Finite Group Databasebeta

← C127×#14723 #44578396

Subgroups — C127×#14723 #44578396

Order 32512.

2558 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
2C22×C4×D4×C127C211yesmaximal, characteristic
3C2×#395×C127C211yesmaximal, characteristic, complemented
4C2×#393×C127C211yesmaximal, characteristic, complemented
5C2×#385×C127C212yesmaximal, complemented
6C127×#1441C211yesmaximal, characteristic, complemented
7C127×#1439C212yesmaximal, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1438C212yesmaximal
10C127×#1436C212yesmaximal, complemented
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×Q8×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C24×C4×C127C2211yescharacteristic
16C2×C22⋊Q8×C127—24no—
17C2×C22⋊Q8×C127—28no—
18C2×C4×D4×C127—24no—
19C2×C4×D4×C127—24no—
20C2×C4×D4×C127—24no—
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2212yes—
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2212yes—
29C22×C22⋊C4×C127C2212yes—
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C42×C127C2211yescharacteristic
32#395×C127—24no—
33#393×C127—24no—
34#385×C127—28no—
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C2×#95×C127C2212yes—
42C2×#95×C127C2212yes—
43C25×C127C2311yescharacteristic
44C25×C127C2311yescharacteristic
45C22×Q8×C127—24no—
46C22×Q8×C127—22no—
47C22×Q8×C127—22no—
48C22×Q8×C127—22no—
49C22×Q8×C127—42no—
50C22×D4×C127—22no—
51C22×D4×C127—22no—
52C22×D4×C127—22no—
53C22×D4×C127—22no—
54C22×D4×C127—22no—
55C22×D4×C127—22no—
56C22×D4×C127Q814yescomplemented
57C23×C4×C127—22no—
58C23×C4×C127—22no—
59C23×C4×C127—22no—
60C23×C4×C127—22no—
61C23×C4×C127—22no—
62C23×C4×C127—24no—
63C23×C4×C127—24no—
64C23×C4×C127—42no—
65C23×C4×C127—42no—
66C23×C4×C127D414yes—
67C23×C4×C127C2312yes—
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2312yes—
70C23×C4×C127C2312yes—
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2312yes—
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C22⋊Q8×C127—232no—
77C4×D4×C127—232no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—24no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—24no—
83C2×C4⋊C4×C127—24no—
84C2×C4⋊C4×C127—24no—
85C2×C4⋊C4×C127—24no—
86C2×C4⋊C4×C127—42no—
87C2×C4⋊C4×C127D414yes—
88C2×C4⋊C4×C127D418yescomplemented
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127—22no—
95C2×C22⋊C4×C127—22no—
96C2×C22⋊C4×C127—24no—
97C2×C22⋊C4×C127—24no—
98C2×C22⋊C4×C127—24no—
99C2×C22⋊C4×C127—24no—
100C2×C22⋊C4×C127—24no—
101C2×C22⋊C4×C127—24no—
102C2×C22⋊C4×C127—24no—
103C2×C22⋊C4×C127—24no—
104C2×C22⋊C4×C127—42no—
105C2×C22⋊C4×C127—42no—
106C2×C22⋊C4×C127D414yes—
107C2×C42×C127—22no—
108C2×C42×C127—22no—
109C2×C42×C127—22no—
110#95×C127—24no—
111#95×C127—24no—
112#95×C127—24no—
113#95×C127—22no—
114#95×C127—22no—
115#95×C127—24no—
116#95×C127—24no—
117#95×C127—24no—
118C24×C127—22no—
119C24×C127—22no—
120C24×C127—21no—
121C24×C127—21no—
122C24×C127—21no—
123C24×C127—21no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—21no—
127C24×C127—21no—
128C24×C127—21no—
129C24×C127—21no—
130C24×C127—22no—
131C24×C127—22no—
132C24×C127—22no—
133C24×C127—22no—
134C24×C127C2×D412yes—
135C24×C127C2×D412yes—
136C24×C127C2×Q812yes—
137C24×C127C2×Q812yes—
138C24×C127#4112yes—
139C24×C127#4112yes—
140C24×C127C2411yescharacteristic
141C2×Q8×C127—28no—
142C2×Q8×C127—48no—
143C2×Q8×C127—48no—
144C2×Q8×C127—44no—
145C2×Q8×C127—44no—
146C2×D4×C127—28no—
147C2×D4×C127—28no—
148C2×D4×C127—28no—
149C2×D4×C127—28no—
150C2×D4×C127—28no—
151C2×D4×C127—28no—
152C2×D4×C127—28no—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127—22no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—22no—
161C22×C4×C127—22no—
162C22×C4×C127—28no—
163C22×C4×C127—22no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—22no—
167C22×C4×C127—22no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—22no—
171C22×C4×C127—22no—
172C22×C4×C127—21no—
173C22×C4×C127—21no—
174C22×C4×C127—22no—
175C22×C4×C127—22no—
176C22×C4×C127—22no—
177C22×C4×C127—22no—
178C22×C4×C127—22no—
179C22×C4×C127—22no—
180C22×C4×C127—22no—
181C22×C4×C127—22no—
182C22×C4×C127—22no—
183C22×C4×C127—22no—
184C22×C4×C127—22no—
185C22×C4×C127—22no—
186C22×C4×C127—22no—
187C22×C4×C127—22no—
188C22×C4×C127—22no—
189C22×C4×C127—28no—
190C22×C4×C127—28no—
191C22×C4×C127—22no—
192C22×C4×C127—22no—
193C22×C4×C127—22no—
194C22×C4×C127—22no—
195C22×C4×C127—22no—
196C22×C4×C127—22no—
197C22×C4×C127—22no—
198C22×C4×C127—44no—
199C22×C4×C127—48no—
200C22×C4×C127—48no—
201C22×C4×C127—48no—
202C22×C4×C127—48no—
203C22×C4×C127—44no—
204C22×C4×C127—44no—
205C22×C4×C127C2×D412yes—
206C22×C4×C127C2×D414yes—
207C22×C4×C127C2×D414yes—
208C22×C4×C127C2×D412yes—
209C22×C4×C127C2×D412yes—
210C22×C4×C127C2×D412yes—
211C22×C4×C127C2×D414yes—
212C22×C4×C127C2×D412yes—
213C22×C4×C127C2×D412yes—
214C22×C4×C127C2×D412yes—
215C22×C4×C127C2×Q812yes—
216C22×C4×C127#4114yes—
217C22×C4×C127#4112yes—
218C4⋊C4×C127—28no—
219C4⋊C4×C127—28no—
220C4⋊C4×C127—216no—
221C4⋊C4×C127—48no—
222C22⋊C4×C127—216no—
223C22⋊C4×C127—28no—
224C22⋊C4×C127—216no—
225C22⋊C4×C127—28no—
226C22⋊C4×C127—48no—
227C22⋊C4×C127—48no—
228C42×C127—28no—
229C23×C127—22no—
230C23×C127—22no—
231C23×C127—22no—
232C23×C127—22no—
233C23×C127—22no—
234C23×C127—22no—
235C23×C127—22no—
236C23×C127—24no—
237C23×C127—22no—
238C23×C127—22no—
239C23×C127—22no—
240C23×C127—22no—
241C23×C127—22no—
242C23×C127—22no—
243C23×C127—22no—
244C23×C127—22no—
245C23×C127—22no—
246C23×C127—24no—
247C23×C127—24no—
248C23×C127—24no—
249C23×C127—24no—
250C23×C127—24no—
251C23×C127—24no—
252C23×C127—24no—
253C23×C127—24no—
254C23×C127—24no—
255C23×C127—41no—
256C23×C127—42no—
257C23×C127—41no—
258C23×C127—42no—
259C23×C127—42no—
260C23×C127—41no—
261C23×C127—41no—
262C23×C127—42no—
263C23×C127—42no—
264C23×C127—42no—
265C23×C127—42no—
266C23×C127—42no—
267C23×C127—42no—
268C23×C127—42no—
269C23×C127—42no—
270C23×C127—42no—
271C23×C127—42no—
272C23×C127—42no—
273C23×C127C22⋊Q814yes—
274C23×C127C22⋊Q814yescomplemented
275C23×C127C22×D411yescharacteristic
276C23×C127C22×D411yescharacteristic
277C23×C127C22×D411yescharacteristic
278C23×C127C22×D412yes—
279C23×C127C22×Q811yescharacteristic
280C23×C127C2×#4111yescharacteristic
281C23×C127C2×#4111yescharacteristic
282C23×C127C2×#4111yescharacteristic
283C23×C127C2×#4112yes—
284C23×C127H(5,𝔽2)12yes—
285C23×C1272−1+412yes—
286Q8×C127—416no—
287D4×C127—232no—
288C2×C4×C127—22no—
289C2×C4×C127—22no—
290C2×C4×C127—22no—
291C2×C4×C127—22no—
292C2×C4×C127—22no—
293C2×C4×C127—22no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—22no—
298C2×C4×C127—24no—
299C2×C4×C127—24no—
300C2×C4×C127—24no—
301C2×C4×C127—24no—
302C2×C4×C127—22no—
303C2×C4×C127—24no—
304C2×C4×C127—22no—
305C2×C4×C127—24no—
306C2×C4×C127—24no—
307C2×C4×C127—24no—
308C2×C4×C127—24no—
309C2×C4×C127—24no—
310C2×C4×C127—24no—
311C2×C4×C127—24no—
312C2×C4×C127—24no—
313C2×C4×C127—24no—
314C2×C4×C127—24no—
315C2×C4×C127—416no—
316C2×C4×C127—416no—
317C2×C4×C127—41no—
318C2×C4×C127—42no—
319C2×C4×C127—42no—
320C2×C4×C127—42no—
321C2×C4×C127—42no—
322C2×C4×C127—42no—
323C2×C4×C127—42no—
324C2×C4×C127—41no—
325C2×C4×C127—41no—
326C2×C4×C127—42no—
327C2×C4×C127—41no—
328C2×C4×C127—42no—
329C2×C4×C127—42no—
330C2×C4×C127—42no—
331C2×C4×C127—42no—
332C2×C4×C127—42no—
333C2×C4×C127—42no—
334C2×C4×C127—42no—
335C2×C4×C127—42no—
336C2×C4×C127—42no—
337C2×C4×C127—42no—
338C2×C4×C127—42no—
339C2×C4×C127—42no—
340C2×C4×C127—42no—
341C2×C4×C127—42no—
342C2×C4×C127#12014yes—
343C2×C4×C127#12014yes—
344C2×C4×C127C22⋊Q814yescomplemented
345C22×C127—24no—
346C22×C127—24no—
347C22×C127—24no—
348C22×C127—24no—
349C22×C127—28no—
350C22×C127—42no—
351C22×C127—42no—
352C22×C127—42no—
353C22×C127—42no—
354C22×C127—42no—
355C22×C127—42no—
356C22×C127—42no—
357C22×C127—42no—
358C22×C127—42no—
359C22×C127—42no—
360C22×C127—44no—
361C22×C127—44no—
362C22×C127—44no—
363C22×C127—44no—
364C22×C127—44no—
365C22×C127—44no—
366C22×C127—44no—
367C22×C127C2×#12011yescharacteristic
368C22×C127C2×#12011yescharacteristic
369C22×C127C2×C22⋊Q811yescharacteristic
370C22×C127C2×C22⋊Q811yescharacteristic
371C22×C127C2×C22⋊Q811yescharacteristic
372C22×C127#52511yescharacteristic
373C22×C127#52511yescharacteristic
374C22×C127#52511yescharacteristic
375C22×C127#52512yes—
376C22×C127#53211yescharacteristic
377C22×C127#53212yes—
378C22×C127#53411yescharacteristic
379C22×C127#53611yescharacteristic
380C22×C127#53912yes—
381C22×C127#54212yes—
382C22×C127D4212yes—
383C22×C127D4212yes—
384C22×C127#54712yes—
385C22×C127#54812yes—
386C22×C127#54812yes—
387C22×C127D4×Q812yes—
388C22×C127#55112yes—
389C22×C127#55412yes—
390C4×C127—24no—
391C4×C127—24no—
392C4×C127—24no—
393C4×C127—44no—
394C4×C127—42no—
395C4×C127—44no—
396C4×C127—42no—
397C4×C127—44no—
398C4×C127—82no—
399#14723C12711yesmaximal, characteristic, direct product factor, Sylow
400C2×C127—44no—
401C2×C127—44no—
402C2×C127#238811yescharacteristic
403C2×C127#240311yescharacteristic
404C2×C127#240911yescharacteristic
405C2×C127#243211yescharacteristic
406C2×C127#244912yes—
407C2×C127#245212yes—
408C2×C127#246112yes—
409C2×C127#246312yes—
410C2×C127#256411yescharacteristic
411C2×C127#263811yescharacteristic
412C2×C127#284811yescharacteristic
413C22×C22⋊Q8C2×C12711yescharacteristic, complemented
414C22×C4×D4C2×C12711yescharacteristic
415C2×#395C2×C12711yescharacteristic, complemented
416C2×#393C2×C12711yescharacteristic, complemented
417C2×#385C2×C12712yescomplemented
418#1441C2×C12711yescharacteristic, complemented
419#1439C2×C12712yescomplemented
420#1439C2×C12711yescharacteristic, complemented
421#1438C2×C12712yes—
422#1436C2×C12712yescomplemented
423C22⋊#95C2×C12711yescharacteristic, complemented
424C127#1472311yescharacteristic, direct product factor, Sylow
425C23×Q8C22×C12711yescharacteristic
426C23×D4C22×C12711yescharacteristic
427C24×C4C22×C12711yescharacteristic
428C24×C4C22×C12711yescharacteristic
429C2×C22⋊Q8—24no—
430C2×C22⋊Q8—28no—
431C2×C4×D4—24no—
432C2×C4×D4—24no—
433C2×C4×D4—24no—
434C22×C4⋊C4C22×C12711yescharacteristic
435C22×C4⋊C4C22×C12712yes—
436C22×C4⋊C4C22×C12711yescharacteristic
437C22×C4⋊C4C22×C12712yes—
438C22×C22⋊C4C22×C12711yescharacteristic
439C22×C22⋊C4C22×C12712yes—
440C22×C22⋊C4C22×C12712yes—
441C22×C22⋊C4C22×C12712yes—
442C22×C22⋊C4C22×C12712yes—
443C22×C22⋊C4C22×C12711yescharacteristic
444C22×C42C22×C12711yescharacteristic
445#395—24no—
446#393—24no—
447#385—28no—
448C2×#95C22×C12711yescharacteristic
449C2×#95C22×C12712yes—
450C2×#95C22×C12711yescharacteristic
451C2×#95C22×C12712yes—
452C2×#95C22×C12712yes—
453C2×#95C22×C12712yes—
454C2×#95C22×C12712yes—
455C2×#95C22×C12712yes—
456C25C23×C12711yescharacteristic
457C25C23×C12711yescharacteristic
458C22×Q8—24no—
459C22×Q8—22no—
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—42no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4Q8×C12714yescomplemented
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—24no—
476C23×C4—24no—
477C23×C4—42no—
478C23×C4—42no—
479C23×C4D4×C12714yes—
480C23×C4C23×C12712yes—
481C23×C4C23×C12712yes—
482C23×C4C23×C12712yes—
483C23×C4C23×C12711yescharacteristic
484C23×C4C23×C12711yescharacteristic
485C23×C4C23×C12712yes—
486C23×C4C23×C12711yescharacteristic
487C23×C4C23×C12711yescharacteristic
488C23×C4C23×C12711yescharacteristic
489C22⋊Q8—232no—
490C4×D4—232no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—24no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—42no—
500C2×C4⋊C4D4×C12714yes—
501C2×C4⋊C4D4×C12718yescomplemented
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4D4×C12714yes—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—22no—
527#95—22no—
528#95—24no—
529#95—24no—
530#95—24no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—22no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24C2×D4×C12712yes—
548C24C2×D4×C12712yes—
549C24C2×Q8×C12712yes—
550C24C2×Q8×C12712yes—
551C24#41×C12712yes—
552C24#41×C12712yes—
553C24C24×C12711yescharacteristic
554C2×Q8—28no—
555C2×Q8—48no—
556C2×Q8—48no—
557C2×Q8—44no—
558C2×Q8—44no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—28no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4C2×D4×C12712yes—
619C22×C4C2×D4×C12714yes—
620C22×C4C2×D4×C12714yes—
621C22×C4C2×D4×C12712yes—
622C22×C4C2×D4×C12712yes—
623C22×C4C2×D4×C12712yes—
624C22×C4C2×D4×C12714yes—
625C22×C4C2×D4×C12712yes—
626C22×C4C2×D4×C12712yes—
627C22×C4C2×D4×C12712yes—
628C22×C4C2×Q8×C12712yes—
629C22×C4#41×C12714yes—
630C22×C4#41×C12712yes—
631C4⋊C4—28no—
632C4⋊C4—28no—
633C4⋊C4—216no—
634C4⋊C4—48no—
635C22⋊C4—216no—
636C22⋊C4—28no—
637C22⋊C4—216no—
638C22⋊C4—28no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C42—28no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—41no—
669C23—42no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23C22⋊Q8×C12714yes—
687C23C22⋊Q8×C12714yescomplemented
688C23C22×D4×C12711yescharacteristic
689C23C22×D4×C12711yescharacteristic
690C23C22×D4×C12711yescharacteristic
691C23C22×D4×C12712yes—
692C23C22×Q8×C12711yescharacteristic
693C23C2×#41×C12711yescharacteristic
694C23C2×#41×C12711yescharacteristic
695C23C2×#41×C12711yescharacteristic
696C23C2×#41×C12712yes—
697C23H(5,𝔽2)×C12712yes—
698C232−1+4×C12712yes—
699Q8—416no—
700D4—232no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4#120×C12714yes—
756C2×C4#120×C12714yes—
757C2×C4C22⋊Q8×C12714yescomplemented
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—42no—
780C22C2×#120×C12711yescharacteristic
781C22C2×#120×C12711yescharacteristic
782C22C2×C22⋊Q8×C12711yescharacteristic
783C22C2×C22⋊Q8×C12711yescharacteristic
784C22C2×C22⋊Q8×C12711yescharacteristic
785C22#525×C12711yescharacteristic
786C22#525×C12711yescharacteristic
787C22#525×C12711yescharacteristic
788C22#525×C12712yes—
789C22#532×C12711yescharacteristic
790C22#532×C12712yes—
791C22#534×C12711yescharacteristic
792C22#536×C12711yescharacteristic
793C22#539×C12712yes—
794C22#542×C12712yes—
795C22D42×C12712yes—
796C22D42×C12712yes—
797C22#547×C12712yes—
798C22#548×C12712yes—
799C22#548×C12712yes—
800C22D4×Q8×C12712yes—
801C22#551×C12712yes—
802C22#554×C12712yes—
803C4—24no—
804C4—24no—
805C4—24no—
806C4—44no—
807C4—42no—
808C4—44no—
809C4—42no—
810C4—44no—
811C4—82no—
812C2—44no—
813C2—44no—
814C2C127×#238811yescharacteristic
815C2C127×#240311yescharacteristic
816C2C127×#240911yescharacteristic
817C2C127×#243211yescharacteristic
818C2C127×#244912yes—
819C2C127×#245212yes—
820C2C127×#246112yes—
821C2C127×#246312yes—
822C2C127×#256411yescharacteristic
823C2C127×#263811yescharacteristic
824C2C127×#284811yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊Q8×C127C2semidirect
3. C2×#395×C127C2semidirect
4. C2×#393×C127C2semidirect
5. C2×#385×C127C2semidirect
6. C127×#1441C2semidirect
7. C127×#1439C2semidirect
8. C127×#1439C2semidirect
10. C127×#1436C2semidirect
11. C127×C22⋊#95C2semidirect
56. C22×D4×C127Q8semidirect
88. C2×C4⋊C4×C127D4semidirect
274. C23×C127C22⋊Q8semidirect
344. C2×C4×C127C22⋊Q8semidirect
399. #14723C127direct (N × H)
413. C22×C22⋊Q8C2×C127semidirect
415. C2×#395C2×C127semidirect
416. C2×#393C2×C127semidirect
417. C2×#385C2×C127semidirect
418. #1441C2×C127semidirect
419. #1439C2×C127semidirect
420. #1439C2×C127semidirect
422. #1436C2×C127semidirect
423. C22⋊#95C2×C127semidirect
424. C127#14723direct (N × H)
469. C22×D4Q8×C127semidirect
501. C2×C4⋊C4D4×C127semidirect
687. C23C22⋊Q8×C127semidirect
757. C2×C4C22⋊Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1272
C22×C4×D4×C1272
C2×#395×C1272
C2×#393×C1272
C2×#385×C1272
C127×#14412
C127×#14392
C127×#14382
C127×#14362
C127×C22⋊#952
#14723127