Finite Group Databasebeta

← C127×#21513 #44585186

Subgroups — C127×#21513 #44585186

Order 32512.

1120 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C127C211yesmaximal, characteristic
2C2×#442×C127C211yesmaximal, characteristic, complemented
3C2×C4×D8×C127C211yesmaximal, characteristic, complemented
4C127×#2328C211yesmaximal, characteristic, complemented
5C127×#2275C211yesmaximal, characteristic, complemented
6C127×#1982C211yesmaximal, characteristic, complemented
7C127×#1949C211yesmaximal, characteristic, complemented
8C127×#1926C211yesmaximal, characteristic, complemented
9C127×#1925C211yesmaximal, characteristic, complemented
10C127×#1879C211yesmaximal, characteristic, complemented
11C127×#1879C211yesmaximal, characteristic, complemented
12C127×#1804C211yesmaximal, characteristic, complemented
13C127×#1768C211yesmaximal, characteristic, complemented
14C127×#1762C211yesmaximal, characteristic, complemented
15C4×#102×C127C211yesmaximal, characteristic, complemented
16C22×D8×C127C2211yescharacteristic
17C22×D8×C127C2211yescharacteristic
18C2×#127×C127C2211yescharacteristic
19C2×C4×D4×C127C2211yescharacteristic
20C2×C4×D4×C127C2211yescharacteristic
21C2×C4×D4×C127C2211yescharacteristic
22C2×C4×D4×C127C2211yescharacteristic
23C2×C4×D4×C127C2211yescharacteristic
24#459×C127C418yescomplemented
25#442×C127—24no—
26C4×D8×C127—24no—
27C2×#107×C127C2211yescharacteristic
28C2×#106×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×#102×C127C2211yescharacteristic
32C2×#102×C127C2211yescharacteristic
33C2×#102×C127C2211yescharacteristic
34C2×#102×C127C2211yescharacteristic
35C2×#102×C127C2211yescharacteristic
36C2×#102×C127C2211yescharacteristic
37C2×#102×C127C2211yescharacteristic
38C2×#102×C127C2211yescharacteristic
39C2×#97×C127C2211yescharacteristic
40C2×C4×C8×C127C2211yescharacteristic
41#390×C127C2211yescharacteristic
42#390×C127C2211yescharacteristic
43#386×C127—21no—
44#386×C127—21no—
45#386×C127—21no—
46#386×C127—21no—
47#382×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×D4×C127—21no—
63C22×D4×C127—21no—
64C22×D4×C127C2311yescharacteristic
65C22×D4×C127C2311yescharacteristic
66C22×D4×C127C2311yescharacteristic
67C23×C4×C127—21no—
68C23×C4×C127—21no—
69C23×C4×C127—21no—
70C23×C4×C127—21no—
71C23×C4×C127—21no—
72C2×D8×C127—22no—
73C2×D8×C127—22no—
74C2×D8×C127—22no—
75C2×D8×C127—22no—
76C2×D8×C127C2×C414yescomplemented
77C2×D8×C127C2×C414yescomplemented
78C22×C8×C127C2311yescharacteristic
79C22×C8×C127C2311yescharacteristic
80C22×C8×C127C2311yescharacteristic
81C22×C8×C127C2311yescharacteristic
82#127×C127—22no—
83#127×C127C2×C414yescomplemented
84C4×D4×C127—22no—
85C4×D4×C127—22no—
86C4×D4×C127—22no—
87C4×D4×C127—22no—
88C4×D4×C127—22no—
89C4×D4×C127—22no—
90C4×D4×C127—22no—
91C4×D4×C127—22no—
92C4×D4×C127C2×C414yescomplemented
93C4×D4×C127D414yescomplemented
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×C22⋊C4×C127—21no—
108C2×C42×C127—21no—
109C2×C42×C127—21no—
110C2×C42×C127—21no—
111C2×C42×C127C2311yescharacteristic
112C2×C42×C127C2311yescharacteristic
113C2×C42×C127C2311yescharacteristic
114#107×C127—22no—
115#106×C127—22no—
116C4⋊C8×C127—22no—
117C4⋊C8×C127C2×C414yescomplemented
118#102×C127—22no—
119#102×C127—22no—
120#102×C127—22no—
121#102×C127—22no—
122#102×C127—22no—
123#102×C127—22no—
124#102×C127C2×C414yescomplemented
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—
139C24×C127—21no—
140C2×D4×C127—24no—
141C2×D4×C127—24no—
142C2×D4×C127—21no—
143C2×D4×C127—21no—
144C2×D4×C127—21no—
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×C127—21no—
154C2×D4×C127—21no—
155C2×D4×C127—81no—
156C2×D4×C127—81no—
157C2×D4×C127—81no—
158C2×D4×C127—81no—
159C2×D4×C127C22×C412yes—
160C2×D4×C127C22×C412yes—
161C2×D4×C127C22×C412yes—
162C2×D4×C127C2×D412yes—
163C2×D4×C127#4112yes—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—24no—
168C22×C4×C127—24no—
169C22×C4×C127—24no—
170C22×C4×C127—21no—
171C22×C4×C127—21no—
172C22×C4×C127—42no—
173C22×C4×C127—42no—
174C22×C4×C127—81no—
175C22×C4×C127—81no—
176C22×C4×C127—81no—
177C22×C4×C127—81no—
178C22×C4×C127—81no—
179C22×C4×C127—81no—
180C22×C4×C127—81no—
181C22×C4×C127—81no—
182C22×C4×C127—81no—
183C22×C4×C127—81no—
184C22×C4×C127C2×D411yescharacteristic
185C22×C4×C127C2×D411yescharacteristic
186C22×C4×C127C2×D411yescharacteristic
187C22×C4×C127C2×D411yescharacteristic
188C22×C4×C127C2×D411yescharacteristic
189C22×C4×C127C2×D411yescharacteristic
190C22×C4×C127C2411yescharacteristic
191D8×C127—28no—
192D8×C127—28no—
193C2×C8×C127—21no—
194C2×C8×C127—21no—
195C2×C8×C127—21no—
196C2×C8×C127—21no—
197C2×C8×C127—21no—
198C2×C8×C127—21no—
199C2×C8×C127—21no—
200C2×C8×C127—21no—
201C2×C8×C127—21no—
202C2×C8×C127—21no—
203C2×C8×C127C22×C412yes—
204C2×C8×C127C22×C412yes—
205C4⋊C4×C127—21no—
206C4⋊C4×C127—21no—
207C4⋊C4×C127—21no—
208C4⋊C4×C127—21no—
209C4⋊C4×C127—21no—
210C4⋊C4×C127—21no—
211C4⋊C4×C127—21no—
212C4⋊C4×C127C22×C412yes—
213C4⋊C4×C127C2×D412yes—
214C4⋊C4×C127#4112yes—
215C22⋊C4×C127—24no—
216C22⋊C4×C127—24no—
217C22⋊C4×C127—24no—
218C22⋊C4×C127—42no—
219C22⋊C4×C127—42no—
220C22⋊C4×C127—81no—
221C22⋊C4×C127—81no—
222C22⋊C4×C127—81no—
223C22⋊C4×C127—81no—
224C42×C127—21no—
225C42×C127—21no—
226C42×C127—81no—
227C42×C127—81no—
228C42×C127—81no—
229C42×C127C22×C412yes—
230C42×C127C2×D412yes—
231C42×C127#4112yes—
232C42×C127#4112yes—
233C23×C127—22no—
234C23×C127—22no—
235C23×C127—22no—
236C23×C127—22no—
237C23×C127—22no—
238C23×C127—41no—
239C23×C127—41no—
240C23×C127—41no—
241C23×C127—41no—
242C23×C127—41no—
243C23×C127—41no—
244C23×C127—41no—
245C23×C127—41no—
246C23×C127—41no—
247C23×C127—41no—
248C23×C127—41no—
249C23×C127—41no—
250C23×C127—41no—
251C23×C127—41no—
252C23×C127—41no—
253C23×C127—41no—
254C23×C127C22×D411yescharacteristic
255D4×C127—22no—
256D4×C127—22no—
257D4×C127—22no—
258D4×C127—22no—
259D4×C127—22no—
260D4×C127—22no—
261D4×C127—22no—
262D4×C127—41no—
263D4×C127—41no—
264D4×C127—41no—
265D4×C127—41no—
266D4×C127—84no—
267D4×C127—84no—
268D4×C127C4×D414yes—
269C2×C4×C127—21no—
270C2×C4×C127—21no—
271C2×C4×C127—21no—
272C2×C4×C127—21no—
273C2×C4×C127—21no—
274C2×C4×C127—21no—
275C2×C4×C127—21no—
276C2×C4×C127—21no—
277C2×C4×C127—22no—
278C2×C4×C127—22no—
279C2×C4×C127—21no—
280C2×C4×C127—21no—
281C2×C4×C127—22no—
282C2×C4×C127—21no—
283C2×C4×C127—21no—
284C2×C4×C127—21no—
285C2×C4×C127—21no—
286C2×C4×C127—41no—
287C2×C4×C127—41no—
288C2×C4×C127—41no—
289C2×C4×C127—41no—
290C2×C4×C127—41no—
291C2×C4×C127—41no—
292C2×C4×C127—41no—
293C2×C4×C127—41no—
294C2×C4×C127—41no—
295C2×C4×C127—41no—
296C2×C4×C127—41no—
297C2×C4×C127—41no—
298C2×C4×C127—84no—
299C2×C4×C127—84no—
300C2×C4×C127—84no—
301C2×C4×C127—84no—
302C2×C4×C127—84no—
303C2×C4×C127C4×D412yes—
304C2×C4×C127C4×D412yes—
305C2×C4×C127#12112yes—
306C2×C4×C127#12112yes—
307C2×C4×C127C23×C411yescharacteristic
308C2×C4×C127C22×D411yescharacteristic
309C2×C4×C127C2×#4111yescharacteristic
310C2×C4×C127C2×#4111yescharacteristic
311C2×C4×C127C2×#4111yescharacteristic
312C2×C4×C127C2×#4111yescharacteristic
313C8×C127—22no—
314C8×C127—22no—
315C8×C127—41no—
316C8×C127—41no—
317C22×C127—24no—
318C22×C127—42no—
319C22×C127—42no—
320C22×C127—42no—
321C22×C127—42no—
322C22×C127—42no—
323C22×C127—42no—
324C22×C127—42no—
325C22×C127—42no—
326C22×C127—42no—
327C22×C127—42no—
328C22×C127—42no—
329C22×C127—42no—
330C22×C127—81no—
331C22×C127—81no—
332C22×C127—81no—
333C22×C127—81no—
334C22×C127—81no—
335C22×C127—81no—
336C22×C127—81no—
337C22×C127—81no—
338C22×C127C2×C4×D411yescharacteristic
339C22×C127C2×#12111yescharacteristic
340C22×C127#52511yescharacteristic
341C22×C127#57611yescharacteristic
342C22×C127#57611yescharacteristic
343C22×C127#57611yescharacteristic
344C22×C127#57711yescharacteristic
345C4×C127—22no—
346C4×C127—22no—
347C4×C127—22no—
348C4×C127—22no—
349C4×C127—41no—
350C4×C127—41no—
351C4×C127—42no—
352C4×C127—42no—
353C4×C127—42no—
354C4×C127—81no—
355C4×C127—81no—
356C4×C127C2×C4×D411yescharacteristic
357C4×C127C4×#4111yescharacteristic
358C4×C127#52911yescharacteristic
359C4×C127#53211yescharacteristic
360#21513C12711yesmaximal, characteristic, direct product factor, Sylow
361C2×C127—44no—
362C2×C127—82no—
363C2×C127—82no—
364C2×C127C4×#12111yescharacteristic
365C2×C127#294611yescharacteristic
366C2×C127#294811yescharacteristic
367C2×C127#304111yescharacteristic
368C2×C127#304511yescharacteristic
369C2×C127#311911yescharacteristic
370C2×C127#312211yescharacteristic
371C2×#459C2×C12711yescharacteristic
372C2×#442C2×C12711yescharacteristic, complemented
373C2×C4×D8C2×C12711yescharacteristic, complemented
374#2328C2×C12711yescharacteristic, complemented
375#2275C2×C12711yescharacteristic, complemented
376#1982C2×C12711yescharacteristic, complemented
377#1949C2×C12711yescharacteristic, complemented
378#1926C2×C12711yescharacteristic, complemented
379#1925C2×C12711yescharacteristic, complemented
380#1879C2×C12711yescharacteristic, complemented
381#1879C2×C12711yescharacteristic, complemented
382#1804C2×C12711yescharacteristic, complemented
383#1768C2×C12711yescharacteristic, complemented
384#1762C2×C12711yescharacteristic, complemented
385C4×#102C2×C12711yescharacteristic, complemented
386C127#2151311yescharacteristic, direct product factor, Sylow
387C22×D8C22×C12711yescharacteristic
388C22×D8C22×C12711yescharacteristic
389C2×#127C22×C12711yescharacteristic
390C2×C4×D4C22×C12711yescharacteristic
391C2×C4×D4C22×C12711yescharacteristic
392C2×C4×D4C22×C12711yescharacteristic
393C2×C4×D4C22×C12711yescharacteristic
394C2×C4×D4C22×C12711yescharacteristic
395#459C4×C12718yescomplemented
396#442—24no—
397C4×D8—24no—
398C2×#107C22×C12711yescharacteristic
399C2×#106C22×C12711yescharacteristic
400C2×C4⋊C8C22×C12711yescharacteristic
401C2×C4⋊C8C22×C12711yescharacteristic
402C2×#102C22×C12711yescharacteristic
403C2×#102C22×C12711yescharacteristic
404C2×#102C22×C12711yescharacteristic
405C2×#102C22×C12711yescharacteristic
406C2×#102C22×C12711yescharacteristic
407C2×#102C22×C12711yescharacteristic
408C2×#102C22×C12711yescharacteristic
409C2×#102C22×C12711yescharacteristic
410C2×#97C22×C12711yescharacteristic
411C2×C4×C8C22×C12711yescharacteristic
412#390C22×C12711yescharacteristic
413#390C22×C12711yescharacteristic
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#382C22×C12711yescharacteristic
419C4×C4⋊C4C22×C12711yescharacteristic
420C4×C4⋊C4C22×C12711yescharacteristic
421C4×C4⋊C4C22×C12711yescharacteristic
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425#376C22×C12711yescharacteristic
426C2×#95—21no—
427#340C22×C12711yescharacteristic
428#340C22×C12711yescharacteristic
429#340C22×C12711yescharacteristic
430#340C22×C12711yescharacteristic
431#336C22×C12711yescharacteristic
432#336C22×C12711yescharacteristic
433C22×D4—21no—
434C22×D4—21no—
435C22×D4C23×C12711yescharacteristic
436C22×D4C23×C12711yescharacteristic
437C22×D4C23×C12711yescharacteristic
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—21no—
443C2×D8—22no—
444C2×D8—22no—
445C2×D8—22no—
446C2×D8—22no—
447C2×D8C2×C4×C12714yescomplemented
448C2×D8C2×C4×C12714yescomplemented
449C22×C8C23×C12711yescharacteristic
450C22×C8C23×C12711yescharacteristic
451C22×C8C23×C12711yescharacteristic
452C22×C8C23×C12711yescharacteristic
453#127—22no—
454#127C2×C4×C12714yescomplemented
455C4×D4—22no—
456C4×D4—22no—
457C4×D4—22no—
458C4×D4—22no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4C2×C4×C12714yescomplemented
464C4×D4D4×C12714yescomplemented
465C2×C4⋊C4C23×C12711yescharacteristic
466C2×C4⋊C4C23×C12711yescharacteristic
467C2×C4⋊C4C23×C12711yescharacteristic
468C2×C4⋊C4C23×C12711yescharacteristic
469C2×C4⋊C4C23×C12711yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—21no—
482C2×C42C23×C12711yescharacteristic
483C2×C42C23×C12711yescharacteristic
484C2×C42C23×C12711yescharacteristic
485#107—22no—
486#106—22no—
487C4⋊C8—22no—
488C4⋊C8C2×C4×C12714yescomplemented
489#102—22no—
490#102—22no—
491#102—22no—
492#102—22no—
493#102—22no—
494#102—22no—
495#102C2×C4×C12714yescomplemented
496#102C2×C4×C12714yescomplemented
497#97—22no—
498C4×C8—22no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95D4×C12711yescharacteristic
505#95D4×C12711yescharacteristic
506#95D4×C12711yescharacteristic
507#95D4×C12711yescharacteristic
508C24—21no—
509C24—21no—
510C24—21no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4—81no—
529C2×D4—81no—
530C2×D4C22×C4×C12712yes—
531C2×D4C22×C4×C12712yes—
532C2×D4C22×C4×C12712yes—
533C2×D4C2×D4×C12712yes—
534C2×D4#41×C12712yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—81no—
555C22×C4C2×D4×C12711yescharacteristic
556C22×C4C2×D4×C12711yescharacteristic
557C22×C4C2×D4×C12711yescharacteristic
558C22×C4C2×D4×C12711yescharacteristic
559C22×C4C2×D4×C12711yescharacteristic
560C22×C4C2×D4×C12711yescharacteristic
561C22×C4C24×C12711yescharacteristic
562D8—28no—
563D8—28no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8C22×C4×C12712yes—
575C2×C8C22×C4×C12712yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4C22×C4×C12712yes—
584C4⋊C4C2×D4×C12712yes—
585C4⋊C4#41×C12712yes—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—81no—
594C22⋊C4—81no—
595C42—21no—
596C42—21no—
597C42—81no—
598C42—81no—
599C42—81no—
600C42C22×C4×C12712yes—
601C42C2×D4×C12712yes—
602C42#41×C12712yes—
603C42#41×C12712yes—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C22×D4×C12711yescharacteristic
626D4—22no—
627D4—22no—
628D4—22no—
629D4—22no—
630D4—22no—
631D4—22no—
632D4—22no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—84no—
638D4—84no—
639D4C4×D4×C12714yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—84no—
670C2×C4—84no—
671C2×C4—84no—
672C2×C4—84no—
673C2×C4—84no—
674C2×C4C4×D4×C12712yes—
675C2×C4C4×D4×C12712yes—
676C2×C4#121×C12712yes—
677C2×C4#121×C12712yes—
678C2×C4C23×C4×C12711yescharacteristic
679C2×C4C22×D4×C12711yescharacteristic
680C2×C4C2×#41×C12711yescharacteristic
681C2×C4C2×#41×C12711yescharacteristic
682C2×C4C2×#41×C12711yescharacteristic
683C2×C4C2×#41×C12711yescharacteristic
684C8—22no—
685C8—22no—
686C8—41no—
687C8—41no—
688C22—24no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22C2×C4×D4×C12711yescharacteristic
710C22C2×#121×C12711yescharacteristic
711C22#525×C12711yescharacteristic
712C22#576×C12711yescharacteristic
713C22#576×C12711yescharacteristic
714C22#576×C12711yescharacteristic
715C22#577×C12711yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—81no—
726C4—81no—
727C4C2×C4×D4×C12711yescharacteristic
728C4C4×#41×C12711yescharacteristic
729C4#529×C12711yescharacteristic
730C4#532×C12711yescharacteristic
731C2—44no—
732C2—82no—
733C2—82no—
734C2C4×#121×C12711yescharacteristic
735C2C127×#294611yescharacteristic
736C2C127×#294811yescharacteristic
737C2C127×#304111yescharacteristic
738C2C127×#304511yescharacteristic
739C2C127×#311911yescharacteristic
740C2C127×#312211yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#459×C127C2
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
2. C2×#442×C127C2semidirect
3. C2×C4×D8×C127C2semidirect
4. C127×#2328C2semidirect
5. C127×#2275C2semidirect
6. C127×#1982C2semidirect
7. C127×#1949C2semidirect
8. C127×#1926C2semidirect
9. C127×#1925C2semidirect
10. C127×#1879C2semidirect
11. C127×#1879C2semidirect
12. C127×#1804C2semidirect
13. C127×#1768C2semidirect
14. C127×#1762C2semidirect
15. C4×#102×C127C2semidirect
24. #459×C127C4semidirect
76. C2×D8×C127C2×C4semidirect
77. C2×D8×C127C2×C4semidirect
83. #127×C127C2×C4semidirect
92. C4×D4×C127C2×C4semidirect
93. C4×D4×C127D4semidirect
117. C4⋊C8×C127C2×C4semidirect
124. #102×C127C2×C4semidirect
125. #102×C127C2×C4semidirect
360. #21513C127direct (N × H)
372. C2×#442C2×C127semidirect
373. C2×C4×D8C2×C127semidirect
374. #2328C2×C127semidirect
375. #2275C2×C127semidirect
376. #1982C2×C127semidirect
377. #1949C2×C127semidirect
378. #1926C2×C127semidirect
379. #1925C2×C127semidirect
380. #1879C2×C127semidirect
381. #1879C2×C127semidirect
382. #1804C2×C127semidirect
383. #1768C2×C127semidirect
384. #1762C2×C127semidirect
385. C4×#102C2×C127semidirect
386. C127#21513direct (N × H)
395. #459C4×C127semidirect
447. C2×D8C2×C4×C127semidirect
448. C2×D8C2×C4×C127semidirect
454. #127C2×C4×C127semidirect
463. C4×D4C2×C4×C127semidirect
464. C4×D4D4×C127semidirect
488. C4⋊C8C2×C4×C127semidirect
495. #102C2×C4×C127semidirect
496. #102C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1272
C2×#442×C1272
C2×C4×D8×C1272
C127×#23282
C127×#22752
C127×#19822
C127×#19492
C127×#19262
C127×#19252
C127×#18792
C127×#18042
C127×#17682
C127×#17622
C4×#102×C1272
#21513127