Finite Group Databasebeta

← C127×#21514 #44585187

Subgroups — C127×#21514 #44585187

Order 32512.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C127C211yesmaximal, characteristic
2C2×#440×C127C211yesmaximal, characteristic
3C2×C4×SD16×C127C211yesmaximal, characteristic
4C127×#2327C211yesmaximal, characteristic, complemented
5C127×#2275C211yesmaximal, characteristic
6C127×#1981C211yesmaximal, characteristic, complemented
7C127×#1949C211yesmaximal, characteristic, complemented
8C127×#1928C211yesmaximal, characteristic, complemented
9C127×#1927C211yesmaximal, characteristic, complemented
10C127×#1877C211yesmaximal, characteristic
11C127×#1877C211yesmaximal, characteristic
12C127×#1804C211yesmaximal, characteristic
13C127×#1768C211yesmaximal, characteristic, complemented
14C127×#1763C211yesmaximal, characteristic, complemented
15C4×#103×C127C211yesmaximal, characteristic, complemented
16C22×SD16×C127C2211yescharacteristic
17C22×SD16×C127C2211yescharacteristic
18C2×C4⋊Q8×C127C2211yescharacteristic
19C2×C4×Q8×C127C2211yescharacteristic
20C2×C4×Q8×C127C2211yescharacteristic
21C2×C4×D4×C127C2211yescharacteristic
22C2×C4×D4×C127C2211yescharacteristic
23C2×C4×D4×C127C2211yescharacteristic
24#461×C127C418yescomplemented
25#440×C127—24no—
26C4×SD16×C127—24no—
27C2×#107×C127C2211yescharacteristic
28C2×#106×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×#103×C127C2211yescharacteristic
32C2×#103×C127C2211yescharacteristic
33C2×#103×C127C2211yescharacteristic
34C2×#103×C127C2211yescharacteristic
35C2×#103×C127C2211yescharacteristic
36C2×#103×C127C2211yescharacteristic
37C2×#102×C127C2211yescharacteristic
38C2×#102×C127C2211yescharacteristic
39C2×#97×C127C2211yescharacteristic
40C2×C4×C8×C127C2211yescharacteristic
41#391×C127C2211yescharacteristic
42#391×C127C2211yescharacteristic
43#387×C127—21no—
44#387×C127—21no—
45#387×C127—21no—
46#387×C127—21no—
47#382×C127C2211yescharacteristic
48C4×C4⋊C4×C127C2211yescharacteristic
49C4×C4⋊C4×C127C2211yescharacteristic
50C4×C4⋊C4×C127C2211yescharacteristic
51C4×C22⋊C4×C127—21no—
52C4×C22⋊C4×C127—21no—
53C4×C22⋊C4×C127—21no—
54#376×C127C2211yescharacteristic
55C2×#95×C127—21no—
56#340×C127C2211yescharacteristic
57#340×C127C2211yescharacteristic
58#340×C127C2211yescharacteristic
59#340×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61#336×C127C2211yescharacteristic
62C22×Q8×C127C2311yescharacteristic
63C22×Q8×C127C2311yescharacteristic
64C22×D4×C127C2311yescharacteristic
65C23×C4×C127—21no—
66C23×C4×C127—21no—
67C23×C4×C127—21no—
68C2×SD16×C127—22no—
69C2×SD16×C127—22no—
70C2×SD16×C127—22no—
71C2×SD16×C127—22no—
72C2×SD16×C127C2×C414yes—
73C2×SD16×C127C2×C414yes—
74C22×C8×C127C2311yescharacteristic
75C22×C8×C127C2311yescharacteristic
76C22×C8×C127C2311yescharacteristic
77C22×C8×C127C2311yescharacteristic
78C4⋊Q8×C127—22no—
79C4⋊Q8×C127C2×C414yescomplemented
80C4×Q8×C127—22no—
81C4×Q8×C127—22no—
82C4×Q8×C127—22no—
83C4×Q8×C127—22no—
84C4×D4×C127—22no—
85C4×D4×C127—22no—
86C4×D4×C127—22no—
87C4×D4×C127—22no—
88C4×D4×C127C2×C414yes—
89C4×D4×C127D414yes—
90C2×C4⋊C4×C127—21no—
91C2×C4⋊C4×C127—21no—
92C2×C4⋊C4×C127—21no—
93C2×C4⋊C4×C127—21no—
94C2×C4⋊C4×C127C2311yescharacteristic
95C2×C4⋊C4×C127C2311yescharacteristic
96C2×C4⋊C4×C127C2311yescharacteristic
97C2×C4⋊C4×C127C2311yescharacteristic
98C2×C4⋊C4×C127C2311yescharacteristic
99C2×C22⋊C4×C127—21no—
100C2×C22⋊C4×C127—21no—
101C2×C22⋊C4×C127—21no—
102C2×C42×C127—21no—
103C2×C42×C127—21no—
104C2×C42×C127—21no—
105C2×C42×C127—21no—
106C2×C42×C127—21no—
107C2×C42×C127C2311yescharacteristic
108C2×C42×C127C2311yescharacteristic
109C2×C42×C127C2311yescharacteristic
110#107×C127—22no—
111#106×C127—22no—
112C4⋊C8×C127—22no—
113C4⋊C8×C127C2×C414yescomplemented
114#103×C127—22no—
115#103×C127—22no—
116#103×C127—22no—
117#103×C127—22no—
118#103×C127C2×C414yescomplemented
119#103×C127C2×C414yescomplemented
120#102×C127—22no—
121#102×C127—22no—
122#97×C127—22no—
123C4×C8×C127—22no—
124#95×C127—21no—
125#95×C127—21no—
126#95×C127—21no—
127#95×C127—21no—
128#95×C127—21no—
129#95×C127—21no—
130#95×C127—21no—
131#95×C127—21no—
132#95×C127—21no—
133#95×C127D411yescharacteristic
134#95×C127D411yescharacteristic
135#95×C127D411yescharacteristic
136#95×C127D411yescharacteristic
137C24×C127—21no—
138C2×Q8×C127—21no—
139C2×Q8×C127—21no—
140C2×Q8×C127—21no—
141C2×Q8×C127—21no—
142C2×Q8×C127—21no—
143C2×Q8×C127—21no—
144C2×Q8×C127—21no—
145C2×Q8×C127—21no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127C22×C412yes—
149C2×Q8×C127C22×C412yes—
150C2×D4×C127—21no—
151C2×D4×C127—21no—
152C2×D4×C127—21no—
153C2×D4×C127C22×C412yes—
154C2×D4×C127C2×D412yes—
155C2×D4×C127#4112yes—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—24no—
162C22×C4×C127—24no—
163C22×C4×C127—24no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—81no—
167C22×C4×C127—81no—
168C22×C4×C127—81no—
169C22×C4×C127—81no—
170C22×C4×C127—81no—
171C22×C4×C127—81no—
172C22×C4×C127C2×D411yescharacteristic
173C22×C4×C127C2×D411yescharacteristic
174C22×C4×C127C2×D411yescharacteristic
175C22×C4×C127C2×D411yescharacteristic
176C22×C4×C127C2×D411yescharacteristic
177C22×C4×C127C2×D411yescharacteristic
178C22×C4×C127C2411yescharacteristic
179SD16×C127—28no—
180SD16×C127—28no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127—21no—
184C2×C8×C127—21no—
185C2×C8×C127—21no—
186C2×C8×C127—21no—
187C2×C8×C127—21no—
188C2×C8×C127—21no—
189C2×C8×C127—21no—
190C2×C8×C127—21no—
191C2×C8×C127C22×C412yes—
192C2×C8×C127C22×C412yes—
193C4⋊C4×C127—24no—
194C4⋊C4×C127—24no—
195C4⋊C4×C127—21no—
196C4⋊C4×C127—21no—
197C4⋊C4×C127—21no—
198C4⋊C4×C127—21no—
199C4⋊C4×C127—21no—
200C4⋊C4×C127—21no—
201C4⋊C4×C127—21no—
202C4⋊C4×C127—42no—
203C4⋊C4×C127—42no—
204C4⋊C4×C127C22×C412yes—
205C4⋊C4×C127C2×D412yes—
206C4⋊C4×C127#4112yes—
207C22⋊C4×C127—24no—
208C22⋊C4×C127—24no—
209C22⋊C4×C127—24no—
210C42×C127—21no—
211C42×C127—21no—
212C42×C127—42no—
213C42×C127—42no—
214C42×C127—81no—
215C42×C127—81no—
216C42×C127—81no—
217C42×C127C22×C412yes—
218C42×C127C2×D412yes—
219C42×C127#4112yes—
220C42×C127#4112yes—
221C23×C127—22no—
222C23×C127—22no—
223C23×C127—22no—
224C23×C127—41no—
225C23×C127—41no—
226C23×C127—41no—
227C23×C127—41no—
228C23×C127C22×D411yescharacteristic
229Q8×C127—22no—
230Q8×C127—22no—
231Q8×C127—22no—
232Q8×C127—22no—
233Q8×C127—41no—
234Q8×C127—41no—
235Q8×C127—41no—
236Q8×C127—41no—
237D4×C127—22no—
238D4×C127—22no—
239D4×C127—22no—
240D4×C127C4×D414yes—
241C2×C4×C127—21no—
242C2×C4×C127—21no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—22no—
250C2×C4×C127—22no—
251C2×C4×C127—22no—
252C2×C4×C127—22no—
253C2×C4×C127—21no—
254C2×C4×C127—21no—
255C2×C4×C127—22no—
256C2×C4×C127—21no—
257C2×C4×C127—21no—
258C2×C4×C127—21no—
259C2×C4×C127—21no—
260C2×C4×C127—41no—
261C2×C4×C127—41no—
262C2×C4×C127—41no—
263C2×C4×C127—41no—
264C2×C4×C127—41no—
265C2×C4×C127—41no—
266C2×C4×C127—41no—
267C2×C4×C127—41no—
268C2×C4×C127—41no—
269C2×C4×C127—41no—
270C2×C4×C127—41no—
271C2×C4×C127—41no—
272C2×C4×C127—41no—
273C2×C4×C127—41no—
274C2×C4×C127—41no—
275C2×C4×C127—41no—
276C2×C4×C127—84no—
277C2×C4×C127—84no—
278C2×C4×C127—84no—
279C2×C4×C127C4×D412yes—
280C2×C4×C127C4×D412yes—
281C2×C4×C127#12112yes—
282C2×C4×C127#12112yes—
283C2×C4×C127C23×C411yescharacteristic
284C2×C4×C127C22×D411yescharacteristic
285C2×C4×C127C2×#4111yescharacteristic
286C2×C4×C127C2×#4111yescharacteristic
287C2×C4×C127C2×#4111yescharacteristic
288C2×C4×C127C2×#4111yescharacteristic
289C8×C127—22no—
290C8×C127—22no—
291C8×C127—41no—
292C8×C127—41no—
293C22×C127—24no—
294C22×C127—42no—
295C22×C127—42no—
296C22×C127—42no—
297C22×C127—42no—
298C22×C127—42no—
299C22×C127—42no—
300C22×C127C2×C4×D411yescharacteristic
301C22×C127C2×#12111yescharacteristic
302C22×C127#52511yescharacteristic
303C22×C127#57711yescharacteristic
304C22×C127#57711yescharacteristic
305C22×C127#57711yescharacteristic
306C22×C127#57811yescharacteristic
307C4×C127—22no—
308C4×C127—22no—
309C4×C127—22no—
310C4×C127—22no—
311C4×C127—41no—
312C4×C127—41no—
313C4×C127—42no—
314C4×C127—42no—
315C4×C127—42no—
316C4×C127—42no—
317C4×C127—42no—
318C4×C127—81no—
319C4×C127—81no—
320C4×C127C2×C4×D411yescharacteristic
321C4×C127C4×#4111yescharacteristic
322C4×C127#52911yescharacteristic
323C4×C127#53211yescharacteristic
324#21514C12711yesmaximal, characteristic, direct product factor, Sylow
325C2×C127—44no—
326C2×C127C4×#12111yescharacteristic
327C2×C127#294711yescharacteristic
328C2×C127#294911yescharacteristic
329C2×C127#304211yescharacteristic
330C2×C127#304611yescharacteristic
331C2×C127#312011yescharacteristic
332C2×C127#312311yescharacteristic
333C2×#461C2×C12711yescharacteristic
334C2×#440C2×C12711yescharacteristic
335C2×C4×SD16C2×C12711yescharacteristic
336#2327C2×C12711yescharacteristic, complemented
337#2275C2×C12711yescharacteristic
338#1981C2×C12711yescharacteristic, complemented
339#1949C2×C12711yescharacteristic, complemented
340#1928C2×C12711yescharacteristic, complemented
341#1927C2×C12711yescharacteristic, complemented
342#1877C2×C12711yescharacteristic
343#1877C2×C12711yescharacteristic
344#1804C2×C12711yescharacteristic
345#1768C2×C12711yescharacteristic, complemented
346#1763C2×C12711yescharacteristic, complemented
347C4×#103C2×C12711yescharacteristic, complemented
348C127#2151411yescharacteristic, direct product factor, Sylow
349C22×SD16C22×C12711yescharacteristic
350C22×SD16C22×C12711yescharacteristic
351C2×C4⋊Q8C22×C12711yescharacteristic
352C2×C4×Q8C22×C12711yescharacteristic
353C2×C4×Q8C22×C12711yescharacteristic
354C2×C4×D4C22×C12711yescharacteristic
355C2×C4×D4C22×C12711yescharacteristic
356C2×C4×D4C22×C12711yescharacteristic
357#461C4×C12718yescomplemented
358#440—24no—
359C4×SD16—24no—
360C2×#107C22×C12711yescharacteristic
361C2×#106C22×C12711yescharacteristic
362C2×C4⋊C8C22×C12711yescharacteristic
363C2×C4⋊C8C22×C12711yescharacteristic
364C2×#103C22×C12711yescharacteristic
365C2×#103C22×C12711yescharacteristic
366C2×#103C22×C12711yescharacteristic
367C2×#103C22×C12711yescharacteristic
368C2×#103C22×C12711yescharacteristic
369C2×#103C22×C12711yescharacteristic
370C2×#102C22×C12711yescharacteristic
371C2×#102C22×C12711yescharacteristic
372C2×#97C22×C12711yescharacteristic
373C2×C4×C8C22×C12711yescharacteristic
374#391C22×C12711yescharacteristic
375#391C22×C12711yescharacteristic
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#382C22×C12711yescharacteristic
381C4×C4⋊C4C22×C12711yescharacteristic
382C4×C4⋊C4C22×C12711yescharacteristic
383C4×C4⋊C4C22×C12711yescharacteristic
384C4×C22⋊C4—21no—
385C4×C22⋊C4—21no—
386C4×C22⋊C4—21no—
387#376C22×C12711yescharacteristic
388C2×#95—21no—
389#340C22×C12711yescharacteristic
390#340C22×C12711yescharacteristic
391#340C22×C12711yescharacteristic
392#340C22×C12711yescharacteristic
393#336C22×C12711yescharacteristic
394#336C22×C12711yescharacteristic
395C22×Q8C23×C12711yescharacteristic
396C22×Q8C23×C12711yescharacteristic
397C22×D4C23×C12711yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4—21no—
401C2×SD16—22no—
402C2×SD16—22no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16C2×C4×C12714yes—
406C2×SD16C2×C4×C12714yes—
407C22×C8C23×C12711yescharacteristic
408C22×C8C23×C12711yescharacteristic
409C22×C8C23×C12711yescharacteristic
410C22×C8C23×C12711yescharacteristic
411C4⋊Q8—22no—
412C4⋊Q8C2×C4×C12714yescomplemented
413C4×Q8—22no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4C2×C4×C12714yes—
422C4×D4D4×C12714yes—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4C23×C12711yescharacteristic
428C2×C4⋊C4C23×C12711yescharacteristic
429C2×C4⋊C4C23×C12711yescharacteristic
430C2×C4⋊C4C23×C12711yescharacteristic
431C2×C4⋊C4C23×C12711yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42—21no—
440C2×C42C23×C12711yescharacteristic
441C2×C42C23×C12711yescharacteristic
442C2×C42C23×C12711yescharacteristic
443#107—22no—
444#106—22no—
445C4⋊C8—22no—
446C4⋊C8C2×C4×C12714yescomplemented
447#103—22no—
448#103—22no—
449#103—22no—
450#103—22no—
451#103C2×C4×C12714yescomplemented
452#103C2×C4×C12714yescomplemented
453#102—22no—
454#102—22no—
455#97—22no—
456C4×C8—22no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95D4×C12711yescharacteristic
467#95D4×C12711yescharacteristic
468#95D4×C12711yescharacteristic
469#95D4×C12711yescharacteristic
470C24—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8C22×C4×C12712yes—
482C2×Q8C22×C4×C12712yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C22×C4×C12712yes—
487C2×D4C2×D4×C12712yes—
488C2×D4#41×C12712yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4C2×D4×C12711yescharacteristic
506C22×C4C2×D4×C12711yescharacteristic
507C22×C4C2×D4×C12711yescharacteristic
508C22×C4C2×D4×C12711yescharacteristic
509C22×C4C2×D4×C12711yescharacteristic
510C22×C4C2×D4×C12711yescharacteristic
511C22×C4C24×C12711yescharacteristic
512SD16—28no—
513SD16—28no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8C22×C4×C12712yes—
525C2×C8C22×C4×C12712yes—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4C22×C4×C12712yes—
538C4⋊C4C2×D4×C12712yes—
539C4⋊C4#41×C12712yes—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—24no—
543C42—21no—
544C42—21no—
545C42—42no—
546C42—42no—
547C42—81no—
548C42—81no—
549C42—81no—
550C42C22×C4×C12712yes—
551C42C2×D4×C12712yes—
552C42#41×C12712yes—
553C42#41×C12712yes—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C22×D4×C12711yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—22no—
565Q8—22no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4C4×D4×C12714yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4C4×D4×C12712yes—
613C2×C4C4×D4×C12712yes—
614C2×C4#121×C12712yes—
615C2×C4#121×C12712yes—
616C2×C4C23×C4×C12711yescharacteristic
617C2×C4C22×D4×C12711yescharacteristic
618C2×C4C2×#41×C12711yescharacteristic
619C2×C4C2×#41×C12711yescharacteristic
620C2×C4C2×#41×C12711yescharacteristic
621C2×C4C2×#41×C12711yescharacteristic
622C8—22no—
623C8—22no—
624C8—41no—
625C8—41no—
626C22—24no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22C2×C4×D4×C12711yescharacteristic
634C22C2×#121×C12711yescharacteristic
635C22#525×C12711yescharacteristic
636C22#577×C12711yescharacteristic
637C22#577×C12711yescharacteristic
638C22#577×C12711yescharacteristic
639C22#578×C12711yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—42no—
647C4—42no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4C2×C4×D4×C12711yescharacteristic
654C4C4×#41×C12711yescharacteristic
655C4#529×C12711yescharacteristic
656C4#532×C12711yescharacteristic
657C2—44no—
658C2C4×#121×C12711yescharacteristic
659C2C127×#294711yescharacteristic
660C2C127×#294911yescharacteristic
661C2C127×#304211yescharacteristic
662C2C127×#304611yescharacteristic
663C2C127×#312011yescharacteristic
664C2C127×#312311yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×D4×C127C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ #376×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#2327C2semidirect
6. C127×#1981C2semidirect
7. C127×#1949C2semidirect
8. C127×#1928C2semidirect
9. C127×#1927C2semidirect
13. C127×#1768C2semidirect
14. C127×#1763C2semidirect
15. C4×#103×C127C2semidirect
24. #461×C127C4semidirect
79. C4⋊Q8×C127C2×C4semidirect
113. C4⋊C8×C127C2×C4semidirect
118. #103×C127C2×C4semidirect
119. #103×C127C2×C4semidirect
324. #21514C127direct (N × H)
336. #2327C2×C127semidirect
338. #1981C2×C127semidirect
339. #1949C2×C127semidirect
340. #1928C2×C127semidirect
341. #1927C2×C127semidirect
345. #1768C2×C127semidirect
346. #1763C2×C127semidirect
347. C4×#103C2×C127semidirect
348. C127#21514direct (N × H)
357. #461C4×C127semidirect
412. C4⋊Q8C2×C4×C127semidirect
446. C4⋊C8C2×C4×C127semidirect
451. #103C2×C4×C127semidirect
452. #103C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1272
C2×#440×C1272
C2×C4×SD16×C1272
C127×#23272
C127×#22752
C127×#19812
C127×#19492
C127×#19282
C127×#19272
C127×#18772
C127×#18042
C127×#17682
C127×#17632
C4×#103×C1272
#21514127