Finite Group Databasebeta

← C127×#14021 #44577694

Subgroups — C127×#14021 #44577694

Order 32512.

1506 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×#391×C127C211yesmaximal, characteristic
2C2×#391×C127C211yesmaximal, characteristic
3C2×#391×C127C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
6C127×#1443C212yesmaximal
7C127×#1442C212yesmaximal
8C127×#1436C212yesmaximal
9C127×C4⋊#95C211yesmaximal, characteristic
10C127×C4⋊#95C211yesmaximal, characteristic
11C127×#1434C212yesmaximal
12C23×Q8×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C42×C127C2211yescharacteristic
19C22×C42×C127C2212yes—
20C22×C42×C127C2211yescharacteristic
21C22×C42×C127C2211yescharacteristic
22#391×C127—24no—
23#391×C127—24no—
24#391×C127C418yescomplemented
25C4×C4⋊C4×C127—24no—
26C4×C4⋊C4×C127—24no—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C22×Q8×C127—22no—
41C22×Q8×C127—22no—
42C22×Q8×C127—22no—
43C22×Q8×C127—22no—
44C22×Q8×C127—22no—
45C22×Q8×C127—22no—
46C22×Q8×C127C2×C414yes—
47C23×C4×C127C2312yes—
48C23×C4×C127C2312yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2312yes—
51C23×C4×C127C2311yescharacteristic
52C23×C4×C127C2312yes—
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C23×C4×C127C2311yescharacteristic
56C23×C4×C127C2311yescharacteristic
57C23×C4×C127C2311yescharacteristic
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127C2×C414yes—
71C2×C4⋊C4×C127D414yes—
72C2×C4⋊C4×C127Q814yescomplemented
73C2×C42×C127—22no—
74C2×C42×C127—22no—
75C2×C42×C127—22no—
76C2×C42×C127—22no—
77C2×C42×C127—24no—
78C2×C42×C127—22no—
79C2×C42×C127—22no—
80C2×C42×C127—24no—
81C2×C42×C127—22no—
82C2×C42×C127—42no—
83C2×C42×C127C2×C414yes—
84C2×C42×C127D414yes—
85#95×C127—24no—
86#95×C127—22no—
87#95×C127—22no—
88#95×C127—24no—
89#95×C127—24no—
90#95×C127—24no—
91#95×C127—24no—
92#95×C127—24no—
93#95×C127—24no—
94#95×C127—42no—
95#95×C127—42no—
96#95×C127C2×C418yes—
97#95×C127C2×C418yes—
98C24×C127C2411yescharacteristic
99C2×Q8×C127—28no—
100C2×Q8×C127—28no—
101C2×Q8×C127—28no—
102C2×Q8×C127—44no—
103C2×Q8×C127—44no—
104C2×Q8×C127—44no—
105C2×Q8×C127—44no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—21no—
128C22×C4×C127—22no—
129C22×C4×C127—21no—
130C22×C4×C127—21no—
131C22×C4×C127—22no—
132C22×C4×C127—21no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—21no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—22no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—22no—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—22no—
157C22×C4×C127—22no—
158C22×C4×C127—22no—
159C22×C4×C127—22no—
160C22×C4×C127—22no—
161C22×C4×C127—22no—
162C22×C4×C127—22no—
163C22×C4×C127C22×C412yes—
164C22×C4×C127C22×C414yes—
165C22×C4×C127C22×C414yes—
166C22×C4×C127C22×C412yes—
167C22×C4×C127C22×C412yes—
168C22×C4×C127C2×D414yes—
169C22×C4×C127C2×D412yes—
170C22×C4×C127C2×D412yes—
171C22×C4×C127C2×D412yes—
172C22×C4×C127C2×D412yes—
173C22×C4×C127C2×Q812yes—
174C22×C4×C127C2×Q812yes—
175C22×C4×C127C2×Q812yes—
176C22×C4×C127#4112yes—
177C22×C4×C127#4112yes—
178C22×C4×C127#4112yes—
179C22×C4×C127#4112yes—
180C22×C4×C127#4112yes—
181C22×C4×C127#4112yes—
182C22×C4×C127#4112yes—
183C4⋊C4×C127—28no—
184C4⋊C4×C127—28no—
185C4⋊C4×C127—28no—
186C4⋊C4×C127—28no—
187C4⋊C4×C127—44no—
188C42×C127—28no—
189C42×C127—28no—
190C42×C127—48no—
191C42×C127—44no—
192C23×C127C23×C411yescharacteristic
193C23×C127C22×D411yescharacteristic
194C23×C127C22×D411yescharacteristic
195C23×C127C22×Q811yescharacteristic
196C23×C127C2×#4111yescharacteristic
197C23×C127C2×#4111yescharacteristic
198C23×C127C2×#4111yescharacteristic
199C23×C127C2×#4111yescharacteristic
200C23×C127C2×#4111yescharacteristic
201C23×C127C2×#4111yescharacteristic
202C23×C127C2×#4111yescharacteristic
203C23×C127H(5,𝔽2)11yescharacteristic
204C23×C1272−1+411yescharacteristic
205C23×C1272−1+411yescharacteristic
206C23×C1272−1+411yescharacteristic
207Q8×C127—416no—
208C2×C4×C127—22no—
209C2×C4×C127—22no—
210C2×C4×C127—22no—
211C2×C4×C127—22no—
212C2×C4×C127—22no—
213C2×C4×C127—22no—
214C2×C4×C127—22no—
215C2×C4×C127—22no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—22no—
220C2×C4×C127—24no—
221C2×C4×C127—22no—
222C2×C4×C127—24no—
223C2×C4×C127—24no—
224C2×C4×C127—24no—
225C2×C4×C127—24no—
226C2×C4×C127—22no—
227C2×C4×C127—22no—
228C2×C4×C127—24no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—24no—
232C2×C4×C127—22no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—24no—
236C2×C4×C127—24no—
237C2×C4×C127—22no—
238C2×C4×C127—22no—
239C2×C4×C127—22no—
240C2×C4×C127—22no—
241C2×C4×C127—41no—
242C2×C4×C127—41no—
243C2×C4×C127—42no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127—42no—
247C2×C4×C127—42no—
248C2×C4×C127—41no—
249C2×C4×C127—41no—
250C2×C4×C127—41no—
251C2×C4×C127—41no—
252C2×C4×C127—41no—
253C2×C4×C127—41no—
254C2×C4×C127—42no—
255C2×C4×C127—42no—
256C2×C4×C127—41no—
257C2×C4×C127—41no—
258C2×C4×C127—41no—
259C2×C4×C127—42no—
260C2×C4×C127—41no—
261C2×C4×C127—41no—
262C2×C4×C127—41no—
263C2×C4×C127—42no—
264C2×C4×C127—41no—
265C2×C4×C127—41no—
266C2×C4×C127—42no—
267C2×C4×C127—42no—
268C2×C4×C127—42no—
269C2×C4×C127—42no—
270C2×C4×C127—42no—
271C2×C4×C127—42no—
272C2×C4×C127—42no—
273C2×C4×C127—42no—
274C2×C4×C127—42no—
275C2×C4×C127—42no—
276C2×C4×C127#11714yes—
277C2×C4×C127C4×D414yes—
278C2×C4×C127C4×D414yes—
279C2×C4×C127C4×Q814yes—
280C2×C4×C127#12114yes—
281C2×C4×C127C22⋊Q814yes—
282C2×C4×C127#12314yes—
283C2×C4×C127#12414yes—
284C2×C4×C127#12614yes—
285C22×C127C2×#11711yescharacteristic
286C22×C127C2×C4×D411yescharacteristic
287C22×C127C2×C4×D411yescharacteristic
288C22×C127C2×C4×Q811yescharacteristic
289C22×C127C4×#4111yescharacteristic
290C22×C127#51911yescharacteristic
291C22×C127#52011yescharacteristic
292C22×C127C2×#12111yescharacteristic
293C22×C127C2×C22⋊Q811yescharacteristic
294C22×C127C2×#12311yescharacteristic
295C22×C127#52511yescharacteristic
296C22×C127C2×#12411yescharacteristic
297C22×C127C2×#12611yescharacteristic
298C22×C127#52911yescharacteristic
299C22×C127#53311yescharacteristic
300C22×C127#53611yescharacteristic
301C22×C127#53711yescharacteristic
302C22×C127#54111yescharacteristic
303C22×C127#54211yescharacteristic
304C22×C127#54611yescharacteristic
305C22×C127#54711yescharacteristic
306C22×C127#54811yescharacteristic
307C22×C127D4×Q811yescharacteristic
308C22×C127#55211yescharacteristic
309C22×C127#55211yescharacteristic
310C22×C127#55411yescharacteristic
311C22×C127#55611yescharacteristic
312C22×C127#55611yescharacteristic
313C22×C127#55611yescharacteristic
314C22×C127#55611yescharacteristic
315C22×C127#55611yescharacteristic
316C22×C127#55711yescharacteristic
317C22×C127#55711yescharacteristic
318C22×C127#55911yescharacteristic
319C22×C127#55911yescharacteristic
320C4×C127—24no—
321C4×C127—24no—
322C4×C127—42no—
323C4×C127—44no—
324C4×C127—42no—
325C4×C127—42no—
326C4×C127—42no—
327C4×C127—44no—
328C4×C127—44no—
329C4×C127—82no—
330C4×C127#38818yes—
331#14021C12711yesmaximal, characteristic, direct product factor, Sylow
332C2×C127C2×#38811yescharacteristic
333C2×C127C4×C22⋊Q811yescharacteristic
334C2×C127#232311yescharacteristic
335C2×C127#235511yescharacteristic
336C2×C127#235611yescharacteristic
337C2×C127#236511yescharacteristic
338C2×C127#236711yescharacteristic
339C2×C127#241511yescharacteristic
340C2×C127#241711yescharacteristic
341C2×C127#244611yescharacteristic
342C2×C127#244711yescharacteristic
343C2×C127#251111yescharacteristic
344C2×C127#251411yescharacteristic
345C2×C127#256811yescharacteristic
346C2×C127#259211yescharacteristic
347C2×#391C2×C12711yescharacteristic
348C2×#391C2×C12711yescharacteristic
349C2×#391C2×C12711yescharacteristic
350C2×C4×C4⋊C4C2×C12711yescharacteristic
351C2×C4×C4⋊C4C2×C12711yescharacteristic
352#1443C2×C12712yes—
353#1442C2×C12712yes—
354#1436C2×C12712yes—
355C4⋊#95C2×C12711yescharacteristic
356C4⋊#95C2×C12711yescharacteristic
357#1434C2×C12712yes—
358C127#1402111yescharacteristic, direct product factor, Sylow
359C23×Q8C22×C12711yescharacteristic
360C22×C4⋊C4C22×C12711yescharacteristic
361C22×C4⋊C4C22×C12711yescharacteristic
362C22×C4⋊C4C22×C12711yescharacteristic
363C22×C4⋊C4C22×C12711yescharacteristic
364C22×C4⋊C4C22×C12711yescharacteristic
365C22×C42C22×C12711yescharacteristic
366C22×C42C22×C12712yes—
367C22×C42C22×C12711yescharacteristic
368C22×C42C22×C12711yescharacteristic
369#391—24no—
370#391—24no—
371#391C4×C12718yescomplemented
372C4×C4⋊C4—24no—
373C4×C4⋊C4—24no—
374C2×#95C22×C12711yescharacteristic
375C2×#95C22×C12712yes—
376C2×#95C22×C12712yes—
377C2×#95C22×C12712yes—
378C2×#95C22×C12712yes—
379C2×#95C22×C12712yes—
380C2×#95C22×C12712yes—
381C2×#95C22×C12712yes—
382C2×#95C22×C12711yescharacteristic
383C2×#95C22×C12712yes—
384C2×#95C22×C12712yes—
385C2×#95C22×C12712yes—
386C2×#95C22×C12712yes—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—22no—
393C22×Q8C2×C4×C12714yes—
394C23×C4C23×C12712yes—
395C23×C4C23×C12712yes—
396C23×C4C23×C12712yes—
397C23×C4C23×C12711yescharacteristic
398C23×C4C23×C12711yescharacteristic
399C23×C4C23×C12712yes—
400C23×C4C23×C12711yescharacteristic
401C23×C4C23×C12711yescharacteristic
402C23×C4C23×C12711yescharacteristic
403C23×C4C23×C12711yescharacteristic
404C23×C4C23×C12711yescharacteristic
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4C2×C4×C12714yes—
418C2×C4⋊C4D4×C12714yes—
419C2×C4⋊C4Q8×C12714yescomplemented
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—42no—
430C2×C42C2×C4×C12714yes—
431C2×C42D4×C12714yes—
432#95—24no—
433#95—22no—
434#95—22no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—42no—
442#95—42no—
443#95C2×C4×C12718yes—
444#95C2×C4×C12718yes—
445C24C24×C12711yescharacteristic
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4C22×C4×C12712yes—
511C22×C4C22×C4×C12714yes—
512C22×C4C22×C4×C12714yes—
513C22×C4C22×C4×C12712yes—
514C22×C4C22×C4×C12712yes—
515C22×C4C2×D4×C12714yes—
516C22×C4C2×D4×C12712yes—
517C22×C4C2×D4×C12712yes—
518C22×C4C2×D4×C12712yes—
519C22×C4C2×D4×C12712yes—
520C22×C4C2×Q8×C12712yes—
521C22×C4C2×Q8×C12712yes—
522C22×C4C2×Q8×C12712yes—
523C22×C4#41×C12712yes—
524C22×C4#41×C12712yes—
525C22×C4#41×C12712yes—
526C22×C4#41×C12712yes—
527C22×C4#41×C12712yes—
528C22×C4#41×C12712yes—
529C22×C4#41×C12712yes—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—44no—
535C42—28no—
536C42—28no—
537C42—48no—
538C42—44no—
539C23C23×C4×C12711yescharacteristic
540C23C22×D4×C12711yescharacteristic
541C23C22×D4×C12711yescharacteristic
542C23C22×Q8×C12711yescharacteristic
543C23C2×#41×C12711yescharacteristic
544C23C2×#41×C12711yescharacteristic
545C23C2×#41×C12711yescharacteristic
546C23C2×#41×C12711yescharacteristic
547C23C2×#41×C12711yescharacteristic
548C23C2×#41×C12711yescharacteristic
549C23C2×#41×C12711yescharacteristic
550C23H(5,𝔽2)×C12711yescharacteristic
551C232−1+4×C12711yescharacteristic
552C232−1+4×C12711yescharacteristic
553C232−1+4×C12711yescharacteristic
554Q8—416no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4#117×C12714yes—
624C2×C4C4×D4×C12714yes—
625C2×C4C4×D4×C12714yes—
626C2×C4C4×Q8×C12714yes—
627C2×C4#121×C12714yes—
628C2×C4C22⋊Q8×C12714yes—
629C2×C4#123×C12714yes—
630C2×C4#124×C12714yes—
631C2×C4#126×C12714yes—
632C22C2×#117×C12711yescharacteristic
633C22C2×C4×D4×C12711yescharacteristic
634C22C2×C4×D4×C12711yescharacteristic
635C22C2×C4×Q8×C12711yescharacteristic
636C22C4×#41×C12711yescharacteristic
637C22#519×C12711yescharacteristic
638C22#520×C12711yescharacteristic
639C22C2×#121×C12711yescharacteristic
640C22C2×C22⋊Q8×C12711yescharacteristic
641C22C2×#123×C12711yescharacteristic
642C22#525×C12711yescharacteristic
643C22C2×#124×C12711yescharacteristic
644C22C2×#126×C12711yescharacteristic
645C22#529×C12711yescharacteristic
646C22#533×C12711yescharacteristic
647C22#536×C12711yescharacteristic
648C22#537×C12711yescharacteristic
649C22#541×C12711yescharacteristic
650C22#542×C12711yescharacteristic
651C22#546×C12711yescharacteristic
652C22#547×C12711yescharacteristic
653C22#548×C12711yescharacteristic
654C22D4×Q8×C12711yescharacteristic
655C22#552×C12711yescharacteristic
656C22#552×C12711yescharacteristic
657C22#554×C12711yescharacteristic
658C22#556×C12711yescharacteristic
659C22#556×C12711yescharacteristic
660C22#556×C12711yescharacteristic
661C22#556×C12711yescharacteristic
662C22#556×C12711yescharacteristic
663C22#557×C12711yescharacteristic
664C22#557×C12711yescharacteristic
665C22#559×C12711yescharacteristic
666C22#559×C12711yescharacteristic
667C4—24no—
668C4—24no—
669C4—42no—
670C4—44no—
671C4—42no—
672C4—42no—
673C4—42no—
674C4—44no—
675C4—44no—
676C4—82no—
677C4#388×C12718yes—
678C2C2×#388×C12711yescharacteristic
679C2C4×C22⋊Q8×C12711yescharacteristic
680C2C127×#232311yescharacteristic
681C2C127×#235511yescharacteristic
682C2C127×#235611yescharacteristic
683C2C127×#236511yescharacteristic
684C2C127×#236711yescharacteristic
685C2C127×#241511yescharacteristic
686C2C127×#241711yescharacteristic
687C2C127×#244611yescharacteristic
688C2C127×#244711yescharacteristic
689C2C127×#251111yescharacteristic
690C2C127×#251411yescharacteristic
691C2C127×#256811yescharacteristic
692C2C127×#259211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
24. #391×C127C4semidirect
72. C2×C4⋊C4×C127Q8semidirect
331. #14021C127direct (N × H)
358. C127#14021direct (N × H)
371. #391C4×C127semidirect
419. C2×C4⋊C4Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C2×C4×C4⋊C4×C1272
C127×#14432
C127×#14422
C127×#14362
C127×C4⋊#952
C127×#14342
#14021127