Finite Group Databasebeta

← C127×#21468 #44585141

Subgroups — C127×#21468 #44585141

Order 32512.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#568×C127C211yesmaximal, characteristic, complemented
2C127×#3002C211yesmaximal, characteristic
3C2×#444×C127C211yesmaximal, characteristic, complemented
4C2×#443×C127C211yesmaximal, characteristic, complemented
5C127×#2930C211yesmaximal, characteristic, complemented
6C127×#1876C211yesmaximal, characteristic, complemented
7C127×#1876C211yesmaximal, characteristic, complemented
8C127×#1871C211yesmaximal, characteristic, complemented
9C127×#1866C211yesmaximal, characteristic, complemented
10C127×#1866C211yesmaximal, characteristic, complemented
11C127×#1855C211yesmaximal, characteristic, complemented
12C127×#1789C211yesmaximal, characteristic, complemented
13C127×#1765C211yesmaximal, characteristic, complemented
14C127×#1764C211yesmaximal, characteristic, complemented
15C127×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C127C2211yescharacteristic
17C2×#135×C127C2211yescharacteristic
18C2×#135×C127C2211yescharacteristic
19#568×C127—24no—
20#568×C127—24no—
21C2×#131×C127—21no—
22C2×#131×C127—21no—
23C2×#131×C127C2211yescharacteristic
24C2×#131×C127C2211yescharacteristic
25C2×#131×C127C2211yescharacteristic
26C2×#131×C127C2211yescharacteristic
27C2×#131×C127C2211yescharacteristic, complemented
28C22×M16×C127—21no—
29C22×M16×C127—21no—
30C22×M16×C127C2211yescharacteristic
31C22×M16×C127C2211yescharacteristic
32#525×C127C2211yescharacteristic
33#452×C127C411yescharacteristic, complemented
34#452×C127C411yescharacteristic, complemented
35#451×C127C411yescharacteristic, complemented
36#450×C127C411yescharacteristic, complemented
37#449×C127C411yescharacteristic, complemented
38#449×C127C411yescharacteristic, complemented
39#448×C127C411yescharacteristic, complemented
40#447×C127C411yescharacteristic, complemented
41#444×C127—24no—
42#443×C127—24no—
43#436×C127—21no—
44#436×C127—21no—
45#435×C127—21no—
46#435×C127—21no—
47C2×#108×C127C2211yescharacteristic, complemented
48C2×#108×C127C2211yescharacteristic, complemented
49#424×C127C2211yescharacteristic, complemented
50C2×#104×C127C2211yescharacteristic
51C2×#104×C127C2211yescharacteristic
52C2×#104×C127C2211yescharacteristic
53C2×#104×C127C2211yescharacteristic
54C2×#104×C127C2211yescharacteristic, complemented
55C2×#104×C127C2211yescharacteristic, complemented
56#416×C127C2211yescharacteristic
57#416×C127C2211yescharacteristic
58#408×C127C2211yescharacteristic, complemented
59#407×C127C2211yescharacteristic
60C2×C22⋊C8×C127C2211yescharacteristic
61#405×C127C2211yescharacteristic, complemented
62C2×#97×C127C2211yescharacteristic, complemented
63C2×C4×C8×C127C2211yescharacteristic, complemented
64C4×C22⋊C4×C127C2211yescharacteristic
65#341×C127C2211yescharacteristic, complemented
66#341×C127C2211yescharacteristic, complemented
67#339×C127C2211yescharacteristic, complemented
68#339×C127C2211yescharacteristic, complemented
69#336×C127C2211yescharacteristic, complemented
70#336×C127C2211yescharacteristic, complemented
71C2×#41×C127—22no—
72C2×#41×C127—22no—
73C2×#41×C127—22no—
74C2×#41×C127—22no—
75C2×#41×C127—21no—
76C2×#41×C127—21no—
77C2×#41×C127C2×C411yescharacteristic
78C2×#41×C127C2×C411yescharacteristic
79C2×#41×C127C2311yescharacteristic
80C2×#41×C127C2311yescharacteristic
81C2×#41×C127C2311yescharacteristic
82C22×Q8×C127C2×C411yescharacteristic
83C22×D4×C127—21no—
84C22×D4×C127C2×C411yescharacteristic
85C23×C4×C127—21no—
86C23×C4×C127C2311yescharacteristic
87#135×C127—22no—
88#135×C127—22no—
89#135×C127—22no—
90#135×C127—22no—
91C2×Q16×C127C2×C411yescharacteristic
92C2×Q16×C127C2×C411yescharacteristic
93C2×SD16×C127C2×C411yescharacteristic
94C2×SD16×C127C2×C411yescharacteristic
95C2×SD16×C127C2×C411yescharacteristic
96C2×SD16×C127C2×C411yescharacteristic
97C2×D8×C127C2×C411yescharacteristic
98C2×D8×C127C2×C411yescharacteristic
99#131×C127—28no—
100#131×C127—28no—
101#131×C127—22no—
102#131×C127—22no—
103#131×C127—22no—
104#131×C127—22no—
105#131×C127—22no—
106#131×C127—22no—
107#131×C127—22no—
108#131×C127—22no—
109#131×C127D414yescomplemented
110#131×C127D414yescomplemented
111C2×M16×C127—28no—
112C2×M16×C127—28no—
113C2×M16×C127—21no—
114C2×M16×C127—22no—
115C2×M16×C127—22no—
116C2×M16×C127—21no—
117C2×M16×C127—21no—
118C2×M16×C127—21no—
119C2×M16×C127—21no—
120C2×M16×C127—22no—
121C2×M16×C127—22no—
122C2×M16×C127—21no—
123C2×M16×C127D411yescharacteristic
124C2×M16×C127D411yescharacteristic
125C2×M16×C127D411yescharacteristic
126C2×M16×C127D411yescharacteristic
127C2×M16×C127C2311yescharacteristic
128C2×M16×C127C2311yescharacteristic
129C2×M16×C127C2311yescharacteristic
130C2×M16×C127C2311yescharacteristic
131C22×C8×C127—21no—
132C22×C8×C127—21no—
133C22×C8×C127—21no—
134C22×C8×C127—21no—
135C22×C8×C127—21no—
136C22×C8×C127—21no—
137C22×C8×C127C2311yescharacteristic
138C22×C8×C127C2311yescharacteristic
139C22×C8×C127C2311yescharacteristic
140C22×C8×C127C2311yescharacteristic
141#123×C127—21no—
142C22⋊Q8×C127C2×C411yescharacteristic
143C22⋊Q8×C127C2×C411yescharacteristic
144#121×C127C2×C411yescharacteristic
145#121×C127C2×C411yescharacteristic
146#120×C127—21no—
147C4×D4×C127—21no—
148C4×D4×C127—21no—
149#117×C127C2311yescharacteristic
150C2×C22⋊C4×C127—21no—
151C2×C42×C127C2311yescharacteristic
152C2×C42×C127C2311yescharacteristic
153#108×C127—22no—
154#108×C127—22no—
155C4⋊C8×C127—21no—
156C4⋊C8×C127—21no—
157#104×C127—22no—
158#104×C127—22no—
159#104×C127—22no—
160#104×C127—22no—
161#104×C127—22no—
162#104×C127—22no—
163#103×C127C2×C411yescharacteristic
164#103×C127C2×C411yescharacteristic
165#103×C127C2×C411yescharacteristic
166#103×C127C2×C411yescharacteristic
167#102×C127C2×C411yescharacteristic
168#102×C127C2×C411yescharacteristic
169#102×C127C2×C411yescharacteristic
170#102×C127C2×C411yescharacteristic
171C22⋊C8×C127—21no—
172C22⋊C8×C127—21no—
173C22⋊C8×C127—21no—
174C22⋊C8×C127—21no—
175C22⋊C8×C127C2×C411yescharacteristic
176C22⋊C8×C127C2×C411yescharacteristic
177C22⋊C8×C127C2×C411yescharacteristic
178C22⋊C8×C127C2×C411yescharacteristic
179#97×C127—22no—
180#97×C127—21no—
181C4×C8×C127—22no—
182C4×C8×C127—21no—
183#95×C127—21no—
184C24×C127—21no—
185C24×C127#4111yescharacteristic
186#41×C127—24no—
187#41×C127—24no—
188#41×C127—24no—
189#41×C127—24no—
190#41×C127—22no—
191#41×C127—22no—
192#41×C127—22no—
193#41×C127—22no—
194#41×C127—21no—
195#41×C127—21no—
196#41×C127—21no—
197#41×C127—21no—
198#41×C127—21no—
199#41×C127—21no—
200#41×C127—21no—
201#41×C127—21no—
202#41×C127C2×D412yes—
203#41×C127C2×D412yes—
204#41×C127#4112yes—
205#41×C127#4112yes—
206C2×Q8×C127—22no—
207C2×Q8×C127—22no—
208C2×Q8×C127—21no—
209C2×Q8×C127C22×C411yescharacteristic
210C2×Q8×C127C22×C411yescharacteristic
211C2×Q8×C127C22×C411yescharacteristic
212C2×D4×C127—24no—
213C2×D4×C127—24no—
214C2×D4×C127—21no—
215C2×D4×C127—21no—
216C2×D4×C127—21no—
217C2×D4×C127—21no—
218C2×D4×C127—22no—
219C2×D4×C127—22no—
220C2×D4×C127—21no—
221C2×D4×C127—21no—
222C2×D4×C127—21no—
223C2×D4×C127—21no—
224C2×D4×C127C22×C411yescharacteristic
225C2×D4×C127C22×C411yescharacteristic
226C2×D4×C127C22×C411yescharacteristic
227C22×C4×C127—24no—
228C22×C4×C127—24no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127C22×C411yescharacteristic
242C22×C4×C127C22×C411yescharacteristic
243C22×C4×C127C2×D411yescharacteristic
244C22×C4×C127C2×D411yescharacteristic
245C22×C4×C127#4111yescharacteristic
246C22×C4×C127C2411yescharacteristic
247Q16×C127—22no—
248Q16×C127—22no—
249SD16×C127—22no—
250SD16×C127—22no—
251SD16×C127—22no—
252SD16×C127—22no—
253D8×C127—22no—
254D8×C127—22no—
255M16×C127—24no—
256M16×C127—24no—
257M16×C127—24no—
258M16×C127—21no—
259M16×C127—21no—
260M16×C127—22no—
261M16×C127—22no—
262M16×C127—24no—
263M16×C127—24no—
264M16×C127—22no—
265M16×C127—22no—
266M16×C127—21no—
267M16×C127—21no—
268M16×C127—21no—
269M16×C127—21no—
270M16×C127—42no—
271M16×C127C2×D412yes—
272M16×C127C2×D412yes—
273C2×C8×C127—24no—
274C2×C8×C127—24no—
275C2×C8×C127—24no—
276C2×C8×C127—21no—
277C2×C8×C127—21no—
278C2×C8×C127—21no—
279C2×C8×C127—21no—
280C2×C8×C127—21no—
281C2×C8×C127—21no—
282C2×C8×C127—21no—
283C2×C8×C127—21no—
284C2×C8×C127—24no—
285C2×C8×C127—24no—
286C2×C8×C127—21no—
287C2×C8×C127—21no—
288C2×C8×C127—42no—
289C2×C8×C127C22×C411yescharacteristic
290C2×C8×C127C22×C411yescharacteristic
291C2×C8×C127C22×C411yescharacteristic
292C2×C8×C127C22×C411yescharacteristic
293C2×C8×C127C2×D411yescharacteristic
294C2×C8×C127C2×D411yescharacteristic
295C2×C8×C127C2×D412yes—
296C2×C8×C127C2×D412yes—
297C2×C8×C127C2×D411yescharacteristic
298C2×C8×C127C2×D411yescharacteristic
299C4⋊C4×C127—21no—
300C4⋊C4×C127—21no—
301C4⋊C4×C127C22×C411yescharacteristic
302C4⋊C4×C127C22×C411yescharacteristic
303C22⋊C4×C127—21no—
304C22⋊C4×C127—21no—
305C22⋊C4×C127—21no—
306C22⋊C4×C127—21no—
307C22⋊C4×C127—21no—
308C22⋊C4×C127—42no—
309C42×C127—21no—
310C42×C127—21no—
311C42×C127—21no—
312C42×C127—21no—
313C42×C127—21no—
314C23×C127—24no—
315C23×C127—21no—
316C23×C127—21no—
317C23×C127—21no—
318C23×C127—21no—
319C23×C127—21no—
320C23×C127—41no—
321C23×C127—41no—
322C23×C127—81no—
323C23×C127—81no—
324C23×C127C4×D411yescharacteristic
325C23×C127C4×D411yescharacteristic
326C23×C127C2×#4111yescharacteristic
327Q8×C127—24no—
328Q8×C127—21no—
329Q8×C127—21no—
330Q8×C127—21no—
331Q8×C127—21no—
332Q8×C127C4×D412yes—
333Q8×C127C4×D412yes—
334D4×C127—24no—
335D4×C127—24no—
336D4×C127—24no—
337D4×C127—22no—
338D4×C127—22no—
339D4×C127—22no—
340D4×C127—22no—
341D4×C127—21no—
342D4×C127—21no—
343D4×C127—21no—
344D4×C127—21no—
345D4×C127—41no—
346D4×C127—41no—
347D4×C127—81no—
348D4×C127—81no—
349D4×C127C4×D412yes—
350D4×C127C4×D412yes—
351C2×C4×C127—24no—
352C2×C4×C127—24no—
353C2×C4×C127—24no—
354C2×C4×C127—21no—
355C2×C4×C127—21no—
356C2×C4×C127—21no—
357C2×C4×C127—21no—
358C2×C4×C127—21no—
359C2×C4×C127—21no—
360C2×C4×C127—21no—
361C2×C4×C127—21no—
362C2×C4×C127—22no—
363C2×C4×C127—22no—
364C2×C4×C127—21no—
365C2×C4×C127—21no—
366C2×C4×C127—21no—
367C2×C4×C127—22no—
368C2×C4×C127—22no—
369C2×C4×C127—21no—
370C2×C4×C127—22no—
371C2×C4×C127—21no—
372C2×C4×C127—21no—
373C2×C4×C127—21no—
374C2×C4×C127—41no—
375C2×C4×C127—41no—
376C2×C4×C127—41no—
377C2×C4×C127—41no—
378C2×C4×C127—41no—
379C2×C4×C127—41no—
380C2×C4×C127—41no—
381C2×C4×C127C4×D411yescharacteristic
382C2×C4×C127C4×D411yescharacteristic
383C2×C4×C127C23×C411yescharacteristic
384C2×C4×C127C22×D411yescharacteristic
385C2×C4×C127C22×D411yescharacteristic
386C2×C4×C127C22×D411yescharacteristic
387C2×C4×C127C2×#4111yescharacteristic
388C2×C4×C127C2×#4111yescharacteristic
389C8×C127—21no—
390C8×C127—21no—
391C8×C127—21no—
392C8×C127—21no—
393C8×C127—22no—
394C8×C127—22no—
395C8×C127—21no—
396C8×C127—21no—
397C8×C127—41no—
398C8×C127—41no—
399C8×C127#12012yes—
400C8×C127#12012yes—
401C22×C127—21no—
402C22×C127—21no—
403C22×C127—21no—
404C22×C127—21no—
405C22×C127—21no—
406C22×C127—21no—
407C22×C127—21no—
408C22×C127—21no—
409C22×C127—22no—
410C22×C127—22no—
411C22×C127—41no—
412C22×C127—41no—
413C22×C127—41no—
414C22×C127—41no—
415C22×C127—41no—
416C22×C127—41no—
417C22×C127—41no—
418C22×C127—81no—
419C22×C127—81no—
420C22×C127—84no—
421C22×C127C2×C4×D411yescharacteristic
422C22×C127#52511yescharacteristic
423C22×C127#52511yescharacteristic
424C4×C127—21no—
425C4×C127—22no—
426C4×C127—22no—
427C4×C127—21no—
428C4×C127—42no—
429C4×C127—41no—
430C4×C127—41no—
431C4×C127—41no—
432C4×C127—81no—
433C4×C127C2×C4×D411yescharacteristic
434C4×C127C2×C4×D411yescharacteristic
435C4×C127C2×#12011yescharacteristic
436C4×C127#52511yescharacteristic
437#21468C12711yesmaximal, characteristic, direct product factor, Sylow
438C2×C127—21no—
439C2×C127—21no—
440C2×C127—41no—
441C2×C127—41no—
442C2×C127—42no—
443C2×C127—42no—
444C2×C127—81no—
445C2×C127C4×#12011yescharacteristic
446C2×C127#295611yescharacteristic
447C2×C127#295711yescharacteristic
448C2×#568C2×C12711yescharacteristic, complemented
449#3002C2×C12711yescharacteristic
450C2×#444C2×C12711yescharacteristic, complemented
451C2×#443C2×C12711yescharacteristic, complemented
452#2930C2×C12711yescharacteristic, complemented
453#1876C2×C12711yescharacteristic, complemented
454#1876C2×C12711yescharacteristic, complemented
455#1871C2×C12711yescharacteristic, complemented
456#1866C2×C12711yescharacteristic, complemented
457#1866C2×C12711yescharacteristic, complemented
458#1855C2×C12711yescharacteristic, complemented
459#1789C2×C12711yescharacteristic, complemented
460#1765C2×C12711yescharacteristic, complemented
461#1764C2×C12711yescharacteristic, complemented
462#1753C2×C12711yescharacteristic, complemented
463C127#2146811yescharacteristic, direct product factor, Sylow
464C22×#41C22×C12711yescharacteristic
465C2×#135C22×C12711yescharacteristic
466C2×#135C22×C12711yescharacteristic
467#568—24no—
468#568—24no—
469C2×#131—21no—
470C2×#131—21no—
471C2×#131C22×C12711yescharacteristic
472C2×#131C22×C12711yescharacteristic
473C2×#131C22×C12711yescharacteristic
474C2×#131C22×C12711yescharacteristic
475C2×#131C22×C12711yescharacteristic, complemented
476C22×M16—21no—
477C22×M16—21no—
478C22×M16C22×C12711yescharacteristic
479C22×M16C22×C12711yescharacteristic
480#525C22×C12711yescharacteristic
481#452C4×C12711yescharacteristic, complemented
482#452C4×C12711yescharacteristic, complemented
483#451C4×C12711yescharacteristic, complemented
484#450C4×C12711yescharacteristic, complemented
485#449C4×C12711yescharacteristic, complemented
486#449C4×C12711yescharacteristic, complemented
487#448C4×C12711yescharacteristic, complemented
488#447C4×C12711yescharacteristic, complemented
489#444—24no—
490#443—24no—
491#436—21no—
492#436—21no—
493#435—21no—
494#435—21no—
495C2×#108C22×C12711yescharacteristic, complemented
496C2×#108C22×C12711yescharacteristic, complemented
497#424C22×C12711yescharacteristic, complemented
498C2×#104C22×C12711yescharacteristic
499C2×#104C22×C12711yescharacteristic
500C2×#104C22×C12711yescharacteristic
501C2×#104C22×C12711yescharacteristic
502C2×#104C22×C12711yescharacteristic, complemented
503C2×#104C22×C12711yescharacteristic, complemented
504#416C22×C12711yescharacteristic
505#416C22×C12711yescharacteristic
506#408C22×C12711yescharacteristic, complemented
507#407C22×C12711yescharacteristic
508C2×C22⋊C8C22×C12711yescharacteristic
509#405C22×C12711yescharacteristic, complemented
510C2×#97C22×C12711yescharacteristic, complemented
511C2×C4×C8C22×C12711yescharacteristic, complemented
512C4×C22⋊C4C22×C12711yescharacteristic
513#341C22×C12711yescharacteristic, complemented
514#341C22×C12711yescharacteristic, complemented
515#339C22×C12711yescharacteristic, complemented
516#339C22×C12711yescharacteristic, complemented
517#336C22×C12711yescharacteristic, complemented
518#336C22×C12711yescharacteristic, complemented
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—21no—
524C2×#41—21no—
525C2×#41C2×C4×C12711yescharacteristic
526C2×#41C2×C4×C12711yescharacteristic
527C2×#41C23×C12711yescharacteristic
528C2×#41C23×C12711yescharacteristic
529C2×#41C23×C12711yescharacteristic
530C22×Q8C2×C4×C12711yescharacteristic
531C22×D4—21no—
532C22×D4C2×C4×C12711yescharacteristic
533C23×C4—21no—
534C23×C4C23×C12711yescharacteristic
535#135—22no—
536#135—22no—
537#135—22no—
538#135—22no—
539C2×Q16C2×C4×C12711yescharacteristic
540C2×Q16C2×C4×C12711yescharacteristic
541C2×SD16C2×C4×C12711yescharacteristic
542C2×SD16C2×C4×C12711yescharacteristic
543C2×SD16C2×C4×C12711yescharacteristic
544C2×SD16C2×C4×C12711yescharacteristic
545C2×D8C2×C4×C12711yescharacteristic
546C2×D8C2×C4×C12711yescharacteristic
547#131—28no—
548#131—28no—
549#131—22no—
550#131—22no—
551#131—22no—
552#131—22no—
553#131—22no—
554#131—22no—
555#131—22no—
556#131—22no—
557#131D4×C12714yescomplemented
558#131D4×C12714yescomplemented
559C2×M16—28no—
560C2×M16—28no—
561C2×M16—21no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—21no—
565C2×M16—21no—
566C2×M16—21no—
567C2×M16—21no—
568C2×M16—22no—
569C2×M16—22no—
570C2×M16—21no—
571C2×M16D4×C12711yescharacteristic
572C2×M16D4×C12711yescharacteristic
573C2×M16D4×C12711yescharacteristic
574C2×M16D4×C12711yescharacteristic
575C2×M16C23×C12711yescharacteristic
576C2×M16C23×C12711yescharacteristic
577C2×M16C23×C12711yescharacteristic
578C2×M16C23×C12711yescharacteristic
579C22×C8—21no—
580C22×C8—21no—
581C22×C8—21no—
582C22×C8—21no—
583C22×C8—21no—
584C22×C8—21no—
585C22×C8C23×C12711yescharacteristic
586C22×C8C23×C12711yescharacteristic
587C22×C8C23×C12711yescharacteristic
588C22×C8C23×C12711yescharacteristic
589#123—21no—
590C22⋊Q8C2×C4×C12711yescharacteristic
591C22⋊Q8C2×C4×C12711yescharacteristic
592#121C2×C4×C12711yescharacteristic
593#121C2×C4×C12711yescharacteristic
594#120—21no—
595C4×D4—21no—
596C4×D4—21no—
597#117C23×C12711yescharacteristic
598C2×C22⋊C4—21no—
599C2×C42C23×C12711yescharacteristic
600C2×C42C23×C12711yescharacteristic
601#108—22no—
602#108—22no—
603C4⋊C8—21no—
604C4⋊C8—21no—
605#104—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#103C2×C4×C12711yescharacteristic
612#103C2×C4×C12711yescharacteristic
613#103C2×C4×C12711yescharacteristic
614#103C2×C4×C12711yescharacteristic
615#102C2×C4×C12711yescharacteristic
616#102C2×C4×C12711yescharacteristic
617#102C2×C4×C12711yescharacteristic
618#102C2×C4×C12711yescharacteristic
619C22⋊C8—21no—
620C22⋊C8—21no—
621C22⋊C8—21no—
622C22⋊C8—21no—
623C22⋊C8C2×C4×C12711yescharacteristic
624C22⋊C8C2×C4×C12711yescharacteristic
625C22⋊C8C2×C4×C12711yescharacteristic
626C22⋊C8C2×C4×C12711yescharacteristic
627#97—22no—
628#97—21no—
629C4×C8—22no—
630C4×C8—21no—
631#95—21no—
632C24—21no—
633C24#41×C12711yescharacteristic
634#41—24no—
635#41—24no—
636#41—24no—
637#41—24no—
638#41—22no—
639#41—22no—
640#41—22no—
641#41—22no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—21no—
647#41—21no—
648#41—21no—
649#41—21no—
650#41C2×D4×C12712yes—
651#41C2×D4×C12712yes—
652#41#41×C12712yes—
653#41#41×C12712yes—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8C22×C4×C12711yescharacteristic
658C2×Q8C22×C4×C12711yescharacteristic
659C2×Q8C22×C4×C12711yescharacteristic
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4C22×C4×C12711yescharacteristic
673C2×D4C22×C4×C12711yescharacteristic
674C2×D4C22×C4×C12711yescharacteristic
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4C22×C4×C12711yescharacteristic
690C22×C4C22×C4×C12711yescharacteristic
691C22×C4C2×D4×C12711yescharacteristic
692C22×C4C2×D4×C12711yescharacteristic
693C22×C4#41×C12711yescharacteristic
694C22×C4C24×C12711yescharacteristic
695Q16—22no—
696Q16—22no—
697SD16—22no—
698SD16—22no—
699SD16—22no—
700SD16—22no—
701D8—22no—
702D8—22no—
703M16—24no—
704M16—24no—
705M16—24no—
706M16—21no—
707M16—21no—
708M16—22no—
709M16—22no—
710M16—24no—
711M16—24no—
712M16—22no—
713M16—22no—
714M16—21no—
715M16—21no—
716M16—21no—
717M16—21no—
718M16—42no—
719M16C2×D4×C12712yes—
720M16C2×D4×C12712yes—
721C2×C8—24no—
722C2×C8—24no—
723C2×C8—24no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8—24no—
733C2×C8—24no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—42no—
737C2×C8C22×C4×C12711yescharacteristic
738C2×C8C22×C4×C12711yescharacteristic
739C2×C8C22×C4×C12711yescharacteristic
740C2×C8C22×C4×C12711yescharacteristic
741C2×C8C2×D4×C12711yescharacteristic
742C2×C8C2×D4×C12711yescharacteristic
743C2×C8C2×D4×C12711yescharacteristic
744C2×C8C2×D4×C12712yes—
745C2×C8C2×D4×C12711yescharacteristic
746C2×C8C2×D4×C12712yes—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4C22×C4×C12711yescharacteristic
750C4⋊C4C22×C4×C12711yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—21no—
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—41no—
769C23—41no—
770C23—81no—
771C23—81no—
772C23C4×D4×C12711yescharacteristic
773C23C4×D4×C12711yescharacteristic
774C23C2×#41×C12711yescharacteristic
775Q8—24no—
776Q8—21no—
777Q8—21no—
778Q8—21no—
779Q8—21no—
780Q8C4×D4×C12712yes—
781Q8C4×D4×C12712yes—
782D4—24no—
783D4—24no—
784D4—24no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—41no—
794D4—41no—
795D4—81no—
796D4—81no—
797D4C4×D4×C12712yes—
798D4C4×D4×C12712yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4C4×D4×C12711yescharacteristic
830C2×C4C4×D4×C12711yescharacteristic
831C2×C4C23×C4×C12711yescharacteristic
832C2×C4C22×D4×C12711yescharacteristic
833C2×C4C22×D4×C12711yescharacteristic
834C2×C4C22×D4×C12711yescharacteristic
835C2×C4C2×#41×C12711yescharacteristic
836C2×C4C2×#41×C12711yescharacteristic
837C8—21no—
838C8—21no—
839C8—21no—
840C8—21no—
841C8—22no—
842C8—22no—
843C8—21no—
844C8—21no—
845C8—41no—
846C8—41no—
847C8#120×C12712yes—
848C8#120×C12712yes—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—84no—
869C22C2×C4×D4×C12711yescharacteristic
870C22#525×C12711yescharacteristic
871C22#525×C12711yescharacteristic
872C4—21no—
873C4—22no—
874C4—22no—
875C4—21no—
876C4—42no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—81no—
881C4C2×C4×D4×C12711yescharacteristic
882C4C2×C4×D4×C12711yescharacteristic
883C4C2×#120×C12711yescharacteristic
884C4#525×C12711yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—42no—
890C2—42no—
891C2—81no—
892C2C4×#120×C12711yescharacteristic
893C2C127×#295611yescharacteristic
894C2C127×#295711yescharacteristic
subgroupG/H
centerC2×C4×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C2×C4×D4
prime radicalC127×#3002C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#568×C127C2semidirect
3. C2×#444×C127C2semidirect
4. C2×#443×C127C2semidirect
5. C127×#2930C2semidirect
6. C127×#1876C2semidirect
7. C127×#1876C2semidirect
8. C127×#1871C2semidirect
9. C127×#1866C2semidirect
10. C127×#1866C2semidirect
11. C127×#1855C2semidirect
12. C127×#1789C2semidirect
13. C127×#1765C2semidirect
14. C127×#1764C2semidirect
15. C127×#1753C2semidirect
27. C2×#131×C127C22semidirect
33. #452×C127C4semidirect
34. #452×C127C4semidirect
35. #451×C127C4semidirect
36. #450×C127C4semidirect
37. #449×C127C4semidirect
38. #449×C127C4semidirect
39. #448×C127C4semidirect
40. #447×C127C4semidirect
47. C2×#108×C127C22semidirect
48. C2×#108×C127C22semidirect
49. #424×C127C22semidirect
54. C2×#104×C127C22semidirect
55. C2×#104×C127C22semidirect
58. #408×C127C22semidirect
61. #405×C127C22semidirect
62. C2×#97×C127C22semidirect
63. C2×C4×C8×C127C22semidirect
65. #341×C127C22semidirect
66. #341×C127C22semidirect
67. #339×C127C22semidirect
68. #339×C127C22semidirect
69. #336×C127C22semidirect
70. #336×C127C22semidirect
109. #131×C127D4semidirect
110. #131×C127D4semidirect
437. #21468C127direct (N × H)
448. C2×#568C2×C127semidirect
450. C2×#444C2×C127semidirect
451. C2×#443C2×C127semidirect
452. #2930C2×C127semidirect
453. #1876C2×C127semidirect
454. #1876C2×C127semidirect
455. #1871C2×C127semidirect
456. #1866C2×C127semidirect
457. #1866C2×C127semidirect
458. #1855C2×C127semidirect
459. #1789C2×C127semidirect
460. #1765C2×C127semidirect
461. #1764C2×C127semidirect
462. #1753C2×C127semidirect
463. C127#21468direct (N × H)
475. C2×#131C22×C127semidirect
481. #452C4×C127semidirect
482. #452C4×C127semidirect
483. #451C4×C127semidirect
484. #450C4×C127semidirect
485. #449C4×C127semidirect
486. #449C4×C127semidirect
487. #448C4×C127semidirect
488. #447C4×C127semidirect
495. C2×#108C22×C127semidirect
496. C2×#108C22×C127semidirect
497. #424C22×C127semidirect
502. C2×#104C22×C127semidirect
503. C2×#104C22×C127semidirect
506. #408C22×C127semidirect
509. #405C22×C127semidirect
510. C2×#97C22×C127semidirect
511. C2×C4×C8C22×C127semidirect
513. #341C22×C127semidirect
514. #341C22×C127semidirect
515. #339C22×C127semidirect
516. #339C22×C127semidirect
517. #336C22×C127semidirect
518. #336C22×C127semidirect
557. #131D4×C127semidirect
558. #131D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#568×C1272
C127×#30022
C2×#444×C1272
C2×#443×C1272
C127×#29302
C127×#18762
C127×#18712
C127×#18662
C127×#18552
C127×#17892
C127×#17652
C127×#17642
C127×#17532
#21468127