Finite Group Databasebeta

← C127×#14019 #44577692

Subgroups — C127×#14019 #44577692

Order 32512.

2538 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C127C211yesmaximal, characteristic, complemented
2C2×#388×C127C212yesmaximal, complemented
3C2×#386×C127C211yesmaximal, characteristic
4C2×#386×C127C211yesmaximal, characteristic
5C2×#386×C127C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
7C127×#1442C212yesmaximal, complemented
8C127×#1439C212yesmaximal, complemented
9C127×#1436C212yesmaximal, complemented
10C127×C22⋊#95C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C24×C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127—24no—
17C22×C4⋊C4×C127—28no—
18C22×C4⋊C4×C127C2212yes—
19C22×C4⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C42×C127C2212yes—
28#388×C127—28no—
29#386×C127—24no—
30#386×C127—24no—
31#386×C127C418yescomplemented
32C4×C22⋊C4×C127—24no—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2212yes—
41C2×#95×C127C2212yes—
42C25×C127C2311yescharacteristic
43C25×C127C2311yescharacteristic
44C22×D4×C127—22no—
45C22×D4×C127—22no—
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127—22no—
49C22×D4×C127—22no—
50C22×D4×C127C2×C414yes—
51C23×C4×C127—22no—
52C23×C4×C127—22no—
53C23×C4×C127—24no—
54C23×C4×C127—24no—
55C23×C4×C127—22no—
56C23×C4×C127—22no—
57C23×C4×C127—22no—
58C23×C4×C127—24no—
59C23×C4×C127—24no—
60C23×C4×C127—22no—
61C23×C4×C127—22no—
62C23×C4×C127—42no—
63C23×C4×C127—42no—
64C23×C4×C127C2×C414yes—
65C23×C4×C127D414yes—
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2312yes—
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2312yes—
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2312yes—
73C23×C4×C127C2312yes—
74C23×C4×C127C2311yescharacteristic
75C2×C4⋊C4×C127—232no—
76C2×C4⋊C4×C127—24no—
77C2×C4⋊C4×C127—24no—
78C2×C4⋊C4×C127—24no—
79C2×C4⋊C4×C127—24no—
80C2×C4⋊C4×C127—24no—
81C2×C4⋊C4×C127D418yescomplemented
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—24no—
87C2×C22⋊C4×C127—24no—
88C2×C22⋊C4×C127—22no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—24no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127—24no—
95C2×C22⋊C4×C127—24no—
96C2×C22⋊C4×C127—42no—
97C2×C22⋊C4×C127—42no—
98C2×C22⋊C4×C127C2×C414yes—
99C2×C22⋊C4×C127C2×C418yescomplemented
100C2×C22⋊C4×C127D414yes—
101C2×C42×C127—24no—
102C2×C42×C127—24no—
103C2×C42×C127—42no—
104#95×C127—24no—
105#95×C127—24no—
106#95×C127—22no—
107#95×C127—22no—
108#95×C127—24no—
109#95×C127—24no—
110#95×C127—24no—
111#95×C127—42no—
112#95×C127C2×C418yescomplemented
113C24×C127—22no—
114C24×C127—22no—
115C24×C127—22no—
116C24×C127—22no—
117C24×C127—22no—
118C24×C127—21no—
119C24×C127—21no—
120C24×C127—22no—
121C24×C127—21no—
122C24×C127—21no—
123C24×C127—21no—
124C24×C127—21no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127C22×C412yes—
128C24×C127C22×C412yes—
129C24×C127C2×D412yes—
130C24×C127C2×D412yes—
131C24×C127#4112yes—
132C24×C127#4112yes—
133C24×C127#4112yes—
134C24×C127#4112yes—
135C24×C127C2411yescharacteristic
136C2×D4×C127—28no—
137C2×D4×C127—28no—
138C2×D4×C127—28no—
139C2×D4×C127—44no—
140C2×D4×C127—44no—
141C2×D4×C127—44no—
142C2×D4×C127—44no—
143C22×C4×C127—28no—
144C22×C4×C127—216no—
145C22×C4×C127—28no—
146C22×C4×C127—28no—
147C22×C4×C127—21no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—21no—
153C22×C4×C127—22no—
154C22×C4×C127—216no—
155C22×C4×C127—28no—
156C22×C4×C127—28no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
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—21no—
173C22×C4×C127—22no—
174C22×C4×C127—21no—
175C22×C4×C127—21no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
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—28no—
186C22×C4×C127—22no—
187C22×C4×C127—21no—
188C22×C4×C127—21no—
189C22×C4×C127—22no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—22no—
195C22×C4×C127—22no—
196C22×C4×C127—44no—
197C22×C4×C127—48no—
198C22×C4×C127—48no—
199C22×C4×C127—48no—
200C22×C4×C127—48no—
201C22×C4×C127—44no—
202C22×C4×C127—44no—
203C22×C4×C127C22×C412yes—
204C22×C4×C127C22×C414yes—
205C22×C4×C127C22×C414yes—
206C22×C4×C127C2×D414yes—
207C22×C4×C127C2×D412yes—
208C22×C4×C127C2×D414yes—
209C22×C4×C127C2×D414yes—
210C22×C4×C127C2×D412yes—
211C22×C4×C127C2×D414yes—
212C22×C4×C127#4114yes—
213C4⋊C4×C127—216no—
214C4⋊C4×C127—216no—
215C22⋊C4×C127—28no—
216C22⋊C4×C127—28no—
217C22⋊C4×C127—216no—
218C22⋊C4×C127—48no—
219C22⋊C4×C127—44no—
220C22⋊C4×C127—44no—
221C22⋊C4×C127—44no—
222C42×C127—48no—
223C23×C127—24no—
224C23×C127—24no—
225C23×C127—22no—
226C23×C127—22no—
227C23×C127—24no—
228C23×C127—22no—
229C23×C127—22no—
230C23×C127—24no—
231C23×C127—24no—
232C23×C127—24no—
233C23×C127—24no—
234C23×C127—24no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—22no—
240C23×C127—24no—
241C23×C127—22no—
242C23×C127—22no—
243C23×C127—24no—
244C23×C127—41no—
245C23×C127—41no—
246C23×C127—41no—
247C23×C127—41no—
248C23×C127—42no—
249C23×C127—41no—
250C23×C127—41no—
251C23×C127—41no—
252C23×C127—41no—
253C23×C127—42no—
254C23×C127—42no—
255C23×C127—42no—
256C23×C127—42no—
257C23×C127—42no—
258C23×C127—42no—
259C23×C127—42no—
260C23×C127—42no—
261C23×C127—42no—
262C23×C127#11714yes—
263C23×C127C4×D414yes—
264C23×C127C4×D414yes—
265C23×C127#12114yes—
266C23×C127#12314yes—
267C23×C127#12414yes—
268C23×C127#12614yes—
269C23×C127C23×C411yescharacteristic
270C23×C127C22×D411yescharacteristic
271C23×C127C22×D412yes—
272C23×C127C22×D411yescharacteristic
273C23×C127C2×#4111yescharacteristic
274C23×C127C2×#4111yescharacteristic
275C23×C127C2×#4111yescharacteristic
276C23×C127C2×#4112yes—
277C23×C127C2×#4111yescharacteristic
278C23×C127H(5,𝔽2)12yes—
279C23×C1272−1+412yes—
280D4×C127—416no—
281C2×C4×C127—232no—
282C2×C4×C127—24no—
283C2×C4×C127—24no—
284C2×C4×C127—24no—
285C2×C4×C127—22no—
286C2×C4×C127—24no—
287C2×C4×C127—24no—
288C2×C4×C127—24no—
289C2×C4×C127—22no—
290C2×C4×C127—24no—
291C2×C4×C127—24no—
292C2×C4×C127—22no—
293C2×C4×C127—24no—
294C2×C4×C127—24no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—24no—
298C2×C4×C127—22no—
299C2×C4×C127—24no—
300C2×C4×C127—22no—
301C2×C4×C127—24no—
302C2×C4×C127—22no—
303C2×C4×C127—24no—
304C2×C4×C127—24no—
305C2×C4×C127—24no—
306C2×C4×C127—24no—
307C2×C4×C127—416no—
308C2×C4×C127—416no—
309C2×C4×C127—42no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—42no—
313C2×C4×C127—41no—
314C2×C4×C127—41no—
315C2×C4×C127—42no—
316C2×C4×C127—42no—
317C2×C4×C127—42no—
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—42no—
325C2×C4×C127—42no—
326C2×C4×C127—42no—
327C2×C4×C127—41no—
328C2×C4×C127—41no—
329C2×C4×C127—41no—
330C2×C4×C127—41no—
331C2×C4×C127—41no—
332C2×C4×C127—41no—
333C2×C4×C127—42no—
334C2×C4×C127—42no—
335C2×C4×C127—42no—
336C2×C4×C127—42no—
337C2×C4×C127C4×D418yes—
338C2×C4×C127#12014yes—
339C22×C127—24no—
340C22×C127—24no—
341C22×C127—28no—
342C22×C127—28no—
343C22×C127—24no—
344C22×C127—24no—
345C22×C127—24no—
346C22×C127—28no—
347C22×C127—28no—
348C22×C127—24no—
349C22×C127—42no—
350C22×C127—44no—
351C22×C127—44no—
352C22×C127—42no—
353C22×C127—42no—
354C22×C127—81no—
355C22×C127—81no—
356C22×C127—81no—
357C22×C127—81no—
358C22×C127—82no—
359C22×C127—82no—
360C22×C127#38818yescomplemented
361C22×C127C2×#11711yescharacteristic
362C22×C127C2×C4×D411yescharacteristic
363C22×C127C2×C4×D412yes—
364C22×C127C2×C4×D411yescharacteristic
365C22×C127#52012yes—
366C22×C127C2×#12011yescharacteristic
367C22×C127C2×#12111yescharacteristic
368C22×C127C2×#12311yescharacteristic
369C22×C127#52511yescharacteristic
370C22×C127#52512yes—
371C22×C127C2×#12411yescharacteristic
372C22×C127C2×#12611yescharacteristic
373C22×C127#53411yescharacteristic
374C22×C127#53611yescharacteristic
375C22×C127#53912yes—
376C22×C127D4212yes—
377C22×C127#54612yes—
378C22×C127#54712yes—
379C22×C127#54812yes—
380C22×C127#54812yes—
381C22×C127#55212yes—
382C22×C127#55312yes—
383C22×C127#55312yes—
384C4×C127—24no—
385C4×C127—28no—
386C4×C127—44no—
387C4×C127—42no—
388C4×C127—44no—
389C4×C127—44no—
390C4×C127—42no—
391C4×C127—81no—
392C4×C127—81no—
393#14019C12711yesmaximal, characteristic, direct product factor, Sylow
394C2×C127—28no—
395C2×C127—82no—
396C2×C127C2×#38811yescharacteristic
397C2×C127C4×#12011yescharacteristic
398C2×C127#232211yescharacteristic
399C2×C127#235212yes—
400C2×C127#236112yes—
401C2×C127#241011yescharacteristic
402C2×C127#241311yescharacteristic
403C2×C127#243611yescharacteristic
404C2×C127#244312yes—
405C2×C127#248112yes—
406C2×C127#259111yescharacteristic
407C23×C4⋊C4C2×C12711yescharacteristic, complemented
408C2×#388C2×C12712yescomplemented
409C2×#386C2×C12711yescharacteristic
410C2×#386C2×C12711yescharacteristic
411C2×#386C2×C12711yescharacteristic
412C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
413#1442C2×C12712yescomplemented
414#1439C2×C12712yescomplemented
415#1436C2×C12712yescomplemented
416C22⋊#95C2×C12711yescharacteristic, complemented
417C22⋊#95C2×C12711yescharacteristic, complemented
418C127#1401911yescharacteristic, direct product factor, Sylow
419C23×D4C22×C12711yescharacteristic
420C24×C4C22×C12711yescharacteristic
421C24×C4C22×C12711yescharacteristic
422C24×C4C22×C12711yescharacteristic
423C22×C4⋊C4—24no—
424C22×C4⋊C4—28no—
425C22×C4⋊C4C22×C12712yes—
426C22×C4⋊C4C22×C12712yes—
427C22×C22⋊C4C22×C12711yescharacteristic
428C22×C22⋊C4C22×C12711yescharacteristic
429C22×C22⋊C4C22×C12712yes—
430C22×C22⋊C4C22×C12711yescharacteristic
431C22×C22⋊C4C22×C12712yes—
432C22×C22⋊C4C22×C12711yescharacteristic
433C22×C22⋊C4C22×C12711yescharacteristic
434C22×C42C22×C12712yes—
435#388—28no—
436#386—24no—
437#386—24no—
438#386C4×C12718yescomplemented
439C4×C22⋊C4—24no—
440C2×#95C22×C12712yes—
441C2×#95C22×C12712yes—
442C2×#95C22×C12712yes—
443C2×#95C22×C12711yescharacteristic
444C2×#95C22×C12712yes—
445C2×#95C22×C12712yes—
446C2×#95C22×C12711yescharacteristic
447C2×#95C22×C12712yes—
448C2×#95C22×C12712yes—
449C25C23×C12711yescharacteristic
450C25C23×C12711yescharacteristic
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4C2×C4×C12714yes—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—24no—
461C23×C4—24no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—42no—
470C23×C4—42no—
471C23×C4C2×C4×C12714yes—
472C23×C4D4×C12714yes—
473C23×C4C23×C12711yescharacteristic
474C23×C4C23×C12711yescharacteristic
475C23×C4C23×C12712yes—
476C23×C4C23×C12711yescharacteristic
477C23×C4C23×C12712yes—
478C23×C4C23×C12711yescharacteristic
479C23×C4C23×C12712yes—
480C23×C4C23×C12712yes—
481C23×C4C23×C12711yescharacteristic
482C2×C4⋊C4—232no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4D4×C12718yescomplemented
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4C2×C4×C12714yes—
506C2×C22⋊C4C2×C4×C12718yescomplemented
507C2×C22⋊C4D4×C12714yes—
508C2×C42—24no—
509C2×C42—24no—
510C2×C42—42no—
511#95—24no—
512#95—24no—
513#95—22no—
514#95—22no—
515#95—24no—
516#95—24no—
517#95—24no—
518#95—42no—
519#95C2×C4×C12718yescomplemented
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—21no—
526C24—21no—
527C24—22no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—22no—
533C24—22no—
534C24C22×C4×C12712yes—
535C24C22×C4×C12712yes—
536C24C2×D4×C12712yes—
537C24C2×D4×C12712yes—
538C24#41×C12712yes—
539C24#41×C12712yes—
540C24#41×C12712yes—
541C24#41×C12712yes—
542C24C24×C12711yescharacteristic
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—28no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C22×C4—28no—
551C22×C4—216no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—216no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—22no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4C22×C4×C12712yes—
611C22×C4C22×C4×C12714yes—
612C22×C4C22×C4×C12714yes—
613C22×C4C2×D4×C12714yes—
614C22×C4C2×D4×C12712yes—
615C22×C4C2×D4×C12714yes—
616C22×C4C2×D4×C12714yes—
617C22×C4C2×D4×C12712yes—
618C22×C4C2×D4×C12714yes—
619C22×C4#41×C12714yes—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C22⋊C4—28no—
623C22⋊C4—28no—
624C22⋊C4—216no—
625C22⋊C4—48no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C42—48no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23#117×C12714yes—
670C23C4×D4×C12714yes—
671C23C4×D4×C12714yes—
672C23#121×C12714yes—
673C23#123×C12714yes—
674C23#124×C12714yes—
675C23#126×C12714yes—
676C23C23×C4×C12711yescharacteristic
677C23C22×D4×C12711yescharacteristic
678C23C22×D4×C12712yes—
679C23C22×D4×C12711yescharacteristic
680C23C2×#41×C12711yescharacteristic
681C23C2×#41×C12711yescharacteristic
682C23C2×#41×C12711yescharacteristic
683C23C2×#41×C12712yes—
684C23C2×#41×C12711yescharacteristic
685C23H(5,𝔽2)×C12712yes—
686C232−1+4×C12712yes—
687D4—416no—
688C2×C4—232no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—416no—
715C2×C4—416no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4C4×D4×C12718yes—
745C2×C4#120×C12714yes—
746C22—24no—
747C22—24no—
748C22—28no—
749C22—28no—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—28no—
754C22—28no—
755C22—24no—
756C22—42no—
757C22—44no—
758C22—44no—
759C22—42no—
760C22—42no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—82no—
766C22—82no—
767C22#388×C12718yescomplemented
768C22C2×#117×C12711yescharacteristic
769C22C2×C4×D4×C12711yescharacteristic
770C22C2×C4×D4×C12712yes—
771C22C2×C4×D4×C12711yescharacteristic
772C22#520×C12712yes—
773C22C2×#120×C12711yescharacteristic
774C22C2×#121×C12711yescharacteristic
775C22C2×#123×C12711yescharacteristic
776C22#525×C12711yescharacteristic
777C22#525×C12712yes—
778C22C2×#124×C12711yescharacteristic
779C22C2×#126×C12711yescharacteristic
780C22#534×C12711yescharacteristic
781C22#536×C12711yescharacteristic
782C22#539×C12712yes—
783C22D42×C12712yes—
784C22#546×C12712yes—
785C22#547×C12712yes—
786C22#548×C12712yes—
787C22#548×C12712yes—
788C22#552×C12712yes—
789C22#553×C12712yes—
790C22#553×C12712yes—
791C4—24no—
792C4—28no—
793C4—44no—
794C4—42no—
795C4—44no—
796C4—44no—
797C4—42no—
798C4—81no—
799C4—81no—
800C2—28no—
801C2—82no—
802C2C2×#388×C12711yescharacteristic
803C2C4×#120×C12711yescharacteristic
804C2C127×#232211yescharacteristic
805C2C127×#235212yes—
806C2C127×#236112yes—
807C2C127×#241011yescharacteristic
808C2C127×#241311yescharacteristic
809C2C127×#243611yescharacteristic
810C2C127×#244312yes—
811C2C127×#248112yes—
812C2C127×#259111yescharacteristic
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
1. C23×C4⋊C4×C127C2semidirect
2. C2×#388×C127C2semidirect
6. C2×C4×C22⋊C4×C127C2semidirect
7. C127×#1442C2semidirect
8. C127×#1439C2semidirect
9. C127×#1436C2semidirect
10. C127×C22⋊#95C2semidirect
11. C127×C22⋊#95C2semidirect
31. #386×C127C4semidirect
81. C2×C4⋊C4×C127D4semidirect
99. C2×C22⋊C4×C127C2×C4semidirect
112. #95×C127C2×C4semidirect
360. C22×C127#388semidirect
393. #14019C127direct (N × H)
407. C23×C4⋊C4C2×C127semidirect
408. C2×#388C2×C127semidirect
412. C2×C4×C22⋊C4C2×C127semidirect
413. #1442C2×C127semidirect
414. #1439C2×C127semidirect
415. #1436C2×C127semidirect
416. C22⋊#95C2×C127semidirect
417. C22⋊#95C2×C127semidirect
418. C127#14019direct (N × H)
438. #386C4×C127semidirect
488. C2×C4⋊C4D4×C127semidirect
506. C2×C22⋊C4C2×C4×C127semidirect
519. #95C2×C4×C127semidirect
767. C22#388×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×#388×C1272
C2×#386×C1272
C2×C4×C22⋊C4×C1272
C127×#14422
C127×#14392
C127×#14362
C127×C22⋊#952
#14019127