Finite Group Databasebeta

← C127×#21510 #44585183

Subgroups — C127×#21510 #44585183

Order 32512.

1056 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C127C211yesmaximal, characteristic
2C2×#442×C127C211yesmaximal, characteristic
3C2×C4×SD16×C127C211yesmaximal, characteristic, complemented
4C127×#2326C211yesmaximal, characteristic, complemented
5C127×#2275C211yesmaximal, characteristic, complemented
6C127×#1983C211yesmaximal, characteristic, complemented
7C127×#1948C211yesmaximal, characteristic, complemented
8C127×#1927C211yesmaximal, characteristic, complemented
9C127×#1926C211yesmaximal, characteristic, complemented
10C127×#1879C211yesmaximal, characteristic
11C127×#1877C211yesmaximal, characteristic, complemented
12C127×#1802C211yesmaximal, characteristic, complemented
13C127×#1768C211yesmaximal, characteristic, complemented
14C127×#1763C211yesmaximal, 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
24#463×C127C418yescomplemented
25#442×C127—24no—
26C4×SD16×C127—24no—
27C2×#106×C127C2211yescharacteristic
28C2×#106×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×#103×C127C2211yescharacteristic
32C2×#103×C127C2211yescharacteristic
33C2×#103×C127C2211yescharacteristic
34C2×#102×C127C2211yescharacteristic
35C2×#102×C127C2211yescharacteristic
36C2×#102×C127C2211yescharacteristic
37C2×#102×C127C2211yescharacteristic
38C2×#102×C127C2211yescharacteristic
39C2×#97×C127C2211yescharacteristic
40C2×C4×C8×C127C2211yescharacteristic
41#391×C127C2211yescharacteristic
42#390×C127C2211yescharacteristic
43#388×C127—21no—
44#388×C127—21no—
45#385×C127—21no—
46#385×C127—21no—
47#384×C127C2211yescharacteristic
48C4×C4⋊C4×C127C2211yescharacteristic
49C4×C4⋊C4×C127C2211yescharacteristic
50C4×C4⋊C4×C127C2211yescharacteristic
51C4×C22⋊C4×C127—21no—
52C4×C22⋊C4×C127—21no—
53C4×C22⋊C4×C127—21no—
54#376×C127C2211yescharacteristic
55C2×#95×C127—21no—
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×C127—21no—
93C2×C4⋊C4×C127—21no—
94C2×C4⋊C4×C127C2311yescharacteristic
95C2×C4⋊C4×C127C2311yescharacteristic
96C2×C4⋊C4×C127C2311yescharacteristic
97C2×C4⋊C4×C127C2311yescharacteristic
98C2×C4⋊C4×C127C2311yescharacteristic
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×C22⋊C4×C127—21no—
106C2×C22⋊C4×C127—21no—
107C2×C42×C127—21no—
108C2×C42×C127—21no—
109C2×C42×C127—21no—
110C2×C42×C127—21no—
111C2×C42×C127C2311yescharacteristic
112C2×C42×C127C2311yescharacteristic
113C2×C42×C127C2311yescharacteristic
114#106×C127—22no—
115#106×C127—22no—
116C4⋊C8×C127—22no—
117C4⋊C8×C127C2×C414yescomplemented
118#103×C127—22no—
119#103×C127—22no—
120#103×C127C2×C414yescomplemented
121#102×C127—22no—
122#102×C127—22no—
123#102×C127—22no—
124#102×C127—22no—
125#102×C127C2×C414yescomplemented
126#97×C127—22no—
127C4×C8×C127—22no—
128#95×C127—21no—
129#95×C127—21no—
130#95×C127—21no—
131#95×C127—21no—
132#95×C127—21no—
133#95×C127D411yescharacteristic
134#95×C127D411yescharacteristic
135#95×C127D411yescharacteristic
136#95×C127D411yescharacteristic
137C24×C127—21no—
138C24×C127—21no—
139C2×Q8×C127—21no—
140C2×Q8×C127—21no—
141C2×Q8×C127—21no—
142C2×Q8×C127—21no—
143C2×Q8×C127—21no—
144C2×Q8×C127C22×C412yes—
145C2×D4×C127—21no—
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×C127C22×C412yes—
154C2×D4×C127C22×C412yes—
155C2×D4×C127C2×D412yes—
156C2×D4×C127#4112yes—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—24no—
162C22×C4×C127—24no—
163C22×C4×C127—24no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—42no—
167C22×C4×C127—81no—
168C22×C4×C127—81no—
169C22×C4×C127—81no—
170C22×C4×C127—81no—
171C22×C4×C127—81no—
172C22×C4×C127—81no—
173C22×C4×C127—81no—
174C22×C4×C127—81no—
175C22×C4×C127C2×D411yescharacteristic
176C22×C4×C127C2×D411yescharacteristic
177C22×C4×C127C2×D411yescharacteristic
178C22×C4×C127C2×D411yescharacteristic
179C22×C4×C127C2×D411yescharacteristic
180C22×C4×C127C2×D411yescharacteristic
181C22×C4×C127C2411yescharacteristic
182SD16×C127—28no—
183D8×C127—28no—
184C2×C8×C127—21no—
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×C127C22×C412yes—
195C2×C8×C127C22×C412yes—
196C4⋊C4×C127—21no—
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—42no—
204C4⋊C4×C127—81no—
205C4⋊C4×C127—81no—
206C4⋊C4×C127C22×C412yes—
207C4⋊C4×C127C2×D412yes—
208C4⋊C4×C127#4112yes—
209C22⋊C4×C127—24no—
210C22⋊C4×C127—24no—
211C22⋊C4×C127—24no—
212C22⋊C4×C127—24no—
213C22⋊C4×C127—24no—
214C22⋊C4×C127—42no—
215C22⋊C4×C127—81no—
216C22⋊C4×C127—81no—
217C42×C127—21no—
218C42×C127—21no—
219C42×C127—42no—
220C42×C127—81no—
221C42×C127—81no—
222C42×C127—81no—
223C42×C127C22×C412yes—
224C42×C127C2×D412yes—
225C42×C127#4112yes—
226C42×C127#4112yes—
227C23×C127—22no—
228C23×C127—22no—
229C23×C127—22no—
230C23×C127—22no—
231C23×C127—41no—
232C23×C127—41no—
233C23×C127—41no—
234C23×C127—41no—
235C23×C127—41no—
236C23×C127—41no—
237C23×C127—41no—
238C23×C127—41no—
239C23×C127—41no—
240C23×C127—41no—
241C23×C127C22×D411yescharacteristic
242Q8×C127—22no—
243Q8×C127—22no—
244Q8×C127—41no—
245Q8×C127—41no—
246D4×C127—22no—
247D4×C127—22no—
248D4×C127—22no—
249D4×C127—22no—
250D4×C127—22no—
251D4×C127—41no—
252D4×C127—41no—
253D4×C127C4×D414yes—
254C2×C4×C127—21no—
255C2×C4×C127—21no—
256C2×C4×C127—21no—
257C2×C4×C127—21no—
258C2×C4×C127—21no—
259C2×C4×C127—21no—
260C2×C4×C127—21no—
261C2×C4×C127—21no—
262C2×C4×C127—22no—
263C2×C4×C127—22no—
264C2×C4×C127—22no—
265C2×C4×C127—21no—
266C2×C4×C127—21no—
267C2×C4×C127—22no—
268C2×C4×C127—21no—
269C2×C4×C127—21no—
270C2×C4×C127—21no—
271C2×C4×C127—21no—
272C2×C4×C127—41no—
273C2×C4×C127—41no—
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—41no—
283C2×C4×C127—41no—
284C2×C4×C127—41no—
285C2×C4×C127—41no—
286C2×C4×C127—84no—
287C2×C4×C127—84no—
288C2×C4×C127—84no—
289C2×C4×C127—84no—
290C2×C4×C127C4×D412yes—
291C2×C4×C127C4×D412yes—
292C2×C4×C127#12112yes—
293C2×C4×C127#12112yes—
294C2×C4×C127C23×C411yescharacteristic
295C2×C4×C127C22×D411yescharacteristic
296C2×C4×C127C2×#4111yescharacteristic
297C2×C4×C127C2×#4111yescharacteristic
298C2×C4×C127C2×#4111yescharacteristic
299C2×C4×C127C2×#4111yescharacteristic
300C8×C127—22no—
301C8×C127—22no—
302C8×C127—41no—
303C8×C127—41no—
304C22×C127—24no—
305C22×C127—42no—
306C22×C127—42no—
307C22×C127—42no—
308C22×C127—42no—
309C22×C127—42no—
310C22×C127—42no—
311C22×C127—42no—
312C22×C127—42no—
313C22×C127—42no—
314C22×C127—81no—
315C22×C127—81no—
316C22×C127—81no—
317C22×C127—81no—
318C22×C127C2×C4×D411yescharacteristic
319C22×C127C2×#12111yescharacteristic
320C22×C127#52511yescharacteristic
321C22×C127#57611yescharacteristic
322C22×C127#57711yescharacteristic
323C22×C127#57711yescharacteristic
324C22×C127#57711yescharacteristic
325C4×C127—22no—
326C4×C127—22no—
327C4×C127—22no—
328C4×C127—22no—
329C4×C127—41no—
330C4×C127—42no—
331C4×C127—41no—
332C4×C127—42no—
333C4×C127—42no—
334C4×C127—42no—
335C4×C127—81no—
336C4×C127—81no—
337C4×C127C2×C4×D411yescharacteristic
338C4×C127C4×#4111yescharacteristic
339C4×C127#52911yescharacteristic
340C4×C127#53211yescharacteristic
341#21510C12711yesmaximal, characteristic, direct product factor, Sylow
342C2×C127—44no—
343C2×C127—82no—
344C2×C127C4×#12111yescharacteristic
345C2×C127#294611yescharacteristic
346C2×C127#295211yescharacteristic
347C2×C127#304211yescharacteristic
348C2×C127#304511yescharacteristic
349C2×C127#311811yescharacteristic
350C2×C127#312511yescharacteristic
351C2×#463C2×C12711yescharacteristic
352C2×#442C2×C12711yescharacteristic
353C2×C4×SD16C2×C12711yescharacteristic, complemented
354#2326C2×C12711yescharacteristic, complemented
355#2275C2×C12711yescharacteristic, complemented
356#1983C2×C12711yescharacteristic, complemented
357#1948C2×C12711yescharacteristic, complemented
358#1927C2×C12711yescharacteristic, complemented
359#1926C2×C12711yescharacteristic, complemented
360#1879C2×C12711yescharacteristic
361#1877C2×C12711yescharacteristic, complemented
362#1802C2×C12711yescharacteristic, complemented
363#1768C2×C12711yescharacteristic, complemented
364#1763C2×C12711yescharacteristic, complemented
365C4×#102C2×C12711yescharacteristic, complemented
366C127#2151011yescharacteristic, direct product factor, Sylow
367C22×SD16C22×C12711yescharacteristic
368C22×D8C22×C12711yescharacteristic
369C2×#124C22×C12711yescharacteristic
370C2×C4×Q8C22×C12711yescharacteristic
371C2×C4×D4C22×C12711yescharacteristic
372C2×C4×D4C22×C12711yescharacteristic
373C2×C4×D4C22×C12711yescharacteristic
374C2×C4×D4C22×C12711yescharacteristic
375#463C4×C12718yescomplemented
376#442—24no—
377C4×SD16—24no—
378C2×#106C22×C12711yescharacteristic
379C2×#106C22×C12711yescharacteristic
380C2×C4⋊C8C22×C12711yescharacteristic
381C2×C4⋊C8C22×C12711yescharacteristic
382C2×#103C22×C12711yescharacteristic
383C2×#103C22×C12711yescharacteristic
384C2×#103C22×C12711yescharacteristic
385C2×#102C22×C12711yescharacteristic
386C2×#102C22×C12711yescharacteristic
387C2×#102C22×C12711yescharacteristic
388C2×#102C22×C12711yescharacteristic
389C2×#102C22×C12711yescharacteristic
390C2×#97C22×C12711yescharacteristic
391C2×C4×C8C22×C12711yescharacteristic
392#391C22×C12711yescharacteristic
393#390C22×C12711yescharacteristic
394#388—21no—
395#388—21no—
396#385—21no—
397#385—21no—
398#384C22×C12711yescharacteristic
399C4×C4⋊C4C22×C12711yescharacteristic
400C4×C4⋊C4C22×C12711yescharacteristic
401C4×C4⋊C4C22×C12711yescharacteristic
402C4×C22⋊C4—21no—
403C4×C22⋊C4—21no—
404C4×C22⋊C4—21no—
405#376C22×C12711yescharacteristic
406C2×#95—21no—
407#340C22×C12711yescharacteristic
408#340C22×C12711yescharacteristic
409#340C22×C12711yescharacteristic
410#340C22×C12711yescharacteristic
411#336C22×C12711yescharacteristic
412#336C22×C12711yescharacteristic
413C22×Q8C23×C12711yescharacteristic
414C22×D4C23×C12711yescharacteristic
415C22×D4C23×C12711yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C23×C4—21no—
419C23×C4—21no—
420C2×SD16—22no—
421C2×SD16—22no—
422C2×SD16C2×C4×C12714yescomplemented
423C2×D8—22no—
424C2×D8—22no—
425C2×D8C2×C4×C12714yes—
426C22×C8C23×C12711yescharacteristic
427C22×C8C23×C12711yescharacteristic
428C22×C8C23×C12711yescharacteristic
429C22×C8C23×C12711yescharacteristic
430#124—22no—
431#124C2×C4×C12714yescomplemented
432C4×Q8—22no—
433C4×Q8—22no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—22no—
440C4×D4C2×C4×C12714yescomplemented
441C4×D4D4×C12714yes—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4C23×C12711yescharacteristic
446C2×C4⋊C4C23×C12711yescharacteristic
447C2×C4⋊C4C23×C12711yescharacteristic
448C2×C4⋊C4C23×C12711yescharacteristic
449C2×C4⋊C4C23×C12711yescharacteristic
450C2×C22⋊C4—21no—
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×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C12711yescharacteristic
463C2×C42C23×C12711yescharacteristic
464C2×C42C23×C12711yescharacteristic
465#106—22no—
466#106—22no—
467C4⋊C8—22no—
468C4⋊C8C2×C4×C12714yescomplemented
469#103—22no—
470#103—22no—
471#103C2×C4×C12714yescomplemented
472#102—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102C2×C4×C12714yescomplemented
477#97—22no—
478C4×C8—22no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95D4×C12711yescharacteristic
485#95D4×C12711yescharacteristic
486#95D4×C12711yescharacteristic
487#95D4×C12711yescharacteristic
488C24—21no—
489C24—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C22×C4×C12712yes—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4C22×C4×C12712yes—
505C2×D4C22×C4×C12712yes—
506C2×D4C2×D4×C12712yes—
507C2×D4#41×C12712yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—42no—
518C22×C4—81no—
519C22×C4—81no—
520C22×C4—81no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4C2×D4×C12711yescharacteristic
527C22×C4C2×D4×C12711yescharacteristic
528C22×C4C2×D4×C12711yescharacteristic
529C22×C4C2×D4×C12711yescharacteristic
530C22×C4C2×D4×C12711yescharacteristic
531C22×C4C2×D4×C12711yescharacteristic
532C22×C4C24×C12711yescharacteristic
533SD16—28no—
534D8—28no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8C22×C4×C12712yes—
546C2×C8C22×C4×C12712yes—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4C22×C4×C12712yes—
558C4⋊C4C2×D4×C12712yes—
559C4⋊C4#41×C12712yes—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C22⋊C4—24no—
564C22⋊C4—24no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C42—21no—
569C42—21no—
570C42—42no—
571C42—81no—
572C42—81no—
573C42—81no—
574C42C22×C4×C12712yes—
575C42C2×D4×C12712yes—
576C42#41×C12712yes—
577C42#41×C12712yes—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C22×D4×C12711yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—41no—
596Q8—41no—
597D4—22no—
598D4—22no—
599D4—22no—
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4C4×D4×C12714yes—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
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—41no—
637C2×C4—84no—
638C2×C4—84no—
639C2×C4—84no—
640C2×C4—84no—
641C2×C4C4×D4×C12712yes—
642C2×C4C4×D4×C12712yes—
643C2×C4#121×C12712yes—
644C2×C4#121×C12712yes—
645C2×C4C23×C4×C12711yescharacteristic
646C2×C4C22×D4×C12711yescharacteristic
647C2×C4C2×#41×C12711yescharacteristic
648C2×C4C2×#41×C12711yescharacteristic
649C2×C4C2×#41×C12711yescharacteristic
650C2×C4C2×#41×C12711yescharacteristic
651C8—22no—
652C8—22no—
653C8—41no—
654C8—41no—
655C22—24no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×C4×D4×C12711yescharacteristic
670C22C2×#121×C12711yescharacteristic
671C22#525×C12711yescharacteristic
672C22#576×C12711yescharacteristic
673C22#577×C12711yescharacteristic
674C22#577×C12711yescharacteristic
675C22#577×C12711yescharacteristic
676C4—22no—
677C4—22no—
678C4—22no—
679C4—22no—
680C4—41no—
681C4—42no—
682C4—41no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—81no—
687C4—81no—
688C4C2×C4×D4×C12711yescharacteristic
689C4C4×#41×C12711yescharacteristic
690C4#529×C12711yescharacteristic
691C4#532×C12711yescharacteristic
692C2—44no—
693C2—82no—
694C2C4×#121×C12711yescharacteristic
695C2C127×#294611yescharacteristic
696C2C127×#295211yescharacteristic
697C2C127×#304211yescharacteristic
698C2C127×#304511yescharacteristic
699C2C127×#311811yescharacteristic
700C2C127×#312511yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×D8×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ #376×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×SD16×C127C2semidirect
4. C127×#2326C2semidirect
5. C127×#2275C2semidirect
6. C127×#1983C2semidirect
7. C127×#1948C2semidirect
8. C127×#1927C2semidirect
9. C127×#1926C2semidirect
11. C127×#1877C2semidirect
12. C127×#1802C2semidirect
13. C127×#1768C2semidirect
14. C127×#1763C2semidirect
15. C4×#102×C127C2semidirect
24. #463×C127C4semidirect
71. C2×SD16×C127C2×C4semidirect
80. #124×C127C2×C4semidirect
89. C4×D4×C127C2×C4semidirect
117. C4⋊C8×C127C2×C4semidirect
120. #103×C127C2×C4semidirect
125. #102×C127C2×C4semidirect
341. #21510C127direct (N × H)
353. C2×C4×SD16C2×C127semidirect
354. #2326C2×C127semidirect
355. #2275C2×C127semidirect
356. #1983C2×C127semidirect
357. #1948C2×C127semidirect
358. #1927C2×C127semidirect
359. #1926C2×C127semidirect
361. #1877C2×C127semidirect
362. #1802C2×C127semidirect
363. #1768C2×C127semidirect
364. #1763C2×C127semidirect
365. C4×#102C2×C127semidirect
366. C127#21510direct (N × H)
375. #463C4×C127semidirect
422. C2×SD16C2×C4×C127semidirect
431. #124C2×C4×C127semidirect
440. C4×D4C2×C4×C127semidirect
468. C4⋊C8C2×C4×C127semidirect
471. #103C2×C4×C127semidirect
476. #102C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1272
C2×#442×C1272
C2×C4×SD16×C1272
C127×#23262
C127×#22752
C127×#19832
C127×#19482
C127×#19272
C127×#19262
C127×#18792
C127×#18772
C127×#18022
C127×#17682
C127×#17632
C4×#102×C1272
#21510127