Finite Group Databasebeta

← C127×#14728 #44578401

Subgroups — C127×#14728 #44578401

Order 32512.

2190 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C127C211yesmaximal, characteristic
2C2×#398×C127C212yesmaximal, complemented
3C2×#385×C127C211yesmaximal, characteristic
4C2×#385×C127C211yesmaximal, characteristic
5C2×#380×C127C211yesmaximal, characteristic
6C127×#1444C212yesmaximal, complemented
7C127×#1442C212yesmaximal, complemented
8C127×#1441C212yesmaximal, complemented
9C127×C22⋊#95C211yesmaximal, characteristic
10C127×C22⋊#95C211yesmaximal, characteristic
11C127×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127—24no—
16C22×C4⋊C4×C127—28no—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2212yes—
19C22×C4⋊C4×C127C2212yes—
20C22×C4⋊C4×C127C2212yes—
21C22×C4⋊C4×C127C2212yes—
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27#398×C127—28no—
28#385×C127—24no—
29#385×C127—24no—
30#380×C127—24no—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C25×C127C2311yescharacteristic
42C23×C4×C127—22no—
43C23×C4×C127—22no—
44C23×C4×C127—24no—
45C23×C4×C127—24no—
46C23×C4×C127—22no—
47C23×C4×C127—22no—
48C23×C4×C127—22no—
49C23×C4×C127—24no—
50C23×C4×C127—24no—
51C23×C4×C127—22no—
52C23×C4×C127—22no—
53C23×C4×C127—42no—
54C23×C4×C127—42no—
55C23×C4×C127D414yes—
56C23×C4×C127Q814yes—
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2312yes—
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2312yes—
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2312yes—
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2312yes—
67C2×C4⋊C4×C127—232no—
68C2×C4⋊C4×C127—24no—
69C2×C4⋊C4×C127—24no—
70C2×C4⋊C4×C127—24no—
71C2×C4⋊C4×C127—24no—
72C2×C4⋊C4×C127—24no—
73C2×C4⋊C4×C127—24no—
74C2×C4⋊C4×C127—24no—
75C2×C4⋊C4×C127—22no—
76C2×C4⋊C4×C127—22no—
77C2×C4⋊C4×C127—24no—
78C2×C4⋊C4×C127—24no—
79C2×C4⋊C4×C127—24no—
80C2×C4⋊C4×C127—42no—
81C2×C4⋊C4×C127—42no—
82C2×C4⋊C4×C127—42no—
83C2×C4⋊C4×C127D418yes—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—22no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127D414yes—
95C2×C22⋊C4×C127Q814yes—
96#95×C127—24no—
97#95×C127—22no—
98#95×C127—22no—
99#95×C127—24no—
100#95×C127—24no—
101#95×C127—24no—
102#95×C127—24no—
103#95×C127—24no—
104#95×C127—24no—
105#95×C127—42no—
106C24×C127—22no—
107C24×C127—22no—
108C24×C127—22no—
109C24×C127—22no—
110C24×C127C2×D412yes—
111C24×C127C2×D412yes—
112C24×C127C2×Q812yes—
113C24×C127C2×Q812yes—
114C24×C127#4112yes—
115C24×C127#4112yes—
116C24×C127#4112yes—
117C24×C127C2411yescharacteristic
118C22×C4×C127—28no—
119C22×C4×C127—216no—
120C22×C4×C127—28no—
121C22×C4×C127—28no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—216no—
130C22×C4×C127—28no—
131C22×C4×C127—28no—
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—22no—
142C22×C4×C127—22no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—21no—
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—28no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—22no—
160C22×C4×C127—22no—
161C22×C4×C127—22no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
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—48no—
176C22×C4×C127—48no—
177C22×C4×C127—48no—
178C22×C4×C127—48no—
179C22×C4×C127—44no—
180C22×C4×C127—44no—
181C22×C4×C127C2×D414yes—
182C22×C4×C127C2×D412yes—
183C22×C4×C127C2×D414yes—
184C22×C4×C127C2×D412yes—
185C22×C4×C127C2×D414yes—
186C22×C4×C127C2×D414yes—
187C22×C4×C127C2×Q812yes—
188C22×C4×C127C2×Q812yes—
189C22×C4×C127C2×Q814yes—
190C22×C4×C127#4114yes—
191C4⋊C4×C127—216no—
192C4⋊C4×C127—216no—
193C4⋊C4×C127—48no—
194C4⋊C4×C127—48no—
195C4⋊C4×C127—44no—
196C4⋊C4×C127—44no—
197C22⋊C4×C127—28no—
198C22⋊C4×C127—28no—
199C22⋊C4×C127—44no—
200C22⋊C4×C127—44no—
201C23×C127—22no—
202C23×C127—24no—
203C23×C127—22no—
204C23×C127—24no—
205C23×C127—22no—
206C23×C127—22no—
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#12114yes—
218C23×C127C22⋊Q814yes—
219C23×C127C22⋊Q814yes—
220C23×C127#12314yes—
221C23×C127#12514yes—
222C23×C127#12514yes—
223C23×C127C4⋊Q814yes—
224C23×C127C22×D411yescharacteristic
225C23×C127C22×D412yes—
226C23×C127C22×D411yescharacteristic
227C23×C127C22×Q811yescharacteristic
228C23×C127C22×Q811yescharacteristic
229C23×C127C2×#4111yescharacteristic
230C23×C127C2×#4111yescharacteristic
231C23×C127C2×#4111yescharacteristic
232C23×C127C2×#4112yes—
233C23×C127H(5,𝔽2)12yes—
234C23×C1272−1+412yes—
235C2×C4×C127—232no—
236C2×C4×C127—24no—
237C2×C4×C127—22no—
238C2×C4×C127—24no—
239C2×C4×C127—24no—
240C2×C4×C127—24no—
241C2×C4×C127—24no—
242C2×C4×C127—24no—
243C2×C4×C127—22no—
244C2×C4×C127—24no—
245C2×C4×C127—24no—
246C2×C4×C127—22no—
247C2×C4×C127—24no—
248C2×C4×C127—22no—
249C2×C4×C127—22no—
250C2×C4×C127—22no—
251C2×C4×C127—24no—
252C2×C4×C127—22no—
253C2×C4×C127—24no—
254C2×C4×C127—24no—
255C2×C4×C127—24no—
256C2×C4×C127—24no—
257C2×C4×C127—24no—
258C2×C4×C127—24no—
259C2×C4×C127—416no—
260C2×C4×C127—416no—
261C2×C4×C127—41no—
262C2×C4×C127—42no—
263C2×C4×C127—41no—
264C2×C4×C127—42no—
265C2×C4×C127—41no—
266C2×C4×C127—42no—
267C2×C4×C127—41no—
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—42no—
277C2×C4×C127—41no—
278C2×C4×C127—41no—
279C2×C4×C127—41no—
280C2×C4×C127—42no—
281C2×C4×C127—41no—
282C2×C4×C127—42no—
283C2×C4×C127—41no—
284C2×C4×C127—41no—
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#12014yes—
295C2×C4×C127C22⋊Q818yes—
296C22×C127—24no—
297C22×C127—24no—
298C22×C127—24no—
299C22×C127—24no—
300C22×C127—24no—
301C22×C127—24no—
302C22×C127—28no—
303C22×C127—28no—
304C22×C127—28no—
305C22×C127—28no—
306C22×C127#39818yescomplemented
307C22×C127C2×#12011yescharacteristic
308C22×C127C2×#12111yescharacteristic
309C22×C127C2×C22⋊Q811yescharacteristic
310C22×C127C2×C22⋊Q811yescharacteristic
311C22×C127C2×C22⋊Q812yes—
312C22×C127C2×#12311yescharacteristic
313C22×C127#52511yescharacteristic
314C22×C127#52512yes—
315C22×C127C2×#12511yescharacteristic
316C22×C127C2×#12511yescharacteristic
317C22×C127C2×C4⋊Q811yescharacteristic
318C22×C127#53411yescharacteristic
319C22×C127#53611yescharacteristic
320C22×C127#53912yes—
321C22×C127#54412yes—
322C22×C127D4212yes—
323C22×C127#54612yes—
324C22×C127#54712yes—
325C22×C127#54812yes—
326C22×C127D4×Q812yes—
327C22×C127#55212yes—
328C22×C127#55312yes—
329C22×C127#55412yes—
330C4×C127—28no—
331C4×C127—24no—
332C4×C127—42no—
333C4×C127—42no—
334C4×C127—42no—
335C4×C127—44no—
336C4×C127—44no—
337C4×C127—81no—
338C4×C127—81no—
339C4×C127—82no—
340#14728C12711yesmaximal, characteristic, direct product factor, Sylow
341C2×C127—28no—
342C2×C127C2×#39811yescharacteristic
343C2×C127#240911yescharacteristic
344C2×C127#241011yescharacteristic
345C2×C127#241311yescharacteristic
346C2×C127#244012yes—
347C2×C127#244212yes—
348C2×C127#244312yes—
349C2×C127#247312yes—
350C2×C127#257911yescharacteristic
351C2×C127#262711yescharacteristic
352C2×C127#284811yescharacteristic
353C23×C4⋊C4C2×C12711yescharacteristic
354C2×#398C2×C12712yescomplemented
355C2×#385C2×C12711yescharacteristic
356C2×#385C2×C12711yescharacteristic
357C2×#380C2×C12711yescharacteristic
358#1444C2×C12712yescomplemented
359#1442C2×C12712yescomplemented
360#1441C2×C12712yescomplemented
361C22⋊#95C2×C12711yescharacteristic
362C22⋊#95C2×C12711yescharacteristic
363C22⋊#95C2×C12711yescharacteristic
364C127#1472811yescharacteristic, direct product factor, Sylow
365C24×C4C22×C12711yescharacteristic
366C24×C4C22×C12711yescharacteristic
367C24×C4C22×C12711yescharacteristic
368C22×C4⋊C4—24no—
369C22×C4⋊C4—28no—
370C22×C4⋊C4C22×C12711yescharacteristic
371C22×C4⋊C4C22×C12712yes—
372C22×C4⋊C4C22×C12712yes—
373C22×C4⋊C4C22×C12712yes—
374C22×C4⋊C4C22×C12712yes—
375C22×C4⋊C4C22×C12711yescharacteristic
376C22×C22⋊C4C22×C12711yescharacteristic
377C22×C22⋊C4C22×C12711yescharacteristic
378C22×C22⋊C4C22×C12711yescharacteristic
379C22×C22⋊C4C22×C12711yescharacteristic
380#398—28no—
381#385—24no—
382#385—24no—
383#380—24no—
384C2×#95C22×C12712yes—
385C2×#95C22×C12712yes—
386C2×#95C22×C12712yes—
387C2×#95C22×C12712yes—
388C2×#95C22×C12712yes—
389C2×#95C22×C12711yescharacteristic
390C2×#95C22×C12712yes—
391C2×#95C22×C12711yescharacteristic
392C2×#95C22×C12712yes—
393C2×#95C22×C12712yes—
394C25C23×C12711yescharacteristic
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4D4×C12714yes—
409C23×C4Q8×C12714yes—
410C23×C4C23×C12711yescharacteristic
411C23×C4C23×C12712yes—
412C23×C4C23×C12711yescharacteristic
413C23×C4C23×C12712yes—
414C23×C4C23×C12711yescharacteristic
415C23×C4C23×C12712yes—
416C23×C4C23×C12711yescharacteristic
417C23×C4C23×C12711yescharacteristic
418C23×C4C23×C12711yescharacteristic
419C23×C4C23×C12712yes—
420C2×C4⋊C4—232no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4D4×C12718yes—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4D4×C12714yes—
448C2×C22⋊C4Q8×C12714yes—
449#95—24no—
450#95—22no—
451#95—22no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—42no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24C2×D4×C12712yes—
464C24C2×D4×C12712yes—
465C24C2×Q8×C12712yes—
466C24C2×Q8×C12712yes—
467C24#41×C12712yes—
468C24#41×C12712yes—
469C24#41×C12712yes—
470C24C24×C12711yescharacteristic
471C22×C4—28no—
472C22×C4—216no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—216no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—28no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—44no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4C2×D4×C12714yes—
535C22×C4C2×D4×C12712yes—
536C22×C4C2×D4×C12714yes—
537C22×C4C2×D4×C12712yes—
538C22×C4C2×D4×C12714yes—
539C22×C4C2×D4×C12714yes—
540C22×C4C2×Q8×C12712yes—
541C22×C4C2×Q8×C12712yes—
542C22×C4C2×Q8×C12714yes—
543C22×C4#41×C12714yes—
544C4⋊C4—216no—
545C4⋊C4—216no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—44no—
549C4⋊C4—44no—
550C22⋊C4—28no—
551C22⋊C4—28no—
552C22⋊C4—44no—
553C22⋊C4—44no—
554C23—22no—
555C23—24no—
556C23—22no—
557C23—24no—
558C23—22no—
559C23—22no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23#121×C12714yes—
571C23C22⋊Q8×C12714yes—
572C23C22⋊Q8×C12714yes—
573C23#123×C12714yes—
574C23#125×C12714yes—
575C23#125×C12714yes—
576C23C4⋊Q8×C12714yes—
577C23C22×D4×C12711yescharacteristic
578C23C22×D4×C12712yes—
579C23C22×D4×C12711yescharacteristic
580C23C22×Q8×C12711yescharacteristic
581C23C22×Q8×C12711yescharacteristic
582C23C2×#41×C12711yescharacteristic
583C23C2×#41×C12711yescharacteristic
584C23C2×#41×C12711yescharacteristic
585C23C2×#41×C12712yes—
586C23H(5,𝔽2)×C12712yes—
587C232−1+4×C12712yes—
588C2×C4—232no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—416no—
613C2×C4—416no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4#120×C12714yes—
648C2×C4C22⋊Q8×C12718yes—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22—24no—
654C22—24no—
655C22—28no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22#398×C12718yescomplemented
660C22C2×#120×C12711yescharacteristic
661C22C2×#121×C12711yescharacteristic
662C22C2×C22⋊Q8×C12711yescharacteristic
663C22C2×C22⋊Q8×C12711yescharacteristic
664C22C2×C22⋊Q8×C12712yes—
665C22C2×#123×C12711yescharacteristic
666C22#525×C12711yescharacteristic
667C22#525×C12712yes—
668C22C2×#125×C12711yescharacteristic
669C22C2×#125×C12711yescharacteristic
670C22C2×C4⋊Q8×C12711yescharacteristic
671C22#534×C12711yescharacteristic
672C22#536×C12711yescharacteristic
673C22#539×C12712yes—
674C22#544×C12712yes—
675C22D42×C12712yes—
676C22#546×C12712yes—
677C22#547×C12712yes—
678C22#548×C12712yes—
679C22D4×Q8×C12712yes—
680C22#552×C12712yes—
681C22#553×C12712yes—
682C22#554×C12712yes—
683C4—28no—
684C4—24no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—44no—
689C4—44no—
690C4—81no—
691C4—81no—
692C4—82no—
693C2—28no—
694C2C2×#398×C12711yescharacteristic
695C2C127×#240911yescharacteristic
696C2C127×#241011yescharacteristic
697C2C127×#241311yescharacteristic
698C2C127×#244012yes—
699C2C127×#244212yes—
700C2C127×#244312yes—
701C2C127×#247312yes—
702C2C127×#257911yescharacteristic
703C2C127×#262711yescharacteristic
704C2C127×#284811yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#398×C127C2semidirect
6. C127×#1444C2semidirect
7. C127×#1442C2semidirect
8. C127×#1441C2semidirect
306. C22×C127#398semidirect
340. #14728C127direct (N × H)
354. C2×#398C2×C127semidirect
358. #1444C2×C127semidirect
359. #1442C2×C127semidirect
360. #1441C2×C127semidirect
364. C127#14728direct (N × H)
659. C22#398×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C1272
C2×#398×C1272
C2×#385×C1272
C2×#380×C1272
C127×#14442
C127×#14422
C127×#14412
C127×C22⋊#952
#14728127