Finite Group Databasebeta

← C127×#14300 #44577973

Subgroups — C127×#14300 #44577973

Order 32512.

2242 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#394×C127C211yesmaximal, characteristic
3C2×#387×C127C211yesmaximal, characteristic, complemented
4C2×#385×C127C212yesmaximal, complemented
5C127×#1444C211yesmaximal, characteristic, complemented
6C127×#1441C211yesmaximal, characteristic, complemented
7C127×#1440C212yesmaximal, complemented
8C127×#1439C212yesmaximal, complemented
9C127×#1438C211yesmaximal, characteristic
10C127×#1434C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C212yesmaximal, complemented
12C23×D4×C127C2211yescharacteristic
13C24×C4×C127C2212yes—
14C2×C4×D4×C127—28no—
15C2×C4×D4×C127—24no—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2212yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C42×C127C2211yescharacteristic
26#394×C127C418yescomplemented
27#387×C127—24no—
28#385×C127—28no—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2211yescharacteristic
40C25×C127C2312yes—
41C22×D4×C127—24no—
42C22×D4×C127—24no—
43C22×D4×C127—22no—
44C22×D4×C127—22no—
45C22×D4×C127C2×C414yes—
46C23×C4×C127—24no—
47C23×C4×C127—24no—
48C23×C4×C127—42no—
49C23×C4×C127—42no—
50C23×C4×C127—42no—
51C23×C4×C127—42no—
52C23×C4×C127D418yes—
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C23×C4×C127C2312yes—
56C23×C4×C127C2311yescharacteristic
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2312yes—
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2312yes—
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C4×D4×C127—232no—
64C2×C4⋊C4×C127—24no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—24no—
69C2×C4⋊C4×C127—24no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127—42no—
72C2×C4⋊C4×C127—42no—
73C2×C4⋊C4×C127C2×C414yescomplemented
74C2×C22⋊C4×C127—24no—
75C2×C22⋊C4×C127—24no—
76C2×C22⋊C4×C127—24no—
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127—24no—
79C2×C22⋊C4×C127—24no—
80C2×C22⋊C4×C127—24no—
81C2×C22⋊C4×C127—42no—
82C2×C22⋊C4×C127—42no—
83C2×C22⋊C4×C127—42no—
84C2×C22⋊C4×C127—42no—
85C2×C22⋊C4×C127—42no—
86C2×C22⋊C4×C127—42no—
87C2×C22⋊C4×C127C2×C418yescomplemented
88C2×C22⋊C4×C127C2×C418yescomplemented
89C2×C42×C127—24no—
90C2×C42×C127D414yes—
91#95×C127—24no—
92#95×C127—24no—
93#95×C127—22no—
94#95×C127—22no—
95#95×C127—22no—
96#95×C127—22no—
97#95×C127—22no—
98#95×C127—42no—
99#95×C127—42no—
100#95×C127—42no—
101#95×C127C2×C414yescomplemented
102C24×C127—22no—
103C24×C127—22no—
104C24×C127—22no—
105C24×C127—22no—
106C24×C127—22no—
107C24×C127—22no—
108C24×C127—22no—
109C24×C127—22no—
110C24×C127—22no—
111C24×C127—22no—
112C24×C127—22no—
113C24×C127—22no—
114C24×C127C22×C414yes—
115C24×C127C2×D414yes—
116C24×C127#4114yes—
117C24×C127C2411yescharacteristic
118C2×D4×C127—28no—
119C2×D4×C127—28no—
120C2×D4×C127—216no—
121C2×D4×C127—216no—
122C2×D4×C127—28no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—21no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—21no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—21no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—21no—
152C22×C4×C127—22no—
153C22×C4×C127—21no—
154C22×C4×C127—216no—
155C22×C4×C127—21no—
156C22×C4×C127—22no—
157C22×C4×C127—21no—
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—21no—
166C22×C4×C127—22no—
167C22×C4×C127—21no—
168C22×C4×C127—22no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—22no—
172C22×C4×C127—48no—
173C22×C4×C127—48no—
174C22×C4×C127—48no—
175C22×C4×C127—48no—
176C22×C4×C127—48no—
177C22×C4×C127—48no—
178C22×C4×C127C22×C414yes—
179C22×C4×C127C22×C412yes—
180C22×C4×C127C22×C412yes—
181C22×C4×C127C22×C412yes—
182C22×C4×C127C2×D412yes—
183C22×C4×C127C2×D414yes—
184C22×C4×C127C2×D412yes—
185C22×C4×C127C2×D414yes—
186C22×C4×C127C2×D412yes—
187C22×C4×C127#4112yes—
188C4⋊C4×C127—28no—
189C4⋊C4×C127—28no—
190C4⋊C4×C127—48no—
191C4⋊C4×C127—44no—
192C22⋊C4×C127—216no—
193C22⋊C4×C127—216no—
194C22⋊C4×C127—48no—
195C22⋊C4×C127—48no—
196C22⋊C4×C127—48no—
197C42×C127—28no—
198C23×C127—24no—
199C23×C127—24no—
200C23×C127—24no—
201C23×C127—24no—
202C23×C127—24no—
203C23×C127—24no—
204C23×C127—24no—
205C23×C127—24no—
206C23×C127—24no—
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—42no—
217C23×C127—42no—
218C23×C127—42no—
219C23×C127—42no—
220C23×C127—42no—
221C23×C127—42no—
222C23×C127—42no—
223C23×C127—42no—
224C23×C127—42no—
225C23×C127—42no—
226C23×C127—42no—
227C23×C127—42no—
228C23×C127—42no—
229C23×C127—42no—
230C23×C127—42no—
231C23×C127—42no—
232C23×C127C4×D418yes—
233C23×C127C23×C411yescharacteristic
234C23×C127C22×D412yes—
235C23×C127C22×D411yescharacteristic
236C23×C127C2×#4112yes—
237C23×C127C2×#4111yescharacteristic
238C23×C127H(5,𝔽2)11yescharacteristic
239C23×C127H(5,𝔽2)11yescharacteristic
240C23×C127H(5,𝔽2)12yes—
241C23×C127H(5,𝔽2)11yescharacteristic
242C23×C1272−1+411yescharacteristic
243C23×C1272−1+412yes—
244D4×C127—232no—
245C2×C4×C127—24no—
246C2×C4×C127—22no—
247C2×C4×C127—22no—
248C2×C4×C127—24no—
249C2×C4×C127—24no—
250C2×C4×C127—24no—
251C2×C4×C127—22no—
252C2×C4×C127—22no—
253C2×C4×C127—24no—
254C2×C4×C127—24no—
255C2×C4×C127—22no—
256C2×C4×C127—22no—
257C2×C4×C127—22no—
258C2×C4×C127—24no—
259C2×C4×C127—22no—
260C2×C4×C127—24no—
261C2×C4×C127—22no—
262C2×C4×C127—24no—
263C2×C4×C127—24no—
264C2×C4×C127—24no—
265C2×C4×C127—22no—
266C2×C4×C127—22no—
267C2×C4×C127—432no—
268C2×C4×C127—41no—
269C2×C4×C127—42no—
270C2×C4×C127—41no—
271C2×C4×C127—42no—
272C2×C4×C127—42no—
273C2×C4×C127—42no—
274C2×C4×C127—41no—
275C2×C4×C127—42no—
276C2×C4×C127—42no—
277C2×C4×C127—42no—
278C2×C4×C127—41no—
279C2×C4×C127—42no—
280C2×C4×C127—42no—
281C2×C4×C127—42no—
282C2×C4×C127—42no—
283C2×C4×C127—41no—
284C2×C4×C127—41no—
285C2×C4×C127—41no—
286C2×C4×C127—42no—
287C2×C4×C127—41no—
288C2×C4×C127—42no—
289C2×C4×C127—42no—
290C2×C4×C127—42no—
291C2×C4×C127—41no—
292C2×C4×C127—41no—
293C2×C4×C127—41no—
294C2×C4×C127—42no—
295C2×C4×C127—41no—
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×C127C4×D414yes—
303C2×C4×C127#12014yes—
304C22×C127—28no—
305C22×C127—28no—
306C22×C127—28no—
307C22×C127—44no—
308C22×C127—44no—
309C22×C127—44no—
310C22×C127—44no—
311C22×C127—44no—
312C22×C127—44no—
313C22×C127—44no—
314C22×C127—44no—
315C22×C127—44no—
316C22×C127—44no—
317C22×C127—44no—
318C22×C127—44no—
319C22×C127C2×C4×D412yes—
320C22×C127C2×C4×D411yescharacteristic
321C22×C127#51811yescharacteristic
322C22×C127#52011yescharacteristic
323C22×C127#52012yes—
324C22×C127C2×#12011yescharacteristic
325C22×C127#52512yes—
326C22×C127#52511yescharacteristic
327C22×C127#53412yes—
328C22×C127#53412yes—
329C22×C127#53511yescharacteristic
330C22×C127#53511yescharacteristic
331C22×C127#53612yes—
332C22×C127#53611yescharacteristic
333C22×C127#53711yescharacteristic
334C22×C127#53712yes—
335C22×C127#53812yes—
336C22×C127#53912yes—
337C22×C127#53912yes—
338C22×C127#53912yes—
339C22×C127#54011yescharacteristic
340C22×C127#54211yescharacteristic
341C22×C127#54212yes—
342C4×C127—24no—
343C4×C127—24no—
344C4×C127—42no—
345C4×C127—44no—
346C4×C127—44no—
347C4×C127—42no—
348C4×C127—42no—
349C4×C127—81no—
350C4×C127—82no—
351C4×C127—81no—
352#14300C12711yesmaximal, characteristic, direct product factor, Sylow
353C2×C127—48no—
354C2×C127C4×#12011yescharacteristic
355C2×C127#232212yes—
356C2×C127#232411yescharacteristic
357C2×C127#232512yes—
358C2×C127#232611yescharacteristic
359C2×C127#261311yescharacteristic
360C2×C127#261611yescharacteristic
361C2×C127#263012yes—
362C2×C127#263311yescharacteristic
363C2×C127#263611yescharacteristic
364C2×C127#263812yes—
365C22×C4×D4C2×C12711yescharacteristic
366C2×#394C2×C12711yescharacteristic
367C2×#387C2×C12711yescharacteristic, complemented
368C2×#385C2×C12712yescomplemented
369#1444C2×C12711yescharacteristic, complemented
370#1441C2×C12711yescharacteristic, complemented
371#1440C2×C12712yescomplemented
372#1439C2×C12712yescomplemented
373#1438C2×C12711yescharacteristic
374#1434C2×C12711yescharacteristic, complemented
375C22⋊#95C2×C12712yescomplemented
376C127#1430011yescharacteristic, direct product factor, Sylow
377C23×D4C22×C12711yescharacteristic
378C24×C4C22×C12712yes—
379C2×C4×D4—28no—
380C2×C4×D4—24no—
381C22×C4⋊C4C22×C12711yescharacteristic
382C22×C4⋊C4C22×C12711yescharacteristic
383C22×C4⋊C4C22×C12711yescharacteristic
384C22×C4⋊C4C22×C12712yes—
385C22×C22⋊C4C22×C12712yes—
386C22×C22⋊C4C22×C12712yes—
387C22×C22⋊C4C22×C12712yes—
388C22×C22⋊C4C22×C12712yes—
389C22×C22⋊C4C22×C12712yes—
390C22×C42C22×C12711yescharacteristic
391#394C4×C12718yescomplemented
392#387—24no—
393#385—28no—
394C2×#95C22×C12711yescharacteristic
395C2×#95C22×C12712yes—
396C2×#95C22×C12711yescharacteristic
397C2×#95C22×C12711yescharacteristic
398C2×#95C22×C12711yescharacteristic
399C2×#95C22×C12711yescharacteristic
400C2×#95C22×C12712yes—
401C2×#95C22×C12712yes—
402C2×#95C22×C12712yes—
403C2×#95C22×C12712yes—
404C2×#95C22×C12711yescharacteristic
405C25C23×C12712yes—
406C22×D4—24no—
407C22×D4—24no—
408C22×D4—22no—
409C22×D4—22no—
410C22×D4C2×C4×C12714yes—
411C23×C4—24no—
412C23×C4—24no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4D4×C12718yes—
418C23×C4C23×C12711yescharacteristic
419C23×C4C23×C12711yescharacteristic
420C23×C4C23×C12712yes—
421C23×C4C23×C12711yescharacteristic
422C23×C4C23×C12711yescharacteristic
423C23×C4C23×C12712yes—
424C23×C4C23×C12711yescharacteristic
425C23×C4C23×C12712yes—
426C23×C4C23×C12711yescharacteristic
427C23×C4C23×C12711yescharacteristic
428C4×D4—232no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4C2×C4×C12714yescomplemented
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—42no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4C2×C4×C12718yescomplemented
453C2×C22⋊C4C2×C4×C12718yescomplemented
454C2×C42—24no—
455C2×C42D4×C12714yes—
456#95—24no—
457#95—24no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95C2×C4×C12714yescomplemented
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24C22×C4×C12714yes—
480C24C2×D4×C12714yes—
481C24#41×C12714yes—
482C24C24×C12711yescharacteristic
483C2×D4—28no—
484C2×D4—28no—
485C2×D4—216no—
486C2×D4—216no—
487C2×D4—28no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—216no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4C22×C4×C12714yes—
544C22×C4C22×C4×C12712yes—
545C22×C4C22×C4×C12712yes—
546C22×C4C22×C4×C12712yes—
547C22×C4C2×D4×C12712yes—
548C22×C4C2×D4×C12714yes—
549C22×C4C2×D4×C12712yes—
550C22×C4C2×D4×C12714yes—
551C22×C4C2×D4×C12712yes—
552C22×C4#41×C12712yes—
553C4⋊C4—28no—
554C4⋊C4—28no—
555C4⋊C4—48no—
556C4⋊C4—44no—
557C22⋊C4—216no—
558C22⋊C4—216no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C42—28no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23C4×D4×C12718yes—
598C23C23×C4×C12711yescharacteristic
599C23C22×D4×C12712yes—
600C23C22×D4×C12711yescharacteristic
601C23C2×#41×C12712yes—
602C23C2×#41×C12711yescharacteristic
603C23H(5,𝔽2)×C12711yescharacteristic
604C23H(5,𝔽2)×C12711yescharacteristic
605C23H(5,𝔽2)×C12712yes—
606C23H(5,𝔽2)×C12711yescharacteristic
607C232−1+4×C12711yescharacteristic
608C232−1+4×C12712yes—
609D4—232no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—432no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4C4×D4×C12714yes—
668C2×C4#120×C12714yes—
669C22—28no—
670C22—28no—
671C22—28no—
672C22—44no—
673C22—44no—
674C22—44no—
675C22—44no—
676C22—44no—
677C22—44no—
678C22—44no—
679C22—44no—
680C22—44no—
681C22—44no—
682C22—44no—
683C22—44no—
684C22C2×C4×D4×C12712yes—
685C22C2×C4×D4×C12711yescharacteristic
686C22#518×C12711yescharacteristic
687C22#520×C12711yescharacteristic
688C22#520×C12712yes—
689C22C2×#120×C12711yescharacteristic
690C22#525×C12712yes—
691C22#525×C12711yescharacteristic
692C22#534×C12712yes—
693C22#534×C12712yes—
694C22#535×C12711yescharacteristic
695C22#535×C12711yescharacteristic
696C22#536×C12712yes—
697C22#536×C12711yescharacteristic
698C22#537×C12711yescharacteristic
699C22#537×C12712yes—
700C22#538×C12712yes—
701C22#539×C12712yes—
702C22#539×C12712yes—
703C22#539×C12712yes—
704C22#540×C12711yescharacteristic
705C22#542×C12711yescharacteristic
706C22#542×C12712yes—
707C4—24no—
708C4—24no—
709C4—42no—
710C4—44no—
711C4—44no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—82no—
716C4—81no—
717C2—48no—
718C2C4×#120×C12711yescharacteristic
719C2C127×#232212yes—
720C2C127×#232411yescharacteristic
721C2C127×#232512yes—
722C2C127×#232611yescharacteristic
723C2C127×#261311yescharacteristic
724C2C127×#261611yescharacteristic
725C2C127×#263012yes—
726C2C127×#263311yescharacteristic
727C2C127×#263611yescharacteristic
728C2C127×#263812yes—
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
3. C2×#387×C127C2semidirect
4. C2×#385×C127C2semidirect
5. C127×#1444C2semidirect
6. C127×#1441C2semidirect
7. C127×#1440C2semidirect
8. C127×#1439C2semidirect
10. C127×#1434C2semidirect
11. C127×C22⋊#95C2semidirect
26. #394×C127C4semidirect
73. C2×C4⋊C4×C127C2×C4semidirect
87. C2×C22⋊C4×C127C2×C4semidirect
88. C2×C22⋊C4×C127C2×C4semidirect
101. #95×C127C2×C4semidirect
352. #14300C127direct (N × H)
367. C2×#387C2×C127semidirect
368. C2×#385C2×C127semidirect
369. #1444C2×C127semidirect
370. #1441C2×C127semidirect
371. #1440C2×C127semidirect
372. #1439C2×C127semidirect
374. #1434C2×C127semidirect
375. C22⋊#95C2×C127semidirect
376. C127#14300direct (N × H)
391. #394C4×C127semidirect
438. C2×C4⋊C4C2×C4×C127semidirect
452. C2×C22⋊C4C2×C4×C127semidirect
453. C2×C22⋊C4C2×C4×C127semidirect
466. #95C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C2×#394×C1272
C2×#387×C1272
C2×#385×C1272
C127×#14442
C127×#14412
C127×#14402
C127×#14392
C127×#14382
C127×#14342
C127×C22⋊#952
#14300127