Finite Group Databasebeta

← C127×#21456 #44585129

Subgroups — C127×#21456 #44585129

Order 32512.

1552 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#41×C127C211yesmaximal, characteristic, complemented
2C2×#449×C127C211yesmaximal, characteristic
3C2×#442×C127C211yesmaximal, characteristic, complemented
4C2×#440×C127C211yesmaximal, characteristic, complemented
5C4×#121×C127C211yesmaximal, characteristic, complemented
6C127×#1880C211yesmaximal, characteristic, complemented
7C127×#1879C211yesmaximal, characteristic, complemented
8C127×#1875C211yesmaximal, characteristic, complemented
9C127×#1865C211yesmaximal, characteristic, complemented
10C127×#1862C211yesmaximal, characteristic, complemented
11C127×#1854C211yesmaximal, characteristic, complemented
12C127×#1788C211yesmaximal, characteristic, complemented
13C127×#1763C211yesmaximal, characteristic, complemented
14C127×#1762C211yesmaximal, characteristic, complemented
15C127×#1749C211yesmaximal, characteristic, complemented
16C22×#41×C127C2211yescharacteristic
17C22×SD16×C127C2211yescharacteristic
18C22×D8×C127C2211yescharacteristic
19C2×#121×C127C2211yescharacteristic
20C4×#41×C127—24no—
21C4×#41×C127—24no—
22C2×C4×Q8×C127C2211yescharacteristic
23C2×C4×Q8×C127C2211yescharacteristic
24C2×C4×D4×C127—21no—
25C2×C4×D4×C127—21no—
26C2×C4×D4×C127—21no—
27C2×C4×D4×C127C2211yescharacteristic
28C2×C4×D4×C127C2211yescharacteristic
29C2×C4×D4×C127C2211yescharacteristic
30C2×#117×C127—21no—
31C2×#117×C127C2211yescharacteristic
32C22×C42×C127—21no—
33C22×C42×C127C2211yescharacteristic
34#449×C127C418yescomplemented
35#442×C127—24no—
36#440×C127—24no—
37C2×#107×C127C2211yescharacteristic
38C2×#106×C127C2211yescharacteristic
39C2×#103×C127C2211yescharacteristic
40C2×#103×C127C2211yescharacteristic
41C2×#103×C127C2211yescharacteristic
42C2×#102×C127C2211yescharacteristic
43C2×#102×C127C2211yescharacteristic
44C2×#102×C127C2211yescharacteristic
45C2×#102×C127C2211yescharacteristic
46C2×#102×C127C2211yescharacteristic
47C2×C22⋊C8×C127C2211yescharacteristic
48C2×C22⋊C8×C127C2211yescharacteristic
49C2×#97×C127C2211yescharacteristic
50C2×#97×C127C2211yescharacteristic
51#390×C127C2211yescharacteristic
52#389×C127C2211yescharacteristic
53#388×C127—21no—
54#386×C127—21no—
55#380×C127C2211yescharacteristic
56C4×C4⋊C4×C127C2211yescharacteristic
57C4×C22⋊C4×C127—21no—
58#340×C127C2211yescharacteristic
59#340×C127C2211yescharacteristic
60#340×C127C2211yescharacteristic
61#340×C127C2211yescharacteristic
62#336×C127C2211yescharacteristic
63#336×C127C2211yescharacteristic
64C2×#41×C127—22no—
65C2×#41×C127—22no—
66C2×#41×C127—22no—
67C2×#41×C127—22no—
68C2×#41×C127—22no—
69C2×#41×C127C2×C414yescomplemented
70C22×Q8×C127C2311yescharacteristic
71C22×D4×C127—21no—
72C22×D4×C127—21no—
73C22×D4×C127C2311yescharacteristic
74C22×D4×C127C2311yescharacteristic
75C23×C4×C127—21no—
76C23×C4×C127—21no—
77C23×C4×C127—21no—
78C23×C4×C127—21no—
79C23×C4×C127D411yescharacteristic
80C23×C4×C127D411yescharacteristic
81C23×C4×C127C2311yescharacteristic
82C2×SD16×C127—22no—
83C2×SD16×C127—22no—
84C2×SD16×C127C2×C414yescomplemented
85C2×D8×C127—22no—
86C2×D8×C127—22no—
87C2×D8×C127C2×C414yescomplemented
88C22×C8×C127C2311yescharacteristic
89C22×C8×C127C2311yescharacteristic
90C22×C8×C127C2311yescharacteristic
91C22×C8×C127C2311yescharacteristic
92#121×C127—22no—
93#121×C127C2×C414yescomplemented
94C4×Q8×C127—22no—
95C4×Q8×C127—22no—
96C4×Q8×C127—22no—
97C4×Q8×C127D414yescomplemented
98C4×D4×C127—28no—
99C4×D4×C127—28no—
100C4×D4×C127—22no—
101C4×D4×C127—22no—
102C4×D4×C127—22no—
103C4×D4×C127—22no—
104C4×D4×C127—22no—
105C4×D4×C127—44no—
106C4×D4×C127D414yescomplemented
107#117×C127—28no—
108#117×C127—22no—
109#117×C127—22no—
110C2×C4⋊C4×C127—21no—
111C2×C4⋊C4×C127—21no—
112C2×C4⋊C4×C127—21no—
113C2×C4⋊C4×C127C2311yescharacteristic
114C2×C4⋊C4×C127C2311yescharacteristic
115C2×C4⋊C4×C127C2311yescharacteristic
116C2×C4⋊C4×C127C2311yescharacteristic
117C2×C4⋊C4×C127C2311yescharacteristic
118C2×C22⋊C4×C127—21no—
119C2×C22⋊C4×C127—21no—
120C2×C22⋊C4×C127—21no—
121C2×C22⋊C4×C127—21no—
122C2×C22⋊C4×C127—21no—
123C2×C22⋊C4×C127—21no—
124C2×C22⋊C4×C127—21no—
125C2×C22⋊C4×C127—21no—
126C2×C42×C127—28no—
127C2×C42×C127—21no—
128C2×C42×C127—21no—
129C2×C42×C127—21no—
130C2×C42×C127—22no—
131C2×C42×C127—22no—
132C2×C42×C127—21no—
133C2×C42×C127D411yescharacteristic
134C2×C42×C127D411yescharacteristic
135C2×C42×C127C2311yescharacteristic
136C2×C42×C127C2311yescharacteristic
137#107×C127—22no—
138#106×C127—22no—
139#103×C127—22no—
140#103×C127—22no—
141#103×C127C2×C414yescomplemented
142#102×C127—22no—
143#102×C127—22no—
144#102×C127—22no—
145#102×C127—22no—
146#102×C127C2×C414yescomplemented
147C22⋊C8×C127—22no—
148C22⋊C8×C127C2×C414yescomplemented
149#97×C127—22no—
150#97×C127—22no—
151#95×C127—21no—
152#95×C127—21no—
153#95×C127—21no—
154C24×C127—21no—
155C24×C127—21no—
156C24×C127C2×D411yescharacteristic
157#41×C127—28no—
158#41×C127—28no—
159#41×C127—28no—
160#41×C127—28no—
161C2×Q8×C127—21no—
162C2×Q8×C127—21no—
163C2×Q8×C127—21no—
164C2×Q8×C127C22×C412yes—
165C2×Q8×C127C2×D412yes—
166C2×Q8×C127#4112yes—
167C2×D4×C127—24no—
168C2×D4×C127—24no—
169C2×D4×C127—24no—
170C2×D4×C127—24no—
171C2×D4×C127—21no—
172C2×D4×C127—21no—
173C2×D4×C127—21no—
174C2×D4×C127—21no—
175C2×D4×C127—21no—
176C2×D4×C127—21no—
177C2×D4×C127—21no—
178C2×D4×C127—21no—
179C2×D4×C127—42no—
180C2×D4×C127—42no—
181C2×D4×C127C22×C412yes—
182C2×D4×C127C22×C412yes—
183C2×D4×C127C2×D412yes—
184C2×D4×C127#4112yes—
185C22×C4×C127—24no—
186C22×C4×C127—24no—
187C22×C4×C127—21no—
188C22×C4×C127—24no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—24no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—22no—
198C22×C4×C127—22no—
199C22×C4×C127—24no—
200C22×C4×C127—22no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—41no—
204C22×C4×C127—41no—
205C22×C4×C127—41no—
206C22×C4×C127—42no—
207C22×C4×C127—42no—
208C22×C4×C127—42no—
209C22×C4×C127—42no—
210C22×C4×C127—42no—
211C22×C4×C127—42no—
212C22×C4×C127—42no—
213C22×C4×C127C22×C412yes—
214C22×C4×C127C2×D411yescharacteristic
215C22×C4×C127C2×D411yescharacteristic
216C22×C4×C127C2×D411yescharacteristic
217C22×C4×C127C2×D411yescharacteristic
218C22×C4×C127C2×D411yescharacteristic
219C22×C4×C127#4112yes—
220C22×C4×C127C2411yescharacteristic
221SD16×C127—28no—
222D8×C127—28no—
223C2×C8×C127—21no—
224C2×C8×C127—21no—
225C2×C8×C127—21no—
226C2×C8×C127—21no—
227C2×C8×C127—21no—
228C2×C8×C127—21no—
229C2×C8×C127—21no—
230C2×C8×C127—21no—
231C2×C8×C127—21no—
232C2×C8×C127—21no—
233C2×C8×C127C22×C412yes—
234C2×C8×C127C22×C412yes—
235C4⋊C4×C127—24no—
236C4⋊C4×C127—24no—
237C4⋊C4×C127—21no—
238C4⋊C4×C127—21no—
239C4⋊C4×C127—21no—
240C4⋊C4×C127—21no—
241C4⋊C4×C127—21no—
242C4⋊C4×C127—21no—
243C4⋊C4×C127—21no—
244C4⋊C4×C127—42no—
245C4⋊C4×C127C22×C412yes—
246C4⋊C4×C127C2×D412yes—
247C4⋊C4×C127C2×D412yes—
248C22⋊C4×C127—24no—
249C22⋊C4×C127—24no—
250C22⋊C4×C127—24no—
251C22⋊C4×C127—24no—
252C22⋊C4×C127—42no—
253C22⋊C4×C127—42no—
254C22⋊C4×C127—42no—
255C22⋊C4×C127—42no—
256C42×C127—24no—
257C42×C127—24no—
258C42×C127—22no—
259C42×C127—24no—
260C42×C127—22no—
261C42×C127—21no—
262C42×C127—21no—
263C42×C127—42no—
264C42×C127C2×D412yes—
265C42×C127C2×D412yes—
266C23×C127—22no—
267C23×C127—21no—
268C23×C127—22no—
269C23×C127—21no—
270C23×C127—22no—
271C23×C127—21no—
272C23×C127—21no—
273C23×C127—21no—
274C23×C127—21no—
275C23×C127—22no—
276C23×C127—41no—
277C23×C127—41no—
278C23×C127—41no—
279C23×C127—41no—
280C23×C127—41no—
281C23×C127—41no—
282C23×C127—41no—
283C23×C127—41no—
284C23×C127—41no—
285C23×C127—41no—
286C23×C127C4×D412yes—
287C23×C127C22×D411yescharacteristic
288Q8×C127—22no—
289Q8×C127—22no—
290Q8×C127—22no—
291Q8×C127C4×D414yescomplemented
292D4×C127—216no—
293D4×C127—22no—
294D4×C127—22no—
295D4×C127—22no—
296D4×C127—22no—
297D4×C127—22no—
298D4×C127—48no—
299D4×C127—41no—
300D4×C127—41no—
301D4×C127C4×D414yescomplemented
302C2×C4×C127—216no—
303C2×C4×C127—22no—
304C2×C4×C127—21no—
305C2×C4×C127—21no—
306C2×C4×C127—22no—
307C2×C4×C127—21no—
308C2×C4×C127—22no—
309C2×C4×C127—21no—
310C2×C4×C127—21no—
311C2×C4×C127—21no—
312C2×C4×C127—21no—
313C2×C4×C127—21no—
314C2×C4×C127—22no—
315C2×C4×C127—22no—
316C2×C4×C127—22no—
317C2×C4×C127—22no—
318C2×C4×C127—22no—
319C2×C4×C127—21no—
320C2×C4×C127—22no—
321C2×C4×C127—22no—
322C2×C4×C127—21no—
323C2×C4×C127—21no—
324C2×C4×C127—44no—
325C2×C4×C127—44no—
326C2×C4×C127—48no—
327C2×C4×C127—48no—
328C2×C4×C127—41no—
329C2×C4×C127—41no—
330C2×C4×C127—41no—
331C2×C4×C127—41no—
332C2×C4×C127—41no—
333C2×C4×C127—41no—
334C2×C4×C127—41no—
335C2×C4×C127—41no—
336C2×C4×C127—41no—
337C2×C4×C127—41no—
338C2×C4×C127—41no—
339C2×C4×C127—41no—
340C2×C4×C127—84no—
341C2×C4×C127C4×D412yes—
342C2×C4×C127#12012yes—
343C2×C4×C127#12012yes—
344C2×C4×C127AGL(1,ℤ/8)12yes—
345C2×C4×C127C23×C411yescharacteristic
346C2×C4×C127C22×D411yescharacteristic
347C2×C4×C127C22×D411yescharacteristic
348C2×C4×C127C2×#4111yescharacteristic
349C2×C4×C127C2×#4111yescharacteristic
350C2×C4×C127C2×#4111yescharacteristic
351C8×C127—22no—
352C8×C127—22no—
353C8×C127—41no—
354C8×C127—41no—
355C22×C127—22no—
356C22×C127—22no—
357C22×C127—22no—
358C22×C127—24no—
359C22×C127—41no—
360C22×C127—42no—
361C22×C127—41no—
362C22×C127—42no—
363C22×C127—42no—
364C22×C127—42no—
365C22×C127—41no—
366C22×C127—42no—
367C22×C127—41no—
368C22×C127—42no—
369C22×C127—42no—
370C22×C127—42no—
371C22×C127—42no—
372C22×C127—81no—
373C22×C127—81no—
374C22×C127—81no—
375C22×C127—81no—
376C22×C127C2×C4×D411yescharacteristic
377C22×C127C2×#12011yescharacteristic
378C22×C127#52511yescharacteristic
379C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C127#57511yescharacteristic
381C22×C127#57511yescharacteristic
382C22×C127#57511yescharacteristic
383C4×C127—22no—
384C4×C127—22no—
385C4×C127—22no—
386C4×C127—22no—
387C4×C127—24no—
388C4×C127—42no—
389C4×C127—41no—
390C4×C127—42no—
391C4×C127—42no—
392C4×C127—81no—
393C4×C127—81no—
394C4×C127C2×C4×D411yescharacteristic
395C4×C127C2×C4×D411yescharacteristic
396C4×C127#52511yescharacteristic
397C4×C127#52511yescharacteristic
398#21456C12711yesmaximal, characteristic, direct product factor, Sylow
399C2×C127—42no—
400C2×C127—44no—
401C2×C127—82no—
402C2×C127C4×#12011yescharacteristic
403C2×C127#294311yescharacteristic
404C2×C127C4×AGL(1,ℤ/8)11yescharacteristic
405C2×C127#300511yescharacteristic
406C2×C127#300611yescharacteristic
407C2×C127#311111yescharacteristic
408C2×C127#311511yescharacteristic
409C2×C4×#41C2×C12711yescharacteristic, complemented
410C2×#449C2×C12711yescharacteristic
411C2×#442C2×C12711yescharacteristic, complemented
412C2×#440C2×C12711yescharacteristic, complemented
413C4×#121C2×C12711yescharacteristic, complemented
414#1880C2×C12711yescharacteristic, complemented
415#1879C2×C12711yescharacteristic, complemented
416#1875C2×C12711yescharacteristic, complemented
417#1865C2×C12711yescharacteristic, complemented
418#1862C2×C12711yescharacteristic, complemented
419#1854C2×C12711yescharacteristic, complemented
420#1788C2×C12711yescharacteristic, complemented
421#1763C2×C12711yescharacteristic, complemented
422#1762C2×C12711yescharacteristic, complemented
423#1749C2×C12711yescharacteristic, complemented
424C127#2145611yescharacteristic, direct product factor, Sylow
425C22×#41C22×C12711yescharacteristic
426C22×SD16C22×C12711yescharacteristic
427C22×D8C22×C12711yescharacteristic
428C2×#121C22×C12711yescharacteristic
429C4×#41—24no—
430C4×#41—24no—
431C2×C4×Q8C22×C12711yescharacteristic
432C2×C4×Q8C22×C12711yescharacteristic
433C2×C4×D4—21no—
434C2×C4×D4—21no—
435C2×C4×D4—21no—
436C2×C4×D4C22×C12711yescharacteristic
437C2×C4×D4C22×C12711yescharacteristic
438C2×C4×D4C22×C12711yescharacteristic
439C2×#117—21no—
440C2×#117C22×C12711yescharacteristic
441C22×C42—21no—
442C22×C42C22×C12711yescharacteristic
443#449C4×C12718yescomplemented
444#442—24no—
445#440—24no—
446C2×#107C22×C12711yescharacteristic
447C2×#106C22×C12711yescharacteristic
448C2×#103C22×C12711yescharacteristic
449C2×#103C22×C12711yescharacteristic
450C2×#103C22×C12711yescharacteristic
451C2×#102C22×C12711yescharacteristic
452C2×#102C22×C12711yescharacteristic
453C2×#102C22×C12711yescharacteristic
454C2×#102C22×C12711yescharacteristic
455C2×#102C22×C12711yescharacteristic
456C2×C22⋊C8C22×C12711yescharacteristic
457C2×C22⋊C8C22×C12711yescharacteristic
458C2×#97C22×C12711yescharacteristic
459C2×#97C22×C12711yescharacteristic
460#390C22×C12711yescharacteristic
461#389C22×C12711yescharacteristic
462#388—21no—
463#386—21no—
464#380C22×C12711yescharacteristic
465C4×C4⋊C4C22×C12711yescharacteristic
466C4×C22⋊C4—21no—
467#340C22×C12711yescharacteristic
468#340C22×C12711yescharacteristic
469#340C22×C12711yescharacteristic
470#340C22×C12711yescharacteristic
471#336C22×C12711yescharacteristic
472#336C22×C12711yescharacteristic
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41C2×C4×C12714yescomplemented
479C22×Q8C23×C12711yescharacteristic
480C22×D4—21no—
481C22×D4—21no—
482C22×D4C23×C12711yescharacteristic
483C22×D4C23×C12711yescharacteristic
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4D4×C12711yescharacteristic
489C23×C4D4×C12711yescharacteristic
490C23×C4C23×C12711yescharacteristic
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16C2×C4×C12714yescomplemented
494C2×D8—22no—
495C2×D8—22no—
496C2×D8C2×C4×C12714yescomplemented
497C22×C8C23×C12711yescharacteristic
498C22×C8C23×C12711yescharacteristic
499C22×C8C23×C12711yescharacteristic
500C22×C8C23×C12711yescharacteristic
501#121—22no—
502#121C2×C4×C12714yescomplemented
503C4×Q8—22no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8D4×C12714yescomplemented
507C4×D4—28no—
508C4×D4—28no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—44no—
515C4×D4D4×C12714yescomplemented
516#117—28no—
517#117—22no—
518#117—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4C23×C12711yescharacteristic
523C2×C4⋊C4C23×C12711yescharacteristic
524C2×C4⋊C4C23×C12711yescharacteristic
525C2×C4⋊C4C23×C12711yescharacteristic
526C2×C4⋊C4C23×C12711yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C42—28no—
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—21no—
542C2×C42D4×C12711yescharacteristic
543C2×C42D4×C12711yescharacteristic
544C2×C42C23×C12711yescharacteristic
545C2×C42C23×C12711yescharacteristic
546#107—22no—
547#106—22no—
548#103—22no—
549#103—22no—
550#103C2×C4×C12714yescomplemented
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102C2×C4×C12714yescomplemented
556C22⋊C8—22no—
557C22⋊C8C2×C4×C12714yescomplemented
558#97—22no—
559#97—22no—
560#95—21no—
561#95—21no—
562#95—21no—
563C24—21no—
564C24—21no—
565C24C2×D4×C12711yescharacteristic
566#41—28no—
567#41—28no—
568#41—28no—
569#41—28no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8C22×C4×C12712yes—
574C2×Q8C2×D4×C12712yes—
575C2×Q8#41×C12712yes—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—24no—
579C2×D4—24no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4C22×C4×C12712yes—
591C2×D4C22×C4×C12712yes—
592C2×D4C2×D4×C12712yes—
593C2×D4#41×C12712yes—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—24no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4C22×C4×C12712yes—
623C22×C4C2×D4×C12711yescharacteristic
624C22×C4C2×D4×C12711yescharacteristic
625C22×C4C2×D4×C12711yescharacteristic
626C22×C4C2×D4×C12711yescharacteristic
627C22×C4C2×D4×C12711yescharacteristic
628C22×C4#41×C12712yes—
629C22×C4C24×C12711yescharacteristic
630SD16—28no—
631D8—28no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8C22×C4×C12712yes—
643C2×C8C22×C4×C12712yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—42no—
654C4⋊C4C22×C4×C12712yes—
655C4⋊C4C2×D4×C12712yes—
656C4⋊C4C2×D4×C12712yes—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C42—24no—
666C42—24no—
667C42—22no—
668C42—24no—
669C42—22no—
670C42—21no—
671C42—21no—
672C42—42no—
673C42C2×D4×C12712yes—
674C42C2×D4×C12712yes—
675C23—22no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23C4×D4×C12712yes—
696C23C22×D4×C12711yescharacteristic
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8C4×D4×C12714yescomplemented
701D4—216no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—22no—
707D4—48no—
708D4—41no—
709D4—41no—
710D4C4×D4×C12714yescomplemented
711C2×C4—216no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—48no—
736C2×C4—48no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—84no—
750C2×C4C4×D4×C12712yes—
751C2×C4#120×C12712yes—
752C2×C4#120×C12712yes—
753C2×C4AGL(1,ℤ/8)×C12712yes—
754C2×C4C23×C4×C12711yescharacteristic
755C2×C4C22×D4×C12711yescharacteristic
756C2×C4C22×D4×C12711yescharacteristic
757C2×C4C2×#41×C12711yescharacteristic
758C2×C4C2×#41×C12711yescharacteristic
759C2×C4C2×#41×C12711yescharacteristic
760C8—22no—
761C8—22no—
762C8—41no—
763C8—41no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—24no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×C4×D4×C12711yescharacteristic
786C22C2×#120×C12711yescharacteristic
787C22#525×C12711yescharacteristic
788C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
789C22#575×C12711yescharacteristic
790C22#575×C12711yescharacteristic
791C22#575×C12711yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—24no—
797C4—42no—
798C4—41no—
799C4—42no—
800C4—42no—
801C4—81no—
802C4—81no—
803C4C2×C4×D4×C12711yescharacteristic
804C4C2×C4×D4×C12711yescharacteristic
805C4#525×C12711yescharacteristic
806C4#525×C12711yescharacteristic
807C2—42no—
808C2—44no—
809C2—82no—
810C2C4×#120×C12711yescharacteristic
811C2C127×#294311yescharacteristic
812C2C4×AGL(1,ℤ/8)×C12711yescharacteristic
813C2C127×#300511yescharacteristic
814C2C127×#300611yescharacteristic
815C2C127×#311111yescharacteristic
816C2C127×#311511yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#449×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C4×#41×C127C2semidirect
3. C2×#442×C127C2semidirect
4. C2×#440×C127C2semidirect
5. C4×#121×C127C2semidirect
6. C127×#1880C2semidirect
7. C127×#1879C2semidirect
8. C127×#1875C2semidirect
9. C127×#1865C2semidirect
10. C127×#1862C2semidirect
11. C127×#1854C2semidirect
12. C127×#1788C2semidirect
13. C127×#1763C2semidirect
14. C127×#1762C2semidirect
15. C127×#1749C2semidirect
34. #449×C127C4semidirect
69. C2×#41×C127C2×C4semidirect
84. C2×SD16×C127C2×C4semidirect
87. C2×D8×C127C2×C4semidirect
93. #121×C127C2×C4semidirect
97. C4×Q8×C127D4semidirect
106. C4×D4×C127D4semidirect
141. #103×C127C2×C4semidirect
146. #102×C127C2×C4semidirect
148. C22⋊C8×C127C2×C4semidirect
291. Q8×C127C4×D4semidirect
301. D4×C127C4×D4semidirect
398. #21456C127direct (N × H)
409. C2×C4×#41C2×C127semidirect
411. C2×#442C2×C127semidirect
412. C2×#440C2×C127semidirect
413. C4×#121C2×C127semidirect
414. #1880C2×C127semidirect
415. #1879C2×C127semidirect
416. #1875C2×C127semidirect
417. #1865C2×C127semidirect
418. #1862C2×C127semidirect
419. #1854C2×C127semidirect
420. #1788C2×C127semidirect
421. #1763C2×C127semidirect
422. #1762C2×C127semidirect
423. #1749C2×C127semidirect
424. C127#21456direct (N × H)
443. #449C4×C127semidirect
478. C2×#41C2×C4×C127semidirect
493. C2×SD16C2×C4×C127semidirect
496. C2×D8C2×C4×C127semidirect
502. #121C2×C4×C127semidirect
506. C4×Q8D4×C127semidirect
515. C4×D4D4×C127semidirect
550. #103C2×C4×C127semidirect
555. #102C2×C4×C127semidirect
557. C22⋊C8C2×C4×C127semidirect
700. Q8C4×D4×C127semidirect
710. D4C4×D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#41×C1272
C2×#449×C1272
C2×#442×C1272
C2×#440×C1272
C4×#121×C1272
C127×#18802
C127×#18792
C127×#18752
C127×#18652
C127×#18622
C127×#18542
C127×#17882
C127×#17632
C127×#17622
C127×#17492
#21456127