Finite Group Databasebeta

← C127×#21460 #44585133

Subgroups — C127×#21460 #44585133

Order 32512.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C127C211yesmaximal, characteristic, complemented
2C2×#449×C127C211yesmaximal, characteristic
3C2×#440×C127C211yesmaximal, characteristic, complemented
4C2×C4×D8×C127C211yesmaximal, characteristic, complemented
5C127×#2324C211yesmaximal, characteristic, complemented
6C127×#1880C211yesmaximal, characteristic, complemented
7C127×#1879C211yesmaximal, characteristic, complemented
8C127×#1874C211yesmaximal, characteristic, complemented
9C127×#1863C211yesmaximal, characteristic, complemented
10C127×#1862C211yesmaximal, characteristic, complemented
11C127×#1852C211yesmaximal, characteristic, complemented
12C127×#1788C211yesmaximal, characteristic, complemented
13C127×#1762C211yesmaximal, characteristic, complemented
14C4×#103×C127C211yesmaximal, characteristic, complemented
15C127×#1750C211yesmaximal, characteristic, complemented
16C22×#41×C127C2211yescharacteristic
17C22×SD16×C127C2211yescharacteristic
18C22×D8×C127C2211yescharacteristic
19C2×#121×C127C2211yescharacteristic
20#520×C127—24no—
21#520×C127—24no—
22C2×C4×Q8×C127C2211yescharacteristic
23C2×C4×Q8×C127C2211yescharacteristic
24C2×C4×D4×C127—21no—
25C2×C4×D4×C127—21no—
26C2×C4×D4×C127C2211yescharacteristic
27C2×C4×D4×C127C2211yescharacteristic
28C2×C4×D4×C127C2211yescharacteristic
29C2×#117×C127—21no—
30C2×#117×C127C2211yescharacteristic
31C22×C4⋊C4×C127—21no—
32C22×C4⋊C4×C127C2211yescharacteristic
33#449×C127C418yescomplemented
34#440×C127—24no—
35C4×D8×C127—24no—
36C2×#107×C127C2211yescharacteristic
37C2×#107×C127C2211yescharacteristic
38C2×#103×C127C2211yescharacteristic
39C2×#103×C127C2211yescharacteristic
40C2×#103×C127C2211yescharacteristic
41C2×#102×C127C2211yescharacteristic
42C2×#102×C127C2211yescharacteristic
43C2×#102×C127C2211yescharacteristic
44C2×#102×C127C2211yescharacteristic
45C2×#102×C127C2211yescharacteristic
46C2×C22⋊C8×C127C2211yescharacteristic
47C2×C22⋊C8×C127C2211yescharacteristic
48C2×#97×C127C2211yescharacteristic
49C2×C4×C8×C127C2211yescharacteristic
50#390×C127—21no—
51#390×C127C2211yescharacteristic
52#389×C127C2211yescharacteristic
53#388×C127—21no—
54#386×C127—21no—
55#385×C127—21no—
56#380×C127C2211yescharacteristic
57C4×C4⋊C4×C127C2211yescharacteristic
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×C127—21no—
80C23×C4×C127C2311yescharacteristic
81C2×SD16×C127—22no—
82C2×SD16×C127—22no—
83C2×SD16×C127C2×C414yescomplemented
84C2×D8×C127—22no—
85C2×D8×C127—22no—
86C2×D8×C127C2×C414yescomplemented
87C22×C8×C127C2311yescharacteristic
88C22×C8×C127C2311yescharacteristic
89C22×C8×C127C2311yescharacteristic
90C22×C8×C127C2311yescharacteristic
91#121×C127—22no—
92#121×C127C2×C414yescomplemented
93C4×Q8×C127—22no—
94C4×Q8×C127—22no—
95C4×Q8×C127—22no—
96C4×Q8×C127D414yescomplemented
97C4×D4×C127—28no—
98C4×D4×C127—28no—
99C4×D4×C127—22no—
100C4×D4×C127—22no—
101C4×D4×C127—22no—
102C4×D4×C127—22no—
103C4×D4×C127—22no—
104C4×D4×C127D414yescomplemented
105#117×C127—28no—
106#117×C127—22no—
107#117×C127—22no—
108C2×C4⋊C4×C127—28no—
109C2×C4⋊C4×C127—21no—
110C2×C4⋊C4×C127—21no—
111C2×C4⋊C4×C127—21no—
112C2×C4⋊C4×C127—22no—
113C2×C4⋊C4×C127—22no—
114C2×C4⋊C4×C127—21no—
115C2×C4⋊C4×C127D411yescharacteristic
116C2×C4⋊C4×C127D411yescharacteristic
117C2×C4⋊C4×C127C2311yescharacteristic
118C2×C4⋊C4×C127C2311yescharacteristic
119C2×C4⋊C4×C127C2311yescharacteristic
120C2×C4⋊C4×C127C2311yescharacteristic
121C2×C4⋊C4×C127C2311yescharacteristic
122C2×C22⋊C4×C127—21no—
123C2×C22⋊C4×C127—21no—
124C2×C22⋊C4×C127—21no—
125C2×C22⋊C4×C127—21no—
126C2×C22⋊C4×C127—21no—
127C2×C22⋊C4×C127—21no—
128C2×C22⋊C4×C127—21no—
129C2×C22⋊C4×C127D411yescharacteristic
130C2×C22⋊C4×C127D411yescharacteristic
131C2×C42×C127—21no—
132C2×C42×C127—21no—
133C2×C42×C127—21no—
134C2×C42×C127C2311yescharacteristic
135C2×C42×C127C2311yescharacteristic
136#107×C127—22no—
137#107×C127—22no—
138#103×C127—22no—
139#103×C127—22no—
140#103×C127C2×C414yescomplemented
141#102×C127—22no—
142#102×C127—22no—
143#102×C127—22no—
144#102×C127—22no—
145#102×C127C2×C414yescomplemented
146C22⋊C8×C127—22no—
147C22⋊C8×C127C2×C414yescomplemented
148#97×C127—22no—
149C4×C8×C127—22no—
150#95×C127—21no—
151#95×C127—21no—
152#95×C127—21no—
153C24×C127—21no—
154C24×C127—21no—
155C24×C127C2×D411yescharacteristic
156#41×C127—28no—
157#41×C127—28no—
158#41×C127—28no—
159#41×C127—28no—
160C2×Q8×C127—21no—
161C2×Q8×C127—21no—
162C2×Q8×C127—21no—
163C2×Q8×C127C22×C412yes—
164C2×Q8×C127C2×D412yes—
165C2×Q8×C127#4112yes—
166C2×D4×C127—24no—
167C2×D4×C127—24no—
168C2×D4×C127—24no—
169C2×D4×C127—24no—
170C2×D4×C127—21no—
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—81no—
179C2×D4×C127—81no—
180C2×D4×C127C22×C412yes—
181C2×D4×C127C22×C412yes—
182C2×D4×C127C2×D412yes—
183C2×D4×C127#4112yes—
184C22×C4×C127—24no—
185C22×C4×C127—24no—
186C22×C4×C127—21no—
187C22×C4×C127—24no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—24no—
196C22×C4×C127—24no—
197C22×C4×C127—24no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—42no—
201C22×C4×C127—81no—
202C22×C4×C127—81no—
203C22×C4×C127—81no—
204C22×C4×C127—81no—
205C22×C4×C127—81no—
206C22×C4×C127—81no—
207C22×C4×C127—81no—
208C22×C4×C127—81no—
209C22×C4×C127C22×C412yes—
210C22×C4×C127C2×D411yescharacteristic
211C22×C4×C127C2×D411yescharacteristic
212C22×C4×C127C2×D411yescharacteristic
213C22×C4×C127C2×D411yescharacteristic
214C22×C4×C127C2×D411yescharacteristic
215C22×C4×C127#4112yes—
216C22×C4×C127C2411yescharacteristic
217SD16×C127—28no—
218D8×C127—28no—
219C2×C8×C127—21no—
220C2×C8×C127—21no—
221C2×C8×C127—21no—
222C2×C8×C127—21no—
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×C127C22×C412yes—
230C2×C8×C127C22×C412yes—
231C4⋊C4×C127—24no—
232C4⋊C4×C127—24no—
233C4⋊C4×C127—22no—
234C4⋊C4×C127—24no—
235C4⋊C4×C127—22no—
236C4⋊C4×C127—21no—
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—81no—
244C4⋊C4×C127C22×C412yes—
245C4⋊C4×C127C2×D412yes—
246C4⋊C4×C127C2×D412yes—
247C22⋊C4×C127—24no—
248C22⋊C4×C127—24no—
249C22⋊C4×C127—24no—
250C22⋊C4×C127—22no—
251C22⋊C4×C127—22no—
252C22⋊C4×C127—42no—
253C22⋊C4×C127—81no—
254C22⋊C4×C127—81no—
255C22⋊C4×C127—81no—
256C42×C127—24no—
257C42×C127—24no—
258C42×C127—21no—
259C42×C127—21no—
260C42×C127—81no—
261C42×C127C2×D412yes—
262C42×C127C2×D412yes—
263C23×C127—22no—
264C23×C127—21no—
265C23×C127—22no—
266C23×C127—21no—
267C23×C127—22no—
268C23×C127—21no—
269C23×C127—21no—
270C23×C127—21no—
271C23×C127—21no—
272C23×C127—22no—
273C23×C127—41no—
274C23×C127—41no—
275C23×C127—41no—
276C23×C127—41no—
277C23×C127—41no—
278C23×C127—41no—
279C23×C127—41no—
280C23×C127—41no—
281C23×C127—41no—
282C23×C127—41no—
283C23×C127C4×D412yes—
284C23×C127C22×D411yescharacteristic
285Q8×C127—22no—
286Q8×C127—22no—
287Q8×C127—22no—
288Q8×C127C4×D414yes—
289D4×C127—216no—
290D4×C127—22no—
291D4×C127—22no—
292D4×C127—22no—
293D4×C127—22no—
294D4×C127—22no—
295D4×C127—41no—
296D4×C127—41no—
297D4×C127—84no—
298D4×C127C4×D414yes—
299C2×C4×C127—216no—
300C2×C4×C127—22no—
301C2×C4×C127—22no—
302C2×C4×C127—21no—
303C2×C4×C127—21no—
304C2×C4×C127—22no—
305C2×C4×C127—21no—
306C2×C4×C127—21no—
307C2×C4×C127—21no—
308C2×C4×C127—21no—
309C2×C4×C127—22no—
310C2×C4×C127—22no—
311C2×C4×C127—22no—
312C2×C4×C127—22no—
313C2×C4×C127—22no—
314C2×C4×C127—21no—
315C2×C4×C127—21no—
316C2×C4×C127—22no—
317C2×C4×C127—22no—
318C2×C4×C127—21no—
319C2×C4×C127—21no—
320C2×C4×C127—21no—
321C2×C4×C127—21no—
322C2×C4×C127—41no—
323C2×C4×C127—41no—
324C2×C4×C127—41no—
325C2×C4×C127—41no—
326C2×C4×C127—41no—
327C2×C4×C127—41no—
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—84no—
335C2×C4×C127—84no—
336C2×C4×C127—84no—
337C2×C4×C127—84no—
338C2×C4×C127C4×D412yes—
339C2×C4×C127#12012yes—
340C2×C4×C127#12012yes—
341C2×C4×C127C23×C411yescharacteristic
342C2×C4×C127C22×D411yescharacteristic
343C2×C4×C127C22×D411yescharacteristic
344C2×C4×C127C2×#4111yescharacteristic
345C2×C4×C127C2×#4111yescharacteristic
346C2×C4×C127C2×#4111yescharacteristic
347C8×C127—22no—
348C8×C127—22no—
349C8×C127—41no—
350C8×C127—41no—
351C22×C127—22no—
352C22×C127—22no—
353C22×C127—22no—
354C22×C127—24no—
355C22×C127—41no—
356C22×C127—42no—
357C22×C127—41no—
358C22×C127—42no—
359C22×C127—42no—
360C22×C127—42no—
361C22×C127—41no—
362C22×C127—42no—
363C22×C127—41no—
364C22×C127—42no—
365C22×C127—42no—
366C22×C127—42no—
367C22×C127—42no—
368C22×C127—81no—
369C22×C127—81no—
370C22×C127—81no—
371C22×C127—81no—
372C22×C127C2×C4×D411yescharacteristic
373C22×C127C2×#12011yescharacteristic
374C22×C127#52511yescharacteristic
375C22×C127#57611yescharacteristic
376C22×C127#57611yescharacteristic
377C22×C127#57711yescharacteristic
378C22×C127#57811yescharacteristic
379C4×C127—22no—
380C4×C127—22no—
381C4×C127—22no—
382C4×C127—24no—
383C4×C127—42no—
384C4×C127—41no—
385C4×C127—42no—
386C4×C127—42no—
387C4×C127—41no—
388C4×C127—81no—
389C4×C127—81no—
390C4×C127C2×C4×D411yescharacteristic
391C4×C127C2×C4×D411yescharacteristic
392C4×C127#52511yescharacteristic
393C4×C127#52511yescharacteristic
394#21460C12711yesmaximal, characteristic, direct product factor, Sylow
395C2×C127—42no—
396C2×C127—44no—
397C2×C127—82no—
398C2×C127C4×#12011yescharacteristic
399C2×C127#294611yescharacteristic
400C2×C127#295111yescharacteristic
401C2×C127#300811yescharacteristic
402C2×C127#301311yescharacteristic
403C2×C127#311911yescharacteristic
404C2×C127#312411yescharacteristic
405C2×#520C2×C12711yescharacteristic, complemented
406C2×#449C2×C12711yescharacteristic
407C2×#440C2×C12711yescharacteristic, complemented
408C2×C4×D8C2×C12711yescharacteristic, complemented
409#2324C2×C12711yescharacteristic, complemented
410#1880C2×C12711yescharacteristic, complemented
411#1879C2×C12711yescharacteristic, complemented
412#1874C2×C12711yescharacteristic, complemented
413#1863C2×C12711yescharacteristic, complemented
414#1862C2×C12711yescharacteristic, complemented
415#1852C2×C12711yescharacteristic, complemented
416#1788C2×C12711yescharacteristic, complemented
417#1762C2×C12711yescharacteristic, complemented
418C4×#103C2×C12711yescharacteristic, complemented
419#1750C2×C12711yescharacteristic, complemented
420C127#2146011yescharacteristic, direct product factor, Sylow
421C22×#41C22×C12711yescharacteristic
422C22×SD16C22×C12711yescharacteristic
423C22×D8C22×C12711yescharacteristic
424C2×#121C22×C12711yescharacteristic
425#520—24no—
426#520—24no—
427C2×C4×Q8C22×C12711yescharacteristic
428C2×C4×Q8C22×C12711yescharacteristic
429C2×C4×D4—21no—
430C2×C4×D4—21no—
431C2×C4×D4C22×C12711yescharacteristic
432C2×C4×D4C22×C12711yescharacteristic
433C2×C4×D4C22×C12711yescharacteristic
434C2×#117—21no—
435C2×#117C22×C12711yescharacteristic
436C22×C4⋊C4—21no—
437C22×C4⋊C4C22×C12711yescharacteristic
438#449C4×C12718yescomplemented
439#440—24no—
440C4×D8—24no—
441C2×#107C22×C12711yescharacteristic
442C2×#107C22×C12711yescharacteristic
443C2×#103C22×C12711yescharacteristic
444C2×#103C22×C12711yescharacteristic
445C2×#103C22×C12711yescharacteristic
446C2×#102C22×C12711yescharacteristic
447C2×#102C22×C12711yescharacteristic
448C2×#102C22×C12711yescharacteristic
449C2×#102C22×C12711yescharacteristic
450C2×#102C22×C12711yescharacteristic
451C2×C22⋊C8C22×C12711yescharacteristic
452C2×C22⋊C8C22×C12711yescharacteristic
453C2×#97C22×C12711yescharacteristic
454C2×C4×C8C22×C12711yescharacteristic
455#390—21no—
456#390C22×C12711yescharacteristic
457#389C22×C12711yescharacteristic
458#388—21no—
459#386—21no—
460#385—21no—
461#380C22×C12711yescharacteristic
462C4×C4⋊C4C22×C12711yescharacteristic
463#340C22×C12711yescharacteristic
464#340C22×C12711yescharacteristic
465#340C22×C12711yescharacteristic
466#340C22×C12711yescharacteristic
467#336C22×C12711yescharacteristic
468#336C22×C12711yescharacteristic
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41C2×C4×C12714yescomplemented
475C22×Q8C23×C12711yescharacteristic
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C12711yescharacteristic
479C22×D4C23×C12711yescharacteristic
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C12711yescharacteristic
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16C2×C4×C12714yescomplemented
489C2×D8—22no—
490C2×D8—22no—
491C2×D8C2×C4×C12714yescomplemented
492C22×C8C23×C12711yescharacteristic
493C22×C8C23×C12711yescharacteristic
494C22×C8C23×C12711yescharacteristic
495C22×C8C23×C12711yescharacteristic
496#121—22no—
497#121C2×C4×C12714yescomplemented
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8D4×C12714yescomplemented
502C4×D4—28no—
503C4×D4—28no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4D4×C12714yescomplemented
510#117—28no—
511#117—22no—
512#117—22no—
513C2×C4⋊C4—28no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C12711yescharacteristic
521C2×C4⋊C4D4×C12711yescharacteristic
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⋊C4D4×C12711yescharacteristic
535C2×C22⋊C4D4×C12711yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42C23×C12711yescharacteristic
540C2×C42C23×C12711yescharacteristic
541#107—22no—
542#107—22no—
543#103—22no—
544#103—22no—
545#103C2×C4×C12714yescomplemented
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102C2×C4×C12714yescomplemented
551C22⋊C8—22no—
552C22⋊C8C2×C4×C12714yescomplemented
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24C2×D4×C12711yescharacteristic
561#41—28no—
562#41—28no—
563#41—28no—
564#41—28no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8C22×C4×C12712yes—
569C2×Q8C2×D4×C12712yes—
570C2×Q8#41×C12712yes—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4C22×C4×C12712yes—
586C2×D4C22×C4×C12712yes—
587C2×D4C2×D4×C12712yes—
588C2×D4#41×C12712yes—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—42no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4C22×C4×C12712yes—
615C22×C4C2×D4×C12711yescharacteristic
616C22×C4C2×D4×C12711yescharacteristic
617C22×C4C2×D4×C12711yescharacteristic
618C22×C4C2×D4×C12711yescharacteristic
619C22×C4C2×D4×C12711yescharacteristic
620C22×C4#41×C12712yes—
621C22×C4C24×C12711yescharacteristic
622SD16—28no—
623D8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8C22×C4×C12712yes—
635C2×C8C22×C4×C12712yes—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—22no—
639C4⋊C4—24no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—81no—
649C4⋊C4C22×C4×C12712yes—
650C4⋊C4C2×D4×C12712yes—
651C4⋊C4C2×D4×C12712yes—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—24no—
662C42—24no—
663C42—21no—
664C42—21no—
665C42—81no—
666C42C2×D4×C12712yes—
667C42C2×D4×C12712yes—
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23C4×D4×C12712yes—
689C23C22×D4×C12711yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8C4×D4×C12714yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4C4×D4×C12714yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4C4×D4×C12712yes—
744C2×C4#120×C12712yes—
745C2×C4#120×C12712yes—
746C2×C4C23×C4×C12711yescharacteristic
747C2×C4C22×D4×C12711yescharacteristic
748C2×C4C22×D4×C12711yescharacteristic
749C2×C4C2×#41×C12711yescharacteristic
750C2×C4C2×#41×C12711yescharacteristic
751C2×C4C2×#41×C12711yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×C4×D4×C12711yescharacteristic
778C22C2×#120×C12711yescharacteristic
779C22#525×C12711yescharacteristic
780C22#576×C12711yescharacteristic
781C22#576×C12711yescharacteristic
782C22#577×C12711yescharacteristic
783C22#578×C12711yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—24no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—41no—
793C4—81no—
794C4—81no—
795C4C2×C4×D4×C12711yescharacteristic
796C4C2×C4×D4×C12711yescharacteristic
797C4#525×C12711yescharacteristic
798C4#525×C12711yescharacteristic
799C2—42no—
800C2—44no—
801C2—82no—
802C2C4×#120×C12711yescharacteristic
803C2C127×#294611yescharacteristic
804C2C127×#295111yescharacteristic
805C2C127×#300811yescharacteristic
806C2C127×#301311yescharacteristic
807C2C127×#311911yescharacteristic
808C2C127×#312411yescharacteristic
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 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#520×C127C2semidirect
3. C2×#440×C127C2semidirect
4. C2×C4×D8×C127C2semidirect
5. C127×#2324C2semidirect
6. C127×#1880C2semidirect
7. C127×#1879C2semidirect
8. C127×#1874C2semidirect
9. C127×#1863C2semidirect
10. C127×#1862C2semidirect
11. C127×#1852C2semidirect
12. C127×#1788C2semidirect
13. C127×#1762C2semidirect
14. C4×#103×C127C2semidirect
15. C127×#1750C2semidirect
33. #449×C127C4semidirect
69. C2×#41×C127C2×C4semidirect
83. C2×SD16×C127C2×C4semidirect
86. C2×D8×C127C2×C4semidirect
92. #121×C127C2×C4semidirect
96. C4×Q8×C127D4semidirect
104. C4×D4×C127D4semidirect
140. #103×C127C2×C4semidirect
145. #102×C127C2×C4semidirect
147. C22⋊C8×C127C2×C4semidirect
394. #21460C127direct (N × H)
405. C2×#520C2×C127semidirect
407. C2×#440C2×C127semidirect
408. C2×C4×D8C2×C127semidirect
409. #2324C2×C127semidirect
410. #1880C2×C127semidirect
411. #1879C2×C127semidirect
412. #1874C2×C127semidirect
413. #1863C2×C127semidirect
414. #1862C2×C127semidirect
415. #1852C2×C127semidirect
416. #1788C2×C127semidirect
417. #1762C2×C127semidirect
418. C4×#103C2×C127semidirect
419. #1750C2×C127semidirect
420. C127#21460direct (N × H)
438. #449C4×C127semidirect
474. C2×#41C2×C4×C127semidirect
488. C2×SD16C2×C4×C127semidirect
491. C2×D8C2×C4×C127semidirect
497. #121C2×C4×C127semidirect
501. C4×Q8D4×C127semidirect
509. C4×D4D4×C127semidirect
545. #103C2×C4×C127semidirect
550. #102C2×C4×C127semidirect
552. C22⋊C8C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#520×C1272
C2×#449×C1272
C2×#440×C1272
C2×C4×D8×C1272
C127×#23242
C127×#18802
C127×#18792
C127×#18742
C127×#18632
C127×#18622
C127×#18522
C127×#17882
C127×#17622
C4×#103×C1272
C127×#17502
#21460127