Finite Group Databasebeta

← C127×#13981 #44577654

Subgroups — C127×#13981 #44577654

Order 32512.

1470 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C211yesmaximal, characteristic
2C2×#387×C127C212yesmaximal
3C2×#384×C127C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
5C127×#1442C212yesmaximal
6C127×#1441C212yesmaximal
7C127×#1436C212yesmaximal
8C127×C4⋊#95C211yesmaximal, characteristic
9C127×C4⋊#95C211yesmaximal, characteristic
10C127×C4⋊#95C211yesmaximal, characteristic
11C4×#95×C127C211yesmaximal, characteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2212yes—
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C42×C127C2211yescharacteristic
20C22×C42×C127C2212yes—
21C22×C42×C127C2211yescharacteristic
22C22×C42×C127C2211yescharacteristic
23#389×C127C418yescomplemented
24#387×C127—28no—
25#384×C127—24no—
26C4×C4⋊C4×C127—24no—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2211yescharacteristic
39C23×C4×C127C2312yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—24no—
59C2×C4⋊C4×C127—24no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—24no—
62C2×C4⋊C4×C127—24no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—42no—
66C2×C4⋊C4×C127—42no—
67C2×C4⋊C4×C127C2×C414yes—
68C2×C4⋊C4×C127C2×C418yes—
69C2×C4⋊C4×C127C2×C414yes—
70C2×C4⋊C4×C127D414yes—
71C2×C42×C127—22no—
72C2×C42×C127—22no—
73C2×C42×C127—22no—
74C2×C42×C127—22no—
75C2×C42×C127—24no—
76C2×C42×C127—24no—
77C2×C42×C127—22no—
78C2×C42×C127—22no—
79C2×C42×C127—22no—
80C2×C42×C127—42no—
81C2×C42×C127C2×C414yes—
82C2×C42×C127Q814yes—
83#95×C127—24no—
84#95×C127—24no—
85#95×C127—24no—
86#95×C127—24no—
87#95×C127—22no—
88#95×C127—22no—
89#95×C127—42no—
90#95×C127—42no—
91#95×C127—42no—
92#95×C127C2×C418yes—
93#95×C127D414yes—
94#95×C127Q814yes—
95C24×C127C2411yescharacteristic
96C22×C4×C127—21no—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—21no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—21no—
134C22×C4×C127—21no—
135C22×C4×C127—21no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—21no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127C22×C414yes—
152C22×C4×C127C22×C414yes—
153C22×C4×C127C22×C412yes—
154C22×C4×C127C22×C412yes—
155C22×C4×C127C22×C412yes—
156C22×C4×C127C2×D412yes—
157C22×C4×C127C2×D414yes—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D412yes—
160C22×C4×C127C2×D412yes—
161C22×C4×C127C2×Q812yes—
162C22×C4×C127C2×Q812yes—
163C22×C4×C127C2×Q812yes—
164C22×C4×C127C2×Q812yes—
165C22×C4×C127C2×Q812yes—
166C22×C4×C127C2×Q812yes—
167C22×C4×C127#4112yes—
168C22×C4×C127#4112yes—
169C22×C4×C127#4112yes—
170C22×C4×C127#4112yes—
171C22×C4×C127#4112yes—
172C22×C4×C127#4112yes—
173C4⋊C4×C127—28no—
174C4⋊C4×C127—216no—
175C4⋊C4×C127—28no—
176C4⋊C4×C127—28no—
177C4⋊C4×C127—48no—
178C4⋊C4×C127—48no—
179C4⋊C4×C127—44no—
180C42×C127—28no—
181C42×C127—28no—
182C42×C127—48no—
183C42×C127—44no—
184C23×C127C23×C411yescharacteristic
185C23×C127C22×D411yescharacteristic
186C23×C127C22×D411yescharacteristic
187C23×C127C22×Q811yescharacteristic
188C23×C127C22×Q811yescharacteristic
189C23×C127C2×#4111yescharacteristic
190C23×C127C2×#4111yescharacteristic
191C23×C127C2×#4111yescharacteristic
192C23×C127C2×#4111yescharacteristic
193C23×C127C2×#4111yescharacteristic
194C23×C127C2×#4111yescharacteristic
195C23×C127H(5,𝔽2)11yescharacteristic
196C23×C127H(5,𝔽2)11yescharacteristic
197C23×C1272−1+411yescharacteristic
198C23×C1272−1+411yescharacteristic
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—22no—
205C2×C4×C127—22no—
206C2×C4×C127—22no—
207C2×C4×C127—22no—
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—24no—
218C2×C4×C127—24no—
219C2×C4×C127—24no—
220C2×C4×C127—24no—
221C2×C4×C127—24no—
222C2×C4×C127—24no—
223C2×C4×C127—22no—
224C2×C4×C127—24no—
225C2×C4×C127—22no—
226C2×C4×C127—22no—
227C2×C4×C127—22no—
228C2×C4×C127—22no—
229C2×C4×C127—24no—
230C2×C4×C127—24no—
231C2×C4×C127—22no—
232C2×C4×C127—22no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—41no—
236C2×C4×C127—41no—
237C2×C4×C127—42no—
238C2×C4×C127—42no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—42no—
242C2×C4×C127—41no—
243C2×C4×C127—42no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127—41no—
247C2×C4×C127—42no—
248C2×C4×C127—42no—
249C2×C4×C127—41no—
250C2×C4×C127—42no—
251C2×C4×C127—41no—
252C2×C4×C127—42no—
253C2×C4×C127—41no—
254C2×C4×C127—41no—
255C2×C4×C127—42no—
256C2×C4×C127—41no—
257C2×C4×C127—41no—
258C2×C4×C127—42no—
259C2×C4×C127—42no—
260C2×C4×C127—42no—
261C2×C4×C127—42no—
262C2×C4×C127—42no—
263C2×C4×C127—42no—
264C2×C4×C127—42no—
265C2×C4×C127—42no—
266C2×C4×C127#11714yes—
267C2×C4×C127C4×D414yes—
268C2×C4×C127C4×D414yes—
269C2×C4×C127C4×Q814yes—
270C2×C4×C127C4×Q814yes—
271C2×C4×C127C22⋊Q814yes—
272C2×C4×C127#12314yes—
273C2×C4×C127#12514yes—
274C2×C4×C127#12614yes—
275C2×C4×C127C4⋊Q814yes—
276C22×C127C2×#11711yescharacteristic
277C22×C127C2×C4×D411yescharacteristic
278C22×C127C2×C4×D411yescharacteristic
279C22×C127C2×C4×Q811yescharacteristic
280C22×C127C2×C4×Q811yescharacteristic
281C22×C127#52011yescharacteristic
282C22×C127#52011yescharacteristic
283C22×C127C2×C22⋊Q811yescharacteristic
284C22×C127C2×#12311yescharacteristic
285C22×C127C2×#12511yescharacteristic
286C22×C127C2×#12611yescharacteristic
287C22×C127C2×C4⋊Q811yescharacteristic
288C22×C127#53211yescharacteristic
289C22×C127#53311yescharacteristic
290C22×C127#53311yescharacteristic
291C22×C127#54011yescharacteristic
292C22×C127#54111yescharacteristic
293C22×C127#54411yescharacteristic
294C22×C127#54411yescharacteristic
295C22×C127D4211yescharacteristic
296C22×C127#54611yescharacteristic
297C22×C127#54711yescharacteristic
298C22×C127#54711yescharacteristic
299C22×C127#54811yescharacteristic
300C22×C127D4×Q811yescharacteristic
301C22×C127#55011yescharacteristic
302C22×C127#55211yescharacteristic
303C22×C127#55311yescharacteristic
304C22×C127#55411yescharacteristic
305C22×C127#55411yescharacteristic
306C22×C127#55511yescharacteristic
307C22×C127#55611yescharacteristic
308C22×C127#55611yescharacteristic
309C22×C127#55711yescharacteristic
310C22×C127#55911yescharacteristic
311C4×C127—24no—
312C4×C127—24no—
313C4×C127—24no—
314C4×C127—44no—
315C4×C127—44no—
316C4×C127—42no—
317C4×C127—44no—
318C4×C127—42no—
319C4×C127—42no—
320C4×C127—82no—
321C4×C127#38718yescomplemented
322#13981C12711yesmaximal, characteristic, direct product factor, Sylow
323C2×C127C2×#38711yescharacteristic
324C2×C127C4×C4⋊Q811yescharacteristic
325C2×C127#233011yescharacteristic
326C2×C127#235411yescharacteristic
327C2×C127#235511yescharacteristic
328C2×C127#236011yescharacteristic
329C2×C127#236111yescharacteristic
330C2×C127#243911yescharacteristic
331C2×C127#244011yescharacteristic
332C2×C127#244511yescharacteristic
333C2×C127#244611yescharacteristic
334C2×C127#249611yescharacteristic
335C2×C127#249711yescharacteristic
336C2×C127#255211yescharacteristic
337C2×C127#257011yescharacteristic
338C2×#389C2×C12711yescharacteristic
339C2×#387C2×C12712yes—
340C2×#384C2×C12711yescharacteristic
341C2×C4×C4⋊C4C2×C12711yescharacteristic
342#1442C2×C12712yes—
343#1441C2×C12712yes—
344#1436C2×C12712yes—
345C4⋊#95C2×C12711yescharacteristic
346C4⋊#95C2×C12711yescharacteristic
347C4⋊#95C2×C12711yescharacteristic
348C4×#95C2×C12711yescharacteristic
349C127#1398111yescharacteristic, direct product factor, Sylow
350C22×C4⋊C4C22×C12711yescharacteristic
351C22×C4⋊C4C22×C12712yes—
352C22×C4⋊C4C22×C12712yes—
353C22×C4⋊C4C22×C12711yescharacteristic
354C22×C4⋊C4C22×C12711yescharacteristic
355C22×C4⋊C4C22×C12712yes—
356C22×C4⋊C4C22×C12711yescharacteristic
357C22×C42C22×C12711yescharacteristic
358C22×C42C22×C12712yes—
359C22×C42C22×C12711yescharacteristic
360C22×C42C22×C12711yescharacteristic
361#389C4×C12718yescomplemented
362#387—28no—
363#384—24no—
364C4×C4⋊C4—24no—
365C2×#95C22×C12711yescharacteristic
366C2×#95C22×C12711yescharacteristic
367C2×#95C22×C12712yes—
368C2×#95C22×C12712yes—
369C2×#95C22×C12712yes—
370C2×#95C22×C12712yes—
371C2×#95C22×C12712yes—
372C2×#95C22×C12712yes—
373C2×#95C22×C12712yes—
374C2×#95C22×C12712yes—
375C2×#95C22×C12711yescharacteristic
376C2×#95C22×C12711yescharacteristic
377C23×C4C23×C12712yes—
378C23×C4C23×C12712yes—
379C23×C4C23×C12712yes—
380C23×C4C23×C12712yes—
381C23×C4C23×C12711yescharacteristic
382C23×C4C23×C12711yescharacteristic
383C23×C4C23×C12711yescharacteristic
384C23×C4C23×C12711yescharacteristic
385C23×C4C23×C12711yescharacteristic
386C23×C4C23×C12711yescharacteristic
387C23×C4C23×C12711yescharacteristic
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—24no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4C2×C4×C12714yes—
406C2×C4⋊C4C2×C4×C12718yes—
407C2×C4⋊C4C2×C4×C12714yes—
408C2×C4⋊C4D4×C12714yes—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—42no—
419C2×C42C2×C4×C12714yes—
420C2×C42Q8×C12714yes—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—22no—
426#95—22no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95C2×C4×C12718yes—
431#95D4×C12714yes—
432#95Q8×C12714yes—
433C24C24×C12711yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
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—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4C22×C4×C12714yes—
490C22×C4C22×C4×C12714yes—
491C22×C4C22×C4×C12712yes—
492C22×C4C22×C4×C12712yes—
493C22×C4C22×C4×C12712yes—
494C22×C4C2×D4×C12712yes—
495C22×C4C2×D4×C12714yes—
496C22×C4C2×D4×C12712yes—
497C22×C4C2×D4×C12712yes—
498C22×C4C2×D4×C12712yes—
499C22×C4C2×Q8×C12712yes—
500C22×C4C2×Q8×C12712yes—
501C22×C4C2×Q8×C12712yes—
502C22×C4C2×Q8×C12712yes—
503C22×C4C2×Q8×C12712yes—
504C22×C4C2×Q8×C12712yes—
505C22×C4#41×C12712yes—
506C22×C4#41×C12712yes—
507C22×C4#41×C12712yes—
508C22×C4#41×C12712yes—
509C22×C4#41×C12712yes—
510C22×C4#41×C12712yes—
511C4⋊C4—28no—
512C4⋊C4—216no—
513C4⋊C4—28no—
514C4⋊C4—28no—
515C4⋊C4—48no—
516C4⋊C4—48no—
517C4⋊C4—44no—
518C42—28no—
519C42—28no—
520C42—48no—
521C42—44no—
522C23C23×C4×C12711yescharacteristic
523C23C22×D4×C12711yescharacteristic
524C23C22×D4×C12711yescharacteristic
525C23C22×Q8×C12711yescharacteristic
526C23C22×Q8×C12711yescharacteristic
527C23C2×#41×C12711yescharacteristic
528C23C2×#41×C12711yescharacteristic
529C23C2×#41×C12711yescharacteristic
530C23C2×#41×C12711yescharacteristic
531C23C2×#41×C12711yescharacteristic
532C23C2×#41×C12711yescharacteristic
533C23H(5,𝔽2)×C12711yescharacteristic
534C23H(5,𝔽2)×C12711yescharacteristic
535C232−1+4×C12711yescharacteristic
536C232−1+4×C12711yescharacteristic
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4#117×C12714yes—
605C2×C4C4×D4×C12714yes—
606C2×C4C4×D4×C12714yes—
607C2×C4C4×Q8×C12714yes—
608C2×C4C4×Q8×C12714yes—
609C2×C4C22⋊Q8×C12714yes—
610C2×C4#123×C12714yes—
611C2×C4#125×C12714yes—
612C2×C4#126×C12714yes—
613C2×C4C4⋊Q8×C12714yes—
614C22C2×#117×C12711yescharacteristic
615C22C2×C4×D4×C12711yescharacteristic
616C22C2×C4×D4×C12711yescharacteristic
617C22C2×C4×Q8×C12711yescharacteristic
618C22C2×C4×Q8×C12711yescharacteristic
619C22#520×C12711yescharacteristic
620C22#520×C12711yescharacteristic
621C22C2×C22⋊Q8×C12711yescharacteristic
622C22C2×#123×C12711yescharacteristic
623C22C2×#125×C12711yescharacteristic
624C22C2×#126×C12711yescharacteristic
625C22C2×C4⋊Q8×C12711yescharacteristic
626C22#532×C12711yescharacteristic
627C22#533×C12711yescharacteristic
628C22#533×C12711yescharacteristic
629C22#540×C12711yescharacteristic
630C22#541×C12711yescharacteristic
631C22#544×C12711yescharacteristic
632C22#544×C12711yescharacteristic
633C22D42×C12711yescharacteristic
634C22#546×C12711yescharacteristic
635C22#547×C12711yescharacteristic
636C22#547×C12711yescharacteristic
637C22#548×C12711yescharacteristic
638C22D4×Q8×C12711yescharacteristic
639C22#550×C12711yescharacteristic
640C22#552×C12711yescharacteristic
641C22#553×C12711yescharacteristic
642C22#554×C12711yescharacteristic
643C22#554×C12711yescharacteristic
644C22#555×C12711yescharacteristic
645C22#556×C12711yescharacteristic
646C22#556×C12711yescharacteristic
647C22#557×C12711yescharacteristic
648C22#559×C12711yescharacteristic
649C4—24no—
650C4—24no—
651C4—24no—
652C4—44no—
653C4—44no—
654C4—42no—
655C4—44no—
656C4—42no—
657C4—42no—
658C4—82no—
659C4#387×C12718yescomplemented
660C2C2×#387×C12711yescharacteristic
661C2C4×C4⋊Q8×C12711yescharacteristic
662C2C127×#233011yescharacteristic
663C2C127×#235411yescharacteristic
664C2C127×#235511yescharacteristic
665C2C127×#236011yescharacteristic
666C2C127×#236111yescharacteristic
667C2C127×#243911yescharacteristic
668C2C127×#244011yescharacteristic
669C2C127×#244511yescharacteristic
670C2C127×#244611yescharacteristic
671C2C127×#249611yescharacteristic
672C2C127×#249711yescharacteristic
673C2C127×#255211yescharacteristic
674C2C127×#257011yescharacteristic
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
23. #389×C127C4semidirect
321. C4×C127#387semidirect
322. #13981C127direct (N × H)
349. C127#13981direct (N × H)
361. #389C4×C127semidirect
659. C4#387×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#387×C1272
C2×#384×C1272
C2×C4×C4⋊C4×C1272
C127×#14422
C127×#14412
C127×#14362
C127×C4⋊#952
C4×#95×C1272
#13981127