Finite Group Databasebeta

← C127×#18252 #44581925

Subgroups — C127×#18252 #44581925

Order 32512.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3534C211yesmaximal, characteristic, complemented
2C127×#3006C211yesmaximal, characteristic, complemented
3C127×#3002C211yesmaximal, characteristic, complemented
4C127×#2430C211yesmaximal, characteristic, complemented
5C127×#1606C211yesmaximal, characteristic, complemented
6C127×#1604C211yesmaximal, characteristic, complemented
7C127×#1603C211yesmaximal, characteristic, complemented
8C127×#1601C211yesmaximal, characteristic, complemented
9C127×#1600C211yesmaximal, characteristic, complemented
10C127×#1598C211yesmaximal, characteristic, complemented
11C127×#1597C211yesmaximal, characteristic, complemented
12C127×#1595C211yesmaximal, characteristic, complemented
13C127×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C127C211yesmaximal, characteristic, complemented
15C127×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C127C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C127—21no—
18C2×#135×C127—21no—
19#562×C127—21no—
20#560×C127—21no—
21#553×C127—21no—
22#551×C127—21no—
23#546×C127—21no—
24#546×C127—21no—
25#546×C127—21no—
26D42×C127—21no—
27#540×C127—21no—
28#539×C127—21no—
29#539×C127C2211yescharacteristic
30#538×C127—21no—
31#538×C127C2211yescharacteristic
32#537×C127C2211yescharacteristic
33#534×C127—21no—
34#534×C127C2211yescharacteristic
35#525×C127C2211yescharacteristic
36C2×#123×C127C2211yescharacteristic
37C2×#121×C127—21no—
38C2×#121×C127C2211yescharacteristic
39#452×C127—21no—
40#451×C127C2211yescharacteristic, complemented
41#450×C127C2211yescharacteristic, complemented
42#449×C127—21no—
43#449×C127—21no—
44#449×C127—21no—
45#448×C127C2211yescharacteristic
46#448×C127C2211yescharacteristic, complemented
47#448×C127C2211yescharacteristic, complemented
48#447×C127C2211yescharacteristic
49#447×C127C2211yescharacteristic, complemented
50#447×C127C2211yescharacteristic, complemented
51#417×C127—21no—
52#416×C127—21no—
53#407×C127C2211yescharacteristic, complemented
54C2×C22⋊C8×C127C2211yescharacteristic, complemented
55#395×C127C2211yescharacteristic, complemented
56#394×C127C2211yescharacteristic, complemented
57#393×C127C2211yescharacteristic, complemented
58#392×C127C2211yescharacteristic, complemented
59#386×C127—21no—
60#386×C127—21no—
61#385×C127—21no—
62C2×#95×C127C2211yescharacteristic, complemented
63#328×C127C2211yescharacteristic, complemented
64#328×C127C2211yescharacteristic, complemented
65#327×C127C2211yescharacteristic
66#327×C127C2211yescharacteristic
67#327×C127C2211yescharacteristic, complemented
68#327×C127C2211yescharacteristic, complemented
69#327×C127C2211yescharacteristic, complemented
70#327×C127C2211yescharacteristic, complemented
71#324×C127C2211yescharacteristic, complemented
72#324×C127C2211yescharacteristic, complemented
73#323×C127C2211yescharacteristic, complemented
74#323×C127C2211yescharacteristic, complemented
75C2×#41×C127—21no—
76C2×#41×C127—21no—
77C2×#41×C127—21no—
78C2×#41×C127—21no—
79C2×#41×C127—21no—
80C2×#41×C127—44no—
81C2×#41×C127D411yescharacteristic, complemented
82C22×Q8×C127C2311yescharacteristic
83C22×D4×C127—21no—
84C22×D4×C127—21no—
85C22×D4×C127—21no—
86C22×D4×C127—21no—
87C22×D4×C127—21no—
88C22×D4×C127D411yescharacteristic
89C22×D4×C127D411yescharacteristic, complemented
90C22×D4×C127C2311yescharacteristic
91C23×C4×C127—21no—
92C23×C4×C127—21no—
93C23×C4×C127C2311yescharacteristic
94AGL(1,ℤ/8)×C127—44no—
95#135×C127—44no—
96C2×Q16×C127—21no—
97C2×SD16×C127—21no—
98C2×SD16×C127—21no—
99C2×SD16×C127—21no—
100C2×SD16×C127—21no—
101C2×D8×C127—21no—
102C2×D8×C127—21no—
103C2×D8×C127—21no—
104C2×M16×C127—21no—
105C22×C8×C127—21no—
106#127×C127—21no—
107#126×C127—21no—
108#126×C127—21no—
109#126×C127—21no—
110#126×C127—21no—
111#125×C127—21no—
112#125×C127—21no—
113#124×C127—21no—
114#124×C127—21no—
115#124×C127—21no—
116#123×C127—21no—
117#123×C127—21no—
118#123×C127—21no—
119#123×C127—21no—
120#123×C127—21no—
121#123×C127—21no—
122#123×C127—21no—
123#123×C127—21no—
124#123×C127—21no—
125#123×C127—21no—
126#123×C127—21no—
127#123×C127—21no—
128#123×C127—21no—
129#123×C127—21no—
130C22⋊Q8×C127—21no—
131C22⋊Q8×C127—21no—
132C22⋊Q8×C127—21no—
133C22⋊Q8×C127—21no—
134C22⋊Q8×C127—21no—
135C22⋊Q8×C127D411yescharacteristic, complemented
136C22⋊Q8×C127C2311yescharacteristic
137#121×C127—21no—
138#121×C127—21no—
139#121×C127—21no—
140#121×C127—21no—
141#121×C127—21no—
142#121×C127—21no—
143#121×C127—21no—
144#121×C127—21no—
145#121×C127—21no—
146#121×C127—21no—
147#121×C127—21no—
148#121×C127—21no—
149#121×C127—21no—
150#121×C127—21no—
151#121×C127—21no—
152#121×C127—44no—
153#121×C127D411yescharacteristic, complemented
154#121×C127D411yescharacteristic, complemented
155#121×C127D411yescharacteristic, complemented
156#121×C127C2311yescharacteristic
157#121×C127C2311yescharacteristic
158#121×C127C2311yescharacteristic
159#120×C127—21no—
160#120×C127—21no—
161#120×C127—21no—
162#120×C127—21no—
163#120×C127—21no—
164#120×C127—21no—
165#120×C127—21no—
166#120×C127—21no—
167C4×D4×C127—21no—
168C4×D4×C127—21no—
169C4×D4×C127—21no—
170C4×D4×C127—21no—
171C4×D4×C127—21no—
172C4×D4×C127—21no—
173C4×D4×C127—21no—
174C4×D4×C127—21no—
175#117×C127—21no—
176#117×C127D411yescharacteristic, complemented
177C2×C4⋊C4×C127—21no—
178C2×C4⋊C4×C127D411yescharacteristic
179C2×C4⋊C4×C127D411yescharacteristic, complemented
180C2×C4⋊C4×C127C2311yescharacteristic
181C2×C22⋊C4×C127—21no—
182C2×C22⋊C4×C127—21no—
183C2×C22⋊C4×C127—21no—
184C2×C22⋊C4×C127—21no—
185C2×C22⋊C4×C127—21no—
186C2×C22⋊C4×C127—21no—
187C2×C22⋊C4×C127—21no—
188C2×C22⋊C4×C127D411yescharacteristic
189C2×C22⋊C4×C127D411yescharacteristic
190C2×C22⋊C4×C127C2311yescharacteristic
191#103×C127—21no—
192#103×C127—21no—
193#103×C127—21no—
194#103×C127—21no—
195#102×C127—21no—
196#102×C127—21no—
197#102×C127—21no—
198#102×C127—21no—
199C22⋊C8×C127—21no—
200C22⋊C8×C127—21no—
201C22⋊C8×C127C2311yescharacteristic
202C22⋊C8×C127C2311yescharacteristic
203C22⋊C8×C127C2311yescharacteristic
204C22⋊C8×C127C2311yescharacteristic
205#95×C127—21no—
206#95×C127—21no—
207#95×C127—21no—
208#95×C127C2311yescharacteristic
209#95×C127C2311yescharacteristic
210C24×C127—21no—
211C24×C127—21no—
212C24×C127—21no—
213C24×C127C2×D411yescharacteristic
214C24×C127C2×D411yescharacteristic
215#41×C127—24no—
216#41×C127—24no—
217#41×C127—42no—
218#41×C127—42no—
219#41×C127—42no—
220#41×C127—42no—
221#41×C127—42no—
222#41×C127—42no—
223#41×C127—42no—
224#41×C127—81no—
225#41×C127—81no—
226C2×Q8×C127—21no—
227C2×Q8×C127—21no—
228C2×Q8×C127—21no—
229C2×Q8×C127—42no—
230C2×Q8×C127C2×D411yescharacteristic
231C2×D4×C127—24no—
232C2×D4×C127—21no—
233C2×D4×C127—21no—
234C2×D4×C127—21no—
235C2×D4×C127—21no—
236C2×D4×C127—21no—
237C2×D4×C127—21no—
238C2×D4×C127—21no—
239C2×D4×C127—21no—
240C2×D4×C127—21no—
241C2×D4×C127—21no—
242C2×D4×C127—21no—
243C2×D4×C127—21no—
244C2×D4×C127—21no—
245C2×D4×C127—21no—
246C2×D4×C127—21no—
247C2×D4×C127—21no—
248C2×D4×C127—21no—
249C2×D4×C127—21no—
250C2×D4×C127—21no—
251C2×D4×C127—42no—
252C2×D4×C127—42no—
253C2×D4×C127—42no—
254C2×D4×C127—42no—
255C2×D4×C127—41no—
256C2×D4×C127—41no—
257C2×D4×C127—42no—
258C2×D4×C127—42no—
259C2×D4×C127—81no—
260C2×D4×C127—81no—
261C2×D4×C127—81no—
262C2×D4×C127—81no—
263C2×D4×C127—81no—
264C2×D4×C127—82no—
265C2×D4×C127C2×D411yescharacteristic
266C2×D4×C127C2×D411yescharacteristic
267C2×D4×C127C2×D411yescharacteristic
268C22×C4×C127—21no—
269C22×C4×C127—21no—
270C22×C4×C127—21no—
271C22×C4×C127—21no—
272C22×C4×C127—21no—
273C22×C4×C127—21no—
274C22×C4×C127—21no—
275C22×C4×C127—21no—
276C22×C4×C127—21no—
277C22×C4×C127—21no—
278C22×C4×C127—42no—
279C22×C4×C127—42no—
280C22×C4×C127—42no—
281C22×C4×C127—42no—
282C22×C4×C127—41no—
283C22×C4×C127—41no—
284C22×C4×C127—42no—
285C22×C4×C127—81no—
286C22×C4×C127C2×D411yescharacteristic
287C22×C4×C127C2×D411yescharacteristic
288C22×C4×C127C2×D411yescharacteristic
289C22×C4×C127C2×D411yescharacteristic
290C22×C4×C127C2×D411yescharacteristic
291C22×C4×C127C2×D411yescharacteristic
292C22×C4×C127C2×D411yescharacteristic
293C22×C4×C127C2×D411yescharacteristic
294C22×C4×C127C2411yescharacteristic
295Q16×C127—42no—
296SD16×C127—42no—
297SD16×C127—42no—
298SD16×C127—42no—
299SD16×C127—42no—
300D8×C127—42no—
301D8×C127—42no—
302D8×C127—42no—
303M16×C127—42no—
304C2×C8×C127—21no—
305C2×C8×C127—21no—
306C2×C8×C127—21no—
307C2×C8×C127—21no—
308C2×C8×C127—42no—
309C4⋊C4×C127—21no—
310C4⋊C4×C127—21no—
311C4⋊C4×C127—21no—
312C4⋊C4×C127—21no—
313C4⋊C4×C127—21no—
314C4⋊C4×C127—21no—
315C4⋊C4×C127—21no—
316C4⋊C4×C127—21no—
317C4⋊C4×C127—21no—
318C4⋊C4×C127—21no—
319C4⋊C4×C127—21no—
320C4⋊C4×C127—21no—
321C4⋊C4×C127—21no—
322C4⋊C4×C127—42no—
323C4⋊C4×C127C2×D411yescharacteristic
324C4⋊C4×C127C2×D411yescharacteristic
325C4⋊C4×C127C2×D411yescharacteristic
326C4⋊C4×C127C2×D411yescharacteristic
327C22⋊C4×C127—21no—
328C22⋊C4×C127—21no—
329C22⋊C4×C127—21no—
330C22⋊C4×C127—21no—
331C22⋊C4×C127—21no—
332C22⋊C4×C127—21no—
333C22⋊C4×C127—21no—
334C22⋊C4×C127—21no—
335C22⋊C4×C127—21no—
336C22⋊C4×C127—21no—
337C22⋊C4×C127—21no—
338C22⋊C4×C127—21no—
339C22⋊C4×C127—21no—
340C22⋊C4×C127—21no—
341C22⋊C4×C127—21no—
342C22⋊C4×C127—21no—
343C22⋊C4×C127—21no—
344C22⋊C4×C127—21no—
345C22⋊C4×C127—21no—
346C22⋊C4×C127—21no—
347C22⋊C4×C127—21no—
348C22⋊C4×C127—21no—
349C22⋊C4×C127—21no—
350C22⋊C4×C127—21no—
351C22⋊C4×C127—21no—
352C22⋊C4×C127—42no—
353C22⋊C4×C127—42no—
354C22⋊C4×C127—42no—
355C22⋊C4×C127—81no—
356C42×C127—21no—
357C42×C127—21no—
358C42×C127—21no—
359C23×C127—21no—
360C23×C127—21no—
361C23×C127—22no—
362C23×C127—22no—
363C23×C127—21no—
364C23×C127—21no—
365C23×C127—21no—
366C23×C127—21no—
367C23×C127—21no—
368C23×C127—21no—
369C23×C127—41no—
370C23×C127—41no—
371C23×C127—41no—
372C23×C127—41no—
373C23×C127—41no—
374C23×C127—41no—
375C23×C127—41no—
376C23×C127—41no—
377C23×C127—41no—
378C23×C127—42no—
379C23×C127—81no—
380C23×C127—81no—
381C23×C127—81no—
382C23×C127—81no—
383C23×C127—81no—
384C23×C127#12011yescharacteristic
385C23×C127#12011yescharacteristic
386C23×C127C22×D411yescharacteristic
387Q8×C127—22no—
388Q8×C127—22no—
389Q8×C127—41no—
390Q8×C127—41no—
391Q8×C127—41no—
392Q8×C127—81no—
393D4×C127—22no—
394D4×C127—22no—
395D4×C127—41no—
396D4×C127—41no—
397D4×C127—41no—
398D4×C127—41no—
399D4×C127—41no—
400D4×C127—44no—
401D4×C127—41no—
402D4×C127—41no—
403D4×C127—41no—
404D4×C127—41no—
405D4×C127—41no—
406D4×C127—41no—
407D4×C127—44no—
408D4×C127—42no—
409D4×C127—42no—
410D4×C127—81no—
411D4×C127—81no—
412D4×C127—81no—
413D4×C127—81no—
414D4×C127—81no—
415D4×C127—81no—
416D4×C127—81no—
417D4×C127—81no—
418D4×C127—81no—
419D4×C127—81no—
420D4×C127—81no—
421D4×C127—81no—
422D4×C127—84no—
423C2×C4×C127—22no—
424C2×C4×C127—22no—
425C2×C4×C127—22no—
426C2×C4×C127—22no—
427C2×C4×C127—21no—
428C2×C4×C127—21no—
429C2×C4×C127—21no—
430C2×C4×C127—21no—
431C2×C4×C127—21no—
432C2×C4×C127—21no—
433C2×C4×C127—21no—
434C2×C4×C127—21no—
435C2×C4×C127—21no—
436C2×C4×C127—21no—
437C2×C4×C127—41no—
438C2×C4×C127—41no—
439C2×C4×C127—41no—
440C2×C4×C127—41no—
441C2×C4×C127—44no—
442C2×C4×C127—44no—
443C2×C4×C127—41no—
444C2×C4×C127—41no—
445C2×C4×C127—41no—
446C2×C4×C127—41no—
447C2×C4×C127—41no—
448C2×C4×C127—41no—
449C2×C4×C127—41no—
450C2×C4×C127—41no—
451C2×C4×C127—41no—
452C2×C4×C127—81no—
453C2×C4×C127—81no—
454C2×C4×C127—81no—
455C2×C4×C127—81no—
456C2×C4×C127—81no—
457C2×C4×C127—81no—
458C2×C4×C127—81no—
459C2×C4×C127—84no—
460C2×C4×C127#12011yescharacteristic
461C2×C4×C127#12011yescharacteristic
462C2×C4×C127C22×D411yescharacteristic
463C2×C4×C127C22×D411yescharacteristic
464C8×C127—41no—
465C8×C127—41no—
466C8×C127—41no—
467C8×C127—41no—
468C22×C127—21no—
469C22×C127—21no—
470C22×C127—21no—
471C22×C127—21no—
472C22×C127—21no—
473C22×C127—21no—
474C22×C127—21no—
475C22×C127—42no—
476C22×C127—42no—
477C22×C127—42no—
478C22×C127—42no—
479C22×C127—41no—
480C22×C127—41no—
481C22×C127—41no—
482C22×C127—41no—
483C22×C127—41no—
484C22×C127—41no—
485C22×C127—41no—
486C22×C127—41no—
487C22×C127—42no—
488C22×C127—41no—
489C22×C127—41no—
490C22×C127—41no—
491C22×C127—41no—
492C22×C127—81no—
493C22×C127—81no—
494C22×C127—81no—
495C22×C127—81no—
496C22×C127—81no—
497C22×C127—81no—
498C22×C127—162no—
499C22×C127—162no—
500C22×C127B(4,𝔽2)12yes—
501C22×C127C2×#12011yescharacteristic
502C22×C127#57611yescharacteristic
503C22×C127#57711yescharacteristic
504C4×C127—21no—
505C4×C127—21no—
506C4×C127—21no—
507C4×C127—21no—
508C4×C127—42no—
509C4×C127—41no—
510C4×C127—41no—
511C4×C127—41no—
512C4×C127—41no—
513C4×C127—41no—
514C4×C127—41no—
515C4×C127—42no—
516C4×C127—41no—
517C4×C127—41no—
518C4×C127—81no—
519#18252C12711yesmaximal, characteristic, direct product factor, Sylow
520C2×C127—21no—
521C2×C127—21no—
522C2×C127—22no—
523C2×C127—41no—
524C2×C127—82no—
525C2×C127—81no—
526C2×C127—81no—
527C2×C127—81no—
528C2×C127—81no—
529C2×C127#301211yescharacteristic
530C2×C127#301811yescharacteristic
531C2×C127C2×B(4,𝔽2)11yescharacteristic
532#3534C2×C12711yescharacteristic, complemented
533#3006C2×C12711yescharacteristic, complemented
534#3002C2×C12711yescharacteristic, complemented
535#2430C2×C12711yescharacteristic, complemented
536#1606C2×C12711yescharacteristic, complemented
537#1604C2×C12711yescharacteristic, complemented
538#1603C2×C12711yescharacteristic, complemented
539#1601C2×C12711yescharacteristic, complemented
540#1600C2×C12711yescharacteristic, complemented
541#1598C2×C12711yescharacteristic, complemented
542#1597C2×C12711yescharacteristic, complemented
543#1595C2×C12711yescharacteristic, complemented
544#1504C2×C12711yescharacteristic, complemented
545C2×#327C2×C12711yescharacteristic, complemented
546#1468C2×C12711yescharacteristic, complemented
547C127#1825211yescharacteristic, direct product factor, Sylow
548C22×#41C22×C12711yescharacteristic, complemented
549C2×AGL(1,ℤ/8)—21no—
550C2×#135—21no—
551#562—21no—
552#560—21no—
553#553—21no—
554#551—21no—
555#546—21no—
556#546—21no—
557#546—21no—
558D42—21no—
559#540—21no—
560#539—21no—
561#539C22×C12711yescharacteristic
562#538—21no—
563#538C22×C12711yescharacteristic
564#537C22×C12711yescharacteristic
565#534—21no—
566#534C22×C12711yescharacteristic
567#525C22×C12711yescharacteristic
568C2×#123C22×C12711yescharacteristic
569C2×#121—21no—
570C2×#121C22×C12711yescharacteristic
571#452—21no—
572#451C22×C12711yescharacteristic, complemented
573#450C22×C12711yescharacteristic, complemented
574#449—21no—
575#449—21no—
576#449—21no—
577#448C22×C12711yescharacteristic
578#448C22×C12711yescharacteristic, complemented
579#448C22×C12711yescharacteristic, complemented
580#447C22×C12711yescharacteristic
581#447C22×C12711yescharacteristic, complemented
582#447C22×C12711yescharacteristic, complemented
583#417—21no—
584#416—21no—
585#407C22×C12711yescharacteristic, complemented
586C2×C22⋊C8C22×C12711yescharacteristic, complemented
587#395C22×C12711yescharacteristic, complemented
588#394C22×C12711yescharacteristic, complemented
589#393C22×C12711yescharacteristic, complemented
590#392C22×C12711yescharacteristic, complemented
591#386—21no—
592#386—21no—
593#385—21no—
594C2×#95C22×C12711yescharacteristic, complemented
595#328C22×C12711yescharacteristic, complemented
596#328C22×C12711yescharacteristic, complemented
597#327C22×C12711yescharacteristic
598#327C22×C12711yescharacteristic
599#327C22×C12711yescharacteristic, complemented
600#327C22×C12711yescharacteristic, complemented
601#327C22×C12711yescharacteristic, complemented
602#327C22×C12711yescharacteristic, complemented
603#324C22×C12711yescharacteristic, complemented
604#324C22×C12711yescharacteristic, complemented
605#323C22×C12711yescharacteristic, complemented
606#323C22×C12711yescharacteristic, complemented
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C12711yescharacteristic, complemented
614C22×Q8C23×C12711yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C12711yescharacteristic
621C22×D4D4×C12711yescharacteristic, complemented
622C22×D4C23×C12711yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C12711yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C12711yescharacteristic, complemented
668C22⋊Q8C23×C12711yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C12711yescharacteristic, complemented
686#121D4×C12711yescharacteristic, complemented
687#121D4×C12711yescharacteristic, complemented
688#121C23×C12711yescharacteristic
689#121C23×C12711yescharacteristic
690#121C23×C12711yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C12711yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C12711yescharacteristic
711C2×C4⋊C4D4×C12711yescharacteristic, complemented
712C2×C4⋊C4C23×C12711yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C12711yescharacteristic
721C2×C22⋊C4D4×C12711yescharacteristic
722C2×C22⋊C4C23×C12711yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C12711yescharacteristic
734C22⋊C8C23×C12711yescharacteristic
735C22⋊C8C23×C12711yescharacteristic
736C22⋊C8C23×C12711yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C12711yescharacteristic
741#95C23×C12711yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C12711yescharacteristic
746C24C2×D4×C12711yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C12711yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C12711yescharacteristic
798C2×D4C2×D4×C12711yescharacteristic
799C2×D4C2×D4×C12711yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C12711yescharacteristic
819C22×C4C2×D4×C12711yescharacteristic
820C22×C4C2×D4×C12711yescharacteristic
821C22×C4C2×D4×C12711yescharacteristic
822C22×C4C2×D4×C12711yescharacteristic
823C22×C4C2×D4×C12711yescharacteristic
824C22×C4C2×D4×C12711yescharacteristic
825C22×C4C2×D4×C12711yescharacteristic
826C22×C4C24×C12711yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C12711yescharacteristic
856C4⋊C4C2×D4×C12711yescharacteristic
857C4⋊C4C2×D4×C12711yescharacteristic
858C4⋊C4C2×D4×C12711yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—21no—
892C23—21no—
893C23—22no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C12711yescharacteristic
917C23#120×C12711yescharacteristic
918C23C22×D4×C12711yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—44no—
940D4—42no—
941D4—42no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C12711yescharacteristic
993C2×C4#120×C12711yescharacteristic
994C2×C4C22×D4×C12711yescharacteristic
995C2×C4C22×D4×C12711yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22B(4,𝔽2)×C12712yes—
1033C22C2×#120×C12711yescharacteristic
1034C22#576×C12711yescharacteristic
1035C22#577×C12711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C127×#301211yescharacteristic
1061C2C127×#301811yescharacteristic
1062C2C2×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×#3534C2semidirect
2. C127×#3006C2semidirect
3. C127×#3002C2semidirect
4. C127×#2430C2semidirect
5. C127×#1606C2semidirect
6. C127×#1604C2semidirect
7. C127×#1603C2semidirect
8. C127×#1601C2semidirect
9. C127×#1600C2semidirect
10. C127×#1598C2semidirect
11. C127×#1597C2semidirect
12. C127×#1595C2semidirect
13. C127×#1504C2semidirect
14. C2×#327×C127C2semidirect
15. C127×#1468C2semidirect
16. C22×#41×C127C22semidirect
40. #451×C127C22semidirect
41. #450×C127C22semidirect
46. #448×C127C22semidirect
47. #448×C127C22semidirect
49. #447×C127C22semidirect
50. #447×C127C22semidirect
53. #407×C127C22semidirect
54. C2×C22⋊C8×C127C22semidirect
55. #395×C127C22semidirect
56. #394×C127C22semidirect
57. #393×C127C22semidirect
58. #392×C127C22semidirect
62. C2×#95×C127C22semidirect
63. #328×C127C22semidirect
64. #328×C127C22semidirect
67. #327×C127C22semidirect
68. #327×C127C22semidirect
69. #327×C127C22semidirect
70. #327×C127C22semidirect
71. #324×C127C22semidirect
72. #324×C127C22semidirect
73. #323×C127C22semidirect
74. #323×C127C22semidirect
81. C2×#41×C127D4semidirect
89. C22×D4×C127D4semidirect
135. C22⋊Q8×C127D4semidirect
153. #121×C127D4semidirect
154. #121×C127D4semidirect
155. #121×C127D4semidirect
176. #117×C127D4semidirect
179. C2×C4⋊C4×C127D4semidirect
519. #18252C127direct (N × H)
532. #3534C2×C127semidirect
533. #3006C2×C127semidirect
534. #3002C2×C127semidirect
535. #2430C2×C127semidirect
536. #1606C2×C127semidirect
537. #1604C2×C127semidirect
538. #1603C2×C127semidirect
539. #1601C2×C127semidirect
540. #1600C2×C127semidirect
541. #1598C2×C127semidirect
542. #1597C2×C127semidirect
543. #1595C2×C127semidirect
544. #1504C2×C127semidirect
545. C2×#327C2×C127semidirect
546. #1468C2×C127semidirect
547. C127#18252direct (N × H)
548. C22×#41C22×C127semidirect
572. #451C22×C127semidirect
573. #450C22×C127semidirect
578. #448C22×C127semidirect
579. #448C22×C127semidirect
581. #447C22×C127semidirect
582. #447C22×C127semidirect
585. #407C22×C127semidirect
586. C2×C22⋊C8C22×C127semidirect
587. #395C22×C127semidirect
588. #394C22×C127semidirect
589. #393C22×C127semidirect
590. #392C22×C127semidirect
594. C2×#95C22×C127semidirect
595. #328C22×C127semidirect
596. #328C22×C127semidirect
599. #327C22×C127semidirect
600. #327C22×C127semidirect
601. #327C22×C127semidirect
602. #327C22×C127semidirect
603. #324C22×C127semidirect
604. #324C22×C127semidirect
605. #323C22×C127semidirect
606. #323C22×C127semidirect
613. C2×#41D4×C127semidirect
621. C22×D4D4×C127semidirect
667. C22⋊Q8D4×C127semidirect
685. #121D4×C127semidirect
686. #121D4×C127semidirect
687. #121D4×C127semidirect
708. #117D4×C127semidirect
711. 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×#35342
C127×#30062
C127×#30022
C127×#24302
C127×#16062
C127×#16042
C127×#16032
C127×#16012
C127×#16002
C127×#15982
C127×#15972
C127×#15952
C127×#15042
C2×#327×C1272
C127×#14682
#18252127