Finite Group Databasebeta

← C127×#14176 #44577849

Subgroups — C127×#14176 #44577849

Order 32512.

2422 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#394×C127C211yesmaximal, characteristic
3C2×#388×C127C212yesmaximal, complemented
4C2×#385×C127C212yesmaximal, complemented
5C2×C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
6C127×#1444C211yesmaximal, characteristic, complemented
7C127×#1441C211yesmaximal, characteristic, complemented
8C127×#1438C211yesmaximal, characteristic
9C127×#1437C212yesmaximal, complemented
10C127×#1434C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2212yes—
14C2×C4×D4×C127—28no—
15C2×C4×D4×C127—24no—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2212yes—
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C42×C127C2211yescharacteristic
26C22×C42×C127C2211yescharacteristic
27C22×C42×C127C2211yescharacteristic
28#394×C127C418yescomplemented
29#388×C127—28no—
30#385×C127—28no—
31C4×C4⋊C4×C127—24no—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2212yes—
40C2×#95×C127C2211yescharacteristic
41C25×C127C2312yes—
42C22×D4×C127—24no—
43C22×D4×C127—24no—
44C22×D4×C127—22no—
45C22×D4×C127—22no—
46C22×D4×C127C2×C414yes—
47C23×C4×C127—24no—
48C23×C4×C127—24no—
49C23×C4×C127—24no—
50C23×C4×C127—24no—
51C23×C4×C127—24no—
52C23×C4×C127—42no—
53C23×C4×C127—42no—
54C23×C4×C127C2312yes—
55C23×C4×C127C2311yescharacteristic
56C23×C4×C127C2312yes—
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2312yes—
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2311yescharacteristic
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2311yescharacteristic
64C4×D4×C127—232no—
65C2×C4⋊C4×C127—24no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127—24no—
72C2×C4⋊C4×C127—24no—
73C2×C4⋊C4×C127—42no—
74C2×C4⋊C4×C127C2×C414yescomplemented
75C2×C4⋊C4×C127D414yescomplemented
76C2×C22⋊C4×C127—24no—
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127—24no—
79C2×C22⋊C4×C127—24no—
80C2×C22⋊C4×C127—24no—
81C2×C22⋊C4×C127—24no—
82C2×C22⋊C4×C127—24no—
83C2×C22⋊C4×C127—24no—
84C2×C22⋊C4×C127—24no—
85C2×C22⋊C4×C127—24no—
86C2×C22⋊C4×C127—42no—
87C2×C22⋊C4×C127—42no—
88C2×C22⋊C4×C127C2×C418yescomplemented
89C2×C22⋊C4×C127C2×C418yescomplemented
90C2×C22⋊C4×C127D418yes—
91C2×C42×C127—24no—
92C2×C42×C127—22no—
93C2×C42×C127—22no—
94C2×C42×C127—22no—
95C2×C42×C127—22no—
96C2×C42×C127—24no—
97C2×C42×C127D414yes—
98#95×C127—22no—
99#95×C127—22no—
100#95×C127—24no—
101#95×C127—24no—
102#95×C127—24no—
103#95×C127—24no—
104#95×C127—22no—
105#95×C127—42no—
106#95×C127C2×C414yescomplemented
107C24×C127—22no—
108C24×C127—22no—
109C24×C127—22no—
110C24×C127—22no—
111C24×C127—22no—
112C24×C127—22no—
113C24×C127—22no—
114C24×C127—22no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—22no—
118C24×C127—22no—
119C24×C127C22×C414yes—
120C24×C127C2×D414yes—
121C24×C127#4114yes—
122C24×C127C2411yescharacteristic
123C2×D4×C127—28no—
124C2×D4×C127—28no—
125C2×D4×C127—216no—
126C2×D4×C127—216no—
127C2×D4×C127—28no—
128C22×C4×C127—21no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—21no—
132C22×C4×C127—21no—
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—216no—
140C22×C4×C127—21no—
141C22×C4×C127—22no—
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—21no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—22no—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
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×C127—22no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—22no—
167C22×C4×C127—22no—
168C22×C4×C127—22no—
169C22×C4×C127—22no—
170C22×C4×C127—22no—
171C22×C4×C127—48no—
172C22×C4×C127—48no—
173C22×C4×C127—48no—
174C22×C4×C127—48no—
175C22×C4×C127—48no—
176C22×C4×C127—48no—
177C22×C4×C127C22×C414yes—
178C22×C4×C127C22×C412yes—
179C22×C4×C127C22×C412yes—
180C22×C4×C127C22×C412yes—
181C22×C4×C127C2×D414yes—
182C22×C4×C127C2×D412yes—
183C22×C4×C127C2×D412yes—
184C22×C4×C127C2×D412yes—
185C22×C4×C127C2×D414yes—
186C22×C4×C127C2×D412yes—
187C22×C4×C127C2×D412yes—
188C22×C4×C127C2×D412yes—
189C22×C4×C127#4112yes—
190C22×C4×C127#4112yes—
191C22×C4×C127#4112yes—
192C22×C4×C127#4112yes—
193C4⋊C4×C127—28no—
194C4⋊C4×C127—28no—
195C4⋊C4×C127—28no—
196C4⋊C4×C127—48no—
197C22⋊C4×C127—216no—
198C22⋊C4×C127—216no—
199C22⋊C4×C127—216no—
200C22⋊C4×C127—48no—
201C22⋊C4×C127—48no—
202C42×C127—28no—
203C42×C127—28no—
204C42×C127—44no—
205C23×C127—24no—
206C23×C127—24no—
207C23×C127—24no—
208C23×C127—24no—
209C23×C127—24no—
210C23×C127—24no—
211C23×C127—24no—
212C23×C127—24no—
213C23×C127—24no—
214C23×C127—24no—
215C23×C127—24no—
216C23×C127—24no—
217C23×C127—24no—
218C23×C127—24no—
219C23×C127—24no—
220C23×C127—24no—
221C23×C127—24no—
222C23×C127—24no—
223C23×C127—42no—
224C23×C127—42no—
225C23×C127—42no—
226C23×C127—42no—
227C23×C127—42no—
228C23×C127—42no—
229C23×C127—42no—
230C23×C127—42no—
231C23×C127—42no—
232C23×C127—42no—
233C23×C127—42no—
234C23×C127—42no—
235C23×C127—42no—
236C23×C127—42no—
237C23×C127—42no—
238C23×C127—42no—
239C23×C127C4×D418yes—
240C23×C127C23×C411yescharacteristic
241C23×C127C22×D411yescharacteristic
242C23×C127C22×D412yes—
243C23×C127C22×D411yescharacteristic
244C23×C127C2×#4111yescharacteristic
245C23×C127C2×#4112yes—
246C23×C127C2×#4111yescharacteristic
247C23×C127C2×#4111yescharacteristic
248C23×C127C2×#4111yescharacteristic
249C23×C127H(5,𝔽2)12yes—
250C23×C1272−1+412yes—
251D4×C127—232no—
252C2×C4×C127—22no—
253C2×C4×C127—24no—
254C2×C4×C127—22no—
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—24no—
262C2×C4×C127—22no—
263C2×C4×C127—22no—
264C2×C4×C127—22no—
265C2×C4×C127—22no—
266C2×C4×C127—24no—
267C2×C4×C127—24no—
268C2×C4×C127—24no—
269C2×C4×C127—24no—
270C2×C4×C127—24no—
271C2×C4×C127—24no—
272C2×C4×C127—24no—
273C2×C4×C127—22no—
274C2×C4×C127—24no—
275C2×C4×C127—24no—
276C2×C4×C127—22no—
277C2×C4×C127—22no—
278C2×C4×C127—24no—
279C2×C4×C127—24no—
280C2×C4×C127—24no—
281C2×C4×C127—24no—
282C2×C4×C127—432no—
283C2×C4×C127—41no—
284C2×C4×C127—41no—
285C2×C4×C127—42no—
286C2×C4×C127—41no—
287C2×C4×C127—41no—
288C2×C4×C127—42no—
289C2×C4×C127—41no—
290C2×C4×C127—41no—
291C2×C4×C127—42no—
292C2×C4×C127—42no—
293C2×C4×C127—42no—
294C2×C4×C127—42no—
295C2×C4×C127—42no—
296C2×C4×C127—42no—
297C2×C4×C127—42no—
298C2×C4×C127—42no—
299C2×C4×C127—42no—
300C2×C4×C127—42no—
301C2×C4×C127—42no—
302C2×C4×C127—42no—
303C2×C4×C127—42no—
304C2×C4×C127—42no—
305C2×C4×C127—42no—
306C2×C4×C127—42no—
307C2×C4×C127C4×D414yes—
308C2×C4×C127C4×D414yescomplemented
309C2×C4×C127#12014yes—
310C2×C4×C127#12114yes—
311C22×C127—28no—
312C22×C127—28no—
313C22×C127—28no—
314C22×C127—44no—
315C22×C127—44no—
316C22×C127—44no—
317C22×C127—44no—
318C22×C127—44no—
319C22×C127—44no—
320C22×C127—44no—
321C22×C127—44no—
322C22×C127—44no—
323C22×C127—44no—
324C22×C127—44no—
325C22×C127—44no—
326C22×C127C2×C4×D411yescharacteristic
327C22×C127C2×C4×D412yes—
328C22×C127C2×C4×D411yescharacteristic
329C22×C127C4×#4111yescharacteristic
330C22×C127#52012yes—
331C22×C127C2×#12011yescharacteristic
332C22×C127C2×#12111yescharacteristic
333C22×C127#52511yescharacteristic
334C22×C127#52511yescharacteristic
335C22×C127#52512yes—
336C22×C127#52911yescharacteristic
337C22×C127#53211yescharacteristic
338C22×C127#53511yescharacteristic
339C22×C127#53611yescharacteristic
340C22×C127#54212yes—
341C22×C127D4212yes—
342C22×C127#54612yes—
343C22×C127#54712yes—
344C22×C127#54712yes—
345C22×C127#54812yes—
346C22×C127#55112yes—
347C22×C127#55212yes—
348C22×C127#55312yes—
349C4×C127—24no—
350C4×C127—24no—
351C4×C127—24no—
352C4×C127—24no—
353C4×C127—42no—
354C4×C127—44no—
355C4×C127—42no—
356C4×C127—44no—
357C4×C127—42no—
358C4×C127—82no—
359#14176C12711yesmaximal, characteristic, direct product factor, Sylow
360C2×C127—48no—
361C2×C127C4×#12011yescharacteristic
362C2×C127C4×#12111yescharacteristic
363C2×C127#232611yescharacteristic
364C2×C127#235912yes—
365C2×C127#236112yes—
366C2×C127#240611yescharacteristic
367C2×C127#240811yescharacteristic
368C2×C127#246112yes—
369C2×C127#246812yes—
370C2×C127#253611yescharacteristic
371C2×C127#259811yescharacteristic
372C22×C4×D4C2×C12711yescharacteristic
373C2×#394C2×C12711yescharacteristic
374C2×#388C2×C12712yescomplemented
375C2×#385C2×C12712yescomplemented
376C2×C4×C4⋊C4C2×C12711yescharacteristic, complemented
377#1444C2×C12711yescharacteristic, complemented
378#1441C2×C12711yescharacteristic, complemented
379#1438C2×C12711yescharacteristic
380#1437C2×C12712yescomplemented
381#1434C2×C12711yescharacteristic, complemented
382C22⋊#95C2×C12712yescomplemented
383C127#1417611yescharacteristic, direct product factor, Sylow
384C23×D4C22×C12711yescharacteristic
385C24×C4C22×C12712yes—
386C2×C4×D4—28no—
387C2×C4×D4—24no—
388C22×C4⋊C4C22×C12711yescharacteristic
389C22×C4⋊C4C22×C12712yes—
390C22×C4⋊C4C22×C12711yescharacteristic
391C22×C4⋊C4C22×C12711yescharacteristic
392C22×C22⋊C4C22×C12712yes—
393C22×C22⋊C4C22×C12712yes—
394C22×C22⋊C4C22×C12712yes—
395C22×C22⋊C4C22×C12712yes—
396C22×C22⋊C4C22×C12712yes—
397C22×C42C22×C12711yescharacteristic
398C22×C42C22×C12711yescharacteristic
399C22×C42C22×C12711yescharacteristic
400#394C4×C12718yescomplemented
401#388—28no—
402#385—28no—
403C4×C4⋊C4—24no—
404C2×#95C22×C12711yescharacteristic
405C2×#95C22×C12712yes—
406C2×#95C22×C12712yes—
407C2×#95C22×C12712yes—
408C2×#95C22×C12711yescharacteristic
409C2×#95C22×C12712yes—
410C2×#95C22×C12711yescharacteristic
411C2×#95C22×C12712yes—
412C2×#95C22×C12711yescharacteristic
413C25C23×C12712yes—
414C22×D4—24no—
415C22×D4—24no—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4C2×C4×C12714yes—
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4C23×C12712yes—
427C23×C4C23×C12712yes—
428C23×C4C23×C12711yescharacteristic
429C23×C4C23×C12711yescharacteristic
430C23×C4C23×C12712yes—
431C23×C4C23×C12711yescharacteristic
432C23×C4C23×C12711yescharacteristic
433C23×C4C23×C12711yescharacteristic
434C23×C4C23×C12711yescharacteristic
435C23×C4C23×C12711yescharacteristic
436C4×D4—232no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4C2×C4×C12714yescomplemented
447C2×C4⋊C4D4×C12714yescomplemented
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4C2×C4×C12718yescomplemented
461C2×C22⋊C4C2×C4×C12718yescomplemented
462C2×C22⋊C4D4×C12718yes—
463C2×C42—24no—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—22no—
468C2×C42—24no—
469C2×C42D4×C12714yes—
470#95—22no—
471#95—22no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—24no—
476#95—22no—
477#95—42no—
478#95C2×C4×C12714yescomplemented
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24C22×C4×C12714yes—
492C24C2×D4×C12714yes—
493C24#41×C12714yes—
494C24C24×C12711yescharacteristic
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—216no—
498C2×D4—216no—
499C2×D4—28no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—216no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4C22×C4×C12714yes—
550C22×C4C22×C4×C12712yes—
551C22×C4C22×C4×C12712yes—
552C22×C4C22×C4×C12712yes—
553C22×C4C2×D4×C12714yes—
554C22×C4C2×D4×C12712yes—
555C22×C4C2×D4×C12712yes—
556C22×C4C2×D4×C12712yes—
557C22×C4C2×D4×C12714yes—
558C22×C4C2×D4×C12712yes—
559C22×C4C2×D4×C12712yes—
560C22×C4C2×D4×C12712yes—
561C22×C4#41×C12712yes—
562C22×C4#41×C12712yes—
563C22×C4#41×C12712yes—
564C22×C4#41×C12712yes—
565C4⋊C4—28no—
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—48no—
569C22⋊C4—216no—
570C22⋊C4—216no—
571C22⋊C4—216no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C42—28no—
575C42—28no—
576C42—44no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23C4×D4×C12718yes—
612C23C23×C4×C12711yescharacteristic
613C23C22×D4×C12711yescharacteristic
614C23C22×D4×C12712yes—
615C23C22×D4×C12711yescharacteristic
616C23C2×#41×C12711yescharacteristic
617C23C2×#41×C12712yes—
618C23C2×#41×C12711yescharacteristic
619C23C2×#41×C12711yescharacteristic
620C23C2×#41×C12711yescharacteristic
621C23H(5,𝔽2)×C12712yes—
622C232−1+4×C12712yes—
623D4—232no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—432no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4C4×D4×C12714yes—
680C2×C4C4×D4×C12714yescomplemented
681C2×C4#120×C12714yes—
682C2×C4#121×C12714yes—
683C22—28no—
684C22—28no—
685C22—28no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22C2×C4×D4×C12711yescharacteristic
699C22C2×C4×D4×C12712yes—
700C22C2×C4×D4×C12711yescharacteristic
701C22C4×#41×C12711yescharacteristic
702C22#520×C12712yes—
703C22C2×#120×C12711yescharacteristic
704C22C2×#121×C12711yescharacteristic
705C22#525×C12711yescharacteristic
706C22#525×C12711yescharacteristic
707C22#525×C12712yes—
708C22#529×C12711yescharacteristic
709C22#532×C12711yescharacteristic
710C22#535×C12711yescharacteristic
711C22#536×C12711yescharacteristic
712C22#542×C12712yes—
713C22D42×C12712yes—
714C22#546×C12712yes—
715C22#547×C12712yes—
716C22#547×C12712yes—
717C22#548×C12712yes—
718C22#551×C12712yes—
719C22#552×C12712yes—
720C22#553×C12712yes—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—42no—
726C4—44no—
727C4—44no—
728C4—42no—
729C4—42no—
730C4—82no—
731C2—48no—
732C2C4×#120×C12711yescharacteristic
733C2C4×#121×C12711yescharacteristic
734C2C127×#232611yescharacteristic
735C2C127×#235912yes—
736C2C127×#236112yes—
737C2C127×#240611yescharacteristic
738C2C127×#240811yescharacteristic
739C2C127×#246112yes—
740C2C127×#246812yes—
741C2C127×#253611yescharacteristic
742C2C127×#259811yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#388×C127C2semidirect
4. C2×#385×C127C2semidirect
5. C2×C4×C4⋊C4×C127C2semidirect
6. C127×#1444C2semidirect
7. C127×#1441C2semidirect
9. C127×#1437C2semidirect
10. C127×#1434C2semidirect
11. C127×C22⋊#95C2semidirect
28. #394×C127C4semidirect
74. C2×C4⋊C4×C127C2×C4semidirect
75. C2×C4⋊C4×C127D4semidirect
88. C2×C22⋊C4×C127C2×C4semidirect
89. C2×C22⋊C4×C127C2×C4semidirect
106. #95×C127C2×C4semidirect
308. C2×C4×C127C4×D4semidirect
359. #14176C127direct (N × H)
374. C2×#388C2×C127semidirect
375. C2×#385C2×C127semidirect
376. C2×C4×C4⋊C4C2×C127semidirect
377. #1444C2×C127semidirect
378. #1441C2×C127semidirect
380. #1437C2×C127semidirect
381. #1434C2×C127semidirect
382. C22⋊#95C2×C127semidirect
383. C127#14176direct (N × H)
400. #394C4×C127semidirect
446. C2×C4⋊C4C2×C4×C127semidirect
447. C2×C4⋊C4D4×C127semidirect
460. C2×C22⋊C4C2×C4×C127semidirect
461. C2×C22⋊C4C2×C4×C127semidirect
478. #95C2×C4×C127semidirect
680. C2×C4C4×D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C2×#394×C1272
C2×#388×C1272
C2×#385×C1272
C2×C4×C4⋊C4×C1272
C127×#14442
C127×#14412
C127×#14382
C127×#14372
C127×#14342
C127×C22⋊#952
#14176127