Finite Group Databasebeta

← C127×#14505 #44578178

Subgroups — C127×#14505 #44578178

Order 32512.

2070 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C211yesmaximal, characteristic
2C2×#390×C127C211yesmaximal, characteristic
3C2×#386×C127C211yesmaximal, characteristic
4C127×#1441C212yesmaximal, complemented
5C127×#1440C212yesmaximal, complemented
6C127×#1440C212yesmaximal, complemented
7C127×#1436C212yesmaximal, complemented
8C127×C22⋊#95C212yesmaximal, complemented
9C127×C22⋊#95C212yesmaximal, complemented
10C23×D4×C127C2211yescharacteristic
11C24×C4×C127C2211yescharacteristic
12C24×C4×C127C2211yescharacteristic
13C2×#123×C127—24no—
14C2×#123×C127—24no—
15C2×#123×C127C418yescomplemented
16C22×C4⋊C4×C127C2212yes—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C42×C127C2211yescharacteristic
25#390×C127—24no—
26#386×C127—24no—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C25×C127C2311yescharacteristic
37C25×C127C2311yescharacteristic
38C22×D4×C127—41no—
39C22×D4×C127—41no—
40C22×D4×C127—41no—
41C22×D4×C127—41no—
42C22×D4×C127C2×C414yes—
43C22×D4×C127D414yes—
44C22×D4×C127D414yes—
45C23×C4×C127—22no—
46C23×C4×C127—22no—
47C23×C4×C127—22no—
48C23×C4×C127—24no—
49C23×C4×C127—41no—
50C23×C4×C127—41no—
51C23×C4×C127—41no—
52C23×C4×C127—41no—
53C23×C4×C127—41no—
54C23×C4×C127—41no—
55C23×C4×C127—42no—
56C23×C4×C127C2×C414yescomplemented
57C23×C4×C127C2312yes—
58C23×C4×C127C2312yes—
59C23×C4×C127C2312yes—
60C23×C4×C127C2312yes—
61C23×C4×C127C2312yes—
62C23×C4×C127C2312yes—
63C23×C4×C127C2311yescharacteristic
64#123×C127—232no—
65C2×C4⋊C4×C127—24no—
66C2×C4⋊C4×C127—24no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—41no—
69C2×C4⋊C4×C127—41no—
70C2×C4⋊C4×C127C2×C418yescomplemented
71C2×C22⋊C4×C127—24no—
72C2×C22⋊C4×C127—24no—
73C2×C22⋊C4×C127—22no—
74C2×C22⋊C4×C127—22no—
75C2×C22⋊C4×C127—24no—
76C2×C22⋊C4×C127—22no—
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—42no—
83C2×C22⋊C4×C127—42no—
84C2×C22⋊C4×C127—42no—
85C2×C22⋊C4×C127—41no—
86C2×C22⋊C4×C127—41no—
87C2×C22⋊C4×C127C2×C418yes—
88C2×C22⋊C4×C127C2×C414yescomplemented
89C2×C42×C127—22no—
90C2×C42×C127—41no—
91C2×C42×C127—41no—
92#95×C127—24no—
93#95×C127—24no—
94#95×C127—24no—
95#95×C127—42no—
96#95×C127—42no—
97#95×C127—42no—
98#95×C127—42no—
99#95×C127—42no—
100#95×C127—42no—
101C24×C127—22no—
102C24×C127—22no—
103C24×C127—22no—
104C24×C127—22no—
105C24×C127—22no—
106C24×C127—22no—
107C24×C127—21no—
108C24×C127—21no—
109C24×C127—21no—
110C24×C127—21no—
111C24×C127—21no—
112C24×C127—21no—
113C24×C127—21no—
114C24×C127—21no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127C22×C412yes—
118C24×C127C22×C412yes—
119C24×C127C2×D412yes—
120C24×C127C2×D412yes—
121C24×C127C2×D412yes—
122C24×C127C2×D412yes—
123C24×C127C2411yescharacteristic
124C2×D4×C127—44no—
125C2×D4×C127—44no—
126C2×D4×C127—44no—
127C2×D4×C127—44no—
128C2×D4×C127—44no—
129C2×D4×C127—44no—
130C2×D4×C127C22⋊C4116yes—
131C22×C4×C127—21no—
132C22×C4×C127—21no—
133C22×C4×C127—21no—
134C22×C4×C127—21no—
135C22×C4×C127—28no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
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×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—22no—
155C22×C4×C127—22no—
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×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—22no—
172C22×C4×C127—22no—
173C22×C4×C127—22no—
174C22×C4×C127—44no—
175C22×C4×C127—44no—
176C22×C4×C127—44no—
177C22×C4×C127—48no—
178C22×C4×C127—48no—
179C22×C4×C127—44no—
180C22×C4×C127—44no—
181C22×C4×C127—44no—
182C22×C4×C127—44no—
183C22×C4×C127—44no—
184C22×C4×C127—44no—
185C22×C4×C127C22×C414yes—
186C22×C4×C127C22×C414yes—
187C22×C4×C127C22×C412yes—
188C22×C4×C127C2×D412yes—
189C22×C4×C127C2×D412yes—
190C22×C4×C127#4114yes—
191C22×C4×C127#4114yes—
192C4⋊C4×C127—216no—
193C4⋊C4×C127—44no—
194C22⋊C4×C127—216no—
195C22⋊C4×C127—28no—
196C22⋊C4×C127—48no—
197C22⋊C4×C127—48no—
198C22⋊C4×C127—48no—
199C22⋊C4×C127—44no—
200C42×C127—44no—
201C23×C127—24no—
202C23×C127—24no—
203C23×C127—22no—
204C23×C127—22no—
205C23×C127—22no—
206C23×C127—22no—
207C23×C127—24no—
208C23×C127—24no—
209C23×C127—22no—
210C23×C127—22no—
211C23×C127—22no—
212C23×C127—22no—
213C23×C127—22no—
214C23×C127—22no—
215C23×C127—22no—
216C23×C127—22no—
217C23×C127—24no—
218C23×C127—24no—
219C23×C127—24no—
220C23×C127—24no—
221C23×C127—24no—
222C23×C127—24no—
223C23×C127—24no—
224C23×C127—24no—
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—41no—
234C23×C127—41no—
235C23×C127—42no—
236C23×C127—42no—
237C23×C127—41no—
238C23×C127—41no—
239C23×C127—41no—
240C23×C127—41no—
241C23×C127—42no—
242C23×C127—42no—
243C23×C127—41no—
244C23×C127—41no—
245C23×C127C2×C22⋊C414yes—
246C23×C127C2×C22⋊C414yes—
247C23×C127C23×C411yescharacteristic
248C23×C127C22×D411yescharacteristic
249C23×C127C22×D411yescharacteristic
250C23×C127C2×#4112yes—
251C23×C127C2×#4112yes—
252C23×C127H(5,𝔽2)11yescharacteristic
253C23×C127H(5,𝔽2)11yescharacteristic
254C23×C127H(5,𝔽2)11yescharacteristic
255C23×C127H(5,𝔽2)11yescharacteristic
256C23×C127H(5,𝔽2)12yes—
257C23×C1272−1+412yes—
258D4×C127—416no—
259C2×C4×C127—22no—
260C2×C4×C127—22no—
261C2×C4×C127—22no—
262C2×C4×C127—22no—
263C2×C4×C127—22no—
264C2×C4×C127—22no—
265C2×C4×C127—24no—
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—24no—
274C2×C4×C127—24no—
275C2×C4×C127—24no—
276C2×C4×C127—24no—
277C2×C4×C127—416no—
278C2×C4×C127—416no—
279C2×C4×C127—42no—
280C2×C4×C127—42no—
281C2×C4×C127—42no—
282C2×C4×C127—42no—
283C2×C4×C127—42no—
284C2×C4×C127—42no—
285C2×C4×C127—42no—
286C2×C4×C127—42no—
287C2×C4×C127—42no—
288C2×C4×C127—42no—
289C2×C4×C127—42no—
290C2×C4×C127—42no—
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×C127—42no—
308C2×C4×C127—42no—
309C2×C4×C127C2×C22⋊C414yes—
310C22×C127—24no—
311C22×C127—24no—
312C22×C127—28no—
313C22×C127—28no—
314C22×C127—44no—
315C22×C127—44no—
316C22×C127—42no—
317C22×C127—42no—
318C22×C127—42no—
319C22×C127—42no—
320C22×C127—42no—
321C22×C127—42no—
322C22×C127—44no—
323C22×C127—44no—
324C22×C127—44no—
325C22×C127—44no—
326C22×C127—42no—
327C22×C127—42no—
328C22×C127—42no—
329C22×C127—42no—
330C22×C127—42no—
331C22×C127—42no—
332C22×C127C22×C22⋊C411yescharacteristic
333C22×C127C4×#4112yes—
334C22×C127#51811yescharacteristic
335C22×C127#51811yescharacteristic
336C22×C127#52012yes—
337C22×C127#53411yescharacteristic
338C22×C127#53411yescharacteristic
339C22×C127#53411yescharacteristic
340C22×C127#53411yescharacteristic
341C22×C127#53812yes—
342C22×C127#53912yes—
343C22×C127#54012yes—
344C22×C127#54212yes—
345C22×C127#54612yes—
346C22×C127#54612yes—
347C22×C127#54712yes—
348C22×C127#54712yes—
349C22×C127#55111yescharacteristic
350C22×C127#55312yes—
351C22×C127#55911yescharacteristic
352C22×C127#56011yescharacteristic
353C22×C127#56212yes—
354C22×C127#56311yescharacteristic
355C4×C127—24no—
356C4×C127—44no—
357C4×C127—44no—
358C4×C127—44no—
359C4×C127—44no—
360C4×C127—82no—
361C4×C127—82no—
362#14505C12711yesmaximal, characteristic, direct product factor, Sylow
363C2×C127—44no—
364C2×C127—44no—
365C2×C127#230811yescharacteristic
366C2×C127#233512yes—
367C2×C127#233912yes—
368C2×C127#237411yescharacteristic
369C2×C127#237611yescharacteristic
370C2×C127#269711yescharacteristic
371C2×C127#270112yes—
372C2×C127#270812yes—
373C2×C127#270911yescharacteristic
374C2×C127#271711yescharacteristic
375C2×C127#272411yescharacteristic
376C22×#123C2×C12711yescharacteristic
377C2×#390C2×C12711yescharacteristic
378C2×#386C2×C12711yescharacteristic
379#1441C2×C12712yescomplemented
380#1440C2×C12712yescomplemented
381#1440C2×C12712yescomplemented
382#1436C2×C12712yescomplemented
383C22⋊#95C2×C12712yescomplemented
384C22⋊#95C2×C12712yescomplemented
385C127#1450511yescharacteristic, direct product factor, Sylow
386C23×D4C22×C12711yescharacteristic
387C24×C4C22×C12711yescharacteristic
388C24×C4C22×C12711yescharacteristic
389C2×#123—24no—
390C2×#123—24no—
391C2×#123C4×C12718yescomplemented
392C22×C4⋊C4C22×C12712yes—
393C22×C4⋊C4C22×C12711yescharacteristic
394C22×C22⋊C4C22×C12712yes—
395C22×C22⋊C4C22×C12712yes—
396C22×C22⋊C4C22×C12712yes—
397C22×C22⋊C4C22×C12712yes—
398C22×C22⋊C4C22×C12711yescharacteristic
399C22×C22⋊C4C22×C12711yescharacteristic
400C22×C42C22×C12711yescharacteristic
401#390—24no—
402#386—24no—
403C2×#95C22×C12712yes—
404C2×#95C22×C12712yes—
405C2×#95C22×C12712yes—
406C2×#95C22×C12712yes—
407C2×#95C22×C12712yes—
408C2×#95C22×C12712yes—
409C2×#95C22×C12712yes—
410C2×#95C22×C12712yes—
411C2×#95C22×C12712yes—
412C25C23×C12711yescharacteristic
413C25C23×C12711yescharacteristic
414C22×D4—41no—
415C22×D4—41no—
416C22×D4—41no—
417C22×D4—41no—
418C22×D4C2×C4×C12714yes—
419C22×D4D4×C12714yes—
420C22×D4D4×C12714yes—
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—24no—
425C23×C4—41no—
426C23×C4—41no—
427C23×C4—41no—
428C23×C4—41no—
429C23×C4—41no—
430C23×C4—41no—
431C23×C4—42no—
432C23×C4C2×C4×C12714yescomplemented
433C23×C4C23×C12712yes—
434C23×C4C23×C12712yes—
435C23×C4C23×C12712yes—
436C23×C4C23×C12712yes—
437C23×C4C23×C12712yes—
438C23×C4C23×C12712yes—
439C23×C4C23×C12711yescharacteristic
440#123—232no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4C2×C4×C12718yescomplemented
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—22no—
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⋊C4—42no—
461C2×C22⋊C4—41no—
462C2×C22⋊C4—41no—
463C2×C22⋊C4C2×C4×C12718yes—
464C2×C22⋊C4C2×C4×C12714yescomplemented
465C2×C42—22no—
466C2×C42—41no—
467C2×C42—41no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95—42no—
476#95—42no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24C22×C4×C12712yes—
494C24C22×C4×C12712yes—
495C24C2×D4×C12712yes—
496C24C2×D4×C12712yes—
497C24C2×D4×C12712yes—
498C24C2×D4×C12712yes—
499C24C24×C12711yescharacteristic
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4C22⋊C4×C127116yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
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—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4C22×C4×C12714yes—
562C22×C4C22×C4×C12714yes—
563C22×C4C22×C4×C12712yes—
564C22×C4C2×D4×C12712yes—
565C22×C4C2×D4×C12712yes—
566C22×C4#41×C12714yes—
567C22×C4#41×C12714yes—
568C4⋊C4—216no—
569C4⋊C4—44no—
570C22⋊C4—216no—
571C22⋊C4—28no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—44no—
576C42—44no—
577C23—24no—
578C23—24no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—41no—
621C23C2×C22⋊C4×C12714yes—
622C23C2×C22⋊C4×C12714yes—
623C23C23×C4×C12711yescharacteristic
624C23C22×D4×C12711yescharacteristic
625C23C22×D4×C12711yescharacteristic
626C23C2×#41×C12712yes—
627C23C2×#41×C12712yes—
628C23H(5,𝔽2)×C12711yescharacteristic
629C23H(5,𝔽2)×C12711yescharacteristic
630C23H(5,𝔽2)×C12711yescharacteristic
631C23H(5,𝔽2)×C12711yescharacteristic
632C23H(5,𝔽2)×C12712yes—
633C232−1+4×C12712yes—
634D4—416no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—416no—
654C2×C4—416no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
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×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4C2×C22⋊C4×C12714yes—
686C22—28no—
687C22—28no—
688C22—24no—
689C22—24no—
690C22—44no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—44no—
699C22—44no—
700C22—44no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22C22×C22⋊C4×C12711yescharacteristic
709C22C4×#41×C12712yes—
710C22#518×C12711yescharacteristic
711C22#518×C12711yescharacteristic
712C22#520×C12712yes—
713C22#534×C12711yescharacteristic
714C22#534×C12711yescharacteristic
715C22#534×C12711yescharacteristic
716C22#534×C12711yescharacteristic
717C22#538×C12712yes—
718C22#539×C12712yes—
719C22#540×C12712yes—
720C22#542×C12712yes—
721C22#546×C12712yes—
722C22#546×C12712yes—
723C22#547×C12712yes—
724C22#547×C12712yes—
725C22#551×C12711yescharacteristic
726C22#553×C12712yes—
727C22#559×C12711yescharacteristic
728C22#560×C12711yescharacteristic
729C22#562×C12712yes—
730C22#563×C12711yescharacteristic
731C4—24no—
732C4—44no—
733C4—44no—
734C4—44no—
735C4—44no—
736C4—82no—
737C4—82no—
738C2—44no—
739C2—44no—
740C2C127×#230811yescharacteristic
741C2C127×#233512yes—
742C2C127×#233912yes—
743C2C127×#237411yescharacteristic
744C2C127×#237611yescharacteristic
745C2C127×#269711yescharacteristic
746C2C127×#270112yes—
747C2C127×#270812yes—
748C2C127×#270911yescharacteristic
749C2C127×#271711yescharacteristic
750C2C127×#272411yescharacteristic
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
4. C127×#1441C2semidirect
5. C127×#1440C2semidirect
6. C127×#1440C2semidirect
7. C127×#1436C2semidirect
8. C127×C22⋊#95C2semidirect
9. C127×C22⋊#95C2semidirect
15. C2×#123×C127C4semidirect
56. C23×C4×C127C2×C4semidirect
70. C2×C4⋊C4×C127C2×C4semidirect
88. C2×C22⋊C4×C127C2×C4semidirect
362. #14505C127direct (N × H)
379. #1441C2×C127semidirect
380. #1440C2×C127semidirect
381. #1440C2×C127semidirect
382. #1436C2×C127semidirect
383. C22⋊#95C2×C127semidirect
384. C22⋊#95C2×C127semidirect
385. C127#14505direct (N × H)
391. C2×#123C4×C127semidirect
432. C23×C4C2×C4×C127semidirect
446. C2×C4⋊C4C2×C4×C127semidirect
464. C2×C22⋊C4C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C2×#390×C1272
C2×#386×C1272
C127×#14412
C127×#14402
C127×#14362
C127×C22⋊#952
#14505127