Finite Group Databasebeta

← C127×#21535 #44585208

Subgroups — C127×#21535 #44585208

Order 32512.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C127C211yesmaximal, characteristic
2C2×C4×SD16×C127C211yesmaximal, characteristic, complemented
3C2×#405×C127C211yesmaximal, characteristic, complemented
4C127×#2324C211yesmaximal, characteristic
5C127×#2323C211yesmaximal, characteristic, complemented
6C127×#1973C211yesmaximal, characteristic, complemented
7C127×#1943C211yesmaximal, characteristic, complemented
8C127×#1934C211yesmaximal, characteristic, complemented
9C127×#1933C211yesmaximal, characteristic, complemented
10C127×#1893C211yesmaximal, characteristic
11C127×#1892C211yesmaximal, characteristic, complemented
12C127×#1809C211yesmaximal, characteristic, complemented
13C4×#107×C127C211yesmaximal, characteristic, complemented
14C127×#1763C211yesmaximal, characteristic, complemented
15C127×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C127C2211yescharacteristic
17C22×M16×C127C2211yescharacteristic
18C23×C8×C127C2211yescharacteristic
19C2×C22⋊Q8×C127C2211yescharacteristic
20C2×#121×C127C2211yescharacteristic
21C2×C4×Q8×C127C2211yescharacteristic
22C2×C4×D4×C127C2211yescharacteristic
23C2×#117×C127C2211yescharacteristic
24#468×C127C418yescomplemented
25C4×SD16×C127—24no—
26C2×#107×C127C2211yescharacteristic
27C2×#107×C127C2211yescharacteristic
28C2×#106×C127C2211yescharacteristic
29C2×#103×C127C2211yescharacteristic
30C2×#103×C127C2211yescharacteristic
31C2×#103×C127C2211yescharacteristic
32C2×#102×C127C2211yescharacteristic
33C2×#102×C127C2211yescharacteristic
34C2×#102×C127C2211yescharacteristic
35#405×C127—24no—
36C2×#97×C127C2211yescharacteristic
37C2×#97×C127C2211yescharacteristic
38C2×C4×C8×C127C2211yescharacteristic
39C2×C4×C8×C127C2211yescharacteristic
40#391×C127C2211yescharacteristic
41#390×C127—21no—
42#390×C127C2211yescharacteristic
43#389×C127—21no—
44#389×C127C2211yescharacteristic
45#389×C127C2211yescharacteristic
46#388×C127—21no—
47#388×C127—21no—
48#388×C127—21no—
49#387×C127—21no—
50#386×C127—21no—
51#385×C127—21no—
52#380×C127C2211yescharacteristic
53#380×C127C2211yescharacteristic
54C4×C4⋊C4×C127C2211yescharacteristic
55C4×C4⋊C4×C127C2211yescharacteristic
56#340×C127C2211yescharacteristic
57#340×C127C2211yescharacteristic
58#340×C127C2211yescharacteristic
59#340×C127C2211yescharacteristic
60#340×C127C2211yescharacteristic
61#340×C127C2211yescharacteristic
62C22×Q8×C127C2311yescharacteristic
63C22×D4×C127—21no—
64C22×D4×C127C2311yescharacteristic
65C23×C4×C127—21no—
66C23×C4×C127C2311yescharacteristic
67C2×SD16×C127—22no—
68C2×SD16×C127—22no—
69C2×SD16×C127C2×C414yes—
70C2×M16×C127—22no—
71C2×M16×C127—22no—
72C2×M16×C127C2×C414yescomplemented
73C22×C8×C127—22no—
74C22×C8×C127—22no—
75C22×C8×C127—22no—
76C22×C8×C127C2311yescharacteristic
77C22×C8×C127C2311yescharacteristic
78C22×C8×C127C2311yescharacteristic
79C22×C8×C127C2311yescharacteristic
80C22⋊Q8×C127—22no—
81C22⋊Q8×C127C2×C414yescomplemented
82#121×C127—22no—
83#121×C127C2×C414yes—
84C4×Q8×C127—22no—
85C4×Q8×C127—22no—
86C4×D4×C127—22no—
87C4×D4×C127—22no—
88#117×C127—22no—
89#117×C127—22no—
90C2×C4⋊C4×C127—21no—
91C2×C4⋊C4×C127—21no—
92C2×C4⋊C4×C127—21no—
93C2×C4⋊C4×C127—21no—
94C2×C4⋊C4×C127D411yescharacteristic
95C2×C4⋊C4×C127D411yescharacteristic
96C2×C4⋊C4×C127C2311yescharacteristic
97C2×C4⋊C4×C127C2311yescharacteristic
98C2×C4⋊C4×C127C2311yescharacteristic
99C2×C4⋊C4×C127C2311yescharacteristic
100C2×C4⋊C4×C127C2311yescharacteristic
101C2×C4⋊C4×C127C2311yescharacteristic
102C2×C22⋊C4×C127—21no—
103C2×C22⋊C4×C127—21no—
104C2×C22⋊C4×C127—21no—
105C2×C22⋊C4×C127—21no—
106C2×C22⋊C4×C127—21no—
107C2×C22⋊C4×C127—21no—
108C2×C22⋊C4×C127—21no—
109C2×C22⋊C4×C127D411yescharacteristic
110C2×C22⋊C4×C127D411yescharacteristic
111C2×C42×C127—21no—
112C2×C42×C127—21no—
113C2×C42×C127—21no—
114C2×C42×C127C2311yescharacteristic
115C2×C42×C127C2311yescharacteristic
116#107×C127—22no—
117#107×C127C2×C414yescomplemented
118#106×C127—22no—
119#103×C127—22no—
120#103×C127—22no—
121#103×C127C2×C414yescomplemented
122#102×C127—22no—
123#102×C127—22no—
124#102×C127C2×C414yes—
125#97×C127—22no—
126#97×C127—22no—
127C4×C8×C127—22no—
128C4×C8×C127D414yescomplemented
129#95×C127—21no—
130#95×C127—21no—
131#95×C127—21no—
132#95×C127—21no—
133#95×C127—21no—
134#95×C127—21no—
135#95×C127—21no—
136#95×C127—21no—
137C24×C127—21no—
138C24×C127C2×D411yescharacteristic
139C2×Q8×C127—21no—
140C2×Q8×C127—21no—
141C2×Q8×C127—21no—
142C2×Q8×C127—21no—
143C2×Q8×C127—21no—
144C2×Q8×C127C22×C412yes—
145C2×D4×C127—24no—
146C2×D4×C127—21no—
147C2×D4×C127—21no—
148C2×D4×C127—21no—
149C2×D4×C127—21no—
150C2×D4×C127—21no—
151C2×D4×C127—81no—
152C2×D4×C127—81no—
153C2×D4×C127C22×C412yes—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—42no—
166C22×C4×C127—81no—
167C22×C4×C127—81no—
168C22×C4×C127C22×C412yes—
169C22×C4×C127C2×D411yescharacteristic
170C22×C4×C127C2×D411yescharacteristic
171C22×C4×C127C2×D411yescharacteristic
172C22×C4×C127C2×D411yescharacteristic
173C22×C4×C127C2×D411yescharacteristic
174C22×C4×C127#4112yes—
175C22×C4×C127C2411yescharacteristic
176SD16×C127—28no—
177M16×C127—28no—
178C2×C8×C127—28no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127—21no—
184C2×C8×C127—21no—
185C2×C8×C127C22×C412yes—
186C2×C8×C127C22×C412yes—
187C2×C8×C127C2×D412yes—
188C2×C8×C127C2×D412yes—
189C2×C8×C127#4112yes—
190C2×C8×C127#4112yes—
191C4⋊C4×C127—24no—
192C4⋊C4×C127—22no—
193C4⋊C4×C127—22no—
194C4⋊C4×C127—21no—
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—21no—
203C4⋊C4×C127—21no—
204C4⋊C4×C127—42no—
205C4⋊C4×C127—81no—
206C4⋊C4×C127—81no—
207C4⋊C4×C127C22×C412yes—
208C4⋊C4×C127C22×C412yes—
209C22⋊C4×C127—24no—
210C22⋊C4×C127—24no—
211C22⋊C4×C127—22no—
212C22⋊C4×C127—22no—
213C22⋊C4×C127—42no—
214C22⋊C4×C127—81no—
215C22⋊C4×C127—81no—
216C22⋊C4×C127—81no—
217C22⋊C4×C127—81no—
218C42×C127—21no—
219C42×C127—21no—
220C42×C127—42no—
221C42×C127—81no—
222C42×C127—81no—
223C42×C127C2×D412yes—
224C42×C127#4112yes—
225C23×C127—21no—
226C23×C127—21no—
227C23×C127—21no—
228C23×C127—21no—
229C23×C127—21no—
230C23×C127—21no—
231C23×C127—22no—
232C23×C127—41no—
233C23×C127—41no—
234C23×C127—41no—
235C23×C127—41no—
236C23×C127—41no—
237C23×C127—41no—
238C23×C127C4×D412yes—
239C23×C127C22×D411yescharacteristic
240Q8×C127—22no—
241Q8×C127—22no—
242Q8×C127—41no—
243Q8×C127—41no—
244D4×C127—22no—
245D4×C127—22no—
246D4×C127—41no—
247D4×C127—41no—
248D4×C127—84no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—21no—
253C2×C4×C127—21no—
254C2×C4×C127—21no—
255C2×C4×C127—22no—
256C2×C4×C127—22no—
257C2×C4×C127—22no—
258C2×C4×C127—22no—
259C2×C4×C127—22no—
260C2×C4×C127—22no—
261C2×C4×C127—22no—
262C2×C4×C127—21no—
263C2×C4×C127—21no—
264C2×C4×C127—21no—
265C2×C4×C127—21no—
266C2×C4×C127—21no—
267C2×C4×C127—21no—
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—41no—
277C2×C4×C127—41no—
278C2×C4×C127—41no—
279C2×C4×C127—41no—
280C2×C4×C127—41no—
281C2×C4×C127—41no—
282C2×C4×C127—41no—
283C2×C4×C127—41no—
284C2×C4×C127—41no—
285C2×C4×C127—41no—
286C2×C4×C127—84no—
287C2×C4×C127C4×D412yes—
288C2×C4×C127#12112yes—
289C2×C4×C127#12112yes—
290C2×C4×C127C23×C411yescharacteristic
291C2×C4×C127C22×D411yescharacteristic
292C2×C4×C127C2×#4111yescharacteristic
293C2×C4×C127C2×#4111yescharacteristic
294C2×C4×C127C2×#4111yescharacteristic
295C2×C4×C127C2×#4111yescharacteristic
296C8×C127—22no—
297C8×C127—22no—
298C8×C127—22no—
299C8×C127C4×D414yes—
300C22×C127—22no—
301C22×C127—22no—
302C22×C127—22no—
303C22×C127—41no—
304C22×C127—41no—
305C22×C127—41no—
306C22×C127—41no—
307C22×C127—42no—
308C22×C127—42no—
309C22×C127—42no—
310C22×C127—81no—
311C22×C127—81no—
312C22×C127—81no—
313C22×C127—81no—
314C22×C127C2×C4×D411yescharacteristic
315C22×C127C2×#12111yescharacteristic
316C22×C127#53211yescharacteristic
317C22×C127#57611yescharacteristic
318C22×C127#57711yescharacteristic
319C22×C127#57711yescharacteristic
320C22×C127#57811yescharacteristic
321C4×C127—22no—
322C4×C127—22no—
323C4×C127—22no—
324C4×C127—42no—
325C4×C127—42no—
326C4×C127—41no—
327C4×C127—41no—
328C4×C127—42no—
329C4×C127—81no—
330C4×C127—81no—
331C4×C127—81no—
332C4×C127—81no—
333C4×C127C2×C4×D411yescharacteristic
334C4×C127C4×#4111yescharacteristic
335C4×C127#52511yescharacteristic
336C4×C127#52911yescharacteristic
337#21535C12711yesmaximal, characteristic, direct product factor, Sylow
338C2×C127—42no—
339C2×C127—82no—
340C2×C127C4×#12111yescharacteristic
341C2×C127#294611yescharacteristic
342C2×C127#294711yescharacteristic
343C2×C127#305711yescharacteristic
344C2×C127#306111yescharacteristic
345C2×C127#317811yescharacteristic
346C2×C127#317911yescharacteristic
347C2×#468C2×C12711yescharacteristic
348C2×C4×SD16C2×C12711yescharacteristic, complemented
349C2×#405C2×C12711yescharacteristic, complemented
350#2324C2×C12711yescharacteristic
351#2323C2×C12711yescharacteristic, complemented
352#1973C2×C12711yescharacteristic, complemented
353#1943C2×C12711yescharacteristic, complemented
354#1934C2×C12711yescharacteristic, complemented
355#1933C2×C12711yescharacteristic, complemented
356#1893C2×C12711yescharacteristic
357#1892C2×C12711yescharacteristic, complemented
358#1809C2×C12711yescharacteristic, complemented
359C4×#107C2×C12711yescharacteristic, complemented
360#1763C2×C12711yescharacteristic, complemented
361#1762C2×C12711yescharacteristic, complemented
362C127#2153511yescharacteristic, direct product factor, Sylow
363C22×SD16C22×C12711yescharacteristic
364C22×M16C22×C12711yescharacteristic
365C23×C8C22×C12711yescharacteristic
366C2×C22⋊Q8C22×C12711yescharacteristic
367C2×#121C22×C12711yescharacteristic
368C2×C4×Q8C22×C12711yescharacteristic
369C2×C4×D4C22×C12711yescharacteristic
370C2×#117C22×C12711yescharacteristic
371#468C4×C12718yescomplemented
372C4×SD16—24no—
373C2×#107C22×C12711yescharacteristic
374C2×#107C22×C12711yescharacteristic
375C2×#106C22×C12711yescharacteristic
376C2×#103C22×C12711yescharacteristic
377C2×#103C22×C12711yescharacteristic
378C2×#103C22×C12711yescharacteristic
379C2×#102C22×C12711yescharacteristic
380C2×#102C22×C12711yescharacteristic
381C2×#102C22×C12711yescharacteristic
382#405—24no—
383C2×#97C22×C12711yescharacteristic
384C2×#97C22×C12711yescharacteristic
385C2×C4×C8C22×C12711yescharacteristic
386C2×C4×C8C22×C12711yescharacteristic
387#391C22×C12711yescharacteristic
388#390—21no—
389#390C22×C12711yescharacteristic
390#389—21no—
391#389C22×C12711yescharacteristic
392#389C22×C12711yescharacteristic
393#388—21no—
394#388—21no—
395#388—21no—
396#387—21no—
397#386—21no—
398#385—21no—
399#380C22×C12711yescharacteristic
400#380C22×C12711yescharacteristic
401C4×C4⋊C4C22×C12711yescharacteristic
402C4×C4⋊C4C22×C12711yescharacteristic
403#340C22×C12711yescharacteristic
404#340C22×C12711yescharacteristic
405#340C22×C12711yescharacteristic
406#340C22×C12711yescharacteristic
407#340C22×C12711yescharacteristic
408#340C22×C12711yescharacteristic
409C22×Q8C23×C12711yescharacteristic
410C22×D4—21no—
411C22×D4C23×C12711yescharacteristic
412C23×C4—21no—
413C23×C4C23×C12711yescharacteristic
414C2×SD16—22no—
415C2×SD16—22no—
416C2×SD16C2×C4×C12714yes—
417C2×M16—22no—
418C2×M16—22no—
419C2×M16C2×C4×C12714yescomplemented
420C22×C8—22no—
421C22×C8—22no—
422C22×C8—22no—
423C22×C8C23×C12711yescharacteristic
424C22×C8C23×C12711yescharacteristic
425C22×C8C23×C12711yescharacteristic
426C22×C8C23×C12711yescharacteristic
427C22⋊Q8—22no—
428C22⋊Q8C2×C4×C12714yescomplemented
429#121—22no—
430#121C2×C4×C12714yes—
431C4×Q8—22no—
432C4×Q8—22no—
433C4×D4—22no—
434C4×D4—22no—
435#117—22no—
436#117—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4D4×C12711yescharacteristic
442C2×C4⋊C4D4×C12711yescharacteristic
443C2×C4⋊C4C23×C12711yescharacteristic
444C2×C4⋊C4C23×C12711yescharacteristic
445C2×C4⋊C4C23×C12711yescharacteristic
446C2×C4⋊C4C23×C12711yescharacteristic
447C2×C4⋊C4C23×C12711yescharacteristic
448C2×C4⋊C4C23×C12711yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C12711yescharacteristic
457C2×C22⋊C4D4×C12711yescharacteristic
458C2×C42—21no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42C23×C12711yescharacteristic
462C2×C42C23×C12711yescharacteristic
463#107—22no—
464#107C2×C4×C12714yescomplemented
465#106—22no—
466#103—22no—
467#103—22no—
468#103C2×C4×C12714yescomplemented
469#102—22no—
470#102—22no—
471#102C2×C4×C12714yes—
472#97—22no—
473#97—22no—
474C4×C8—22no—
475C4×C8D4×C12714yescomplemented
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484C24—21no—
485C24C2×D4×C12711yescharacteristic
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8C22×C4×C12712yes—
492C2×D4—24no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—81no—
499C2×D4—81no—
500C2×D4C22×C4×C12712yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4C22×C4×C12712yes—
516C22×C4C2×D4×C12711yescharacteristic
517C22×C4C2×D4×C12711yescharacteristic
518C22×C4C2×D4×C12711yescharacteristic
519C22×C4C2×D4×C12711yescharacteristic
520C22×C4C2×D4×C12711yescharacteristic
521C22×C4#41×C12712yes—
522C22×C4C24×C12711yescharacteristic
523SD16—28no—
524M16—28no—
525C2×C8—28no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8C22×C4×C12712yes—
533C2×C8C22×C4×C12712yes—
534C2×C8C2×D4×C12712yes—
535C2×C8C2×D4×C12712yes—
536C2×C8#41×C12712yes—
537C2×C8#41×C12712yes—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4C22×C4×C12712yes—
555C4⋊C4C22×C4×C12712yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—42no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C42—21no—
566C42—21no—
567C42—42no—
568C42—81no—
569C42—81no—
570C42C2×D4×C12712yes—
571C42#41×C12712yes—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23C4×D4×C12712yes—
586C23C22×D4×C12711yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—84no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—84no—
634C2×C4C4×D4×C12712yes—
635C2×C4#121×C12712yes—
636C2×C4#121×C12712yes—
637C2×C4C23×C4×C12711yescharacteristic
638C2×C4C22×D4×C12711yescharacteristic
639C2×C4C2×#41×C12711yescharacteristic
640C2×C4C2×#41×C12711yescharacteristic
641C2×C4C2×#41×C12711yescharacteristic
642C2×C4C2×#41×C12711yescharacteristic
643C8—22no—
644C8—22no—
645C8—22no—
646C8C4×D4×C12714yes—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×C4×D4×C12711yescharacteristic
662C22C2×#121×C12711yescharacteristic
663C22#532×C12711yescharacteristic
664C22#576×C12711yescharacteristic
665C22#577×C12711yescharacteristic
666C22#577×C12711yescharacteristic
667C22#578×C12711yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—42no—
672C4—42no—
673C4—41no—
674C4—41no—
675C4—42no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4C2×C4×D4×C12711yescharacteristic
681C4C4×#41×C12711yescharacteristic
682C4#525×C12711yescharacteristic
683C4#529×C12711yescharacteristic
684C2—42no—
685C2—82no—
686C2C4×#121×C12711yescharacteristic
687C2C127×#294611yescharacteristic
688C2C127×#294711yescharacteristic
689C2C127×#305711yescharacteristic
690C2C127×#306111yescharacteristic
691C2C127×#317811yescharacteristic
692C2C127×#317911yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#121×C127C22
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
2. C2×C4×SD16×C127C2semidirect
3. C2×#405×C127C2semidirect
5. C127×#2323C2semidirect
6. C127×#1973C2semidirect
7. C127×#1943C2semidirect
8. C127×#1934C2semidirect
9. C127×#1933C2semidirect
11. C127×#1892C2semidirect
12. C127×#1809C2semidirect
13. C4×#107×C127C2semidirect
14. C127×#1763C2semidirect
15. C127×#1762C2semidirect
24. #468×C127C4semidirect
72. C2×M16×C127C2×C4semidirect
81. C22⋊Q8×C127C2×C4semidirect
117. #107×C127C2×C4semidirect
121. #103×C127C2×C4semidirect
128. C4×C8×C127D4semidirect
337. #21535C127direct (N × H)
348. C2×C4×SD16C2×C127semidirect
349. C2×#405C2×C127semidirect
351. #2323C2×C127semidirect
352. #1973C2×C127semidirect
353. #1943C2×C127semidirect
354. #1934C2×C127semidirect
355. #1933C2×C127semidirect
357. #1892C2×C127semidirect
358. #1809C2×C127semidirect
359. C4×#107C2×C127semidirect
360. #1763C2×C127semidirect
361. #1762C2×C127semidirect
362. C127#21535direct (N × H)
371. #468C4×C127semidirect
419. C2×M16C2×C4×C127semidirect
428. C22⋊Q8C2×C4×C127semidirect
464. #107C2×C4×C127semidirect
468. #103C2×C4×C127semidirect
475. C4×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1272
C2×C4×SD16×C1272
C2×#405×C1272
C127×#23242
C127×#23232
C127×#19732
C127×#19432
C127×#19342
C127×#19332
C127×#18932
C127×#18922
C127×#18092
C4×#107×C1272
C127×#17632
C127×#17622
#21535127