Finite Group Databasebeta

← C127×#18254 #44581927

Subgroups — C127×#18254 #44581927

Order 32512.

1508 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3537C211yesmaximal, characteristic, complemented
2C127×#3003C211yesmaximal, characteristic, complemented
3C2×#447×C127C211yesmaximal, characteristic, complemented
4C127×#2433C211yesmaximal, characteristic, complemented
5C127×#1600C214yesmaximal, complemented
6C127×#1595C214yesmaximal, complemented
7C127×#1507C211yesmaximal, characteristic, complemented
8C127×#1501C211yesmaximal, characteristic, complemented
9C127×#1471C211yesmaximal, characteristic, complemented
10C23×D4×C127C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C127—21no—
12C22×D8×C127—21no—
13#560×C127—22no—
14#553×C127—21no—
15#553×C127—21no—
16D42×C127—22no—
17D42×C127—21no—
18D42×C127—21no—
19#540×C127—21no—
20#538×C127—21no—
21#538×C127C2212yescomplemented
22#535×C127—21no—
23#534×C127—21no—
24#534×C127C2212yescomplemented
25C2×#127×C127—21no—
26#525×C127C2211yescharacteristic
27C2×#121×C127C2211yescharacteristic
28C2×#121×C127C2211yescharacteristic
29C2×#120×C127—22no—
30#450×C127—21no—
31#450×C127C2212yescomplemented
32#447×C127—22no—
33#447×C127—21no—
34#447×C127C2212yescomplemented
35#447×C127C2214yescomplemented
36#418×C127—21no—
37C2×#102×C127—21no—
38#407×C127C2211yescharacteristic, complemented
39C2×C22⋊C8×C127C2211yescharacteristic, complemented
40#392×C127C2214yescomplemented
41#390×C127—21no—
42C4×C22⋊C4×C127C2211yescharacteristic, complemented
43#328×C127C2212yescomplemented
44#327×C127C2212yescomplemented
45#327×C127C2214yescomplemented
46#323×C127C2214yescomplemented
47C25×C127—21no—
48C2×#41×C127D411yescharacteristic, complemented
49C22×D4×C127—22no—
50C22×D4×C127—21no—
51C22×D4×C127—21no—
52C22×D4×C127—22no—
53C22×D4×C127—24no—
54C22×D4×C127—21no—
55C22×D4×C127—21no—
56C22×D4×C127—21no—
57C22×D4×C127—21no—
58C22×D4×C127—21no—
59C22×D4×C127—44no—
60C22×D4×C127D412yes—
61C22×D4×C127D411yescharacteristic
62C22×D4×C127D411yescharacteristic, complemented
63C22×D4×C127C2312yes—
64C23×C4×C127C2311yescharacteristic
65AGL(1,ℤ/8)×C127—44no—
66C2×SD16×C127—22no—
67C2×D8×C127—24no—
68C2×D8×C127—22no—
69C2×D8×C127—44no—
70C2×M16×C127—21no—
71C22×C8×C127—21no—
72#127×C127—22no—
73#127×C127—21no—
74#127×C127—44no—
75#126×C127—22no—
76#126×C127—22no—
77#125×C127—21no—
78#124×C127—22no—
79#123×C127—22no—
80#123×C127—21no—
81#123×C127—22no—
82#123×C127—22no—
83#123×C127—22no—
84C22⋊Q8×C127D411yescharacteristic, complemented
85C22⋊Q8×C127C2311yescharacteristic
86#121×C127—22no—
87#121×C127—21no—
88#121×C127—21no—
89#121×C127—22no—
90#121×C127—22no—
91#121×C127—22no—
92#121×C127—22no—
93#121×C127—21no—
94#121×C127—21no—
95#121×C127—21no—
96#121×C127—21no—
97#121×C127—21no—
98#121×C127—21no—
99#121×C127—22no—
100#121×C127D412yescomplemented
101#121×C127D411yescharacteristic, complemented
102#121×C127C2312yes—
103#121×C127C2311yescharacteristic
104#120×C127—22no—
105#120×C127—22no—
106#120×C127—22no—
107#120×C127—21no—
108#120×C127—22no—
109#120×C127—22no—
110#120×C127—22no—
111#120×C127—48no—
112C4×D4×C127—22no—
113C4×D4×C127—21no—
114C4×D4×C127—21no—
115C4×D4×C127—21no—
116C4×D4×C127—21no—
117C4×D4×C127—22no—
118#117×C127—21no—
119#117×C127D411yescharacteristic, complemented
120C2×C4⋊C4×C127D411yescharacteristic
121C2×C4⋊C4×C127D411yescharacteristic, complemented
122C2×C22⋊C4×C127—21no—
123C2×C22⋊C4×C127—21no—
124C2×C22⋊C4×C127—24no—
125C2×C22⋊C4×C127C2312yes—
126C2×C42×C127—21no—
127#102×C127—24no—
128#102×C127—22no—
129#102×C127—22no—
130C22⋊C8×C127—21no—
131C22⋊C8×C127—21no—
132C22⋊C8×C127C2312yes—
133C22⋊C8×C127C2312yes—
134#95×C127C2312yes—
135C24×C127—22no—
136C24×C127—22no—
137C24×C127—21no—
138C24×C127—44no—
139C24×C127—44no—
140C24×C127—41no—
141C24×C127—41no—
142C24×C127—82no—
143C24×C127C2×D411yescharacteristic
144C24×C127C2×D412yes—
145#41×C127—42no—
146C2×Q8×C127C2×D411yescharacteristic
147C2×D4×C127—24no—
148C2×D4×C127—24no—
149C2×D4×C127—24no—
150C2×D4×C127—22no—
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—22no—
154C2×D4×C127—22no—
155C2×D4×C127—22no—
156C2×D4×C127—22no—
157C2×D4×C127—22no—
158C2×D4×C127—22no—
159C2×D4×C127—21no—
160C2×D4×C127—22no—
161C2×D4×C127—22no—
162C2×D4×C127—21no—
163C2×D4×C127—21no—
164C2×D4×C127—21no—
165C2×D4×C127—22no—
166C2×D4×C127—22no—
167C2×D4×C127—42no—
168C2×D4×C127—42no—
169C2×D4×C127—42no—
170C2×D4×C127—42no—
171C2×D4×C127—42no—
172C2×D4×C127—48no—
173C2×D4×C127—44no—
174C2×D4×C127—44no—
175C2×D4×C127—44no—
176C2×D4×C127—44no—
177C2×D4×C127—48no—
178C2×D4×C127—41no—
179C2×D4×C127—41no—
180C2×D4×C127—82no—
181C2×D4×C127—84no—
182C2×D4×C127—82no—
183C2×D4×C127—84no—
184C2×D4×C127—84no—
185C2×D4×C127C2×D411yescharacteristic
186C2×D4×C127C2×D412yes—
187C22×C4×C127—22no—
188C22×C4×C127—22no—
189C22×C4×C127—22no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—42no—
193C22×C4×C127C2×D411yescharacteristic
194C22×C4×C127C2×D411yescharacteristic
195C22×C4×C127C2×D411yescharacteristic
196C22×C4×C127C2×D412yes—
197C22×C4×C127C2×D411yescharacteristic
198C22×C4×C127C2×D411yescharacteristic
199C22×C4×C127C2411yescharacteristic
200SD16×C127—44no—
201D8×C127—48no—
202D8×C127—44no—
203M16×C127—42no—
204C2×C8×C127—22no—
205C2×C8×C127—22no—
206C2×C8×C127—42no—
207C4⋊C4×C127—22no—
208C4⋊C4×C127—22no—
209C4⋊C4×C127—21no—
210C4⋊C4×C127—21no—
211C4⋊C4×C127—21no—
212C4⋊C4×C127—21no—
213C4⋊C4×C127—21no—
214C4⋊C4×C127C2×D412yes—
215C4⋊C4×C127C2×D411yescharacteristic
216C4⋊C4×C127C2×D411yescharacteristic
217C22⋊C4×C127—24no—
218C22⋊C4×C127—22no—
219C22⋊C4×C127—22no—
220C22⋊C4×C127—22no—
221C22⋊C4×C127—22no—
222C22⋊C4×C127—22no—
223C22⋊C4×C127—21no—
224C22⋊C4×C127—21no—
225C22⋊C4×C127—21no—
226C22⋊C4×C127—22no—
227C22⋊C4×C127—21no—
228C22⋊C4×C127—22no—
229C22⋊C4×C127—22no—
230C22⋊C4×C127—22no—
231C22⋊C4×C127—21no—
232C22⋊C4×C127—48no—
233C42×C127—22no—
234C42×C127—21no—
235C42×C127—42no—
236C23×C127—22no—
237C23×C127—22no—
238C23×C127—24no—
239C23×C127—22no—
240C23×C127—22no—
241C23×C127—21no—
242C23×C127—24no—
243C23×C127—41no—
244C23×C127—44no—
245C23×C127—44no—
246C23×C127—44no—
247C23×C127—42no—
248C23×C127—42no—
249C23×C127—42no—
250C23×C127—42no—
251C23×C127—44no—
252C23×C127—42no—
253C23×C127—81no—
254C23×C127—81no—
255C23×C127—82no—
256C23×C127—82no—
257C23×C127—82no—
258C23×C127—82no—
259C23×C127—82no—
260C23×C127—82no—
261C23×C127—816no—
262C23×C127—82no—
263C23×C127#12011yescharacteristic
264C23×C127#12011yescharacteristic
265C23×C127C22×D411yescharacteristic
266Q8×C127—41no—
267D4×C127—24no—
268D4×C127—24no—
269D4×C127—42no—
270D4×C127—41no—
271D4×C127—42no—
272D4×C127—42no—
273D4×C127—44no—
274D4×C127—44no—
275D4×C127—42no—
276D4×C127—44no—
277D4×C127—42no—
278D4×C127—44no—
279D4×C127—42no—
280D4×C127—42no—
281D4×C127—81no—
282D4×C127—82no—
283D4×C127—82no—
284D4×C127—81no—
285D4×C127—82no—
286D4×C127—82no—
287D4×C127—82no—
288D4×C127—82no—
289D4×C127—82no—
290D4×C127—816no—
291C2×C4×C127—22no—
292C2×C4×C127—22no—
293C2×C4×C127—22no—
294C2×C4×C127—24no—
295C2×C4×C127—21no—
296C2×C4×C127—22no—
297C2×C4×C127—22no—
298C2×C4×C127—21no—
299C2×C4×C127—21no—
300C2×C4×C127—41no—
301C2×C4×C127—41no—
302C2×C4×C127—41no—
303C2×C4×C127—42no—
304C2×C4×C127—42no—
305C2×C4×C127—42no—
306C2×C4×C127—42no—
307C2×C4×C127—81no—
308C2×C4×C127—82no—
309C2×C4×C127—82no—
310C2×C4×C127#12011yescharacteristic
311C2×C4×C127#12011yescharacteristic
312C2×C4×C127C22×D411yescharacteristic
313C2×C4×C127C22×D411yescharacteristic
314C8×C127—42no—
315C8×C127—42no—
316C22×C127—21no—
317C22×C127—21no—
318C22×C127—21no—
319C22×C127—21no—
320C22×C127—21no—
321C22×C127—21no—
322C22×C127—21no—
323C22×C127—44no—
324C22×C127—48no—
325C22×C127—42no—
326C22×C127—42no—
327C22×C127—41no—
328C22×C127—42no—
329C22×C127—42no—
330C22×C127—41no—
331C22×C127—41no—
332C22×C127—44no—
333C22×C127—42no—
334C22×C127—42no—
335C22×C127—84no—
336C22×C127—84no—
337C22×C127—88no—
338C22×C127—88no—
339C22×C127—82no—
340C22×C127—82no—
341C22×C127—162no—
342C22×C127—164no—
343C22×C127#45312yes—
344C22×C127C2×#12011yescharacteristic
345C22×C127#57612yes—
346C4×C127—21no—
347C4×C127—21no—
348C4×C127—21no—
349C4×C127—44no—
350C4×C127—42no—
351C4×C127—41no—
352C4×C127—42no—
353C4×C127—41no—
354C4×C127—41no—
355C4×C127B(4,𝔽2)12yes—
356#18254C12711yesmaximal, characteristic, direct product factor, Sylow
357C2×C127—22no—
358C2×C127—22no—
359C2×C127—41no—
360C2×C127—84no—
361C2×C127—82no—
362C2×C127—82no—
363C2×C127—81no—
364C2×C127#300811yescharacteristic
365C2×C127C2×#45311yescharacteristic
366C2×C127C2×B(4,𝔽2)11yescharacteristic
367#3537C2×C12711yescharacteristic, complemented
368#3003C2×C12711yescharacteristic, complemented
369C2×#447C2×C12711yescharacteristic, complemented
370#2433C2×C12711yescharacteristic, complemented
371#1600C2×C12714yescomplemented
372#1595C2×C12714yescomplemented
373#1507C2×C12711yescharacteristic, complemented
374#1501C2×C12711yescharacteristic, complemented
375#1471C2×C12711yescharacteristic, complemented
376C127#1825411yescharacteristic, direct product factor, Sylow
377C23×D4C22×C12711yescharacteristic, complemented
378C2×AGL(1,ℤ/8)—21no—
379C22×D8—21no—
380#560—22no—
381#553—21no—
382#553—21no—
383D42—22no—
384D42—21no—
385D42—21no—
386#540—21no—
387#538—21no—
388#538C22×C12712yescomplemented
389#535—21no—
390#534—21no—
391#534C22×C12712yescomplemented
392C2×#127—21no—
393#525C22×C12711yescharacteristic
394C2×#121C22×C12711yescharacteristic
395C2×#121C22×C12711yescharacteristic
396C2×#120—22no—
397#450—21no—
398#450C22×C12712yescomplemented
399#447—22no—
400#447—21no—
401#447C22×C12712yescomplemented
402#447C22×C12714yescomplemented
403#418—21no—
404C2×#102—21no—
405#407C22×C12711yescharacteristic, complemented
406C2×C22⋊C8C22×C12711yescharacteristic, complemented
407#392C22×C12714yescomplemented
408#390—21no—
409C4×C22⋊C4C22×C12711yescharacteristic, complemented
410#328C22×C12712yescomplemented
411#327C22×C12712yescomplemented
412#327C22×C12714yescomplemented
413#323C22×C12714yescomplemented
414C25—21no—
415C2×#41D4×C12711yescharacteristic, complemented
416C22×D4—22no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4—22no—
420C22×D4—24no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—44no—
427C22×D4D4×C12712yes—
428C22×D4D4×C12711yescharacteristic
429C22×D4D4×C12711yescharacteristic, complemented
430C22×D4C23×C12712yes—
431C23×C4C23×C12711yescharacteristic
432AGL(1,ℤ/8)—44no—
433C2×SD16—22no—
434C2×D8—24no—
435C2×D8—22no—
436C2×D8—44no—
437C2×M16—21no—
438C22×C8—21no—
439#127—22no—
440#127—21no—
441#127—44no—
442#126—22no—
443#126—22no—
444#125—21no—
445#124—22no—
446#123—22no—
447#123—21no—
448#123—22no—
449#123—22no—
450#123—22no—
451C22⋊Q8D4×C12711yescharacteristic, complemented
452C22⋊Q8C23×C12711yescharacteristic
453#121—22no—
454#121—21no—
455#121—21no—
456#121—22no—
457#121—22no—
458#121—22no—
459#121—22no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121—22no—
467#121D4×C12712yescomplemented
468#121D4×C12711yescharacteristic, complemented
469#121C23×C12712yes—
470#121C23×C12711yescharacteristic
471#120—22no—
472#120—22no—
473#120—22no—
474#120—21no—
475#120—22no—
476#120—22no—
477#120—22no—
478#120—48no—
479C4×D4—22no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—22no—
485#117—21no—
486#117D4×C12711yescharacteristic, complemented
487C2×C4⋊C4D4×C12711yescharacteristic
488C2×C4⋊C4D4×C12711yescharacteristic, complemented
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4C23×C12712yes—
493C2×C42—21no—
494#102—24no—
495#102—22no—
496#102—22no—
497C22⋊C8—21no—
498C22⋊C8—21no—
499C22⋊C8C23×C12712yes—
500C22⋊C8C23×C12712yes—
501#95C23×C12712yes—
502C24—22no—
503C24—22no—
504C24—21no—
505C24—44no—
506C24—44no—
507C24—41no—
508C24—41no—
509C24—82no—
510C24C2×D4×C12711yescharacteristic
511C24C2×D4×C12712yes—
512#41—42no—
513C2×Q8C2×D4×C12711yescharacteristic
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—21no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—48no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—44no—
544C2×D4—48no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—82no—
548C2×D4—84no—
549C2×D4—82no—
550C2×D4—84no—
551C2×D4—84no—
552C2×D4C2×D4×C12711yescharacteristic
553C2×D4C2×D4×C12712yes—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—42no—
560C22×C4C2×D4×C12711yescharacteristic
561C22×C4C2×D4×C12711yescharacteristic
562C22×C4C2×D4×C12711yescharacteristic
563C22×C4C2×D4×C12712yes—
564C22×C4C2×D4×C12711yescharacteristic
565C22×C4C2×D4×C12711yescharacteristic
566C22×C4C24×C12711yescharacteristic
567SD16—44no—
568D8—48no—
569D8—44no—
570M16—42no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—42no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4C2×D4×C12712yes—
582C4⋊C4C2×D4×C12711yescharacteristic
583C4⋊C4C2×D4×C12711yescharacteristic
584C22⋊C4—24no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—21no—
591C22⋊C4—21no—
592C22⋊C4—21no—
593C22⋊C4—22no—
594C22⋊C4—21no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—21no—
599C22⋊C4—48no—
600C42—22no—
601C42—21no—
602C42—42no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—21no—
609C23—24no—
610C23—41no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—44no—
619C23—42no—
620C23—81no—
621C23—81no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—816no—
629C23—82no—
630C23#120×C12711yescharacteristic
631C23#120×C12711yescharacteristic
632C23C22×D4×C12711yescharacteristic
633Q8—41no—
634D4—24no—
635D4—24no—
636D4—42no—
637D4—41no—
638D4—42no—
639D4—42no—
640D4—44no—
641D4—44no—
642D4—42no—
643D4—44no—
644D4—42no—
645D4—44no—
646D4—42no—
647D4—42no—
648D4—81no—
649D4—82no—
650D4—82no—
651D4—81no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—82no—
657D4—816no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—81no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4#120×C12711yescharacteristic
678C2×C4#120×C12711yescharacteristic
679C2×C4C22×D4×C12711yescharacteristic
680C2×C4C22×D4×C12711yescharacteristic
681C8—42no—
682C8—42no—
683C22—21no—
684C22—21no—
685C22—21no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—44no—
691C22—48no—
692C22—42no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—41no—
698C22—41no—
699C22—44no—
700C22—42no—
701C22—42no—
702C22—84no—
703C22—84no—
704C22—88no—
705C22—88no—
706C22—82no—
707C22—82no—
708C22—162no—
709C22—164no—
710C22#453×C12712yes—
711C22C2×#120×C12711yescharacteristic
712C22#576×C12712yes—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—44no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—41no—
722C4B(4,𝔽2)×C12712yes—
723C2—22no—
724C2—22no—
725C2—41no—
726C2—84no—
727C2—82no—
728C2—82no—
729C2—81no—
730C2C127×#300811yescharacteristic
731C2C2×#453×C12711yescharacteristic
732C2C2×B(4,𝔽2)×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3537C2semidirect
2. C127×#3003C2semidirect
3. C2×#447×C127C2semidirect
4. C127×#2433C2semidirect
5. C127×#1600C2semidirect
6. C127×#1595C2semidirect
7. C127×#1507C2semidirect
8. C127×#1501C2semidirect
9. C127×#1471C2semidirect
10. C23×D4×C127C22semidirect
21. #538×C127C22semidirect
24. #534×C127C22semidirect
31. #450×C127C22semidirect
34. #447×C127C22semidirect
35. #447×C127C22semidirect
38. #407×C127C22semidirect
39. C2×C22⋊C8×C127C22semidirect
40. #392×C127C22semidirect
42. C4×C22⋊C4×C127C22semidirect
43. #328×C127C22semidirect
44. #327×C127C22semidirect
45. #327×C127C22semidirect
46. #323×C127C22semidirect
48. C2×#41×C127D4semidirect
62. C22×D4×C127D4semidirect
84. C22⋊Q8×C127D4semidirect
100. #121×C127D4semidirect
101. #121×C127D4semidirect
119. #117×C127D4semidirect
121. C2×C4⋊C4×C127D4semidirect
356. #18254C127direct (N × H)
367. #3537C2×C127semidirect
368. #3003C2×C127semidirect
369. C2×#447C2×C127semidirect
370. #2433C2×C127semidirect
371. #1600C2×C127semidirect
372. #1595C2×C127semidirect
373. #1507C2×C127semidirect
374. #1501C2×C127semidirect
375. #1471C2×C127semidirect
376. C127#18254direct (N × H)
377. C23×D4C22×C127semidirect
388. #538C22×C127semidirect
391. #534C22×C127semidirect
398. #450C22×C127semidirect
401. #447C22×C127semidirect
402. #447C22×C127semidirect
405. #407C22×C127semidirect
406. C2×C22⋊C8C22×C127semidirect
407. #392C22×C127semidirect
409. C4×C22⋊C4C22×C127semidirect
410. #328C22×C127semidirect
411. #327C22×C127semidirect
412. #327C22×C127semidirect
413. #323C22×C127semidirect
415. C2×#41D4×C127semidirect
429. C22×D4D4×C127semidirect
451. C22⋊Q8D4×C127semidirect
467. #121D4×C127semidirect
468. #121D4×C127semidirect
486. #117D4×C127semidirect
488. C2×C4⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35372
C127×#30032
C2×#447×C1272
C127×#24332
C127×#16002
C127×#15952
C127×#15072
C127×#15012
C127×#14712
#18254127