Finite Group Databasebeta

← C127×#18448 #44582121

Subgroups — C127×#18448 #44582121

Order 32512.

968 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3535C211yesmaximal, characteristic, complemented
2C127×#3193C211yesmaximal, characteristic, complemented
3C127×#3188C211yesmaximal, characteristic, complemented
4C127×#2813C211yesmaximal, characteristic, complemented
5C127×#1618C211yesmaximal, characteristic, complemented
6C127×#1617C211yesmaximal, characteristic, complemented
7C127×#1615C211yesmaximal, characteristic, complemented
8C127×#1614C211yesmaximal, characteristic, complemented
9C127×#1600C211yesmaximal, characteristic, complemented
10C127×#1599C211yesmaximal, characteristic, complemented
11C127×#1597C211yesmaximal, characteristic, complemented
12C127×#1596C211yesmaximal, characteristic, complemented
13C127×#1520C211yesmaximal, characteristic, complemented
14C127×#1513C211yesmaximal, characteristic, complemented
15C127×#1468C211yesmaximal, characteristic, complemented
16#563×C127—21no—
17#562×C127—21no—
18#554×C127—21no—
19#552×C127—21no—
20#551×C127—21no—
21#551×C127—21no—
22#547×C127—21no—
23#546×C127—21no—
24#544×C127C2211yescharacteristic
25#543×C127C2211yescharacteristic
26#542×C127—21no—
27#539×C127—21no—
28#539×C127—21no—
29#539×C127C2211yescharacteristic
30#538×C127C2211yescharacteristic
31#536×C127—21no—
32#525×C127C2211yescharacteristic
33C2×#123×C127C2211yescharacteristic
34C2×C22⋊Q8×C127C2211yescharacteristic
35C2×#121×C127C2211yescharacteristic
36#484×C127C2211yescharacteristic
37#484×C127C2211yescharacteristic
38#484×C127C2211yescharacteristic
39#482×C127—21no—
40#481×C127C2211yescharacteristic
41#480×C127—21no—
42#468×C127—21no—
43#468×C127—21no—
44#466×C127—21no—
45#465×C127—21no—
46#450×C127C2211yescharacteristic
47#450×C127C2211yescharacteristic
48#450×C127C2211yescharacteristic
49#449×C127—21no—
50#448×C127—21no—
51#447×C127C2211yescharacteristic
52#407×C127C2211yescharacteristic
53C2×C22⋊C8×C127C2211yescharacteristic
54#400×C127C2211yescharacteristic
55#399×C127C2211yescharacteristic
56#396×C127—21no—
57#394×C127—21no—
58#394×C127—21no—
59#394×C127C2211yescharacteristic
60#392×C127—21no—
61#392×C127C2211yescharacteristic
62#380×C127C2211yescharacteristic
63#328×C127C2211yescharacteristic
64#328×C127C2211yescharacteristic
65#328×C127C2211yescharacteristic
66#328×C127C2211yescharacteristic
67#328×C127C2211yescharacteristic
68#328×C127C2211yescharacteristic
69#327×C127C2211yescharacteristic
70#327×C127C2211yescharacteristic
71#324×C127C2211yescharacteristic
72#324×C127C2211yescharacteristic
73#323×C127C2211yescharacteristic
74#323×C127C2211yescharacteristic
75C2×#41×C127—21no—
76C2×#41×C127D411yescharacteristic, complemented
77C22×Q8×C127D411yescharacteristic, complemented
78C22×D4×C127—21no—
79C22×D4×C127—21no—
80C22×D4×C127D411yescharacteristic
81C22×D4×C127C2311yescharacteristic
82C23×C4×C127C2311yescharacteristic
83C2×SD16×C127—21no—
84C2×SD16×C127—21no—
85C2×SD16×C127—21no—
86C2×D8×C127—21no—
87C2×M16×C127—21no—
88C22×C8×C127—21no—
89C4⋊Q8×C127—21no—
90C4⋊Q8×C127—21no—
91C4⋊Q8×C127—21no—
92#126×C127—21no—
93#126×C127—21no—
94#126×C127—21no—
95#126×C127—21no—
96#126×C127—21no—
97#126×C127—21no—
98#125×C127—21no—
99#125×C127—21no—
100#125×C127—21no—
101#125×C127—21no—
102#125×C127—21no—
103#124×C127—21no—
104#124×C127—21no—
105#124×C127—21no—
106#124×C127—21no—
107#123×C127—21no—
108#123×C127—21no—
109#123×C127—21no—
110#123×C127—21no—
111#123×C127—21no—
112#123×C127—21no—
113#123×C127—21no—
114#123×C127—21no—
115#123×C127—21no—
116#123×C127—21no—
117#123×C127—21no—
118#123×C127—21no—
119#123×C127—21no—
120#123×C127—21no—
121C22⋊Q8×C127—21no—
122C22⋊Q8×C127—21no—
123C22⋊Q8×C127—21no—
124C22⋊Q8×C127—21no—
125C22⋊Q8×C127—21no—
126C22⋊Q8×C127—21no—
127C22⋊Q8×C127—21no—
128C22⋊Q8×C127—21no—
129C22⋊Q8×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×C127D411yescharacteristic, complemented
137C22⋊Q8×C127D411yescharacteristic, complemented
138C22⋊Q8×C127C2311yescharacteristic
139C22⋊Q8×C127C2311yescharacteristic
140C22⋊Q8×C127C2311yescharacteristic
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×C127D411yescharacteristic, complemented
150#121×C127C2311yescharacteristic
151#120×C127—21no—
152#120×C127—21no—
153C4×Q8×C127—21no—
154C4×D4×C127—21no—
155C4×D4×C127—21no—
156C4×D4×C127—21no—
157C4×D4×C127—21no—
158C4×D4×C127—21no—
159C4×D4×C127—21no—
160C4×D4×C127—21no—
161#117×C127—21no—
162#117×C127—21no—
163#117×C127—21no—
164#117×C127D411yescharacteristic, complemented
165C2×C4⋊C4×C127—21no—
166C2×C4⋊C4×C127—21no—
167C2×C4⋊C4×C127—21no—
168C2×C4⋊C4×C127—21no—
169C2×C4⋊C4×C127D411yescharacteristic
170C2×C4⋊C4×C127D411yescharacteristic, complemented
171C2×C4⋊C4×C127C2311yescharacteristic
172C2×C4⋊C4×C127C2311yescharacteristic
173C2×C22⋊C4×C127—21no—
174C2×C22⋊C4×C127—21no—
175C2×C22⋊C4×C127—21no—
176C2×C22⋊C4×C127—21no—
177C2×C22⋊C4×C127—21no—
178C2×C22⋊C4×C127—21no—
179C2×C22⋊C4×C127—21no—
180C2×C22⋊C4×C127—21no—
181C2×C22⋊C4×C127D411yescharacteristic
182C2×C22⋊C4×C127D411yescharacteristic
183C2×C22⋊C4×C127C2311yescharacteristic
184#107×C127—21no—
185#107×C127—21no—
186#107×C127—21no—
187#106×C127—21no—
188#103×C127—21no—
189#103×C127—21no—
190#103×C127—21no—
191#102×C127—21no—
192#102×C127—21no—
193#102×C127—21no—
194#102×C127—21no—
195#102×C127—21no—
196C22⋊C8×C127—21no—
197C22⋊C8×C127—21no—
198C22⋊C8×C127C2311yescharacteristic
199C22⋊C8×C127C2311yescharacteristic
200C22⋊C8×C127C2311yescharacteristic
201C22⋊C8×C127C2311yescharacteristic
202#95×C127—21no—
203#95×C127—21no—
204#95×C127C2311yescharacteristic
205#95×C127C2311yescharacteristic
206C24×C127—21no—
207C24×C127C2×D411yescharacteristic
208C24×C127C2×D411yescharacteristic
209#41×C127—82no—
210#41×C127—81no—
211C2×Q8×C127—21no—
212C2×Q8×C127—21no—
213C2×Q8×C127—21no—
214C2×Q8×C127—81no—
215C2×Q8×C127C2×D411yescharacteristic
216C2×Q8×C127C2×D411yescharacteristic
217C2×Q8×C127C2×D411yescharacteristic
218C2×D4×C127—21no—
219C2×D4×C127—21no—
220C2×D4×C127—21no—
221C2×D4×C127—21no—
222C2×D4×C127—21no—
223C2×D4×C127—21no—
224C2×D4×C127—21no—
225C2×D4×C127—21no—
226C2×D4×C127—21no—
227C2×D4×C127—41no—
228C2×D4×C127—41no—
229C2×D4×C127—81no—
230C2×D4×C127—81no—
231C2×D4×C127—81no—
232C2×D4×C127—81no—
233C2×D4×C127—81no—
234C2×D4×C127—81no—
235C2×D4×C127—81no—
236C2×D4×C127C2×D411yescharacteristic
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—81no—
248C22×C4×C127C2×D411yescharacteristic
249C22×C4×C127C2×D411yescharacteristic
250C22×C4×C127C2×D411yescharacteristic
251C22×C4×C127C2×D411yescharacteristic
252C22×C4×C127C2×D411yescharacteristic
253C22×C4×C127C2×D411yescharacteristic
254C22×C4×C127C2×D411yescharacteristic
255C22×C4×C127C2×D411yescharacteristic
256C22×C4×C127C2411yescharacteristic
257SD16×C127—81no—
258SD16×C127—81no—
259SD16×C127—81no—
260D8×C127—81no—
261M16×C127—81no—
262C2×C8×C127—21no—
263C2×C8×C127—21no—
264C2×C8×C127—21no—
265C2×C8×C127—21no—
266C2×C8×C127—81no—
267C4⋊C4×C127—21no—
268C4⋊C4×C127—21no—
269C4⋊C4×C127—21no—
270C4⋊C4×C127—21no—
271C4⋊C4×C127—21no—
272C4⋊C4×C127—21no—
273C4⋊C4×C127—21no—
274C4⋊C4×C127—21no—
275C4⋊C4×C127—21no—
276C4⋊C4×C127—21no—
277C4⋊C4×C127—21no—
278C4⋊C4×C127—21no—
279C4⋊C4×C127—21no—
280C4⋊C4×C127—21no—
281C4⋊C4×C127—21no—
282C4⋊C4×C127—21no—
283C4⋊C4×C127—21no—
284C4⋊C4×C127—21no—
285C4⋊C4×C127—21no—
286C4⋊C4×C127—21no—
287C4⋊C4×C127—21no—
288C4⋊C4×C127—21no—
289C4⋊C4×C127—21no—
290C4⋊C4×C127—21no—
291C4⋊C4×C127—21no—
292C4⋊C4×C127—81no—
293C4⋊C4×C127—81no—
294C4⋊C4×C127C2×D411yescharacteristic
295C4⋊C4×C127C2×D411yescharacteristic
296C4⋊C4×C127C2×D411yescharacteristic
297C4⋊C4×C127C2×D411yescharacteristic
298C22⋊C4×C127—21no—
299C22⋊C4×C127—21no—
300C22⋊C4×C127—21no—
301C22⋊C4×C127—21no—
302C22⋊C4×C127—21no—
303C22⋊C4×C127—21no—
304C22⋊C4×C127—21no—
305C22⋊C4×C127—21no—
306C22⋊C4×C127—21no—
307C22⋊C4×C127—21no—
308C22⋊C4×C127—21no—
309C22⋊C4×C127—21no—
310C22⋊C4×C127—21no—
311C22⋊C4×C127—21no—
312C22⋊C4×C127—21no—
313C22⋊C4×C127—21no—
314C22⋊C4×C127—21no—
315C22⋊C4×C127—21no—
316C22⋊C4×C127—21no—
317C22⋊C4×C127—21no—
318C22⋊C4×C127—21no—
319C22⋊C4×C127—21no—
320C22⋊C4×C127—21no—
321C22⋊C4×C127—41no—
322C22⋊C4×C127—41no—
323C22⋊C4×C127—81no—
324C22⋊C4×C127—81no—
325C22⋊C4×C127—81no—
326C22⋊C4×C127—81no—
327C22⋊C4×C127—81no—
328C42×C127—21no—
329C42×C127—21no—
330C42×C127—21no—
331C42×C127—21no—
332C42×C127—21no—
333C23×C127—21no—
334C23×C127—21no—
335C23×C127—21no—
336C23×C127—21no—
337C23×C127—21no—
338C23×C127—21no—
339C23×C127—41no—
340C23×C127—41no—
341C23×C127—41no—
342C23×C127—41no—
343C23×C127—41no—
344C23×C127—41no—
345C23×C127—41no—
346C23×C127—41no—
347C23×C127—41no—
348C23×C127—41no—
349C23×C127—41no—
350C23×C127#12011yescharacteristic
351C23×C127#12011yescharacteristic
352C23×C127C22×D411yescharacteristic
353Q8×C127—41no—
354Q8×C127—41no—
355Q8×C127—41no—
356Q8×C127—81no—
357Q8×C127—81no—
358Q8×C127—81no—
359D4×C127—41no—
360D4×C127—41no—
361D4×C127—41no—
362D4×C127—41no—
363D4×C127—41no—
364D4×C127—42no—
365D4×C127—42no—
366D4×C127—41no—
367D4×C127—41no—
368D4×C127—81no—
369D4×C127—81no—
370D4×C127—81no—
371D4×C127—81no—
372D4×C127—82no—
373D4×C127—82no—
374D4×C127—84no—
375C2×C4×C127—21no—
376C2×C4×C127—21no—
377C2×C4×C127—21no—
378C2×C4×C127—21no—
379C2×C4×C127—21no—
380C2×C4×C127—21no—
381C2×C4×C127—21no—
382C2×C4×C127—21no—
383C2×C4×C127—21no—
384C2×C4×C127—21no—
385C2×C4×C127—21no—
386C2×C4×C127—21no—
387C2×C4×C127—41no—
388C2×C4×C127—41no—
389C2×C4×C127—41no—
390C2×C4×C127—41no—
391C2×C4×C127—41no—
392C2×C4×C127—41no—
393C2×C4×C127—42no—
394C2×C4×C127—41no—
395C2×C4×C127—41no—
396C2×C4×C127—41no—
397C2×C4×C127—41no—
398C2×C4×C127—41no—
399C2×C4×C127—41no—
400C2×C4×C127—41no—
401C2×C4×C127—41no—
402C2×C4×C127—41no—
403C2×C4×C127—41no—
404C2×C4×C127—41no—
405C2×C4×C127—81no—
406C2×C4×C127—81no—
407C2×C4×C127—81no—
408C2×C4×C127—81no—
409C2×C4×C127—81no—
410C2×C4×C127—81no—
411C2×C4×C127#12011yescharacteristic
412C2×C4×C127#12011yescharacteristic
413C2×C4×C127C22×D411yescharacteristic
414C2×C4×C127C22×D411yescharacteristic
415C8×C127—41no—
416C8×C127—41no—
417C8×C127—41no—
418C8×C127—41no—
419C22×C127—21no—
420C22×C127—21no—
421C22×C127—21no—
422C22×C127—21no—
423C22×C127—21no—
424C22×C127—21no—
425C22×C127—21no—
426C22×C127—21no—
427C22×C127—41no—
428C22×C127—41no—
429C22×C127—41no—
430C22×C127—41no—
431C22×C127—41no—
432C22×C127—41no—
433C22×C127—81no—
434C22×C127—81no—
435C22×C127—81no—
436C22×C127—81no—
437C22×C127—81no—
438C22×C127—81no—
439C22×C127—81no—
440C22×C127—81no—
441C22×C127—81no—
442C22×C127—81no—
443C22×C127—81no—
444C22×C127C2×#12011yescharacteristic
445C22×C127#57711yescharacteristic
446C22×C127#57811yescharacteristic
447C4×C127—21no—
448C4×C127—21no—
449C4×C127—21no—
450C4×C127—21no—
451C4×C127—41no—
452C4×C127—41no—
453C4×C127—41no—
454C4×C127—41no—
455C4×C127—41no—
456C4×C127—41no—
457C4×C127—41no—
458C4×C127—41no—
459C4×C127—41no—
460C4×C127—41no—
461C4×C127—81no—
462C4×C127—81no—
463C4×C127—81no—
464#18448C12711yesmaximal, characteristic, direct product factor, Sylow
465C2×C127—21no—
466C2×C127—21no—
467C2×C127—41no—
468C2×C127—41no—
469C2×C127—81no—
470C2×C127—81no—
471C2×C127—161no—
472C2×C127#301311yescharacteristic
473C2×C127#302111yescharacteristic
474C2×C127#302611yescharacteristic
475#3535C2×C12711yescharacteristic, complemented
476#3193C2×C12711yescharacteristic, complemented
477#3188C2×C12711yescharacteristic, complemented
478#2813C2×C12711yescharacteristic, complemented
479#1618C2×C12711yescharacteristic, complemented
480#1617C2×C12711yescharacteristic, complemented
481#1615C2×C12711yescharacteristic, complemented
482#1614C2×C12711yescharacteristic, complemented
483#1600C2×C12711yescharacteristic, complemented
484#1599C2×C12711yescharacteristic, complemented
485#1597C2×C12711yescharacteristic, complemented
486#1596C2×C12711yescharacteristic, complemented
487#1520C2×C12711yescharacteristic, complemented
488#1513C2×C12711yescharacteristic, complemented
489#1468C2×C12711yescharacteristic, complemented
490C127#1844811yescharacteristic, direct product factor, Sylow
491#563—21no—
492#562—21no—
493#554—21no—
494#552—21no—
495#551—21no—
496#551—21no—
497#547—21no—
498#546—21no—
499#544C22×C12711yescharacteristic
500#543C22×C12711yescharacteristic
501#542—21no—
502#539—21no—
503#539—21no—
504#539C22×C12711yescharacteristic
505#538C22×C12711yescharacteristic
506#536—21no—
507#525C22×C12711yescharacteristic
508C2×#123C22×C12711yescharacteristic
509C2×C22⋊Q8C22×C12711yescharacteristic
510C2×#121C22×C12711yescharacteristic
511#484C22×C12711yescharacteristic
512#484C22×C12711yescharacteristic
513#484C22×C12711yescharacteristic
514#482—21no—
515#481C22×C12711yescharacteristic
516#480—21no—
517#468—21no—
518#468—21no—
519#466—21no—
520#465—21no—
521#450C22×C12711yescharacteristic
522#450C22×C12711yescharacteristic
523#450C22×C12711yescharacteristic
524#449—21no—
525#448—21no—
526#447C22×C12711yescharacteristic
527#407C22×C12711yescharacteristic
528C2×C22⋊C8C22×C12711yescharacteristic
529#400C22×C12711yescharacteristic
530#399C22×C12711yescharacteristic
531#396—21no—
532#394—21no—
533#394—21no—
534#394C22×C12711yescharacteristic
535#392—21no—
536#392C22×C12711yescharacteristic
537#380C22×C12711yescharacteristic
538#328C22×C12711yescharacteristic
539#328C22×C12711yescharacteristic
540#328C22×C12711yescharacteristic
541#328C22×C12711yescharacteristic
542#328C22×C12711yescharacteristic
543#328C22×C12711yescharacteristic
544#327C22×C12711yescharacteristic
545#327C22×C12711yescharacteristic
546#324C22×C12711yescharacteristic
547#324C22×C12711yescharacteristic
548#323C22×C12711yescharacteristic
549#323C22×C12711yescharacteristic
550C2×#41—21no—
551C2×#41D4×C12711yescharacteristic, complemented
552C22×Q8D4×C12711yescharacteristic, complemented
553C22×D4—21no—
554C22×D4—21no—
555C22×D4D4×C12711yescharacteristic
556C22×D4C23×C12711yescharacteristic
557C23×C4C23×C12711yescharacteristic
558C2×SD16—21no—
559C2×SD16—21no—
560C2×SD16—21no—
561C2×D8—21no—
562C2×M16—21no—
563C22×C8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#126—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#125—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#124—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8D4×C12711yescharacteristic, complemented
611C22⋊Q8D4×C12711yescharacteristic, complemented
612C22⋊Q8D4×C12711yescharacteristic, complemented
613C22⋊Q8C23×C12711yescharacteristic
614C22⋊Q8C23×C12711yescharacteristic
615C22⋊Q8C23×C12711yescharacteristic
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121D4×C12711yescharacteristic, complemented
625#121C23×C12711yescharacteristic
626#120—21no—
627#120—21no—
628C4×Q8—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635C4×D4—21no—
636#117—21no—
637#117—21no—
638#117—21no—
639#117D4×C12711yescharacteristic, complemented
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4D4×C12711yescharacteristic
645C2×C4⋊C4D4×C12711yescharacteristic, complemented
646C2×C4⋊C4C23×C12711yescharacteristic
647C2×C4⋊C4C23×C12711yescharacteristic
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4D4×C12711yescharacteristic
657C2×C22⋊C4D4×C12711yescharacteristic
658C2×C22⋊C4C23×C12711yescharacteristic
659#107—21no—
660#107—21no—
661#107—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#103—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C12711yescharacteristic
674C22⋊C8C23×C12711yescharacteristic
675C22⋊C8C23×C12711yescharacteristic
676C22⋊C8C23×C12711yescharacteristic
677#95—21no—
678#95—21no—
679#95C23×C12711yescharacteristic
680#95C23×C12711yescharacteristic
681C24—21no—
682C24C2×D4×C12711yescharacteristic
683C24C2×D4×C12711yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C12711yescharacteristic
691C2×Q8C2×D4×C12711yescharacteristic
692C2×Q8C2×D4×C12711yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C12711yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C12711yescharacteristic
724C22×C4C2×D4×C12711yescharacteristic
725C22×C4C2×D4×C12711yescharacteristic
726C22×C4C2×D4×C12711yescharacteristic
727C22×C4C2×D4×C12711yescharacteristic
728C22×C4C2×D4×C12711yescharacteristic
729C22×C4C2×D4×C12711yescharacteristic
730C22×C4C2×D4×C12711yescharacteristic
731C22×C4C24×C12711yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C12711yescharacteristic
770C4⋊C4C2×D4×C12711yescharacteristic
771C4⋊C4C2×D4×C12711yescharacteristic
772C4⋊C4C2×D4×C12711yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—41no—
797C22⋊C4—41no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C22⋊C4—81no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23#120×C12711yescharacteristic
826C23#120×C12711yescharacteristic
827C23C22×D4×C12711yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—82no—
848D4—82no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4#120×C12711yescharacteristic
887C2×C4#120×C12711yescharacteristic
888C2×C4C22×D4×C12711yescharacteristic
889C2×C4C22×D4×C12711yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×#120×C12711yescharacteristic
920C22#577×C12711yescharacteristic
921C22#578×C12711yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C127×#301311yescharacteristic
947C2C127×#302111yescharacteristic
948C2C127×#302611yescharacteristic
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×#3535C2semidirect
2. C127×#3193C2semidirect
3. C127×#3188C2semidirect
4. C127×#2813C2semidirect
5. C127×#1618C2semidirect
6. C127×#1617C2semidirect
7. C127×#1615C2semidirect
8. C127×#1614C2semidirect
9. C127×#1600C2semidirect
10. C127×#1599C2semidirect
11. C127×#1597C2semidirect
12. C127×#1596C2semidirect
13. C127×#1520C2semidirect
14. C127×#1513C2semidirect
15. C127×#1468C2semidirect
76. C2×#41×C127D4semidirect
77. C22×Q8×C127D4semidirect
135. C22⋊Q8×C127D4semidirect
136. C22⋊Q8×C127D4semidirect
137. C22⋊Q8×C127D4semidirect
149. #121×C127D4semidirect
164. #117×C127D4semidirect
170. C2×C4⋊C4×C127D4semidirect
464. #18448C127direct (N × H)
475. #3535C2×C127semidirect
476. #3193C2×C127semidirect
477. #3188C2×C127semidirect
478. #2813C2×C127semidirect
479. #1618C2×C127semidirect
480. #1617C2×C127semidirect
481. #1615C2×C127semidirect
482. #1614C2×C127semidirect
483. #1600C2×C127semidirect
484. #1599C2×C127semidirect
485. #1597C2×C127semidirect
486. #1596C2×C127semidirect
487. #1520C2×C127semidirect
488. #1513C2×C127semidirect
489. #1468C2×C127semidirect
490. C127#18448direct (N × H)
551. C2×#41D4×C127semidirect
552. C22×Q8D4×C127semidirect
610. C22⋊Q8D4×C127semidirect
611. C22⋊Q8D4×C127semidirect
612. C22⋊Q8D4×C127semidirect
624. #121D4×C127semidirect
639. #117D4×C127semidirect
645. 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×#35352
C127×#31932
C127×#31882
C127×#28132
C127×#16182
C127×#16172
C127×#16152
C127×#16142
C127×#16002
C127×#15992
C127×#15972
C127×#15962
C127×#15202
C127×#15132
C127×#14682
#18448127