C23×C127—432no—
339C23×C127—432no—
340C23×C127—432no—
341C23×C127—432no—
342C23×C127—432no—
343C23×C127—432no—
344C23×C127—41no—
345C23×C127—42no—
346C23×C127—42no—
347C23×C127—42no—
348C23×C127—41no—
349C23×C127—41no—
350C23×C127—42no—
351C23×C127—42no—
352C23×C127—42no—
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—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—42no—
376C23×C127—42no—
377C23×C127—42no—
378C23×C127—41no—
379C23×C127—42no—
380C23×C127—41no—
381C23×C127—42no—
382C23×C127—41no—
383C23×C127—42no—
384C23×C127—41no—
385C23×C127—42no—
386C23×C127—42no—
387C23×C127—42no—
388C23×C127—42no—
389C23×C127—42no—
390C23×C127—42no—
391C23×C127—42no—
392C23×C127—42no—
393C23×C127—42no—
394C23×C127#12014yes—
395C23×C127#12014yescomplemented
396C23×C127#12118yescomplemented
397C23×C127C22×D411yescharacteristic
398C23×C127C22×D411yescharacteristic
399C23×C127C22×D412yes—
400C23×C127C22×D412yes—
401C23×C127C22×D411yescharacteristic
402C23×C127C2×#4112yes—
403C23×C127H(5,𝔽2)12yes—
404C23×C127H(5,𝔽2)12yes—
405C23×C127H(5,𝔽2)12yes—
406D4×C127—416no—
407D4×C127—416no—
408D4×C127—432no—
409D4×C127—416no—
410D4×C127—432no—
411C2×C4×C127—22no—
412C2×C4×C127—22no—
413C2×C4×C127—24no—
414C2×C4×C127—24no—
415C2×C4×C127—22no—
416C2×C4×C127—22no—
417C2×C4×C127—24no—
418C2×C4×C127—24no—
419C2×C4×C127—22no—
420C2×C4×C127—22no—
421C2×C4×C127—24no—
422C2×C4×C127—24no—
423C2×C4×C127—22no—
424C2×C4×C127—24no—
425C2×C4×C127—24no—
426C2×C4×C127—24no—
427C2×C4×C127—24no—
428C2×C4×C127—416no—
429C2×C4×C127—41no—
430C2×C4×C127—41no—
431C2×C4×C127—42no—
432C2×C4×C127—41no—
433C2×C4×C127—41no—
434C2×C4×C127—42no—
435C2×C4×C127—42no—
436C2×C4×C127—42no—
437C2×C4×C127—42no—
438C2×C4×C127—42no—
439C2×C4×C127—42no—
440C2×C4×C127—42no—
441C2×C4×C127—42no—
442C2×C4×C127—42no—
443C2×C4×C127—42no—
444C2×C4×C127—42no—
445C2×C4×C127—42no—
446C2×C4×C127—42no—
447C2×C4×C127—42no—
448C2×C4×C127—42no—
449C2×C4×C127—42no—
450C2×C4×C127—42no—
451C2×C4×C127—42no—
452C2×C4×C127#12014yescomplemented
453C22×C127—24no—
454C22×C127—24no—
455C22×C127—24no—
456C22×C127—24no—
457C22×C127—28no—
458C22×C127—28no—
459C22×C127—28no—
460C22×C127—28no—
461C22×C127—464no—
462C22×C127—42no—
463C22×C127—44no—
464C22×C127—44no—
465C22×C127—42no—
466C22×C127—44no—
467C22×C127—44no—
468C22×C127—44no—
469C22×C127—44no—
470C22×C127—44no—
471C22×C127—44no—
472C22×C127—44no—
473C22×C127—44no—
474C22×C127—44no—
475C22×C127—44no—
476C22×C127—44no—
477C22×C127—44no—
478C22×C127—44no—
479C22×C127—44no—
480C22×C127—44no—
481C22×C127—44no—
482C22×C127—44no—
483C22×C127—44no—
484C22×C127—44no—
485C22×C127—44no—
486C22×C127—44no—
487C22×C127—42no—
488C22×C127—42no—
489C22×C127—42no—
490C22×C127—44no—
491C22×C127—44no—
492C22×C127—82no—
493C22×C127—82no—
494C22×C127—82no—
495C22×C127—82no—
496C22×C127C2×#12011yescharacteristic
497C22×C127C2×#12011yescharacteristic
498C22×C127C2×#12011yescharacteristic
499C22×C127C2×#12112yes—
500C22×C127#52511yescharacteristic
501C22×C127#53411yescharacteristic
502C22×C127#53411yescharacteristic
503C22×C127#53412yes—
504C22×C127#53511yescharacteristic
505C22×C127#53512yes—
506C22×C127#53812yes—
507C22×C127D4212yes—
508C22×C127D4212yes—
509C22×C127D4212yes—
510C22×C127D4212yes—
511C22×C127D4212yes—
512C22×C127#54612yes—
513C22×C127#54612yes—
514C22×C127#54612yes—
515C22×C127#54612yes—
516C22×C127#56012yes—
517C4×C127—24no—
518C4×C127—42no—
519C4×C127—42no—
520C4×C127—42no—
521C4×C127—44no—
522C4×C127—44no—
523C4×C127—82no—
524#15257C12711yesmaximal, characteristic, direct product factor, Sylow
525C2×C127—44no—
526C2×C127—44no—
527C2×C127—48no—
528C2×C127—82no—
529C2×C127#240311yescharacteristic
530C2×C127#240311yescharacteristic
531C2×C127#240411yescharacteristic
532C2×C127#240812yes—
533C2×C127#241012yes—
534C2×C127#242412yes—
535C2×C127#266812yes—
536C2×C127#266912yes—
537C2×C127#267812yes—
538C22×#121C2×C12711yescharacteristic, complemented
539C22×#120C2×C12711yescharacteristic, complemented
540C22×#120C2×C12711yescharacteristic, complemented
541C2×#392C2×C12712yescomplemented
542C2×#386C2×C12712yescomplemented
543C2×#379C2×C12711yescharacteristic, complemented
544#1440C2×C12711yescharacteristic, complemented
545#1439C2×C12712yescomplemented
546#1438C2×C12712yescomplemented
547#1438C2×C12711yescharacteristic, complemented
548#1438C2×C12711yescharacteristic, complemented
549C127#1525711yescharacteristic, direct product factor, Sylow
550C26C22×C12711yescharacteristic
551C23×D4C22×C12712yes—
552C23×D4C22×C12712yes—
553C23×D4C22×C12711yescharacteristic
554C23×D4C22×C12711yescharacteristic
555C23×D4C22×C12711yescharacteristic, complemented
556C24×C4C22×C12711yescharacteristic, complemented
557C2×#121—24no—
558C2×#121—24no—
559C2×#121—24no—
560C2×#120—24no—
561C2×#120—24no—
562C2×#120—28no—
563C2×#120—28no—
564C22×C4⋊C4C22×C12711yescharacteristic, complemented
565C22×C22⋊C4C22×C12712yes—
566C22×C22⋊C4C22×C12711yescharacteristic
567C22×C22⋊C4C22×C12711yescharacteristic
568C22×C22⋊C4C22×C12712yes—
569C22×C22⋊C4C22×C12712yes—
570C22×C22⋊C4C22×C12712yes—
571C22×C22⋊C4C22×C12711yescharacteristic
572C22×C22⋊C4C22×C12711yescharacteristic
573C22×C22⋊C4C22×C12711yescharacteristic, complemented
574C22×C22⋊C4C22×C12712yescomplemented
575C22×C22⋊C4C22×C12712yescomplemented
576#392—28no—
577#386—28no—
578#379—24no—
579C2×#95C22×C12712yescomplemented
580C2×#95C22×C12712yescomplemented
581C2×#95C22×C12712yescomplemented
582C2×#95C22×C12712yescomplemented
583C25—22no—
584C25—22no—
585C25—24no—
586C25—24no—
587C25—22no—
588C25—24no—
589C25—42no—
590C25—42no—
591C25—42no—
592C25C23×C12711yescharacteristic
593C25C23×C12711yescharacteristic
594C25C23×C12711yescharacteristic
595C25C23×C12712yes—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—24no—
600C22×D4—24no—
601C22×D4—22no—
602C22×D4—22no—
603C22×D4—22no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—24no—
608C22×D4—24no—
609C22×D4—24no—
610C22×D4—24no—
611C22×D4—24no—
612C22×D4—24no—
613C22×D4—24no—
614C22×D4—22no—
615C22×D4—42no—
616C22×D4—42no—
617C22×D4—42no—
618C22×D4—42no—
619C22×D4—42no—
620C22×D4—42no—
621C22×D4—42no—
622C22×D4D4×C12714yescomplemented
623C22×D4D4×C12714yescomplemented
624C22×D4D4×C12718yescomplemented
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—22no—
628C23×C4—24no—
629C23×C4—42no—
630C23×C4C23×C12712yes—
631C23×C4C23×C12711yescharacteristic
632C23×C4C23×C12711yescharacteristic
633C23×C4C23×C12711yescharacteristic
634C23×C4C23×C12712yes—
635C23×C4C23×C12712yes—
636C23×C4C23×C12711yescharacteristic
637#121—232no—
638#120—232no—
639#120—232no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—24no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—24no—
665C2×C22⋊C4—42no—
666C2×C22⋊C4—42no—
667C2×C22⋊C4—42no—
668C2×C22⋊C4—42no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4—42no—
671C2×C22⋊C4D4×C12718yescomplemented
672C2×C22⋊C4D4×C12714yescomplemented
673#95—24no—
674#95—24no—
675#95—24no—
676#95—42no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—28no—
703C24—28no—
704C24—28no—
705C24—21no—
706C24—21no—
707C24—22no—
708C24—22no—
709C24—22no—
710C24—22no—
711C24—22no—
712C24—22no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—44no—
723C24—44no—
724C24—48no—
725C24—44no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—44no—
730C24—48no—
731C24C2×D4×C12712yes—
732C24C2×D4×C12712yes—
733C24C2×D4×C12712yes—
734C24C2×D4×C12712yes—
735C24C2×D4×C12714yes—
736C24C2×D4×C12712yes—
737C24C2×D4×C12714yes—
738C24C2×D4×C12714yes—
739C24#41×C12714yes—
740C24C24×C12711yescharacteristic
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—216no—
747C2×D4—216no—
748C2×D4—28no—
749C2×D4—44no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—48no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—28no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4C2×D4×C12714yes—
810C22×C4C2×D4×C12714yes—
811C22×C4C2×D4×C12712yes—
812C22×C4C2×D4×C12712yes—
813C22×C4C2×D4×C12712yes—
814C22×C4C2×D4×C12714yes—
815C22×C4C2×D4×C12712yes—
816C4⋊C4—28no—
817C22⋊C4—216no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—216no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C23—22no—
829C23—22no—
830C23—24no—
831C23—24no—
832C23—22no—
833C23—24no—
834C23—22no—
835C23—24no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—24no—
840C23—24no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—432no—
879C23—432no—
880C23—432no—
881C23—432no—
882C23—41no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—41no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23—42no—
906C23—42no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—42no—
915C23—42no—
916C23—41no—
917C23—42no—
918C23—41no—
919C23—42no—
920C23—41no—
921C23—42no—
922C23—41no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—42no—
930C23—42no—
931C23—42no—
932C23#120×C12714yes—
933C23#120×C12714yescomplemented
934C23#121×C12718yescomplemented
935C23C22×D4×C12711yescharacteristic
936C23C22×D4×C12711yescharacteristic
937C23C22×D4×C12712yes—
938C23C22×D4×C12712yes—
939C23C22×D4×C12711yescharacteristic
940C23C2×#41×C12712yes—
941C23H(5,𝔽2)×C12712yes—
942C23H(5,𝔽2)×C12712yes—
943C23H(5,𝔽2)×C12712yes—
944D4—416no—
945D4—416no—
946D4—432no—
947D4—416no—
948D4—432no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—416no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4#120×C12714yescomplemented
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—28no—
996C22—28no—
997C22—28no—
998C22—28no—
999C22—464no—
1000C22—42no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—42no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—44no—
1029C22—44no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—82no—
1034C22C2×#120×C12711yescharacteristic
1035C22C2×#120×C12711yescharacteristic
1036C22C2×#120×C12711yescharacteristic
1037C22C2×#121×C12712yes—
1038C22#525×C12711yescharacteristic
1039C22#534×C12711yescharacteristic
1040C22#534×C12711yescharacteristic
1041C22#534×C12712yes—
1042C22#535×C12711yescharacteristic
1043C22#535×C12712yes—
1044C22#538×C12712yes—
1045C22D42×C12712yes—
1046C22D42×C12712yes—
1047C22D42×C12712yes—
1048C22D42×C12712yes—
1049C22D42×C12712yes—
1050C22#546×C12712yes—
1051C22#546×C12712yes—
1052C22#546×C12712yes—
1053C22#546×C12712yes—
1054C22#560×C12712yes—
1055C4—24no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—82no—
1062C2—44no—
1063C2—48no—
1064C2—44no—
1065C2—82no—
1066C2C127×#240311yescharacteristic
1067C2C127×#240311yescharacteristic
1068C2C127×#240411yescharacteristic
1069C2C127×#240812yes—
1070C2C127×#241012yes—
1071C2C127×#242412yes—
1072C2C127×#266812yes—
1073C2C127×#266912yes—
1074C2C127×#267812yes—
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. C22×#120×C127C2semidirect
3. C22×#120×C127C2semidirect
4. C2×#392×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#379×C127C2semidirect
7. C127×#1440C2semidirect
8. C127×#1439C2semidirect
9. C127×#1438C2semidirect
10. C127×#1438C2semidirect
11. C127×#1438C2semidirect
17. C23×D4×C127C22semidirect
18. C24×C4×C127C22semidirect
26. C22×C4⋊C4×C127C22semidirect
35. C22×C22⋊C4×C127C22semidirect
36. C22×C22⋊C4×C127C22semidirect
37. C22×C22⋊C4×C127C22semidirect
41. C2×#95×C127C22semidirect
42. C2×#95×C127C22semidirect
43. C2×#95×C127C22semidirect
44. C2×#95×C127C22semidirect
84. C22×D4×C127D4semidirect
85. C22×D4×C127D4semidirect
86. C22×D4×C127D4semidirect
133. C2×C22⋊C4×C127D4semidirect
134. C2×C22⋊C4×C127D4semidirect
395. C23×C127#120semidirect
396. C23×C127#121semidirect
452. C2×C4×C127#120semidirect
524. #15257C127direct (N × H)
538. C22×#121C2×C127semidirect
539. C22×#120C2×C127semidirect
540. C22×#120C2×C127semidirect
541. C2×#392C2×C127semidirect
542. C2×#386C2×C127semidirect
543. C2×#379C2×C127semidirect
544. #1440C2×C127semidirect
545. #1439C2×C127semidirect
546. #1438C2×C127semidirect
547. #1438C2×C127semidirect
548. #1438C2×C127semidirect
549. C127#15257direct (N × H)
555. C23×D4C22×C127semidirect
556. C24×C4C22×C127semidirect
564. C22×C4⋊C4C22×C127semidirect
573. C22×C22⋊C4C22×C127semidirect
574. C22×C22⋊C4C22×C127semidirect
575. C22×C22⋊C4C22×C127semidirect
579. C2×#95C22×C127semidirect
580. C2×#95C22×C127semidirect
581. C2×#95C22×C127semidirect
582. C2×#95C22×C127semidirect
622. C22×D4D4×C127semidirect
623. C22×D4D4×C127semidirect
624. C22×D4D4×C127semidirect
671. C2×C22⋊C4D4×C127semidirect
672. C2×C22⋊C4D4×C127semidirect
933. C23#120×C127semidirect
934. C23#121×C127semidirect
990. C2×C4#120×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1272
C22×#120×C1272
C2×#392×C1272
C2×#386×C1272
C2×#379×C1272
C127×#14402
C127×#14392
C127×#14382
#15257127