Finite Group Databasebeta

← C127×#21458 #44585131

Subgroups — C127×#21458 #44585131

Order 32512.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C127C211yesmaximal, characteristic, complemented
2C2×#447×C127C211yesmaximal, characteristic
3C2×#442×C127C211yesmaximal, characteristic, complemented
4C2×C4×D8×C127C211yesmaximal, characteristic, complemented
5C127×#2324C211yesmaximal, characteristic, complemented
6C127×#1879C211yesmaximal, characteristic, complemented
7C127×#1879C211yesmaximal, characteristic, complemented
8C127×#1875C211yesmaximal, characteristic, complemented
9C127×#1864C211yesmaximal, characteristic, complemented
10C127×#1862C211yesmaximal, characteristic, complemented
11C127×#1854C211yesmaximal, characteristic, complemented
12C127×#1786C211yesmaximal, characteristic, complemented
13C127×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C127C211yesmaximal, characteristic, complemented
15C127×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C22×D8×C127C2211yescharacteristic
18C22×D8×C127C2211yescharacteristic
19C2×#121×C127C2211yescharacteristic
20#518×C127—24no—
21#518×C127—24no—
22C2×C4×D4×C127—21no—
23C2×C4×D4×C127—21no—
24C2×C4×D4×C127C2211yescharacteristic
25C2×C4×D4×C127C2211yescharacteristic
26C2×C4×D4×C127C2211yescharacteristic
27C2×C4×D4×C127C2211yescharacteristic
28C2×C4×D4×C127C2211yescharacteristic, complemented
29C2×#117×C127C2211yescharacteristic
30C2×#117×C127C2211yescharacteristic
31C22×C22⋊C4×C127—21no—
32C22×C22⋊C4×C127—21no—
33#447×C127C418yescomplemented
34#442×C127—24no—
35C4×D8×C127—24no—
36C2×#107×C127C2211yescharacteristic, complemented
37C2×#106×C127C2211yescharacteristic, complemented
38C2×#102×C127C2211yescharacteristic
39C2×#102×C127C2211yescharacteristic
40C2×#102×C127C2211yescharacteristic
41C2×#102×C127C2211yescharacteristic
42C2×#102×C127C2211yescharacteristic
43C2×#102×C127C2211yescharacteristic
44C2×#102×C127C2211yescharacteristic, complemented
45C2×#102×C127C2211yescharacteristic, complemented
46C2×C22⋊C8×C127C2211yescharacteristic
47C2×C22⋊C8×C127C2211yescharacteristic
48C2×#97×C127C2211yescharacteristic, complemented
49C2×C4×C8×C127C2211yescharacteristic, complemented
50#390×C127—21no—
51#390×C127C2211yescharacteristic, complemented
52#389×C127C2211yescharacteristic, complemented
53#388×C127—21no—
54#386×C127—21no—
55#385×C127—21no—
56#380×C127C2211yescharacteristic
57C4×C4⋊C4×C127C2211yescharacteristic, complemented
58#340×C127C2211yescharacteristic, complemented
59#340×C127C2211yescharacteristic, complemented
60#340×C127C2211yescharacteristic, complemented
61#340×C127C2211yescharacteristic, complemented
62#336×C127C2211yescharacteristic, complemented
63#336×C127C2211yescharacteristic, complemented
64C25×C127—21no—
65C22×D4×C127—22no—
66C22×D4×C127—22no—
67C22×D4×C127—22no—
68C22×D4×C127—22no—
69C22×D4×C127—21no—
70C22×D4×C127—21no—
71C22×D4×C127—22no—
72C22×D4×C127C2×C414yescomplemented
73C22×D4×C127C2311yescharacteristic
74C22×D4×C127C2311yescharacteristic
75C22×D4×C127C2311yescharacteristic
76C23×C4×C127—21no—
77C23×C4×C127—21no—
78C23×C4×C127—21no—
79C23×C4×C127—21no—
80C23×C4×C127—21no—
81C23×C4×C127C2311yescharacteristic
82C2×D8×C127—22no—
83C2×D8×C127—22no—
84C2×D8×C127—22no—
85C2×D8×C127—22no—
86C2×D8×C127C2×C414yescomplemented
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×D4×C127—28no—
95C4×D4×C127—28no—
96C4×D4×C127—22no—
97C4×D4×C127—22no—
98C4×D4×C127—22no—
99C4×D4×C127—22no—
100C4×D4×C127—22no—
101C4×D4×C127—22no—
102C4×D4×C127—22no—
103C4×D4×C127—22no—
104C4×D4×C127D414yescomplemented
105C4×D4×C127D414yescomplemented
106#117×C127—22no—
107#117×C127—22no—
108#117×C127—22no—
109#117×C127—22no—
110C2×C4⋊C4×C127—21no—
111C2×C4⋊C4×C127D411yescharacteristic
112C2×C4⋊C4×C127D411yescharacteristic
113C2×C4⋊C4×C127C2311yescharacteristic
114C2×C4⋊C4×C127C2311yescharacteristic
115C2×C4⋊C4×C127C2311yescharacteristic
116C2×C4⋊C4×C127C2311yescharacteristic
117C2×C4⋊C4×C127C2311yescharacteristic
118C2×C22⋊C4×C127—28no—
119C2×C22⋊C4×C127—28no—
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×C22⋊C4×C127—21no—
127C2×C22⋊C4×C127—21no—
128C2×C22⋊C4×C127—21no—
129C2×C22⋊C4×C127—21no—
130C2×C22⋊C4×C127D411yescharacteristic
131C2×C22⋊C4×C127D411yescharacteristic
132C2×C42×C127—21no—
133C2×C42×C127—21no—
134C2×C42×C127C2311yescharacteristic
135C2×C42×C127C2311yescharacteristic
136#107×C127—22no—
137#106×C127—22no—
138#102×C127—22no—
139#102×C127—22no—
140#102×C127—22no—
141#102×C127—22no—
142#102×C127—22no—
143#102×C127—22no—
144#102×C127C2×C414yescomplemented
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—24no—
154C24×C127—24no—
155C24×C127—21no—
156C24×C127—21no—
157C24×C127—24no—
158C24×C127—21no—
159C24×C127—81no—
160C24×C127—81no—
161C24×C127—81no—
162C24×C127—81no—
163C24×C127C2×D411yescharacteristic
164C2×D4×C127—24no—
165C2×D4×C127—24no—
166C2×D4×C127—28no—
167C2×D4×C127—28no—
168C2×D4×C127—28no—
169C2×D4×C127—28no—
170C2×D4×C127—24no—
171C2×D4×C127—24no—
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—21no—
180C2×D4×C127—21no—
181C2×D4×C127—21no—
182C2×D4×C127—21no—
183C2×D4×C127—81no—
184C2×D4×C127—81no—
185C2×D4×C127C22×C412yes—
186C2×D4×C127C22×C412yes—
187C2×D4×C127C22×C412yes—
188C2×D4×C127C2×D412yes—
189C2×D4×C127C2×D412yes—
190C2×D4×C127#4112yes—
191C2×D4×C127#4112yes—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—24no—
200C22×C4×C127—24no—
201C22×C4×C127—24no—
202C22×C4×C127—24no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—42no—
206C22×C4×C127—81no—
207C22×C4×C127—81no—
208C22×C4×C127—81no—
209C22×C4×C127—81no—
210C22×C4×C127—81no—
211C22×C4×C127—81no—
212C22×C4×C127—81no—
213C22×C4×C127—81no—
214C22×C4×C127—81no—
215C22×C4×C127—81no—
216C22×C4×C127C22×C412yes—
217C22×C4×C127C2×D411yescharacteristic
218C22×C4×C127C2×D411yescharacteristic
219C22×C4×C127C2×D411yescharacteristic
220C22×C4×C127C2×D411yescharacteristic
221C22×C4×C127C2×D411yescharacteristic
222C22×C4×C127#4112yes—
223C22×C4×C127C2411yescharacteristic
224D8×C127—28no—
225D8×C127—28no—
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×C127—21no—
234C2×C8×C127—21no—
235C2×C8×C127—21no—
236C2×C8×C127C22×C412yes—
237C2×C8×C127C22×C412yes—
238C4⋊C4×C127—22no—
239C4⋊C4×C127—22no—
240C4⋊C4×C127—21no—
241C4⋊C4×C127—21no—
242C4⋊C4×C127—21no—
243C4⋊C4×C127—21no—
244C4⋊C4×C127—21no—
245C4⋊C4×C127—21no—
246C4⋊C4×C127—21no—
247C4⋊C4×C127—81no—
248C4⋊C4×C127C22×C412yes—
249C4⋊C4×C127C2×D412yes—
250C4⋊C4×C127C2×D412yes—
251C22⋊C4×C127—24no—
252C22⋊C4×C127—24no—
253C22⋊C4×C127—24no—
254C22⋊C4×C127—24no—
255C22⋊C4×C127—22no—
256C22⋊C4×C127—22no—
257C22⋊C4×C127—24no—
258C22⋊C4×C127—24no—
259C22⋊C4×C127—42no—
260C22⋊C4×C127—81no—
261C22⋊C4×C127—81no—
262C22⋊C4×C127—81no—
263C42×C127—24no—
264C42×C127—21no—
265C42×C127—21no—
266C42×C127—81no—
267C42×C127C2×D412yes—
268C42×C127C2×D412yes—
269C23×C127—216no—
270C23×C127—22no—
271C23×C127—22no—
272C23×C127—21no—
273C23×C127—22no—
274C23×C127—22no—
275C23×C127—21no—
276C23×C127—22no—
277C23×C127—22no—
278C23×C127—21no—
279C23×C127—21no—
280C23×C127—21no—
281C23×C127—21no—
282C23×C127—22no—
283C23×C127—41no—
284C23×C127—41no—
285C23×C127—41no—
286C23×C127—41no—
287C23×C127—41no—
288C23×C127—41no—
289C23×C127—41no—
290C23×C127—41no—
291C23×C127—41no—
292C23×C127—41no—
293C23×C127—41no—
294C23×C127—41no—
295C23×C127—41no—
296C23×C127—41no—
297C23×C127—84no—
298C23×C127—84no—
299C23×C127—84no—
300C23×C127—84no—
301C23×C127—84no—
302C23×C127—84no—
303C23×C127C4×D412yes—
304C23×C127C22×D411yescharacteristic
305D4×C127—216no—
306D4×C127—22no—
307D4×C127—22no—
308D4×C127—22no—
309D4×C127—22no—
310D4×C127—22no—
311D4×C127—22no—
312D4×C127—22no—
313D4×C127—22no—
314D4×C127—41no—
315D4×C127—41no—
316D4×C127—84no—
317D4×C127C4×D414yes—
318D4×C127C4×D414yes—
319C2×C4×C127—21no—
320C2×C4×C127—21no—
321C2×C4×C127—21no—
322C2×C4×C127—21no—
323C2×C4×C127—21no—
324C2×C4×C127—21no—
325C2×C4×C127—22no—
326C2×C4×C127—22no—
327C2×C4×C127—22no—
328C2×C4×C127—22no—
329C2×C4×C127—22no—
330C2×C4×C127—21no—
331C2×C4×C127—21no—
332C2×C4×C127—22no—
333C2×C4×C127—22no—
334C2×C4×C127—21no—
335C2×C4×C127—21no—
336C2×C4×C127—21no—
337C2×C4×C127—21no—
338C2×C4×C127—41no—
339C2×C4×C127—41no—
340C2×C4×C127—41no—
341C2×C4×C127—41no—
342C2×C4×C127—41no—
343C2×C4×C127—41no—
344C2×C4×C127—41no—
345C2×C4×C127—41no—
346C2×C4×C127—41no—
347C2×C4×C127—41no—
348C2×C4×C127—41no—
349C2×C4×C127—41no—
350C2×C4×C127—84no—
351C2×C4×C127—84no—
352C2×C4×C127—84no—
353C2×C4×C127—84no—
354C2×C4×C127—84no—
355C2×C4×C127C4×D412yes—
356C2×C4×C127#12012yes—
357C2×C4×C127#12012yes—
358C2×C4×C127C23×C411yescharacteristic
359C2×C4×C127C22×D411yescharacteristic
360C2×C4×C127C22×D411yescharacteristic
361C2×C4×C127C2×#4111yescharacteristic
362C2×C4×C127C2×#4111yescharacteristic
363C2×C4×C127C2×#4111yescharacteristic
364C8×C127—22no—
365C8×C127—22no—
366C8×C127—41no—
367C8×C127—41no—
368C22×C127—22no—
369C22×C127—22no—
370C22×C127—22no—
371C22×C127—24no—
372C22×C127—24no—
373C22×C127—41no—
374C22×C127—42no—
375C22×C127—42no—
376C22×C127—41no—
377C22×C127—42no—
378C22×C127—42no—
379C22×C127—42no—
380C22×C127—42no—
381C22×C127—42no—
382C22×C127—42no—
383C22×C127—42no—
384C22×C127—42no—
385C22×C127—41no—
386C22×C127—42no—
387C22×C127—42no—
388C22×C127—41no—
389C22×C127—42no—
390C22×C127—42no—
391C22×C127—42no—
392C22×C127—816no—
393C22×C127—81no—
394C22×C127—81no—
395C22×C127—81no—
396C22×C127—81no—
397C22×C127C2×C4×D411yescharacteristic
398C22×C127C2×#12011yescharacteristic
399C22×C127#52511yescharacteristic
400C22×C127#57611yescharacteristic
401C22×C127#57611yescharacteristic
402C22×C127#57611yescharacteristic
403C22×C127#57711yescharacteristic
404C4×C127—22no—
405C4×C127—22no—
406C4×C127—22no—
407C4×C127—42no—
408C4×C127—41no—
409C4×C127—42no—
410C4×C127—41no—
411C4×C127—42no—
412C4×C127—81no—
413C4×C127—81no—
414C4×C127C2×C4×D411yescharacteristic
415C4×C127C2×C4×D411yescharacteristic
416C4×C127#52511yescharacteristic
417C4×C127#52511yescharacteristic
418#21458C12711yesmaximal, characteristic, direct product factor, Sylow
419C2×C127—42no—
420C2×C127—44no—
421C2×C127—44no—
422C2×C127—82no—
423C2×C127C4×#12011yescharacteristic
424C2×C127#294611yescharacteristic
425C2×C127#294811yescharacteristic
426C2×C127#300811yescharacteristic
427C2×C127#301211yescharacteristic
428C2×C127#311811yescharacteristic
429C2×C127#312211yescharacteristic
430C2×#518C2×C12711yescharacteristic, complemented
431C2×#447C2×C12711yescharacteristic
432C2×#442C2×C12711yescharacteristic, complemented
433C2×C4×D8C2×C12711yescharacteristic, complemented
434#2324C2×C12711yescharacteristic, complemented
435#1879C2×C12711yescharacteristic, complemented
436#1879C2×C12711yescharacteristic, complemented
437#1875C2×C12711yescharacteristic, complemented
438#1864C2×C12711yescharacteristic, complemented
439#1862C2×C12711yescharacteristic, complemented
440#1854C2×C12711yescharacteristic, complemented
441#1786C2×C12711yescharacteristic, complemented
442#1762C2×C12711yescharacteristic, complemented
443C4×#102C2×C12711yescharacteristic, complemented
444#1750C2×C12711yescharacteristic, complemented
445C127#2145811yescharacteristic, direct product factor, Sylow
446C23×D4C22×C12711yescharacteristic
447C22×D8C22×C12711yescharacteristic
448C22×D8C22×C12711yescharacteristic
449C2×#121C22×C12711yescharacteristic
450#518—24no—
451#518—24no—
452C2×C4×D4—21no—
453C2×C4×D4—21no—
454C2×C4×D4C22×C12711yescharacteristic
455C2×C4×D4C22×C12711yescharacteristic
456C2×C4×D4C22×C12711yescharacteristic
457C2×C4×D4C22×C12711yescharacteristic
458C2×C4×D4C22×C12711yescharacteristic, complemented
459C2×#117C22×C12711yescharacteristic
460C2×#117C22×C12711yescharacteristic
461C22×C22⋊C4—21no—
462C22×C22⋊C4—21no—
463#447C4×C12718yescomplemented
464#442—24no—
465C4×D8—24no—
466C2×#107C22×C12711yescharacteristic, complemented
467C2×#106C22×C12711yescharacteristic, complemented
468C2×#102C22×C12711yescharacteristic
469C2×#102C22×C12711yescharacteristic
470C2×#102C22×C12711yescharacteristic
471C2×#102C22×C12711yescharacteristic
472C2×#102C22×C12711yescharacteristic
473C2×#102C22×C12711yescharacteristic
474C2×#102C22×C12711yescharacteristic, complemented
475C2×#102C22×C12711yescharacteristic, complemented
476C2×C22⋊C8C22×C12711yescharacteristic
477C2×C22⋊C8C22×C12711yescharacteristic
478C2×#97C22×C12711yescharacteristic, complemented
479C2×C4×C8C22×C12711yescharacteristic, complemented
480#390—21no—
481#390C22×C12711yescharacteristic, complemented
482#389C22×C12711yescharacteristic, complemented
483#388—21no—
484#386—21no—
485#385—21no—
486#380C22×C12711yescharacteristic
487C4×C4⋊C4C22×C12711yescharacteristic, complemented
488#340C22×C12711yescharacteristic, complemented
489#340C22×C12711yescharacteristic, complemented
490#340C22×C12711yescharacteristic, complemented
491#340C22×C12711yescharacteristic, complemented
492#336C22×C12711yescharacteristic, complemented
493#336C22×C12711yescharacteristic, complemented
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4C2×C4×C12714yescomplemented
503C22×D4C23×C12711yescharacteristic
504C22×D4C23×C12711yescharacteristic
505C22×D4C23×C12711yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C23×C12711yescharacteristic
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8C2×C4×C12714yescomplemented
517C2×D8C2×C4×C12714yescomplemented
518C22×C8C23×C12711yescharacteristic
519C22×C8C23×C12711yescharacteristic
520C22×C8C23×C12711yescharacteristic
521C22×C8C23×C12711yescharacteristic
522#121—22no—
523#121C2×C4×C12714yescomplemented
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4D4×C12714yescomplemented
535C4×D4D4×C12714yescomplemented
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C12711yescharacteristic
542C2×C4⋊C4D4×C12711yescharacteristic
543C2×C4⋊C4C23×C12711yescharacteristic
544C2×C4⋊C4C23×C12711yescharacteristic
545C2×C4⋊C4C23×C12711yescharacteristic
546C2×C4⋊C4C23×C12711yescharacteristic
547C2×C4⋊C4C23×C12711yescharacteristic
548C2×C22⋊C4—28no—
549C2×C22⋊C4—28no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4D4×C12711yescharacteristic
561C2×C22⋊C4D4×C12711yescharacteristic
562C2×C42—21no—
563C2×C42—21no—
564C2×C42C23×C12711yescharacteristic
565C2×C42C23×C12711yescharacteristic
566#107—22no—
567#106—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102C2×C4×C12714yescomplemented
575#102C2×C4×C12714yescomplemented
576C22⋊C8—22no—
577C22⋊C8C2×C4×C12714yescomplemented
578#97—22no—
579C4×C8—22no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—21no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—81no—
593C24C2×D4×C12711yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4C22×C4×C12712yes—
616C2×D4C22×C4×C12712yes—
617C2×D4C22×C4×C12712yes—
618C2×D4C2×D4×C12712yes—
619C2×D4C2×D4×C12712yes—
620C2×D4#41×C12712yes—
621C2×D4#41×C12712yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C22×C4×C12712yes—
647C22×C4C2×D4×C12711yescharacteristic
648C22×C4C2×D4×C12711yescharacteristic
649C22×C4C2×D4×C12711yescharacteristic
650C22×C4C2×D4×C12711yescharacteristic
651C22×C4C2×D4×C12711yescharacteristic
652C22×C4#41×C12712yes—
653C22×C4C24×C12711yescharacteristic
654D8—28no—
655D8—28no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C22×C4×C12712yes—
667C2×C8C22×C4×C12712yes—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—81no—
678C4⋊C4C22×C4×C12712yes—
679C4⋊C4C2×D4×C12712yes—
680C4⋊C4C2×D4×C12712yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—42no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—81no—
697C42C2×D4×C12712yes—
698C42C2×D4×C12712yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23C4×D4×C12712yes—
734C23C22×D4×C12711yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4C4×D4×C12714yes—
748D4C4×D4×C12714yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4C4×D4×C12712yes—
786C2×C4#120×C12712yes—
787C2×C4#120×C12712yes—
788C2×C4C23×C4×C12711yescharacteristic
789C2×C4C22×D4×C12711yescharacteristic
790C2×C4C22×D4×C12711yescharacteristic
791C2×C4C2×#41×C12711yescharacteristic
792C2×C4C2×#41×C12711yescharacteristic
793C2×C4C2×#41×C12711yescharacteristic
794C8—22no—
795C8—22no—
796C8—41no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—24no—
802C22—24no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22C2×C4×D4×C12711yescharacteristic
828C22C2×#120×C12711yescharacteristic
829C22#525×C12711yescharacteristic
830C22#576×C12711yescharacteristic
831C22#576×C12711yescharacteristic
832C22#576×C12711yescharacteristic
833C22#577×C12711yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—42no—
838C4—41no—
839C4—42no—
840C4—41no—
841C4—42no—
842C4—81no—
843C4—81no—
844C4C2×C4×D4×C12711yescharacteristic
845C4C2×C4×D4×C12711yescharacteristic
846C4#525×C12711yescharacteristic
847C4#525×C12711yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—82no—
852C2C4×#120×C12711yescharacteristic
853C2C127×#294611yescharacteristic
854C2C127×#294811yescharacteristic
855C2C127×#300811yescharacteristic
856C2C127×#301211yescharacteristic
857C2C127×#311811yescharacteristic
858C2C127×#312211yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#447×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×#518×C127C2semidirect
3. C2×#442×C127C2semidirect
4. C2×C4×D8×C127C2semidirect
5. C127×#2324C2semidirect
6. C127×#1879C2semidirect
7. C127×#1879C2semidirect
8. C127×#1875C2semidirect
9. C127×#1864C2semidirect
10. C127×#1862C2semidirect
11. C127×#1854C2semidirect
12. C127×#1786C2semidirect
13. C127×#1762C2semidirect
14. C4×#102×C127C2semidirect
15. C127×#1750C2semidirect
28. C2×C4×D4×C127C22semidirect
33. #447×C127C4semidirect
36. C2×#107×C127C22semidirect
37. C2×#106×C127C22semidirect
44. C2×#102×C127C22semidirect
45. C2×#102×C127C22semidirect
48. C2×#97×C127C22semidirect
49. C2×C4×C8×C127C22semidirect
51. #390×C127C22semidirect
52. #389×C127C22semidirect
57. C4×C4⋊C4×C127C22semidirect
58. #340×C127C22semidirect
59. #340×C127C22semidirect
60. #340×C127C22semidirect
61. #340×C127C22semidirect
62. #336×C127C22semidirect
63. #336×C127C22semidirect
72. C22×D4×C127C2×C4semidirect
86. C2×D8×C127C2×C4semidirect
87. C2×D8×C127C2×C4semidirect
93. #121×C127C2×C4semidirect
104. C4×D4×C127D4semidirect
105. C4×D4×C127D4semidirect
144. #102×C127C2×C4semidirect
145. #102×C127C2×C4semidirect
147. C22⋊C8×C127C2×C4semidirect
418. #21458C127direct (N × H)
430. C2×#518C2×C127semidirect
432. C2×#442C2×C127semidirect
433. C2×C4×D8C2×C127semidirect
434. #2324C2×C127semidirect
435. #1879C2×C127semidirect
436. #1879C2×C127semidirect
437. #1875C2×C127semidirect
438. #1864C2×C127semidirect
439. #1862C2×C127semidirect
440. #1854C2×C127semidirect
441. #1786C2×C127semidirect
442. #1762C2×C127semidirect
443. C4×#102C2×C127semidirect
444. #1750C2×C127semidirect
445. C127#21458direct (N × H)
458. C2×C4×D4C22×C127semidirect
463. #447C4×C127semidirect
466. C2×#107C22×C127semidirect
467. C2×#106C22×C127semidirect
474. C2×#102C22×C127semidirect
475. C2×#102C22×C127semidirect
478. C2×#97C22×C127semidirect
479. C2×C4×C8C22×C127semidirect
481. #390C22×C127semidirect
482. #389C22×C127semidirect
487. C4×C4⋊C4C22×C127semidirect
488. #340C22×C127semidirect
489. #340C22×C127semidirect
490. #340C22×C127semidirect
491. #340C22×C127semidirect
492. #336C22×C127semidirect
493. #336C22×C127semidirect
502. C22×D4C2×C4×C127semidirect
516. C2×D8C2×C4×C127semidirect
517. C2×D8C2×C4×C127semidirect
523. #121C2×C4×C127semidirect
534. C4×D4D4×C127semidirect
535. C4×D4D4×C127semidirect
574. #102C2×C4×C127semidirect
575. #102C2×C4×C127semidirect
577. 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×#518×C1272
C2×#447×C1272
C2×#442×C1272
C2×C4×D8×C1272
C127×#23242
C127×#18792
C127×#18752
C127×#18642
C127×#18622
C127×#18542
C127×#17862
C127×#17622
C4×#102×C1272
C127×#17502
#21458127