Finite Group Databasebeta

← C4×#463×C127 #44585174

Subgroups — C4×#463×C127 #44585174

Order 32512.

1136 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C127C211yesmaximal, characteristic
2C2×C4×SD16×C127C211yesmaximal, characteristic, complemented
3C2×C4×D8×C127C211yesmaximal, characteristic
4C4×#124×C127C211yesmaximal, characteristic, complemented
5C42×D4×C127C211yesmaximal, characteristic, complemented
6C127×#1983C211yesmaximal, characteristic, complemented
7C127×#1949C211yesmaximal, characteristic, complemented
8C127×#1928C211yesmaximal, characteristic, complemented
9C127×#1926C211yesmaximal, characteristic, complemented
10C127×#1879C211yesmaximal, characteristic
11C127×#1877C211yesmaximal, characteristic, complemented
12C127×#1804C211yesmaximal, characteristic, complemented
13C4×C4⋊C8×C127C211yesmaximal, characteristic, complemented
14C4×#103×C127C211yesmaximal, characteristic, complemented
15C4×#102×C127C211yesmaximal, characteristic, complemented
16C22×SD16×C127C2211yescharacteristic
17C22×D8×C127C2211yescharacteristic
18C2×#124×C127C2211yescharacteristic
19C2×C4×Q8×C127C2211yescharacteristic
20C2×C4×D4×C127C2211yescharacteristic
21C2×C4×D4×C127C2211yescharacteristic
22C2×C4×D4×C127C2211yescharacteristic
23C2×C4×D4×C127C2211yescharacteristic
24C22×C42×C127—21no—
25#463×C127C418yesdirect product factor
26C4×SD16×C127—24no—
27C4×D8×C127—24no—
28C2×#107×C127C2211yescharacteristic
29C2×#106×C127C2211yescharacteristic
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×#103×C127C2211yescharacteristic
33C2×#103×C127C2211yescharacteristic
34C2×#103×C127C2211yescharacteristic
35C2×#102×C127C2211yescharacteristic
36C2×#102×C127C2211yescharacteristic
37C2×#102×C127C2211yescharacteristic
38C2×#102×C127C2211yescharacteristic
39C2×#102×C127C2211yescharacteristic
40C2×C4×C8×C127C2211yescharacteristic
41C2×C4×C8×C127C2211yescharacteristic
42#391×C127C2211yescharacteristic
43#390×C127C2211yescharacteristic
44#388×C127—21no—
45#388×C127—21no—
46#382×C127C2211yescharacteristic
47C4×C4⋊C4×C127C2211yescharacteristic
48C4×C4⋊C4×C127C2211yescharacteristic
49C4×C4⋊C4×C127C2211yescharacteristic
50C4×C22⋊C4×C127—21no—
51C4×C22⋊C4×C127—21no—
52C4×C22⋊C4×C127—21no—
53C4×C22⋊C4×C127—21no—
54C4×C22⋊C4×C127—21no—
55C43×C127C2211yescharacteristic
56#340×C127C2211yescharacteristic
57#340×C127C2211yescharacteristic
58#340×C127C2211yescharacteristic
59#340×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61#336×C127C2211yescharacteristic
62C22×Q8×C127C2311yescharacteristic
63C22×D4×C127C2311yescharacteristic
64C22×D4×C127C2311yescharacteristic
65C23×C4×C127—21no—
66C23×C4×C127—21no—
67C23×C4×C127—21no—
68C23×C4×C127—21no—
69C2×SD16×C127—22no—
70C2×SD16×C127—22no—
71C2×SD16×C127C2×C414yescomplemented
72C2×D8×C127—22no—
73C2×D8×C127—22no—
74C2×D8×C127C2×C414yes—
75C22×C8×C127C2311yescharacteristic
76C22×C8×C127C2311yescharacteristic
77C22×C8×C127C2311yescharacteristic
78C22×C8×C127C2311yescharacteristic
79#124×C127—22no—
80#124×C127C2×C414yescomplemented
81C4×Q8×C127—22no—
82C4×Q8×C127—22no—
83C4×D4×C127—22no—
84C4×D4×C127—22no—
85C4×D4×C127—22no—
86C4×D4×C127—22no—
87C4×D4×C127—22no—
88C4×D4×C127—22no—
89C4×D4×C127C2×C414yescomplemented
90C4×D4×C127D414yes—
91C2×C4⋊C4×C127—21no—
92C2×C4⋊C4×C127C2311yescharacteristic
93C2×C4⋊C4×C127C2311yescharacteristic
94C2×C4⋊C4×C127C2311yescharacteristic
95C2×C4⋊C4×C127C2311yescharacteristic
96C2×C4⋊C4×C127C2311yescharacteristic
97C2×C22⋊C4×C127—21no—
98C2×C22⋊C4×C127—21no—
99C2×C22⋊C4×C127—21no—
100C2×C22⋊C4×C127—21no—
101C2×C22⋊C4×C127—21no—
102C2×C22⋊C4×C127—21no—
103C2×C22⋊C4×C127—21no—
104C2×C22⋊C4×C127—21no—
105C2×C42×C127—21no—
106C2×C42×C127—21no—
107C2×C42×C127—21no—
108C2×C42×C127—21no—
109C2×C42×C127—44no—
110C2×C42×C127D411yescharacteristic
111C2×C42×C127D411yescharacteristic
112C2×C42×C127D411yescharacteristic
113C2×C42×C127D411yescharacteristic
114C2×C42×C127C2311yescharacteristic
115C2×C42×C127C2311yescharacteristic
116C2×C42×C127C2311yescharacteristic
117#107×C127—22no—
118#106×C127—22no—
119C4⋊C8×C127—22no—
120C4⋊C8×C127C2×C414yescomplemented
121#103×C127—22no—
122#103×C127—22no—
123#103×C127C2×C414yescomplemented
124#102×C127—22no—
125#102×C127—22no—
126#102×C127—22no—
127#102×C127—22no—
128#102×C127C2×C414yescomplemented
129C4×C8×C127—22no—
130C4×C8×C127—22no—
131#95×C127—21no—
132#95×C127—21no—
133#95×C127—21no—
134#95×C127—21no—
135#95×C127—21no—
136#95×C127—21no—
137#95×C127—21no—
138C24×C127—21no—
139C24×C127—21no—
140C2×Q8×C127—21no—
141C2×Q8×C127—21no—
142C2×Q8×C127—21no—
143C2×Q8×C127—21no—
144C2×Q8×C127—21no—
145C2×Q8×C127C22×C412yes—
146C2×D4×C127—21no—
147C2×D4×C127—21no—
148C2×D4×C127—21no—
149C2×D4×C127—21no—
150C2×D4×C127—21no—
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127—21no—
154C2×D4×C127C22×C412yes—
155C2×D4×C127C22×C412yes—
156C2×D4×C127C2×D412yes—
157C2×D4×C127#4112yes—
158C22×C4×C127—24no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—24no—
164C22×C4×C127—24no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—42no—
168C22×C4×C127—42no—
169C22×C4×C127—42no—
170C22×C4×C127—42no—
171C22×C4×C127—42no—
172C22×C4×C127—42no—
173C22×C4×C127—42no—
174C22×C4×C127—42no—
175C22×C4×C127—42no—
176C22×C4×C127C2×D411yescharacteristic
177C22×C4×C127C2×D411yescharacteristic
178C22×C4×C127C2×D411yescharacteristic
179C22×C4×C127C2×D411yescharacteristic
180C22×C4×C127C2×D411yescharacteristic
181C22×C4×C127C2×D411yescharacteristic
182C22×C4×C127C2411yescharacteristic
183SD16×C127—28no—
184D8×C127—28no—
185C2×C8×C127—21no—
186C2×C8×C127—21no—
187C2×C8×C127—21no—
188C2×C8×C127—21no—
189C2×C8×C127—21no—
190C2×C8×C127—21no—
191C2×C8×C127—21no—
192C2×C8×C127—21no—
193C2×C8×C127—21no—
194C2×C8×C127—21no—
195C2×C8×C127C22×C412yes—
196C2×C8×C127C22×C412yes—
197C4⋊C4×C127—21no—
198C4⋊C4×C127—21no—
199C4⋊C4×C127—21no—
200C4⋊C4×C127—21no—
201C4⋊C4×C127—21no—
202C4⋊C4×C127—21no—
203C4⋊C4×C127—21no—
204C4⋊C4×C127—42no—
205C4⋊C4×C127C22×C412yes—
206C4⋊C4×C127C2×D412yes—
207C4⋊C4×C127#4112yes—
208C22⋊C4×C127—24no—
209C22⋊C4×C127—24no—
210C22⋊C4×C127—24no—
211C22⋊C4×C127—24no—
212C22⋊C4×C127—24no—
213C22⋊C4×C127—42no—
214C22⋊C4×C127—42no—
215C22⋊C4×C127—42no—
216C42×C127—22no—
217C42×C127—22no—
218C42×C127—22no—
219C42×C127—21no—
220C42×C127—21no—
221C42×C127—41no—
222C42×C127—42no—
223C42×C127—42no—
224C42×C127—42no—
225C42×C127—42no—
226C42×C127C22×C412yes—
227C42×C127C2×D412yes—
228C42×C127#4112yes—
229C42×C127#4112yes—
230C23×C127—22no—
231C23×C127—22no—
232C23×C127—22no—
233C23×C127—22no—
234C23×C127—41no—
235C23×C127—41no—
236C23×C127—41no—
237C23×C127—41no—
238C23×C127—41no—
239C23×C127—41no—
240C23×C127—41no—
241C23×C127—41no—
242C23×C127—41no—
243C23×C127—41no—
244C23×C127C22×D411yescharacteristic
245Q8×C127—22no—
246Q8×C127—22no—
247Q8×C127—41no—
248Q8×C127—41no—
249D4×C127—22no—
250D4×C127—22no—
251D4×C127—22no—
252D4×C127—22no—
253D4×C127—22no—
254D4×C127—41no—
255D4×C127—41no—
256D4×C127C4×D414yes—
257C2×C4×C127—21no—
258C2×C4×C127—21no—
259C2×C4×C127—21no—
260C2×C4×C127—21no—
261C2×C4×C127—21no—
262C2×C4×C127—21no—
263C2×C4×C127—21no—
264C2×C4×C127—21no—
265C2×C4×C127—22no—
266C2×C4×C127—22no—
267C2×C4×C127—22no—
268C2×C4×C127—21no—
269C2×C4×C127—22no—
270C2×C4×C127—21no—
271C2×C4×C127—21no—
272C2×C4×C127—48no—
273C2×C4×C127—48no—
274C2×C4×C127—41no—
275C2×C4×C127—41no—
276C2×C4×C127—41no—
277C2×C4×C127—41no—
278C2×C4×C127—41no—
279C2×C4×C127—41no—
280C2×C4×C127—41no—
281C2×C4×C127—41no—
282C2×C4×C127—48no—
283C2×C4×C127—41no—
284C2×C4×C127—41no—
285C2×C4×C127—41no—
286C2×C4×C127—41no—
287C2×C4×C127—41no—
288C2×C4×C127—41no—
289C2×C4×C127—84no—
290C2×C4×C127C4×D412yes—
291C2×C4×C127C4×D412yes—
292C2×C4×C127#12112yes—
293C2×C4×C127#12112yes—
294C2×C4×C127#13512yes—
295C2×C4×C127#13512yes—
296C2×C4×C127AGL(1,ℤ/8)12yes—
297C2×C4×C127C23×C411yescharacteristic
298C2×C4×C127C22×D411yescharacteristic
299C2×C4×C127C2×#4111yescharacteristic
300C2×C4×C127C2×#4111yescharacteristic
301C2×C4×C127C2×#4111yescharacteristic
302C2×C4×C127C2×#4111yescharacteristic
303C8×C127—22no—
304C8×C127—22no—
305C8×C127—41no—
306C8×C127—41no—
307C22×C127—24no—
308C22×C127—42no—
309C22×C127—42no—
310C22×C127—42no—
311C22×C127—42no—
312C22×C127—42no—
313C22×C127—42no—
314C22×C127—42no—
315C22×C127—42no—
316C22×C127—42no—
317C22×C127—81no—
318C22×C127—81no—
319C22×C127—81no—
320C22×C127—81no—
321C22×C127C2×C4×D411yescharacteristic
322C22×C127C2×#12111yescharacteristic
323C22×C127#52511yescharacteristic
324C22×C127C2×#13511yescharacteristic
325C22×C127C2×#13511yescharacteristic
326C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C127#57511yescharacteristic
328C4×C127—22no—
329C4×C127—22no—
330C4×C127—22no—
331C4×C127—22no—
332C4×C127—41no—
333C4×C127—42no—
334C4×C127—42no—
335C4×C127—42no—
336C4×C127—42no—
337C4×C127—81no—
338C4×C127—81no—
339C4×C127#46314yesdirect product factor
340C4×C127C2×C4×D411yescharacteristic
341C4×C127C4×#4111yescharacteristic
342C4×C127#52911yescharacteristic
343C4×C127#53211yescharacteristic
344C4×#463C12711yesmaximal, characteristic, direct product factor, Sylow
345C2×C127—44no—
346C2×C127—82no—
347C2×C127C4×#12111yescharacteristic
348C2×C127C4×#13511yescharacteristic
349C2×C127C4×AGL(1,ℤ/8)11yescharacteristic
350C2×C127C2×#46311yescharacteristic
351C2×C127#303511yescharacteristic
352C2×C127#310211yescharacteristic
353C2×C127#310511yescharacteristic
354C2×#463C2×C12711yescharacteristic
355C2×C4×SD16C2×C12711yescharacteristic, complemented
356C2×C4×D8C2×C12711yescharacteristic
357C4×#124C2×C12711yescharacteristic, complemented
358C42×D4C2×C12711yescharacteristic, complemented
359#1983C2×C12711yescharacteristic, complemented
360#1949C2×C12711yescharacteristic, complemented
361#1928C2×C12711yescharacteristic, complemented
362#1926C2×C12711yescharacteristic, complemented
363#1879C2×C12711yescharacteristic
364#1877C2×C12711yescharacteristic, complemented
365#1804C2×C12711yescharacteristic, complemented
366C4×C4⋊C8C2×C12711yescharacteristic, complemented
367C4×#103C2×C12711yescharacteristic, complemented
368C4×#102C2×C12711yescharacteristic, complemented
369C127C4×#46311yescharacteristic, direct product factor, Sylow
370C22×SD16C22×C12711yescharacteristic
371C22×D8C22×C12711yescharacteristic
372C2×#124C22×C12711yescharacteristic
373C2×C4×Q8C22×C12711yescharacteristic
374C2×C4×D4C22×C12711yescharacteristic
375C2×C4×D4C22×C12711yescharacteristic
376C2×C4×D4C22×C12711yescharacteristic
377C2×C4×D4C22×C12711yescharacteristic
378C22×C42—21no—
379#463C4×C12718yesdirect product factor
380C4×SD16—24no—
381C4×D8—24no—
382C2×#107C22×C12711yescharacteristic
383C2×#106C22×C12711yescharacteristic
384C2×C4⋊C8C22×C12711yescharacteristic
385C2×C4⋊C8C22×C12711yescharacteristic
386C2×#103C22×C12711yescharacteristic
387C2×#103C22×C12711yescharacteristic
388C2×#103C22×C12711yescharacteristic
389C2×#102C22×C12711yescharacteristic
390C2×#102C22×C12711yescharacteristic
391C2×#102C22×C12711yescharacteristic
392C2×#102C22×C12711yescharacteristic
393C2×#102C22×C12711yescharacteristic
394C2×C4×C8C22×C12711yescharacteristic
395C2×C4×C8C22×C12711yescharacteristic
396#391C22×C12711yescharacteristic
397#390C22×C12711yescharacteristic
398#388—21no—
399#388—21no—
400#382C22×C12711yescharacteristic
401C4×C4⋊C4C22×C12711yescharacteristic
402C4×C4⋊C4C22×C12711yescharacteristic
403C4×C4⋊C4C22×C12711yescharacteristic
404C4×C22⋊C4—21no—
405C4×C22⋊C4—21no—
406C4×C22⋊C4—21no—
407C4×C22⋊C4—21no—
408C4×C22⋊C4—21no—
409C43C22×C12711yescharacteristic
410#340C22×C12711yescharacteristic
411#340C22×C12711yescharacteristic
412#340C22×C12711yescharacteristic
413#340C22×C12711yescharacteristic
414#336C22×C12711yescharacteristic
415#336C22×C12711yescharacteristic
416C22×Q8C23×C12711yescharacteristic
417C22×D4C23×C12711yescharacteristic
418C22×D4C23×C12711yescharacteristic
419C23×C4—21no—
420C23×C4—21no—
421C23×C4—21no—
422C23×C4—21no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16C2×C4×C12714yescomplemented
426C2×D8—22no—
427C2×D8—22no—
428C2×D8C2×C4×C12714yes—
429C22×C8C23×C12711yescharacteristic
430C22×C8C23×C12711yescharacteristic
431C22×C8C23×C12711yescharacteristic
432C22×C8C23×C12711yescharacteristic
433#124—22no—
434#124C2×C4×C12714yescomplemented
435C4×Q8—22no—
436C4×Q8—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4—22no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4C2×C4×C12714yescomplemented
444C4×D4D4×C12714yes—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C23×C12711yescharacteristic
447C2×C4⋊C4C23×C12711yescharacteristic
448C2×C4⋊C4C23×C12711yescharacteristic
449C2×C4⋊C4C23×C12711yescharacteristic
450C2×C4⋊C4C23×C12711yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42—44no—
464C2×C42D4×C12711yescharacteristic
465C2×C42D4×C12711yescharacteristic
466C2×C42D4×C12711yescharacteristic
467C2×C42D4×C12711yescharacteristic
468C2×C42C23×C12711yescharacteristic
469C2×C42C23×C12711yescharacteristic
470C2×C42C23×C12711yescharacteristic
471#107—22no—
472#106—22no—
473C4⋊C8—22no—
474C4⋊C8C2×C4×C12714yescomplemented
475#103—22no—
476#103—22no—
477#103C2×C4×C12714yescomplemented
478#102—22no—
479#102—22no—
480#102—22no—
481#102—22no—
482#102C2×C4×C12714yescomplemented
483C4×C8—22no—
484C4×C8—22no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492C24—21no—
493C24—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C22×C4×C12712yes—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C22×C4×C12712yes—
509C2×D4C22×C4×C12712yes—
510C2×D4C2×D4×C12712yes—
511C2×D4#41×C12712yes—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4C2×D4×C12711yescharacteristic
531C22×C4C2×D4×C12711yescharacteristic
532C22×C4C2×D4×C12711yescharacteristic
533C22×C4C2×D4×C12711yescharacteristic
534C22×C4C2×D4×C12711yescharacteristic
535C22×C4C2×D4×C12711yescharacteristic
536C22×C4C24×C12711yescharacteristic
537SD16—28no—
538D8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8C22×C4×C12712yes—
550C2×C8C22×C4×C12712yes—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4C22×C4×C12712yes—
560C4⋊C4C2×D4×C12712yes—
561C4⋊C4#41×C12712yes—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—24no—
566C22⋊C4—24no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—21no—
574C42—21no—
575C42—41no—
576C42—42no—
577C42—42no—
578C42—42no—
579C42—42no—
580C42C22×C4×C12712yes—
581C42C2×D4×C12712yes—
582C42#41×C12712yes—
583C42#41×C12712yes—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C22×D4×C12711yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4C4×D4×C12714yes—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—48no—
627C2×C4—48no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—48no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4C4×D4×C12712yes—
645C2×C4C4×D4×C12712yes—
646C2×C4#121×C12712yes—
647C2×C4#121×C12712yes—
648C2×C4#135×C12712yes—
649C2×C4#135×C12712yes—
650C2×C4AGL(1,ℤ/8)×C12712yes—
651C2×C4C23×C4×C12711yescharacteristic
652C2×C4C22×D4×C12711yescharacteristic
653C2×C4C2×#41×C12711yescharacteristic
654C2×C4C2×#41×C12711yescharacteristic
655C2×C4C2×#41×C12711yescharacteristic
656C2×C4C2×#41×C12711yescharacteristic
657C8—22no—
658C8—22no—
659C8—41no—
660C8—41no—
661C22—24no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22C2×C4×D4×C12711yescharacteristic
676C22C2×#121×C12711yescharacteristic
677C22#525×C12711yescharacteristic
678C22C2×#135×C12711yescharacteristic
679C22C2×#135×C12711yescharacteristic
680C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
681C22#575×C12711yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—41no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4#463×C12714yesdirect product factor
694C4C2×C4×D4×C12711yescharacteristic
695C4C4×#41×C12711yescharacteristic
696C4#529×C12711yescharacteristic
697C4#532×C12711yescharacteristic
698C2—44no—
699C2—82no—
700C2C4×#121×C12711yescharacteristic
701C2C4×#135×C12711yescharacteristic
702C2C4×AGL(1,ℤ/8)×C12711yescharacteristic
703C2C2×#463×C12711yescharacteristic
704C2C127×#303511yescharacteristic
705C2C127×#310211yescharacteristic
706C2C127×#310511yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C22×D4
prime radicalC22×D8×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C127C2semidirect
4. C4×#124×C127C2semidirect
5. C42×D4×C127C2semidirect
6. C127×#1983C2semidirect
7. C127×#1949C2semidirect
8. C127×#1928C2semidirect
9. C127×#1926C2semidirect
11. C127×#1877C2semidirect
12. C127×#1804C2semidirect
13. C4×C4⋊C8×C127C2semidirect
14. C4×#103×C127C2semidirect
15. C4×#102×C127C2semidirect
25. #463×C127C4direct (N × H)
71. C2×SD16×C127C2×C4semidirect
80. #124×C127C2×C4semidirect
89. C4×D4×C127C2×C4semidirect
120. C4⋊C8×C127C2×C4semidirect
123. #103×C127C2×C4semidirect
128. #102×C127C2×C4semidirect
339. C4×C127#463direct (N × H)
344. C4×#463C127direct (N × H)
355. C2×C4×SD16C2×C127semidirect
357. C4×#124C2×C127semidirect
358. C42×D4C2×C127semidirect
359. #1983C2×C127semidirect
360. #1949C2×C127semidirect
361. #1928C2×C127semidirect
362. #1926C2×C127semidirect
364. #1877C2×C127semidirect
365. #1804C2×C127semidirect
366. C4×C4⋊C8C2×C127semidirect
367. C4×#103C2×C127semidirect
368. C4×#102C2×C127semidirect
369. C127C4×#463direct (N × H)
379. #463C4×C127direct (N × H)
425. C2×SD16C2×C4×C127semidirect
434. #124C2×C4×C127semidirect
443. C4×D4C2×C4×C127semidirect
474. C4⋊C8C2×C4×C127semidirect
477. #103C2×C4×C127semidirect
482. #102C2×C4×C127semidirect
693. C4#463×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#463×C1272
C2×C4×SD16×C1272
C2×C4×D8×C1272
C4×#124×C1272
C42×D4×C1272
C127×#19832
C127×#19492
C127×#19282
C127×#19262
C127×#18792
C127×#18772
C127×#18042
C4×C4⋊C8×C1272
C4×#103×C1272
C4×#102×C1272
C4×#463127