Finite Group Databasebeta

← C127×#15673 #44579346

Subgroups — C127×#15673 #44579346

Order 32512.

2602 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C127C211yesmaximal, characteristic, complemented
2C22×#121×C127C211yesmaximal, characteristic
3C2×#395×C127C211yesmaximal, characteristic, complemented
4C2×#394×C127C212yesmaximal, complemented
5C2×#393×C127C211yesmaximal, characteristic, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1438C212yesmaximal, complemented
8C127×#1438C211yesmaximal, characteristic, complemented
9C127×#1437C211yesmaximal, characteristic, complemented
10C127×#1436C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C212yesmaximal, complemented
12C23×Q8×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C23×D4×C127C2211yescharacteristic
15C23×D4×C127C2211yescharacteristic
16C24×C4×C127C2211yescharacteristic
17C2×#124×C127—24no—
18C2×#124×C127—28no—
19C2×#121×C127—24no—
20C2×#121×C127—24no—
21C2×#121×C127—24no—
22C22×C4⋊C4×C127C2212yes—
23C22×C4⋊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×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2212yes—
31C22×C22⋊C4×C127C2212yes—
32C22×C42×C127C2211yescharacteristic
33#395×C127—24no—
34#394×C127—28no—
35#393×C127—24no—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2212yes—
42C2×#95×C127C2212yes—
43C25×C127C2311yescharacteristic
44C25×C127C2311yescharacteristic
45C25×C127C2311yescharacteristic
46C22×Q8×C127—24no—
47C22×Q8×C127—22no—
48C22×Q8×C127—22no—
49C22×Q8×C127—22no—
50C22×Q8×C127—42no—
51C22×D4×C127—22no—
52C22×D4×C127—22no—
53C22×D4×C127—22no—
54C22×D4×C127—22no—
55C22×D4×C127—24no—
56C22×D4×C127—24no—
57C22×D4×C127—22no—
58C22×D4×C127—22no—
59C22×D4×C127—22no—
60C22×D4×C127—22no—
61C22×D4×C127—24no—
62C22×D4×C127—42no—
63C22×D4×C127—42no—
64C22×D4×C127—42no—
65C22×D4×C127D414yes—
66C23×C4×C127—22no—
67C23×C4×C127—22no—
68C23×C4×C127—22no—
69C23×C4×C127—24no—
70C23×C4×C127—42no—
71C23×C4×C127C2312yes—
72C23×C4×C127C2312yes—
73C23×C4×C127C2312yes—
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2312yes—
77C23×C4×C127C2311yescharacteristic
78C23×C4×C127C2311yescharacteristic
79#124×C127—232no—
80#121×C127—232no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—24no—
84C2×C4⋊C4×C127—24no—
85C2×C4⋊C4×C127—42no—
86C2×C4⋊C4×C127D414yes—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—24no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127—22no—
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—42no—
105C2×C22⋊C4×C127—42no—
106C2×C22⋊C4×C127—42no—
107C2×C22⋊C4×C127—42no—
108C2×C22⋊C4×C127—42no—
109C2×C22⋊C4×C127D414yes—
110C2×C22⋊C4×C127D418yescomplemented
111C2×C42×C127—24no—
112C2×C42×C127—22no—
113#95×C127—24no—
114#95×C127—22no—
115#95×C127—24no—
116#95×C127—22no—
117#95×C127—24no—
118#95×C127—24no—
119#95×C127—42no—
120C24×C127—21no—
121C24×C127—21no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—22no—
128C24×C127—22no—
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×C127C2×D412yes—
144C24×C127C2×D412yes—
145C24×C127C2×D414yes—
146C24×C127C2×D412yes—
147C24×C127C2411yescharacteristic
148C2×Q8×C127—28no—
149C2×Q8×C127—48no—
150C2×Q8×C127—48no—
151C2×Q8×C127—44no—
152C2×Q8×C127—44no—
153C2×D4×C127—28no—
154C2×D4×C127—28no—
155C2×D4×C127—28no—
156C2×D4×C127—28no—
157C2×D4×C127—44no—
158C2×D4×C127—48no—
159C2×D4×C127—48no—
160C2×D4×C127—48no—
161C2×D4×C127—48no—
162C2×D4×C127—48no—
163C2×D4×C127—44no—
164C2×D4×C127—48no—
165C2×D4×C127—44no—
166C2×D4×C127—44no—
167C2×D4×C127—44no—
168C22×C4×C127—22no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—22no—
172C22×C4×C127—22no—
173C22×C4×C127—28no—
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—21no—
182C22×C4×C127—21no—
183C22×C4×C127—22no—
184C22×C4×C127—22no—
185C22×C4×C127—21no—
186C22×C4×C127—21no—
187C22×C4×C127—22no—
188C22×C4×C127—22no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127—22no—
192C22×C4×C127—22no—
193C22×C4×C127—22no—
194C22×C4×C127—22no—
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—22no—
205C22×C4×C127—22no—
206C22×C4×C127—22no—
207C22×C4×C127—48no—
208C22×C4×C127—48no—
209C22×C4×C127—44no—
210C22×C4×C127—44no—
211C22×C4×C127C2×D412yes—
212C22×C4×C127C2×D414yes—
213C22×C4×C127C2×D414yes—
214C22×C4×C127C2×D412yes—
215C22×C4×C127C2×D412yes—
216C22×C4×C127C2×D412yes—
217C22×C4×C127C2×D412yes—
218C22×C4×C127C2×D412yes—
219C22×C4×C127#4114yes—
220C22×C4×C127#4114yes—
221C4⋊C4×C127—28no—
222C4⋊C4×C127—48no—
223C22⋊C4×C127—28no—
224C22⋊C4×C127—216no—
225C22⋊C4×C127—216no—
226C22⋊C4×C127—28no—
227C22⋊C4×C127—48no—
228C22⋊C4×C127—48no—
229C22⋊C4×C127—48no—
230C22⋊C4×C127—48no—
231C42×C127—28no—
232C23×C127—22no—
233C23×C127—24no—
234C23×C127—22no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—24no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—22no—
243C23×C127—22no—
244C23×C127—22no—
245C23×C127—22no—
246C23×C127—22no—
247C23×C127—22no—
248C23×C127—24no—
249C23×C127—24no—
250C23×C127—24no—
251C23×C127—24no—
252C23×C127—41no—
253C23×C127—41no—
254C23×C127—41no—
255C23×C127—41no—
256C23×C127—42no—
257C23×C127—42no—
258C23×C127—42no—
259C23×C127—42no—
260C23×C127—42no—
261C23×C127—42no—
262C23×C127—41no—
263C23×C127—41no—
264C23×C127—41no—
265C23×C127—42no—
266C23×C127—41no—
267C23×C127—42no—
268C23×C127—41no—
269C23×C127—41no—
270C23×C127—41no—
271C23×C127—41no—
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#12014yes—
295C23×C127C22×D411yescharacteristic
296C23×C127C22×D411yescharacteristic
297C23×C127C22×D411yescharacteristic
298C23×C127C22×D412yes—
299C23×C127C2×#4112yes—
300C23×C127C2×#4112yes—
301C23×C127H(5,𝔽2)12yes—
302C23×C127H(5,𝔽2)12yes—
303C23×C1272−1+412yes—
304Q8×C127—416no—
305D4×C127—416no—
306D4×C127—416no—
307D4×C127—416no—
308C2×C4×C127—22no—
309C2×C4×C127—22no—
310C2×C4×C127—22no—
311C2×C4×C127—22no—
312C2×C4×C127—24no—
313C2×C4×C127—24no—
314C2×C4×C127—24no—
315C2×C4×C127—24no—
316C2×C4×C127—24no—
317C2×C4×C127—22no—
318C2×C4×C127—24no—
319C2×C4×C127—22no—
320C2×C4×C127—24no—
321C2×C4×C127—24no—
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—24no—
329C2×C4×C127—416no—
330C2×C4×C127—41no—
331C2×C4×C127—42no—
332C2×C4×C127—41no—
333C2×C4×C127—42no—
334C2×C4×C127—41no—
335C2×C4×C127—42no—
336C2×C4×C127—42no—
337C2×C4×C127—41no—
338C2×C4×C127—42no—
339C2×C4×C127—42no—
340C2×C4×C127—42no—
341C2×C4×C127—42no—
342C2×C4×C127—42no—
343C2×C4×C127—42no—
344C2×C4×C127—42no—
345C2×C4×C127—42no—
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—42no—
354C2×C4×C127—42no—
355C2×C4×C127#12014yes—
356C2×C4×C127#12414yescomplemented
357C22×C127—24no—
358C22×C127—28no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—44no—
362C22×C127—42no—
363C22×C127—42no—
364C22×C127—44no—
365C22×C127—44no—
366C22×C127—42no—
367C22×C127—42no—
368C22×C127—44no—
369C22×C127—44no—
370C22×C127—44no—
371C22×C127—42no—
372C22×C127—42no—
373C22×C127—42no—
374C22×C127—42no—
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×#12011yescharacteristic
385C22×C127C2×#12011yescharacteristic
386C22×C127C2×#12411yescharacteristic
387C22×C127#53212yes—
388C22×C127#53211yescharacteristic
389C22×C127#53411yescharacteristic
390C22×C127#53511yescharacteristic
391C22×C127#53611yescharacteristic
392C22×C127#53712yes—
393C22×C127#53812yes—
394C22×C127#54212yes—
395C22×C127D4212yes—
396C22×C127D4212yes—
397C22×C127#54612yes—
398C22×C127#54612yes—
399C22×C127#54612yes—
400C22×C127#54712yes—
401C22×C127#54712yes—
402C22×C127#54812yes—
403C22×C127#55512yes—
404C22×C127#56212yes—
405C4×C127—24no—
406C4×C127—24no—
407C4×C127—42no—
408C4×C127—44no—
409C4×C127—44no—
410C4×C127—44no—
411C4×C127—42no—
412C4×C127—82no—
413#15673C12711yesmaximal, characteristic, direct product factor, Sylow
414C2×C127—44no—
415C2×C127—82no—
416C2×C127—82no—
417C2×C127#240311yescharacteristic
418C2×C127#243012yes—
419C2×C127#243211yescharacteristic
420C2×C127#243511yescharacteristic
421C2×C127#249112yes—
422C2×C127#255512yes—
423C2×C127#267212yes—
424C2×C127#267612yes—
425C2×C127#268612yes—
426C22×#124C2×C12711yescharacteristic, complemented
427C22×#121C2×C12711yescharacteristic
428C2×#395C2×C12711yescharacteristic, complemented
429C2×#394C2×C12712yescomplemented
430C2×#393C2×C12711yescharacteristic, complemented
431#1439C2×C12712yescomplemented
432#1438C2×C12712yescomplemented
433#1438C2×C12711yescharacteristic, complemented
434#1437C2×C12711yescharacteristic, complemented
435#1436C2×C12711yescharacteristic, complemented
436C22⋊#95C2×C12712yescomplemented
437C127#1567311yescharacteristic, direct product factor, Sylow
438C23×Q8C22×C12711yescharacteristic
439C23×D4C22×C12711yescharacteristic
440C23×D4C22×C12711yescharacteristic
441C23×D4C22×C12711yescharacteristic
442C24×C4C22×C12711yescharacteristic
443C2×#124—24no—
444C2×#124—28no—
445C2×#121—24no—
446C2×#121—24no—
447C2×#121—24no—
448C22×C4⋊C4C22×C12712yes—
449C22×C4⋊C4C22×C12711yescharacteristic
450C22×C22⋊C4C22×C12711yescharacteristic
451C22×C22⋊C4C22×C12712yes—
452C22×C22⋊C4C22×C12712yes—
453C22×C22⋊C4C22×C12712yes—
454C22×C22⋊C4C22×C12712yes—
455C22×C22⋊C4C22×C12711yescharacteristic
456C22×C22⋊C4C22×C12712yes—
457C22×C22⋊C4C22×C12712yes—
458C22×C42C22×C12711yescharacteristic
459#395—24no—
460#394—28no—
461#393—24no—
462C2×#95C22×C12712yes—
463C2×#95C22×C12711yescharacteristic
464C2×#95C22×C12712yes—
465C2×#95C22×C12712yes—
466C2×#95C22×C12711yescharacteristic
467C2×#95C22×C12712yes—
468C2×#95C22×C12712yes—
469C25C23×C12711yescharacteristic
470C25C23×C12711yescharacteristic
471C25C23×C12711yescharacteristic
472C22×Q8—24no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8—42no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—24no—
482C22×D4—24no—
483C22×D4—22no—
484C22×D4—22no—
485C22×D4—22no—
486C22×D4—22no—
487C22×D4—24no—
488C22×D4—42no—
489C22×D4—42no—
490C22×D4—42no—
491C22×D4D4×C12714yes—
492C23×C4—22no—
493C23×C4—22no—
494C23×C4—22no—
495C23×C4—24no—
496C23×C4—42no—
497C23×C4C23×C12712yes—
498C23×C4C23×C12712yes—
499C23×C4C23×C12712yes—
500C23×C4C23×C12711yescharacteristic
501C23×C4C23×C12711yescharacteristic
502C23×C4C23×C12712yes—
503C23×C4C23×C12711yescharacteristic
504C23×C4C23×C12711yescharacteristic
505#124—232no—
506#121—232no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4D4×C12714yes—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
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—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4D4×C12714yes—
536C2×C22⋊C4D4×C12718yescomplemented
537C2×C42—24no—
538C2×C42—22no—
539#95—24no—
540#95—22no—
541#95—24no—
542#95—22no—
543#95—24no—
544#95—24no—
545#95—42no—
546C24—21no—
547C24—21no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24C2×D4×C12712yes—
570C24C2×D4×C12712yes—
571C24C2×D4×C12714yes—
572C24C2×D4×C12712yes—
573C24C24×C12711yescharacteristic
574C2×Q8—28no—
575C2×Q8—48no—
576C2×Q8—48no—
577C2×Q8—44no—
578C2×Q8—44no—
579C2×D4—28no—
580C2×D4—28no—
581C2×D4—28no—
582C2×D4—28no—
583C2×D4—44no—
584C2×D4—48no—
585C2×D4—48no—
586C2×D4—48no—
587C2×D4—48no—
588C2×D4—48no—
589C2×D4—44no—
590C2×D4—48no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—44no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—28no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4C2×D4×C12712yes—
638C22×C4C2×D4×C12714yes—
639C22×C4C2×D4×C12714yes—
640C22×C4C2×D4×C12712yes—
641C22×C4C2×D4×C12712yes—
642C22×C4C2×D4×C12712yes—
643C22×C4C2×D4×C12712yes—
644C22×C4C2×D4×C12712yes—
645C22×C4#41×C12714yes—
646C22×C4#41×C12714yes—
647C4⋊C4—28no—
648C4⋊C4—48no—
649C22⋊C4—28no—
650C22⋊C4—216no—
651C22⋊C4—216no—
652C22⋊C4—28no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C42—28no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
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#120×C12714yes—
721C23C22×D4×C12711yescharacteristic
722C23C22×D4×C12711yescharacteristic
723C23C22×D4×C12711yescharacteristic
724C23C22×D4×C12712yes—
725C23C2×#41×C12712yes—
726C23C2×#41×C12712yes—
727C23H(5,𝔽2)×C12712yes—
728C23H(5,𝔽2)×C12712yes—
729C232−1+4×C12712yes—
730Q8—416no—
731D4—416no—
732D4—416no—
733D4—416no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—416no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4#120×C12714yes—
782C2×C4#124×C12714yescomplemented
783C22—24no—
784C22—28no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—42no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22C2×#120×C12711yescharacteristic
811C22C2×#120×C12711yescharacteristic
812C22C2×#124×C12711yescharacteristic
813C22#532×C12712yes—
814C22#532×C12711yescharacteristic
815C22#534×C12711yescharacteristic
816C22#535×C12711yescharacteristic
817C22#536×C12711yescharacteristic
818C22#537×C12712yes—
819C22#538×C12712yes—
820C22#542×C12712yes—
821C22D42×C12712yes—
822C22D42×C12712yes—
823C22#546×C12712yes—
824C22#546×C12712yes—
825C22#546×C12712yes—
826C22#547×C12712yes—
827C22#547×C12712yes—
828C22#548×C12712yes—
829C22#555×C12712yes—
830C22#562×C12712yes—
831C4—24no—
832C4—24no—
833C4—42no—
834C4—44no—
835C4—44no—
836C4—44no—
837C4—42no—
838C4—82no—
839C2—44no—
840C2—82no—
841C2—82no—
842C2C127×#240311yescharacteristic
843C2C127×#243012yes—
844C2C127×#243211yescharacteristic
845C2C127×#243511yescharacteristic
846C2C127×#249112yes—
847C2C127×#255512yes—
848C2C127×#267212yes—
849C2C127×#267612yes—
850C2C127×#268612yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC22×#121×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#124×C127C2semidirect
3. C2×#395×C127C2semidirect
4. C2×#394×C127C2semidirect
5. C2×#393×C127C2semidirect
6. C127×#1439C2semidirect
7. C127×#1438C2semidirect
8. C127×#1438C2semidirect
9. C127×#1437C2semidirect
10. C127×#1436C2semidirect
11. C127×C22⋊#95C2semidirect
110. C2×C22⋊C4×C127D4semidirect
356. C2×C4×C127#124semidirect
413. #15673C127direct (N × H)
426. C22×#124C2×C127semidirect
428. C2×#395C2×C127semidirect
429. C2×#394C2×C127semidirect
430. C2×#393C2×C127semidirect
431. #1439C2×C127semidirect
432. #1438C2×C127semidirect
433. #1438C2×C127semidirect
434. #1437C2×C127semidirect
435. #1436C2×C127semidirect
436. C22⋊#95C2×C127semidirect
437. C127#15673direct (N × H)
536. C2×C22⋊C4D4×C127semidirect
782. C2×C4#124×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1272
C22×#121×C1272
C2×#395×C1272
C2×#394×C1272
C2×#393×C1272
C127×#14392
C127×#14382
C127×#14372
C127×#14362
C127×C22⋊#952
#15673127