Finite Group Databasebeta

← C127×#15453 #44579126

Subgroups — C127×#15453 #44579126

Order 32512.

2506 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
2C2×#394×C127C211yesmaximal, characteristic, complemented
3C2×#393×C127C212yesmaximal, complemented
4C2×#392×C127C211yesmaximal, characteristic
5C2×#390×C127C211yesmaximal, characteristic, complemented
6C2×#386×C127C212yesmaximal, complemented
7C127×#1445C211yesmaximal, characteristic, complemented
8C127×#1439C212yesmaximal, complemented
9C127×#1438C212yesmaximal, complemented
10C127×#1437C211yesmaximal, characteristic, complemented
11C127×#1436C211yesmaximal, characteristic, complemented
12C23×Q8×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C23×D4×C127C2212yes—
15C24×C4×C127C2211yescharacteristic
16C2×C22⋊Q8×C127—24no—
17C2×C22⋊Q8×C127—24no—
18C2×C22⋊Q8×C127—24no—
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2212yes—
27C22×C22⋊C4×C127C2212yes—
28C22×C22⋊C4×C127C2212yes—
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C42×C127C2211yescharacteristic
31#394×C127—24no—
32#393×C127—28no—
33#392×C127—24no—
34#390×C127—24no—
35#386×C127—28no—
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2212yes—
41C2×#95×C127C2212yes—
42C2×#95×C127C2212yes—
43C25×C127C2312yes—
44C25×C127C2311yescharacteristic
45C22×Q8×C127—22no—
46C22×Q8×C127—22no—
47C22×Q8×C127—22no—
48C22×Q8×C127—24no—
49C22×Q8×C127—42no—
50C22×D4×C127—24no—
51C22×D4×C127—24no—
52C22×D4×C127—24no—
53C22×D4×C127—24no—
54C22×D4×C127—24no—
55C22×D4×C127—24no—
56C22×D4×C127—22no—
57C22×D4×C127—22no—
58C22×D4×C127—22no—
59C22×D4×C127—42no—
60C22×D4×C127—42no—
61C22×D4×C127—42no—
62C23×C4×C127—22no—
63C23×C4×C127—22no—
64C23×C4×C127—22no—
65C23×C4×C127—24no—
66C23×C4×C127—42no—
67C23×C4×C127C2312yes—
68C23×C4×C127C2312yes—
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2312yes—
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C22⋊Q8×C127—232no—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127D414yescomplemented
85C2×C4⋊C4×C127D414yescomplemented
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—24no—
92C2×C22⋊C4×C127—24no—
93C2×C22⋊C4×C127—24no—
94C2×C22⋊C4×C127—24no—
95C2×C22⋊C4×C127—24no—
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×C127—42no—
107C2×C22⋊C4×C127—42no—
108C2×C22⋊C4×C127—42no—
109C2×C22⋊C4×C127D414yes—
110C2×C42×C127—22no—
111C2×C42×C127—42no—
112#95×C127—24no—
113#95×C127—22no—
114#95×C127—24no—
115#95×C127—24no—
116#95×C127—22no—
117#95×C127—42no—
118#95×C127D418yescomplemented
119C24×C127—21no—
120C24×C127—21no—
121C24×C127—22no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—22no—
127C24×C127—22no—
128C24×C127—22no—
129C24×C127—22no—
130C24×C127—22no—
131C24×C127—22no—
132C24×C127—22no—
133C24×C127—22no—
134C24×C127—22no—
135C24×C127—22no—
136C24×C127—22no—
137C24×C127—22no—
138C24×C127—22no—
139C24×C127—22no—
140C24×C127C2×D412yes—
141C24×C127#4114yes—
142C24×C127#4114yes—
143C24×C127C2411yescharacteristic
144C2×Q8×C127—28no—
145C2×Q8×C127—48no—
146C2×Q8×C127—48no—
147C2×Q8×C127—44no—
148C2×Q8×C127—44no—
149C2×D4×C127—28no—
150C2×D4×C127—216no—
151C2×D4×C127—48no—
152C2×D4×C127—48no—
153C2×D4×C127—48no—
154C2×D4×C127—48no—
155C2×D4×C127—44no—
156C2×D4×C127—48no—
157C2×D4×C127—48no—
158C2×D4×C127—48no—
159C2×D4×C127—48no—
160C2×D4×C127—44no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—22no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—28no—
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—21no—
174C22×C4×C127—21no—
175C22×C4×C127—21no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
178C22×C4×C127—21no—
179C22×C4×C127—21no—
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—22no—
190C22×C4×C127—22no—
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—22no—
199C22×C4×C127—22no—
200C22×C4×C127—22no—
201C22×C4×C127—22no—
202C22×C4×C127—48no—
203C22×C4×C127—48no—
204C22×C4×C127—44no—
205C22×C4×C127—44no—
206C22×C4×C127C2×D414yes—
207C22×C4×C127C2×D414yes—
208C22×C4×C127C2×D412yes—
209C22×C4×C127C2×D412yes—
210C22×C4×C127C2×D412yes—
211C22×C4×C127C2×D412yes—
212C22×C4×C127C2×D412yes—
213C22×C4×C127C2×D412yes—
214C22×C4×C127C2×D412yes—
215C22×C4×C127C2×D414yes—
216C22×C4×C127C2×D412yes—
217C4⋊C4×C127—28no—
218C4⋊C4×C127—28no—
219C4⋊C4×C127—28no—
220C22⋊C4×C127—28no—
221C22⋊C4×C127—28no—
222C22⋊C4×C127—48no—
223C22⋊C4×C127—48no—
224C22⋊C4×C127—48no—
225C22⋊C4×C127—48no—
226C22⋊C4×C127—48no—
227C22⋊C4×C127—48no—
228C42×C127—44no—
229C23×C127—22no—
230C23×C127—24no—
231C23×C127—22no—
232C23×C127—24no—
233C23×C127—24no—
234C23×C127—24no—
235C23×C127—24no—
236C23×C127—24no—
237C23×C127—24no—
238C23×C127—24no—
239C23×C127—24no—
240C23×C127—24no—
241C23×C127—24no—
242C23×C127—24no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—24no—
246C23×C127—41no—
247C23×C127—41no—
248C23×C127—41no—
249C23×C127—41no—
250C23×C127—42no—
251C23×C127—42no—
252C23×C127—42no—
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—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×C127—42no—
274C23×C127—42no—
275C23×C127—42no—
276C23×C127—42no—
277C23×C127—42no—
278C23×C127—42no—
279C23×C127—42no—
280C23×C127—42no—
281C23×C127—42no—
282C23×C127—42no—
283C23×C127—42no—
284C23×C127#12414yes—
285C23×C127C22×D411yescharacteristic
286C23×C127C22×D411yescharacteristic
287C23×C127C22×D411yescharacteristic
288C23×C127C22×D412yes—
289C23×C127C2×#4112yes—
290C23×C127C2×#4112yes—
291C23×C127H(5,𝔽2)12yes—
292C23×C127H(5,𝔽2)12yes—
293C23×C1272−1+412yes—
294Q8×C127—416no—
295D4×C127—416no—
296D4×C127—432no—
297C2×C4×C127—22no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
300C2×C4×C127—22no—
301C2×C4×C127—24no—
302C2×C4×C127—24no—
303C2×C4×C127—24no—
304C2×C4×C127—24no—
305C2×C4×C127—22no—
306C2×C4×C127—22no—
307C2×C4×C127—22no—
308C2×C4×C127—22no—
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—24no—
316C2×C4×C127—24no—
317C2×C4×C127—24no—
318C2×C4×C127—24no—
319C2×C4×C127—416no—
320C2×C4×C127—41no—
321C2×C4×C127—42no—
322C2×C4×C127—41no—
323C2×C4×C127—41no—
324C2×C4×C127—41no—
325C2×C4×C127—42no—
326C2×C4×C127—41no—
327C2×C4×C127—41no—
328C2×C4×C127—41no—
329C2×C4×C127—41no—
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—42no—
343C2×C4×C127—42no—
344C2×C4×C127—42no—
345C2×C4×C127—42no—
346C2×C4×C127—42no—
347C2×C4×C127#12014yes—
348C2×C4×C127#12714yes—
349C22×C127—24no—
350C22×C127—28no—
351C22×C127—42no—
352C22×C127—44no—
353C22×C127—44no—
354C22×C127—42no—
355C22×C127—44no—
356C22×C127—44no—
357C22×C127—44no—
358C22×C127—44no—
359C22×C127—44no—
360C22×C127—44no—
361C22×C127—44no—
362C22×C127—44no—
363C22×C127—44no—
364C22×C127—44no—
365C22×C127—82no—
366C22×C127—82no—
367C22×C127—82no—
368C22×C127—82no—
369C22×C127—82no—
370C22×C127—82no—
371C22×C127—82no—
372C22×C127—82no—
373C22×C127C2×#12011yescharacteristic
374C22×C127#52511yescharacteristic
375C22×C127#52512yes—
376C22×C127C2×#12411yescharacteristic
377C22×C127C2×#12711yescharacteristic
378C22×C127#53511yescharacteristic
379C22×C127#53511yescharacteristic
380C22×C127#53611yescharacteristic
381C22×C127#53712yes—
382C22×C127#53812yes—
383C22×C127#53912yes—
384C22×C127D4212yes—
385C22×C127D4212yes—
386C22×C127#54612yes—
387C22×C127#54612yes—
388C22×C127#54612yes—
389C22×C127#54812yes—
390C22×C127#54812yes—
391C22×C127#54812yes—
392C22×C127#55112yes—
393C22×C127#56212yes—
394C4×C127—24no—
395C4×C127—24no—
396C4×C127—42no—
397C4×C127—44no—
398C4×C127—42no—
399C4×C127—42no—
400C4×C127—42no—
401C4×C127—44no—
402C4×C127—82no—
403#15453C12711yesmaximal, characteristic, direct product factor, Sylow
404C2×C127—44no—
405C2×C127—84no—
406C2×C127#240411yescharacteristic
407C2×C127#243311yescharacteristic
408C2×C127#243611yescharacteristic
409C2×C127#246312yes—
410C2×C127#247212yes—
411C2×C127#254012yes—
412C2×C127#267612yes—
413C2×C127#268112yes—
414C2×C127#269612yes—
415C22×C22⋊Q8C2×C12711yescharacteristic, complemented
416C2×#394C2×C12711yescharacteristic, complemented
417C2×#393C2×C12712yescomplemented
418C2×#392C2×C12711yescharacteristic
419C2×#390C2×C12711yescharacteristic, complemented
420C2×#386C2×C12712yescomplemented
421#1445C2×C12711yescharacteristic, complemented
422#1439C2×C12712yescomplemented
423#1438C2×C12712yescomplemented
424#1437C2×C12711yescharacteristic, complemented
425#1436C2×C12711yescharacteristic, complemented
426C127#1545311yescharacteristic, direct product factor, Sylow
427C23×Q8C22×C12711yescharacteristic
428C23×D4C22×C12711yescharacteristic
429C23×D4C22×C12712yes—
430C24×C4C22×C12711yescharacteristic
431C2×C22⋊Q8—24no—
432C2×C22⋊Q8—24no—
433C2×C22⋊Q8—24no—
434C22×C4⋊C4C22×C12711yescharacteristic
435C22×C4⋊C4C22×C12711yescharacteristic
436C22×C4⋊C4C22×C12711yescharacteristic
437C22×C22⋊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×C12712yes—
444C22×C22⋊C4C22×C12711yescharacteristic
445C22×C42C22×C12711yescharacteristic
446#394—24no—
447#393—28no—
448#392—24no—
449#390—24no—
450#386—28no—
451C2×#95C22×C12711yescharacteristic
452C2×#95C22×C12712yes—
453C2×#95C22×C12712yes—
454C2×#95C22×C12711yescharacteristic
455C2×#95C22×C12712yes—
456C2×#95C22×C12712yes—
457C2×#95C22×C12712yes—
458C25C23×C12712yes—
459C25C23×C12711yescharacteristic
460C22×Q8—22no—
461C22×Q8—22no—
462C22×Q8—22no—
463C22×Q8—24no—
464C22×Q8—42no—
465C22×D4—24no—
466C22×D4—24no—
467C22×D4—24no—
468C22×D4—24no—
469C22×D4—24no—
470C22×D4—24no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—42no—
475C22×D4—42no—
476C22×D4—42no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—24no—
481C23×C4—42no—
482C23×C4C23×C12712yes—
483C23×C4C23×C12711yescharacteristic
484C23×C4C23×C12711yescharacteristic
485C23×C4C23×C12711yescharacteristic
486C23×C4C23×C12712yes—
487C23×C4C23×C12711yescharacteristic
488C23×C4C23×C12712yes—
489C23×C4C23×C12711yescharacteristic
490C23×C4C23×C12711yescharacteristic
491C22⋊Q8—232no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4D4×C12714yescomplemented
500C2×C4⋊C4D4×C12714yescomplemented
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
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—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4D4×C12714yes—
525C2×C42—22no—
526C2×C42—42no—
527#95—24no—
528#95—22no—
529#95—24no—
530#95—24no—
531#95—22no—
532#95—42no—
533#95D4×C12718yescomplemented
534C24—21no—
535C24—21no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24C2×D4×C12712yes—
556C24#41×C12714yes—
557C24#41×C12714yes—
558C24C24×C12711yescharacteristic
559C2×Q8—28no—
560C2×Q8—48no—
561C2×Q8—48no—
562C2×Q8—44no—
563C2×Q8—44no—
564C2×D4—28no—
565C2×D4—216no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—44no—
571C2×D4—48no—
572C2×D4—48no—
573C2×D4—48no—
574C2×D4—48no—
575C2×D4—44no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4C2×D4×C12714yes—
622C22×C4C2×D4×C12714yes—
623C22×C4C2×D4×C12712yes—
624C22×C4C2×D4×C12712yes—
625C22×C4C2×D4×C12712yes—
626C22×C4C2×D4×C12712yes—
627C22×C4C2×D4×C12712yes—
628C22×C4C2×D4×C12712yes—
629C22×C4C2×D4×C12712yes—
630C22×C4C2×D4×C12714yes—
631C22×C4C2×D4×C12712yes—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—28no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C42—44no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23#124×C12714yes—
700C23C22×D4×C12711yescharacteristic
701C23C22×D4×C12711yescharacteristic
702C23C22×D4×C12711yescharacteristic
703C23C22×D4×C12712yes—
704C23C2×#41×C12712yes—
705C23C2×#41×C12712yes—
706C23H(5,𝔽2)×C12712yes—
707C23H(5,𝔽2)×C12712yes—
708C232−1+4×C12712yes—
709Q8—416no—
710D4—416no—
711D4—432no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—416no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
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—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4#120×C12714yes—
763C2×C4#127×C12714yes—
764C22—24no—
765C22—28no—
766C22—42no—
767C22—44no—
768C22—44no—
769C22—42no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22C2×#120×C12711yescharacteristic
789C22#525×C12711yescharacteristic
790C22#525×C12712yes—
791C22C2×#124×C12711yescharacteristic
792C22C2×#127×C12711yescharacteristic
793C22#535×C12711yescharacteristic
794C22#535×C12711yescharacteristic
795C22#536×C12711yescharacteristic
796C22#537×C12712yes—
797C22#538×C12712yes—
798C22#539×C12712yes—
799C22D42×C12712yes—
800C22D42×C12712yes—
801C22#546×C12712yes—
802C22#546×C12712yes—
803C22#546×C12712yes—
804C22#548×C12712yes—
805C22#548×C12712yes—
806C22#548×C12712yes—
807C22#551×C12712yes—
808C22#562×C12712yes—
809C4—24no—
810C4—24no—
811C4—42no—
812C4—44no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—44no—
817C4—82no—
818C2—44no—
819C2—84no—
820C2C127×#240411yescharacteristic
821C2C127×#243311yescharacteristic
822C2C127×#243611yescharacteristic
823C2C127×#246312yes—
824C2C127×#247212yes—
825C2C127×#254012yes—
826C2C127×#267612yes—
827C2C127×#268112yes—
828C2C127×#269612yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
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
2. C2×#394×C127C2semidirect
3. C2×#393×C127C2semidirect
5. C2×#390×C127C2semidirect
6. C2×#386×C127C2semidirect
7. C127×#1445C2semidirect
8. C127×#1439C2semidirect
9. C127×#1438C2semidirect
10. C127×#1437C2semidirect
11. C127×#1436C2semidirect
84. C2×C4⋊C4×C127D4semidirect
85. C2×C4⋊C4×C127D4semidirect
118. #95×C127D4semidirect
403. #15453C127direct (N × H)
415. C22×C22⋊Q8C2×C127semidirect
416. C2×#394C2×C127semidirect
417. C2×#393C2×C127semidirect
419. C2×#390C2×C127semidirect
420. C2×#386C2×C127semidirect
421. #1445C2×C127semidirect
422. #1439C2×C127semidirect
423. #1438C2×C127semidirect
424. #1437C2×C127semidirect
425. #1436C2×C127semidirect
426. C127#15453direct (N × H)
499. C2×C4⋊C4D4×C127semidirect
500. C2×C4⋊C4D4×C127semidirect
533. #95D4×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
C2×#394×C1272
C2×#393×C1272
C2×#392×C1272
C2×#390×C1272
C2×#386×C1272
C127×#14452
C127×#14392
C127×#14382
C127×#14372
C127×#14362
#15453127