Finite Group Databasebeta

← C127×#10994 #44574667

Subgroups — C127×#10994 #44574667

Order 32512.

1494 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C127C211yesmaximal, characteristic
2C2×#421×C127C211yesmaximal, characteristic, complemented
3C127×#2896C211yesmaximal, characteristic, complemented
4C2×#407×C127C211yesmaximal, characteristic, complemented
5C127×#2280C211yesmaximal, characteristic, complemented
6C127×#1733C211yesmaximal, characteristic, complemented
7C2×H(3,ℤ/4)×C127C211yesmaximal, characteristic, complemented
8C22×#41×C127C2211yescharacteristic
9C24×C4×C127C2211yescharacteristic
10C22×M16×C127C2211yescharacteristic
11C22×M16×C127C2211yescharacteristic
12#525×C127—22no—
13#525×C127—22no—
14#525×C127—22no—
15#525×C127C414yescomplemented
16C2×#123×C127—21no—
17C2×C22⋊Q8×C127—21no—
18C2×#121×C127—21no—
19C2×#120×C127—21no—
20C2×C4×D4×C127—22no—
21C2×#117×C127C2211yescharacteristic
22C2×#117×C127C2211yescharacteristic
23C2×#117×C127C2211yescharacteristic
24#421×C127—22no—
25#421×C127—22no—
26C2×#104×C127—22no—
27#419×C127—21no—
28#418×C127—21no—
29#417×C127—22no—
30#416×C127—22no—
31#407×C127—22no—
32#407×C127—22no—
33C2×C22⋊C8×C127—22no—
34#381×C127—21no—
35#380×C127—22no—
36#379×C127—21no—
37C4×C22⋊C4×C127—22no—
38#339×C127—22no—
39H(3,ℤ/4)×C127—22no—
40C25×C127D411yescharacteristic
41C2×#41×C127—21no—
42C2×#41×C127—21no—
43C2×#41×C127—21no—
44C2×#41×C127—21no—
45C2×#41×C127—21no—
46C2×#41×C127—21no—
47C2×#41×C127—21no—
48C2×#41×C127—21no—
49C2×#41×C127—21no—
50C2×#41×C127—21no—
51C2×#41×C127C2×C412yes—
52C2×#41×C127D412yes—
53C22×Q8×C127D411yescharacteristic
54C22×D4×C127—22no—
55C22×D4×C127—21no—
56C22×D4×C127D411yescharacteristic
57C23×C4×C127—21no—
58C23×C4×C127—21no—
59C23×C4×C127—21no—
60C23×C4×C127—21no—
61C23×C4×C127—21no—
62C23×C4×C127—21no—
63C23×C4×C127—21no—
64C23×C4×C127—21no—
65C23×C4×C127—21no—
66C23×C4×C127—21no—
67C23×C4×C127—21no—
68C23×C4×C127—21no—
69C23×C4×C127—21no—
70C23×C4×C127C2×C412yes—
71C23×C4×C127D411yescharacteristic
72C23×C4×C127D412yes—
73C23×C4×C127C2311yescharacteristic
74C2×M16×C127—21no—
75C2×M16×C127—21no—
76C2×M16×C127—21no—
77C2×M16×C127—21no—
78C2×M16×C127—21no—
79C2×M16×C127—21no—
80C2×M16×C127—21no—
81C2×M16×C127—21no—
82C2×M16×C127—21no—
83C2×M16×C127—21no—
84C2×M16×C127—21no—
85C2×M16×C127D412yescomplemented
86C22×C8×C127—21no—
87C22×C8×C127D412yescomplemented
88#123×C127—24no—
89#123×C127—24no—
90C22⋊Q8×C127—24no—
91C22⋊Q8×C127—24no—
92#121×C127—24no—
93#121×C127—24no—
94#120×C127—24no—
95#120×C127—24no—
96C4×D4×C127—28no—
97C4×D4×C127—28no—
98#117×C127—21no—
99#117×C127—21no—
100#117×C127—21no—
101#117×C127—21no—
102#117×C127—21no—
103#117×C127—21no—
104#117×C127—21no—
105#117×C127—21no—
106#117×C127—21no—
107#117×C127—21no—
108#117×C127C2×C412yes—
109#117×C127D412yes—
110C2×C4⋊C4×C127—22no—
111C2×C4⋊C4×C127—21no—
112C2×C4⋊C4×C127—21no—
113C2×C4⋊C4×C127D412yescomplemented
114C2×C22⋊C4×C127—22no—
115C2×C22⋊C4×C127—22no—
116C2×C22⋊C4×C127—21no—
117C2×C22⋊C4×C127—24no—
118C2×C22⋊C4×C127—21no—
119C2×C22⋊C4×C127—21no—
120C2×C42×C127—21no—
121C2×C42×C127D412yes—
122C2×C42×C127D412yescomplemented
123#104×C127—28no—
124#103×C127—24no—
125#102×C127—24no—
126C22⋊C8×C127—28no—
127#95×C127—24no—
128C24×C127—21no—
129C24×C127—21no—
130C24×C127—21no—
131C24×C127—21no—
132C24×C127—21no—
133C24×C127—21no—
134C24×C127—21no—
135C24×C127—44no—
136C24×C127C22⋊C412yes—
137C24×C127C2×D411yescharacteristic
138#41×C127—22no—
139#41×C127—22no—
140#41×C127—22no—
141#41×C127—22no—
142#41×C127—22no—
143#41×C127—22no—
144#41×C127—22no—
145#41×C127—22no—
146#41×C127—41no—
147#41×C127—41no—
148#41×C127—41no—
149#41×C127—41no—
150#41×C127—41no—
151#41×C127—41no—
152#41×C127—41no—
153#41×C127—41no—
154C2×Q8×C127—21no—
155C2×Q8×C127—21no—
156C2×Q8×C127—21no—
157C2×Q8×C127—21no—
158C2×Q8×C127—21no—
159C2×Q8×C127C22⋊C412yescomplemented
160C2×D4×C127—28no—
161C2×D4×C127—22no—
162C2×D4×C127—22no—
163C2×D4×C127—21no—
164C2×D4×C127—21no—
165C2×D4×C127—21no—
166C2×D4×C127—21no—
167C2×D4×C127—21no—
168C2×D4×C127—48no—
169C2×D4×C127—41no—
170C2×D4×C127—41no—
171C2×D4×C127—41no—
172C2×D4×C127—41no—
173C2×D4×C127C22⋊C412yescomplemented
174C22×C4×C127—21no—
175C22×C4×C127—22no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
178C22×C4×C127—21no—
179C22×C4×C127—21no—
180C22×C4×C127—21no—
181C22×C4×C127—21no—
182C22×C4×C127—22no—
183C22×C4×C127—22no—
184C22×C4×C127—22no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
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—41no—
199C22×C4×C127—41no—
200C22×C4×C127—41no—
201C22×C4×C127—41no—
202C22×C4×C127—41no—
203C22×C4×C127—41no—
204C22×C4×C127—41no—
205C22×C4×C127—41no—
206C22×C4×C127—41no—
207C22×C4×C127—41no—
208C22×C4×C127—41no—
209C22×C4×C127—41no—
210C22×C4×C127—41no—
211C22×C4×C127—41no—
212C22×C4×C127—41no—
213C22×C4×C127—41no—
214C22×C4×C127—41no—
215C22×C4×C127—41no—
216C22×C4×C127—41no—
217C22×C4×C127—41no—
218C22×C4×C127C22⋊C412yes—
219C22×C4×C127C22×C411yescharacteristic
220C22×C4×C127C2×D411yescharacteristic
221C22×C4×C127C2×D411yescharacteristic
222C22×C4×C127C2×D411yescharacteristic
223C22×C4×C127C2×D411yescharacteristic
224C22×C4×C127C2×D411yescharacteristic
225C22×C4×C127C2×D411yescharacteristic
226C22×C4×C127C2×D411yescharacteristic
227C22×C4×C127C2×D411yescharacteristic
228C22×C4×C127C2×D411yescharacteristic
229C22×C4×C127#4111yescharacteristic
230C22×C4×C127#4111yescharacteristic
231C22×C4×C127#4111yescharacteristic
232C22×C4×C127#4111yescharacteristic
233M16×C127—22no—
234M16×C127—22no—
235M16×C127—41no—
236M16×C127—41no—
237M16×C127—41no—
238M16×C127—41no—
239M16×C127—41no—
240M16×C127—41no—
241C2×C8×C127—22no—
242C2×C8×C127—22no—
243C2×C8×C127—22no—
244C2×C8×C127—22no—
245C2×C8×C127—41no—
246C2×C8×C127—41no—
247C4⋊C4×C127—28no—
248C4⋊C4×C127—22no—
249C4⋊C4×C127—22no—
250C4⋊C4×C127—22no—
251C4⋊C4×C127—22no—
252C4⋊C4×C127—41no—
253C4⋊C4×C127—41no—
254C22⋊C4×C127—28no—
255C22⋊C4×C127—28no—
256C22⋊C4×C127—22no—
257C22⋊C4×C127—22no—
258C22⋊C4×C127—48no—
259C22⋊C4×C127—41no—
260C22⋊C4×C127—41no—
261C22⋊C4×C127—41no—
262C22⋊C4×C127—41no—
263C42×C127—22no—
264C42×C127—22no—
265C42×C127—22no—
266C42×C127—41no—
267C42×C127—41no—
268C42×C127C22⋊C414yescomplemented
269C23×C127—24no—
270C23×C127—24no—
271C23×C127—24no—
272C23×C127—22no—
273C23×C127—22no—
274C23×C127—22no—
275C23×C127—22no—
276C23×C127—44no—
277C23×C127—42no—
278C23×C127—42no—
279C23×C127—42no—
280C23×C127—42no—
281C23×C127—44no—
282C23×C127—44no—
283C23×C127—44no—
284C23×C127—44no—
285C23×C127—41no—
286C23×C127—41no—
287C23×C127—41no—
288C23×C127—41no—
289C23×C127—41no—
290C23×C127—41no—
291C23×C127C2×C22⋊C411yescharacteristic
292C23×C127#12011yescharacteristic
293C23×C127#12011yescharacteristic
294C23×C127#12011yescharacteristic
295C23×C127#12111yescharacteristic
296C23×C127#12111yescharacteristic
297C23×C127#12311yescharacteristic
298Q8×C127—22no—
299Q8×C127—22no—
300Q8×C127—41no—
301Q8×C127—41no—
302D4×C127—22no—
303D4×C127—22no—
304D4×C127—416no—
305D4×C127—42no—
306D4×C127—42no—
307D4×C127—42no—
308D4×C127—42no—
309D4×C127—41no—
310D4×C127—41no—
311C2×C4×C127—24no—
312C2×C4×C127—22no—
313C2×C4×C127—22no—
314C2×C4×C127—22no—
315C2×C4×C127—22no—
316C2×C4×C127—44no—
317C2×C4×C127—41no—
318C2×C4×C127—41no—
319C2×C4×C127—41no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—41no—
323C2×C4×C127—42no—
324C2×C4×C127—42no—
325C2×C4×C127—42no—
326C2×C4×C127—42no—
327C2×C4×C127—42no—
328C2×C4×C127—42no—
329C2×C4×C127—42no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127—42no—
334C2×C4×C127—42no—
335C2×C4×C127—44no—
336C2×C4×C127—44no—
337C2×C4×C127—42no—
338C2×C4×C127—42no—
339C2×C4×C127C2×C22⋊C411yescharacteristic
340C2×C4×C127C2×C22⋊C411yescharacteristic
341C2×C4×C127C4×D411yescharacteristic
342C2×C4×C127C4×D411yescharacteristic
343C2×C4×C127C4×D411yescharacteristic
344C2×C4×C127C4×D411yescharacteristic
345C2×C4×C127#12011yescharacteristic
346C2×C4×C127#12011yescharacteristic
347C2×C4×C127#12011yescharacteristic
348C2×C4×C127#12011yescharacteristic
349C2×C4×C127#12011yescharacteristic
350C2×C4×C127#12111yescharacteristic
351C2×C4×C127#12111yescharacteristic
352C2×C4×C127#12111yescharacteristic
353C2×C4×C127#12111yescharacteristic
354C2×C4×C127#12111yescharacteristic
355C2×C4×C127#12111yescharacteristic
356C2×C4×C127#12111yescharacteristic
357C2×C4×C127#12111yescharacteristic
358C2×C4×C127#12111yescharacteristic
359C2×C4×C127#12111yescharacteristic
360C2×C4×C127#12311yescharacteristic
361C2×C4×C127#12311yescharacteristic
362C2×C4×C127#12311yescharacteristic
363C2×C4×C127#12411yescharacteristic
364C2×C4×C127#12411yescharacteristic
365C2×C4×C127#12711yescharacteristic
366C2×C4×C127#12711yescharacteristic
367C8×C127—42no—
368C8×C127—42no—
369C22×C127—22no—
370C22×C127—22no—
371C22×C127—22no—
372C22×C127—24no—
373C22×C127—24no—
374C22×C127—24no—
375C22×C127—41no—
376C22×C127—41no—
377C22×C127—41no—
378C22×C127—41no—
379C22×C127—42no—
380C22×C127—44no—
381C22×C127—42no—
382C22×C127—42no—
383C22×C127—44no—
384C22×C127—44no—
385C22×C127—44no—
386C22×C127—42no—
387C22×C127—44no—
388C22×C127—42no—
389C22×C127—82no—
390C22×C127—82no—
391C22×C127#37911yescharacteristic
392C22×C127#38611yescharacteristic
393C22×C127#38611yescharacteristic
394C22×C127#39211yescharacteristic
395C22×C127#39211yescharacteristic
396C22×C127#39411yescharacteristic
397C22×C127#39411yescharacteristic
398C4×C127—44no—
399C4×C127—42no—
400C4×C127—42no—
401C4×C127—82no—
402C4×C127—82no—
403C4×C127#38611yescharacteristic
404C4×C127#38611yescharacteristic
405C4×C127#39011yescharacteristic
406C4×C127#39011yescharacteristic
407C4×C127#39211yescharacteristic
408C4×C127#39211yescharacteristic
409C4×C127#39411yescharacteristic
410C4×C127#39411yescharacteristic
411#10994C12711yesmaximal, characteristic, direct product factor, Sylow
412C2×C127—21no—
413C2×C127—21no—
414C2×C127—21no—
415C2×C127—21no—
416C2×C127—21no—
417C2×C127—21no—
418C2×C127—44no—
419C2×C127—82no—
420C2×C127#143811yescharacteristic
421C2×C127#201012yes—
422C2×#525C2×C12711yescharacteristic
423C2×#421C2×C12711yescharacteristic, complemented
424#2896C2×C12711yescharacteristic, complemented
425C2×#407C2×C12711yescharacteristic, complemented
426#2280C2×C12711yescharacteristic, complemented
427#1733C2×C12711yescharacteristic, complemented
428C2×H(3,ℤ/4)C2×C12711yescharacteristic, complemented
429C127#1099411yescharacteristic, direct product factor, Sylow
430C22×#41C22×C12711yescharacteristic
431C24×C4C22×C12711yescharacteristic
432C22×M16C22×C12711yescharacteristic
433C22×M16C22×C12711yescharacteristic
434#525—22no—
435#525—22no—
436#525—22no—
437#525C4×C12714yescomplemented
438C2×#123—21no—
439C2×C22⋊Q8—21no—
440C2×#121—21no—
441C2×#120—21no—
442C2×C4×D4—22no—
443C2×#117C22×C12711yescharacteristic
444C2×#117C22×C12711yescharacteristic
445C2×#117C22×C12711yescharacteristic
446#421—22no—
447#421—22no—
448C2×#104—22no—
449#419—21no—
450#418—21no—
451#417—22no—
452#416—22no—
453#407—22no—
454#407—22no—
455C2×C22⋊C8—22no—
456#381—21no—
457#380—22no—
458#379—21no—
459C4×C22⋊C4—22no—
460#339—22no—
461H(3,ℤ/4)—22no—
462C25D4×C12711yescharacteristic
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41C2×C4×C12712yes—
474C2×#41D4×C12712yes—
475C22×Q8D4×C12711yescharacteristic
476C22×D4—22no—
477C22×D4—21no—
478C22×D4D4×C12711yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4C2×C4×C12712yes—
493C23×C4D4×C12711yescharacteristic
494C23×C4D4×C12712yes—
495C23×C4C23×C12711yescharacteristic
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16D4×C12712yescomplemented
508C22×C8—21no—
509C22×C8D4×C12712yescomplemented
510#123—24no—
511#123—24no—
512C22⋊Q8—24no—
513C22⋊Q8—24no—
514#121—24no—
515#121—24no—
516#120—24no—
517#120—24no—
518C4×D4—28no—
519C4×D4—28no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117—21no—
524#117—21no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—21no—
529#117—21no—
530#117C2×C4×C12712yes—
531#117D4×C12712yes—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4D4×C12712yescomplemented
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C42—21no—
543C2×C42D4×C12712yes—
544C2×C42D4×C12712yescomplemented
545#104—28no—
546#103—24no—
547#102—24no—
548C22⋊C8—28no—
549#95—24no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24—44no—
558C24C22⋊C4×C12712yes—
559C24C2×D4×C12711yescharacteristic
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C22⋊C4×C12712yescomplemented
582C2×D4—28no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—48no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4C22⋊C4×C12712yescomplemented
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4C22⋊C4×C12712yes—
641C22×C4C22×C4×C12711yescharacteristic
642C22×C4C2×D4×C12711yescharacteristic
643C22×C4C2×D4×C12711yescharacteristic
644C22×C4C2×D4×C12711yescharacteristic
645C22×C4C2×D4×C12711yescharacteristic
646C22×C4C2×D4×C12711yescharacteristic
647C22×C4C2×D4×C12711yescharacteristic
648C22×C4C2×D4×C12711yescharacteristic
649C22×C4C2×D4×C12711yescharacteristic
650C22×C4C2×D4×C12711yescharacteristic
651C22×C4#41×C12711yescharacteristic
652C22×C4#41×C12711yescharacteristic
653C22×C4#41×C12711yescharacteristic
654C22×C4#41×C12711yescharacteristic
655M16—22no—
656M16—22no—
657M16—41no—
658M16—41no—
659M16—41no—
660M16—41no—
661M16—41no—
662M16—41no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—41no—
668C2×C8—41no—
669C4⋊C4—28no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—48no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—41no—
689C42—41no—
690C42C22⋊C4×C12714yescomplemented
691C23—24no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—44no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23C2×C22⋊C4×C12711yescharacteristic
714C23#120×C12711yescharacteristic
715C23#120×C12711yescharacteristic
716C23#120×C12711yescharacteristic
717C23#121×C12711yescharacteristic
718C23#121×C12711yescharacteristic
719C23#123×C12711yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—416no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—41no—
732D4—41no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4C2×C22⋊C4×C12711yescharacteristic
762C2×C4C2×C22⋊C4×C12711yescharacteristic
763C2×C4C4×D4×C12711yescharacteristic
764C2×C4C4×D4×C12711yescharacteristic
765C2×C4C4×D4×C12711yescharacteristic
766C2×C4C4×D4×C12711yescharacteristic
767C2×C4#120×C12711yescharacteristic
768C2×C4#120×C12711yescharacteristic
769C2×C4#120×C12711yescharacteristic
770C2×C4#120×C12711yescharacteristic
771C2×C4#120×C12711yescharacteristic
772C2×C4#121×C12711yescharacteristic
773C2×C4#121×C12711yescharacteristic
774C2×C4#121×C12711yescharacteristic
775C2×C4#121×C12711yescharacteristic
776C2×C4#121×C12711yescharacteristic
777C2×C4#121×C12711yescharacteristic
778C2×C4#121×C12711yescharacteristic
779C2×C4#121×C12711yescharacteristic
780C2×C4#121×C12711yescharacteristic
781C2×C4#121×C12711yescharacteristic
782C2×C4#123×C12711yescharacteristic
783C2×C4#123×C12711yescharacteristic
784C2×C4#123×C12711yescharacteristic
785C2×C4#124×C12711yescharacteristic
786C2×C4#124×C12711yescharacteristic
787C2×C4#127×C12711yescharacteristic
788C2×C4#127×C12711yescharacteristic
789C8—42no—
790C8—42no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—44no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—42no—
811C22—82no—
812C22—82no—
813C22#379×C12711yescharacteristic
814C22#386×C12711yescharacteristic
815C22#386×C12711yescharacteristic
816C22#392×C12711yescharacteristic
817C22#392×C12711yescharacteristic
818C22#394×C12711yescharacteristic
819C22#394×C12711yescharacteristic
820C4—44no—
821C4—42no—
822C4—42no—
823C4—82no—
824C4—82no—
825C4#386×C12711yescharacteristic
826C4#386×C12711yescharacteristic
827C4#390×C12711yescharacteristic
828C4#390×C12711yescharacteristic
829C4#392×C12711yescharacteristic
830C4#392×C12711yescharacteristic
831C4#394×C12711yescharacteristic
832C4#394×C12711yescharacteristic
833C2—21no—
834C2—21no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—44no—
840C2—82no—
841C2C127×#143811yescharacteristic
842C2C127×#201012yes—
subgroupG/H
centerC2×C4×C127#127
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
socleC22×C127#392
prime radicalC2×#525×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#421×C127C2semidirect
3. C127×#2896C2semidirect
4. C2×#407×C127C2semidirect
5. C127×#2280C2semidirect
6. C127×#1733C2semidirect
7. C2×H(3,ℤ/4)×C127C2semidirect
15. #525×C127C4semidirect
85. C2×M16×C127D4semidirect
87. C22×C8×C127D4semidirect
113. C2×C4⋊C4×C127D4semidirect
122. C2×C42×C127D4semidirect
159. C2×Q8×C127C22⋊C4semidirect
173. C2×D4×C127C22⋊C4semidirect
268. C42×C127C22⋊C4semidirect
411. #10994C127direct (N × H)
423. C2×#421C2×C127semidirect
424. #2896C2×C127semidirect
425. C2×#407C2×C127semidirect
426. #2280C2×C127semidirect
427. #1733C2×C127semidirect
428. C2×H(3,ℤ/4)C2×C127semidirect
429. C127#10994direct (N × H)
437. #525C4×C127semidirect
507. C2×M16D4×C127semidirect
509. C22×C8D4×C127semidirect
535. C2×C4⋊C4D4×C127semidirect
544. C2×C42D4×C127semidirect
581. C2×Q8C22⋊C4×C127semidirect
595. C2×D4C22⋊C4×C127semidirect
690. C42C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1272
C2×#421×C1272
C127×#28962
C2×#407×C1272
C127×#22802
C127×#17332
C2×H(3,ℤ/4)×C1272
#10994127