Finite Group Databasebeta

← C127×#13991 #44577664

Subgroups — C127×#13991 #44577664

Order 32512.

3526 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C2×#388×C127C212yesmaximal, complemented
3C2×#385×C127C211yesmaximal, characteristic, complemented
4C2×#379×C127C211yesmaximal, characteristic
5C2×#379×C127C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
7C127×#1440C212yesmaximal, complemented
8C127×#1439C212yesmaximal, complemented
9C127×#1437C212yesmaximal, complemented
10C127×C22⋊#95C211yesmaximal, characteristic, complemented
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2212yescomplemented
16C22×C22⋊C4×C127—24no—
17C22×C22⋊C4×C127—28no—
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2212yes—
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2212yes—
28C22×C42×C127C2211yescharacteristic, complemented
29C22×C42×C127C2211yescharacteristic, complemented
30#388×C127—28no—
31#385×C127—24no—
32#379×C127—24no—
33#379×C127C418yescomplemented
34C4×C22⋊C4×C127—24no—
35C2×#95×C127C2212yescomplemented
36C2×#95×C127C2212yescomplemented
37C2×#95×C127C2212yescomplemented
38C2×#95×C127C2211yescharacteristic, complemented
39C2×#95×C127C2211yescharacteristic, complemented
40C2×#95×C127C2212yescomplemented
41C2×#95×C127C2212yescomplemented
42C25×C127—24no—
43C25×C127—22no—
44C25×C127—24no—
45C25×C127—22no—
46C25×C127—22no—
47C25×C127—22no—
48C25×C127—22no—
49C25×C127—22no—
50C25×C127—42no—
51C25×C127—42no—
52C25×C127C2×C414yes—
53C25×C127C2312yes—
54C25×C127C2311yescharacteristic
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×C127D414yes—
65C23×C4×C127C2312yes—
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2312yes—
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2312yes—
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74C2×C4⋊C4×C127—24no—
75C2×C4⋊C4×C127—24no—
76C2×C4⋊C4×C127—42no—
77C2×C22⋊C4×C127—232no—
78C2×C22⋊C4×C127—24no—
79C2×C22⋊C4×C127—22no—
80C2×C22⋊C4×C127—22no—
81C2×C22⋊C4×C127—22no—
82C2×C22⋊C4×C127—24no—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—24no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—24no—
88C2×C22⋊C4×C127—24no—
89C2×C22⋊C4×C127—24no—
90C2×C22⋊C4×C127—24no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—24no—
93C2×C22⋊C4×C127—24no—
94C2×C22⋊C4×C127—22no—
95C2×C22⋊C4×C127—22no—
96C2×C22⋊C4×C127—24no—
97C2×C22⋊C4×C127—24no—
98C2×C22⋊C4×C127—42no—
99C2×C22⋊C4×C127—42no—
100C2×C22⋊C4×C127—42no—
101C2×C22⋊C4×C127—42no—
102C2×C22⋊C4×C127C2×C414yes—
103C2×C22⋊C4×C127C2×C414yes—
104C2×C22⋊C4×C127C2×C418yescomplemented
105C2×C22⋊C4×C127C2×C418yescomplemented
106C2×C22⋊C4×C127D418yes—
107C2×C22⋊C4×C127D414yes—
108C2×C42×C127—22no—
109C2×C42×C127—22no—
110C2×C42×C127—24no—
111C2×C42×C127—42no—
112#95×C127—22no—
113#95×C127—22no—
114#95×C127—24no—
115#95×C127—24no—
116#95×C127—24no—
117#95×C127—42no—
118#95×C127—42no—
119C24×C127—22no—
120C24×C127—22no—
121C24×C127—22no—
122C24×C127—22no—
123C24×C127—28no—
124C24×C127—28no—
125C24×C127—216no—
126C24×C127—216no—
127C24×C127—28no—
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×C127—28no—
141C24×C127—28no—
142C24×C127—48no—
143C24×C127—48no—
144C24×C127—48no—
145C24×C127—48no—
146C24×C127—48no—
147C24×C127—48no—
148C24×C127—48no—
149C24×C127—48no—
150C24×C127—48no—
151C24×C127—44no—
152C24×C127—44no—
153C24×C127—48no—
154C24×C127—44no—
155C24×C127—44no—
156C24×C127—44no—
157C24×C127—44no—
158C24×C127C22×C414yes—
159C24×C127C22×C412yes—
160C24×C127C2×D414yes—
161C24×C127C2×D412yes—
162C24×C127C2×D412yes—
163C24×C127#4114yes—
164C24×C127#4112yes—
165C24×C127#4112yes—
166C24×C127#4112yes—
167C24×C127#4112yes—
168C24×C127C2411yescharacteristic
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—22no—
172C22×C4×C127—28no—
173C22×C4×C127—28no—
174C22×C4×C127—21no—
175C22×C4×C127—22no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
178C22×C4×C127—21no—
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—21no—
187C22×C4×C127—22no—
188C22×C4×C127—21no—
189C22×C4×C127—22no—
190C22×C4×C127—22no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—22no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
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—22no—
203C22×C4×C127—22no—
204C22×C4×C127—22no—
205C22×C4×C127—22no—
206C22×C4×C127—28no—
207C22×C4×C127—22no—
208C22×C4×C127—22no—
209C22×C4×C127—22no—
210C22×C4×C127—22no—
211C22×C4×C127—22no—
212C22×C4×C127—22no—
213C22×C4×C127—22no—
214C22×C4×C127—44no—
215C22×C4×C127—48no—
216C22×C4×C127—48no—
217C22×C4×C127—48no—
218C22×C4×C127—48no—
219C22×C4×C127—44no—
220C22×C4×C127—44no—
221C22×C4×C127C22×C412yes—
222C22×C4×C127C22×C414yes—
223C22×C4×C127C22×C412yes—
224C22×C4×C127C2×D412yes—
225C22×C4×C127C2×D412yes—
226C22×C4×C127C2×D414yes—
227C22×C4×C127C2×D412yes—
228C22×C4×C127C2×D414yes—
229C22×C4×C127C2×D412yes—
230C4⋊C4×C127—48no—
231C22⋊C4×C127—216no—
232C22⋊C4×C127—28no—
233C22⋊C4×C127—28no—
234C22⋊C4×C127—216no—
235C22⋊C4×C127—28no—
236C22⋊C4×C127—216no—
237C22⋊C4×C127—48no—
238C22⋊C4×C127—48no—
239C22⋊C4×C127—48no—
240C22⋊C4×C127—44no—
241C42×C127—44no—
242C42×C127—44no—
243C23×C127—24no—
244C23×C127—24no—
245C23×C127—22no—
246C23×C127—22no—
247C23×C127—24no—
248C23×C127—22no—
249C23×C127—22no—
250C23×C127—24no—
251C23×C127—24no—
252C23×C127—24no—
253C23×C127—24no—
254C23×C127—24no—
255C23×C127—24no—
256C23×C127—24no—
257C23×C127—24no—
258C23×C127—24no—
259C23×C127—232no—
260C23×C127—24no—
261C23×C127—24no—
262C23×C127—24no—
263C23×C127—24no—
264C23×C127—24no—
265C23×C127—24no—
266C23×C127—24no—
267C23×C127—24no—
268C23×C127—24no—
269C23×C127—24no—
270C23×C127—24no—
271C23×C127—24no—
272C23×C127—24no—
273C23×C127—24no—
274C23×C127—24no—
275C23×C127—24no—
276C23×C127—24no—
277C23×C127—24no—
278C23×C127—432no—
279C23×C127—432no—
280C23×C127—416no—
281C23×C127—416no—
282C23×C127—416no—
283C23×C127—432no—
284C23×C127—432no—
285C23×C127—416no—
286C23×C127—416no—
287C23×C127—42no—
288C23×C127—42no—
289C23×C127—42no—
290C23×C127—42no—
291C23×C127—42no—
292C23×C127—42no—
293C23×C127—42no—
294C23×C127—42no—
295C23×C127—42no—
296C23×C127—42no—
297C23×C127—42no—
298C23×C127—42no—
299C23×C127—42no—
300C23×C127—42no—
301C23×C127—42no—
302C23×C127—42no—
303C23×C127—416no—
304C23×C127#11714yes—
305C23×C127C4×D418yes—
306C23×C127C4×D414yes—
307C23×C127C4×D414yes—
308C23×C127#12114yes—
309C23×C127#12314yes—
310C23×C127#12414yes—
311C23×C127#12614yes—
312C23×C127C23×C411yescharacteristic
313C23×C127C22×D411yescharacteristic
314C23×C127C22×D412yes—
315C23×C127C22×D411yescharacteristic
316C23×C127C2×#4111yescharacteristic
317C23×C127C2×#4111yescharacteristic
318C23×C127C2×#4111yescharacteristic
319C23×C127C2×#4111yescharacteristic
320C23×C127C2×#4112yes—
321C23×C127H(5,𝔽2)12yes—
322C23×C127H(5,𝔽2)12yes—
323C2×C4×C127—22no—
324C2×C4×C127—22no—
325C2×C4×C127—24no—
326C2×C4×C127—24no—
327C2×C4×C127—22no—
328C2×C4×C127—24no—
329C2×C4×C127—24no—
330C2×C4×C127—22no—
331C2×C4×C127—24no—
332C2×C4×C127—24no—
333C2×C4×C127—24no—
334C2×C4×C127—22no—
335C2×C4×C127—24no—
336C2×C4×C127—22no—
337C2×C4×C127—22no—
338C2×C4×C127—22no—
339C2×C4×C127—22no—
340C2×C4×C127—24no—
341C2×C4×C127—24no—
342C2×C4×C127—24no—
343C2×C4×C127—24no—
344C2×C4×C127—416no—
345C2×C4×C127—416no—
346C2×C4×C127—41no—
347C2×C4×C127—41no—
348C2×C4×C127—42no—
349C2×C4×C127—41no—
350C2×C4×C127—42no—
351C2×C4×C127—41no—
352C2×C4×C127—41no—
353C2×C4×C127—41no—
354C2×C4×C127—41no—
355C2×C4×C127—41no—
356C2×C4×C127—42no—
357C2×C4×C127—42no—
358C2×C4×C127—42no—
359C2×C4×C127—42no—
360C2×C4×C127—42no—
361C2×C4×C127—42no—
362C2×C4×C127—42no—
363C2×C4×C127—42no—
364C2×C4×C127—42no—
365C2×C4×C127—42no—
366C2×C4×C127—42no—
367C2×C4×C127—42no—
368C2×C4×C127—42no—
369C2×C4×C127—42no—
370C2×C4×C127—42no—
371C2×C4×C127—42no—
372C2×C4×C127—42no—
373C2×C4×C127—42no—
374C2×C4×C127—42no—
375C2×C4×C127#12014yes—
376C22×C127—24no—
377C22×C127—28no—
378C22×C127—28no—
379C22×C127—24no—
380C22×C127—24no—
381C22×C127—28no—
382C22×C127—28no—
383C22×C127—24no—
384C22×C127—24no—
385C22×C127—24no—
386C22×C127—28no—
387C22×C127—28no—
388C22×C127—28no—
389C22×C127—464no—
390C22×C127—44no—
391C22×C127—44no—
392C22×C127—44no—
393C22×C127—44no—
394C22×C127—44no—
395C22×C127—44no—
396C22×C127—44no—
397C22×C127—44no—
398C22×C127—44no—
399C22×C127—44no—
400C22×C127—44no—
401C22×C127—44no—
402C22×C127#38818yescomplemented
403C22×C127C2×#11711yescharacteristic
404C22×C127C2×C4×D411yescharacteristic
405C22×C127C2×C4×D412yes—
406C22×C127C2×C4×D411yescharacteristic
407C22×C127#51812yes—
408C22×C127C2×#12011yescharacteristic
409C22×C127C2×#12111yescharacteristic
410C22×C127C2×#12311yescharacteristic
411C22×C127#52512yes—
412C22×C127#52511yescharacteristic
413C22×C127C2×#12411yescharacteristic
414C22×C127C2×#12611yescharacteristic
415C22×C127#53411yescharacteristic
416C22×C127#53511yescharacteristic
417C22×C127#53812yes—
418C22×C127D4212yes—
419C22×C127#54612yes—
420C22×C127#54612yes—
421C22×C127#54612yes—
422C22×C127#54612yes—
423C22×C127#55112yes—
424C22×C127#55112yes—
425C22×C127#55112yes—
426C4×C127—24no—
427C4×C127—42no—
428C4×C127—44no—
429C4×C127—42no—
430C4×C127—42no—
431C4×C127—44no—
432C4×C127—42no—
433C4×C127—42no—
434C4×C127—82no—
435#13991C12711yesmaximal, characteristic, direct product factor, Sylow
436C2×C127—28no—
437C2×C127—48no—
438C2×C127C2×#38811yescharacteristic
439C2×C127C4×#12011yescharacteristic
440C2×C127#232111yescharacteristic
441C2×C127#234212yes—
442C2×C127#235812yes—
443C2×C127#240511yescharacteristic
444C2×C127#240811yescharacteristic
445C2×C127#247212yes—
446C2×C127#248012yes—
447C2×C127#248211yescharacteristic
448C2×C127#253411yescharacteristic
449C23×C22⋊C4C2×C12711yescharacteristic
450C2×#388C2×C12712yescomplemented
451C2×#385C2×C12711yescharacteristic, complemented
452C2×#379C2×C12711yescharacteristic
453C2×#379C2×C12711yescharacteristic
454C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
455#1440C2×C12712yescomplemented
456#1439C2×C12712yescomplemented
457#1437C2×C12712yescomplemented
458C22⋊#95C2×C12711yescharacteristic, complemented
459C22⋊#95C2×C12711yescharacteristic, complemented
460C127#1399111yescharacteristic, direct product factor, Sylow
461C26C22×C12711yescharacteristic
462C24×C4C22×C12711yescharacteristic
463C24×C4C22×C12711yescharacteristic
464C22×C4⋊C4C22×C12712yescomplemented
465C22×C22⋊C4—24no—
466C22×C22⋊C4—28no—
467C22×C22⋊C4C22×C12712yes—
468C22×C22⋊C4C22×C12711yescharacteristic
469C22×C22⋊C4C22×C12712yes—
470C22×C22⋊C4C22×C12712yes—
471C22×C22⋊C4C22×C12711yescharacteristic
472C22×C22⋊C4C22×C12711yescharacteristic
473C22×C22⋊C4C22×C12712yes—
474C22×C22⋊C4C22×C12712yes—
475C22×C22⋊C4C22×C12711yescharacteristic
476C22×C22⋊C4C22×C12712yes—
477C22×C42C22×C12711yescharacteristic, complemented
478C22×C42C22×C12711yescharacteristic, complemented
479#388—28no—
480#385—24no—
481#379—24no—
482#379C4×C12718yescomplemented
483C4×C22⋊C4—24no—
484C2×#95C22×C12712yescomplemented
485C2×#95C22×C12712yescomplemented
486C2×#95C22×C12712yescomplemented
487C2×#95C22×C12711yescharacteristic, complemented
488C2×#95C22×C12711yescharacteristic, complemented
489C2×#95C22×C12712yescomplemented
490C2×#95C22×C12712yescomplemented
491C25—24no—
492C25—22no—
493C25—24no—
494C25—22no—
495C25—22no—
496C25—22no—
497C25—22no—
498C25—22no—
499C25—42no—
500C25—42no—
501C25C2×C4×C12714yes—
502C25C23×C12712yes—
503C25C23×C12711yescharacteristic
504C23×C4—22no—
505C23×C4—22no—
506C23×C4—22no—
507C23×C4—24no—
508C23×C4—24no—
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—42no—
512C23×C4—42no—
513C23×C4D4×C12714yes—
514C23×C4C23×C12712yes—
515C23×C4C23×C12712yes—
516C23×C4C23×C12711yescharacteristic
517C23×C4C23×C12711yescharacteristic
518C23×C4C23×C12711yescharacteristic
519C23×C4C23×C12711yescharacteristic
520C23×C4C23×C12712yes—
521C23×C4C23×C12711yescharacteristic
522C23×C4C23×C12711yescharacteristic
523C2×C4⋊C4—24no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—42no—
526C2×C22⋊C4—232no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4C2×C4×C12714yes—
552C2×C22⋊C4C2×C4×C12714yes—
553C2×C22⋊C4C2×C4×C12718yescomplemented
554C2×C22⋊C4C2×C4×C12718yescomplemented
555C2×C22⋊C4D4×C12718yes—
556C2×C22⋊C4D4×C12714yes—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—24no—
560C2×C42—42no—
561#95—22no—
562#95—22no—
563#95—24no—
564#95—24no—
565#95—24no—
566#95—42no—
567#95—42no—
568C24—22no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—28no—
573C24—28no—
574C24—216no—
575C24—216no—
576C24—28no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—28no—
590C24—28no—
591C24—48no—
592C24—48no—
593C24—48no—
594C24—48no—
595C24—48no—
596C24—48no—
597C24—48no—
598C24—48no—
599C24—48no—
600C24—44no—
601C24—44no—
602C24—48no—
603C24—44no—
604C24—44no—
605C24—44no—
606C24—44no—
607C24C22×C4×C12714yes—
608C24C22×C4×C12712yes—
609C24C2×D4×C12714yes—
610C24C2×D4×C12712yes—
611C24C2×D4×C12712yes—
612C24#41×C12714yes—
613C24#41×C12712yes—
614C24#41×C12712yes—
615C24#41×C12712yes—
616C24#41×C12712yes—
617C24C24×C12711yescharacteristic
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—21no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—28no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—44no—
664C22×C4—48no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4C22×C4×C12712yes—
671C22×C4C22×C4×C12714yes—
672C22×C4C22×C4×C12712yes—
673C22×C4C2×D4×C12712yes—
674C22×C4C2×D4×C12712yes—
675C22×C4C2×D4×C12714yes—
676C22×C4C2×D4×C12712yes—
677C22×C4C2×D4×C12714yes—
678C22×C4C2×D4×C12712yes—
679C4⋊C4—48no—
680C22⋊C4—216no—
681C22⋊C4—28no—
682C22⋊C4—28no—
683C22⋊C4—216no—
684C22⋊C4—28no—
685C22⋊C4—216no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—44no—
690C42—44no—
691C42—44no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—232no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—432no—
728C23—432no—
729C23—416no—
730C23—416no—
731C23—416no—
732C23—432no—
733C23—432no—
734C23—416no—
735C23—416no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—416no—
753C23#117×C12714yes—
754C23C4×D4×C12718yes—
755C23C4×D4×C12714yes—
756C23C4×D4×C12714yes—
757C23#121×C12714yes—
758C23#123×C12714yes—
759C23#124×C12714yes—
760C23#126×C12714yes—
761C23C23×C4×C12711yescharacteristic
762C23C22×D4×C12711yescharacteristic
763C23C22×D4×C12712yes—
764C23C22×D4×C12711yescharacteristic
765C23C2×#41×C12711yescharacteristic
766C23C2×#41×C12711yescharacteristic
767C23C2×#41×C12711yescharacteristic
768C23C2×#41×C12711yescharacteristic
769C23C2×#41×C12712yes—
770C23H(5,𝔽2)×C12712yes—
771C23H(5,𝔽2)×C12712yes—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—416no—
794C2×C4—416no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4#120×C12714yes—
825C22—24no—
826C22—28no—
827C22—28no—
828C22—24no—
829C22—24no—
830C22—28no—
831C22—28no—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—28no—
836C22—28no—
837C22—28no—
838C22—464no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22#388×C12718yescomplemented
852C22C2×#117×C12711yescharacteristic
853C22C2×C4×D4×C12711yescharacteristic
854C22C2×C4×D4×C12712yes—
855C22C2×C4×D4×C12711yescharacteristic
856C22#518×C12712yes—
857C22C2×#120×C12711yescharacteristic
858C22C2×#121×C12711yescharacteristic
859C22C2×#123×C12711yescharacteristic
860C22#525×C12712yes—
861C22#525×C12711yescharacteristic
862C22C2×#124×C12711yescharacteristic
863C22C2×#126×C12711yescharacteristic
864C22#534×C12711yescharacteristic
865C22#535×C12711yescharacteristic
866C22#538×C12712yes—
867C22D42×C12712yes—
868C22#546×C12712yes—
869C22#546×C12712yes—
870C22#546×C12712yes—
871C22#546×C12712yes—
872C22#551×C12712yes—
873C22#551×C12712yes—
874C22#551×C12712yes—
875C4—24no—
876C4—42no—
877C4—44no—
878C4—42no—
879C4—44no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—82no—
884C2—28no—
885C2—48no—
886C2C2×#388×C12711yescharacteristic
887C2C4×#120×C12711yescharacteristic
888C2C127×#232111yescharacteristic
889C2C127×#234212yes—
890C2C127×#235812yes—
891C2C127×#240511yescharacteristic
892C2C127×#240811yescharacteristic
893C2C127×#247212yes—
894C2C127×#248012yes—
895C2C127×#248211yescharacteristic
896C2C127×#253411yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C127C2semidirect
3. C2×#385×C127C2semidirect
6. C2×C4×C22⋊C4×C127C2semidirect
7. C127×#1440C2semidirect
8. C127×#1439C2semidirect
9. C127×#1437C2semidirect
10. C127×C22⋊#95C2semidirect
11. C127×C22⋊#95C2semidirect
15. C22×C4⋊C4×C127C22semidirect
28. C22×C42×C127C22semidirect
29. C22×C42×C127C22semidirect
33. #379×C127C4semidirect
35. C2×#95×C127C22semidirect
36. C2×#95×C127C22semidirect
37. C2×#95×C127C22semidirect
38. C2×#95×C127C22semidirect
39. C2×#95×C127C22semidirect
40. C2×#95×C127C22semidirect
41. C2×#95×C127C22semidirect
104. C2×C22⋊C4×C127C2×C4semidirect
105. C2×C22⋊C4×C127C2×C4semidirect
402. C22×C127#388semidirect
435. #13991C127direct (N × H)
450. C2×#388C2×C127semidirect
451. C2×#385C2×C127semidirect
454. C2×C4×C22⋊C4C2×C127semidirect
455. #1440C2×C127semidirect
456. #1439C2×C127semidirect
457. #1437C2×C127semidirect
458. C22⋊#95C2×C127semidirect
459. C22⋊#95C2×C127semidirect
460. C127#13991direct (N × H)
464. C22×C4⋊C4C22×C127semidirect
477. C22×C42C22×C127semidirect
478. C22×C42C22×C127semidirect
482. #379C4×C127semidirect
484. C2×#95C22×C127semidirect
485. C2×#95C22×C127semidirect
486. C2×#95C22×C127semidirect
487. C2×#95C22×C127semidirect
488. C2×#95C22×C127semidirect
489. C2×#95C22×C127semidirect
490. C2×#95C22×C127semidirect
553. C2×C22⋊C4C2×C4×C127semidirect
554. C2×C22⋊C4C2×C4×C127semidirect
851. C22#388×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1272
C2×#388×C1272
C2×#385×C1272
C2×#379×C1272
C2×C4×C22⋊C4×C1272
C127×#14402
C127×#14392
C127×#14372
C127×C22⋊#952
#13991127