Finite Group Databasebeta

← C127×#14726 #44578399

Subgroups — C127×#14726 #44578399

Order 32512.

3494 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C2×#396×C127C212yesmaximal, complemented
3C2×#385×C127C211yesmaximal, characteristic, complemented
4C2×#385×C127C211yesmaximal, characteristic, complemented
5C2×#380×C127C211yesmaximal, characteristic, complemented
6C2×#379×C127C211yesmaximal, characteristic
7C2×#379×C127C211yesmaximal, characteristic
8C127×#1439C212yesmaximal, complemented
9C127×#1439C212yesmaximal, complemented
10C127×#1439C212yesmaximal, complemented
11C127×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C127C2211yescharacteristic
13C24×C4×C127C2211yescharacteristic
14C24×C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic, complemented
16C22×C4⋊C4×C127C2212yescomplemented
17C22×C4⋊C4×C127C2212yescomplemented
18C22×C4⋊C4×C127C2211yescharacteristic, complemented
19C22×C22⋊C4×C127—24no—
20C22×C22⋊C4×C127—28no—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2211yescharacteristic
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×C22⋊C4×C127C2211yescharacteristic
31#396×C127—28no—
32#385×C127—24no—
33#385×C127—24no—
34#380×C127—24no—
35#379×C127—24no—
36#379×C127—24no—
37C2×#95×C127C2212yescomplemented
38C2×#95×C127C2212yescomplemented
39C2×#95×C127C2211yescharacteristic, complemented
40C2×#95×C127C2211yescharacteristic, complemented
41C2×#95×C127C2212yescomplemented
42C2×#95×C127C2212yescomplemented
43C25×C127—24no—
44C25×C127—22no—
45C25×C127—24no—
46C25×C127—22no—
47C25×C127—22no—
48C25×C127—22no—
49C25×C127—22no—
50C25×C127—22no—
51C25×C127—42no—
52C25×C127—42no—
53C25×C127Q814yes—
54C25×C127C2312yes—
55C25×C127C2311yescharacteristic
56C23×C4×C127—22no—
57C23×C4×C127—22no—
58C23×C4×C127—22no—
59C23×C4×C127—24no—
60C23×C4×C127—24no—
61C23×C4×C127—22no—
62C23×C4×C127—22no—
63C23×C4×C127—42no—
64C23×C4×C127—42no—
65C23×C4×C127D414yes—
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2312yes—
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2312yes—
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2312yes—
74C23×C4×C127C2311yescharacteristic
75C2×C4⋊C4×C127—24no—
76C2×C4⋊C4×C127—24no—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—24no—
80C2×C4⋊C4×C127—24no—
81C2×C4⋊C4×C127—24no—
82C2×C4⋊C4×C127—42no—
83C2×C4⋊C4×C127—42no—
84C2×C4⋊C4×C127—42no—
85C2×C22⋊C4×C127—232no—
86C2×C22⋊C4×C127—24no—
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—22no—
96C2×C22⋊C4×C127—22no—
97C2×C22⋊C4×C127—22no—
98C2×C22⋊C4×C127—22no—
99C2×C22⋊C4×C127—24no—
100C2×C22⋊C4×C127—24no—
101C2×C22⋊C4×C127—24no—
102C2×C22⋊C4×C127—24no—
103C2×C22⋊C4×C127—22no—
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127—24no—
106C2×C22⋊C4×C127—24no—
107C2×C22⋊C4×C127—24no—
108C2×C22⋊C4×C127—24no—
109C2×C22⋊C4×C127—42no—
110C2×C22⋊C4×C127—42no—
111C2×C22⋊C4×C127—42no—
112C2×C22⋊C4×C127—42no—
113C2×C22⋊C4×C127D418yes—
114C2×C22⋊C4×C127D414yes—
115C2×C22⋊C4×C127D414yes—
116#95×C127—24no—
117#95×C127—24no—
118#95×C127—22no—
119#95×C127—22no—
120#95×C127—24no—
121#95×C127—42no—
122C24×C127—22no—
123C24×C127—22no—
124C24×C127—22no—
125C24×C127—22no—
126C24×C127—28no—
127C24×C127—28no—
128C24×C127—216no—
129C24×C127—216no—
130C24×C127—28no—
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—22no—
141C24×C127—22no—
142C24×C127—22no—
143C24×C127—28no—
144C24×C127—28no—
145C24×C127—48no—
146C24×C127—48no—
147C24×C127—48no—
148C24×C127—48no—
149C24×C127—48no—
150C24×C127—48no—
151C24×C127—48no—
152C24×C127—48no—
153C24×C127—48no—
154C24×C127—44no—
155C24×C127—44no—
156C24×C127—48no—
157C24×C127—44no—
158C24×C127—44no—
159C24×C127—44no—
160C24×C127—44no—
161C24×C127C2×D414yes—
162C24×C127C2×D412yes—
163C24×C127C2×D412yes—
164C24×C127C2×D412yes—
165C24×C127C2×Q814yes—
166C24×C127C2×Q812yes—
167C24×C127#4114yes—
168C24×C127#4112yes—
169C24×C127#4112yes—
170C24×C127#4112yes—
171C24×C127C2411yescharacteristic
172C22×C4×C127—21no—
173C22×C4×C127—21no—
174C22×C4×C127—22no—
175C22×C4×C127—28no—
176C22×C4×C127—28no—
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—21no—
189C22×C4×C127—21no—
190C22×C4×C127—22no—
191C22×C4×C127—22no—
192C22×C4×C127—21no—
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—28no—
202C22×C4×C127—21no—
203C22×C4×C127—22no—
204C22×C4×C127—22no—
205C22×C4×C127—22no—
206C22×C4×C127—21no—
207C22×C4×C127—22no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—22no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
213C22×C4×C127—22no—
214C22×C4×C127—22no—
215C22×C4×C127—22no—
216C22×C4×C127—22no—
217C22×C4×C127—22no—
218C22×C4×C127—22no—
219C22×C4×C127—44no—
220C22×C4×C127—48no—
221C22×C4×C127—48no—
222C22×C4×C127—48no—
223C22×C4×C127—48no—
224C22×C4×C127—44no—
225C22×C4×C127—44no—
226C22×C4×C127C2×D412yes—
227C22×C4×C127C2×D414yes—
228C22×C4×C127C2×D412yes—
229C22×C4×C127C2×D414yes—
230C22×C4×C127C2×D412yes—
231C22×C4×C127C2×D412yes—
232C22×C4×C127C2×D414yes—
233C4⋊C4×C127—48no—
234C4⋊C4×C127—48no—
235C4⋊C4×C127—44no—
236C4⋊C4×C127—44no—
237C22⋊C4×C127—216no—
238C22⋊C4×C127—28no—
239C22⋊C4×C127—28no—
240C22⋊C4×C127—216no—
241C22⋊C4×C127—48no—
242C22⋊C4×C127—48no—
243C22⋊C4×C127—48no—
244C22⋊C4×C127—48no—
245C22⋊C4×C127—44no—
246C22⋊C4×C127—44no—
247C23×C127—22no—
248C23×C127—24no—
249C23×C127—22no—
250C23×C127—24no—
251C23×C127—22no—
252C23×C127—22no—
253C23×C127—24no—
254C23×C127—24no—
255C23×C127—24no—
256C23×C127—24no—
257C23×C127—24no—
258C23×C127—24no—
259C23×C127—24no—
260C23×C127—24no—
261C23×C127—24no—
262C23×C127—24no—
263C23×C127—232no—
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—24no—
279C23×C127—24no—
280C23×C127—24no—
281C23×C127—24no—
282C23×C127—432no—
283C23×C127—432no—
284C23×C127—416no—
285C23×C127—416no—
286C23×C127—416no—
287C23×C127—416no—
288C23×C127—432no—
289C23×C127—432no—
290C23×C127—416no—
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—42no—
304C23×C127—42no—
305C23×C127—42no—
306C23×C127—42no—
307C23×C127—416no—
308C23×C127#12114yes—
309C23×C127#12114yes—
310C23×C127#12114yes—
311C23×C127C22⋊Q818yes—
312C23×C127C22⋊Q814yes—
313C23×C127C22⋊Q814yes—
314C23×C127C22⋊Q814yes—
315C23×C127#12614yes—
316C23×C127C22×D411yescharacteristic
317C23×C127C22×D412yes—
318C23×C127C22×D411yescharacteristic
319C23×C127C22×D411yescharacteristic
320C23×C127C22×Q811yescharacteristic
321C23×C127C2×#4111yescharacteristic
322C23×C127C2×#4111yescharacteristic
323C23×C127C2×#4111yescharacteristic
324C23×C127C2×#4112yes—
325C23×C127H(5,𝔽2)12yes—
326C23×C127H(5,𝔽2)12yes—
327C2×C4×C127—22no—
328C2×C4×C127—22no—
329C2×C4×C127—24no—
330C2×C4×C127—24no—
331C2×C4×C127—24no—
332C2×C4×C127—22no—
333C2×C4×C127—22no—
334C2×C4×C127—24no—
335C2×C4×C127—22no—
336C2×C4×C127—22no—
337C2×C4×C127—22no—
338C2×C4×C127—24no—
339C2×C4×C127—24no—
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—42no—
348C2×C4×C127—42no—
349C2×C4×C127—41no—
350C2×C4×C127—41no—
351C2×C4×C127—41no—
352C2×C4×C127—42no—
353C2×C4×C127—42no—
354C2×C4×C127—42no—
355C2×C4×C127—42no—
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—41no—
363C2×C4×C127—41no—
364C2×C4×C127—41no—
365C2×C4×C127—42no—
366C2×C4×C127—41no—
367C2×C4×C127—42no—
368C2×C4×C127—41no—
369C2×C4×C127—41no—
370C2×C4×C127—42no—
371C2×C4×C127—42no—
372C2×C4×C127—42no—
373C2×C4×C127—42no—
374C2×C4×C127—42no—
375C2×C4×C127—42no—
376C2×C4×C127—42no—
377C2×C4×C127—42no—
378C2×C4×C127—42no—
379C2×C4×C127#12014yes—
380C22×C127—24no—
381C22×C127—24no—
382C22×C127—24no—
383C22×C127—24no—
384C22×C127—24no—
385C22×C127—28no—
386C22×C127—28no—
387C22×C127—28no—
388C22×C127—28no—
389C22×C127—24no—
390C22×C127—28no—
391C22×C127—28no—
392C22×C127—28no—
393C22×C127—464no—
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—44no—
403C22×C127—44no—
404C22×C127—44no—
405C22×C127—44no—
406C22×C127#39618yescomplemented
407C22×C127C2×#12011yescharacteristic
408C22×C127C2×#12111yescharacteristic
409C22×C127C2×#12111yescharacteristic
410C22×C127C2×#12111yescharacteristic
411C22×C127C2×C22⋊Q811yescharacteristic
412C22×C127C2×C22⋊Q812yes—
413C22×C127C2×C22⋊Q811yescharacteristic
414C22×C127C2×C22⋊Q811yescharacteristic
415C22×C127#52511yescharacteristic
416C22×C127#52512yes—
417C22×C127C2×#12611yescharacteristic
418C22×C127#53411yescharacteristic
419C22×C127#53511yescharacteristic
420C22×C127#53812yes—
421C22×C127#54312yes—
422C22×C127D4212yes—
423C22×C127D4212yes—
424C22×C127#54612yes—
425C22×C127#54612yes—
426C22×C127#54612yes—
427C22×C127#54612yes—
428C22×C127#55112yes—
429C22×C127#55112yes—
430C4×C127—24no—
431C4×C127—42no—
432C4×C127—44no—
433C4×C127—42no—
434C4×C127—44no—
435C4×C127—42no—
436C4×C127—81no—
437C4×C127—81no—
438C4×C127—82no—
439#14726C12711yesmaximal, characteristic, direct product factor, Sylow
440C2×C127—28no—
441C2×C127—48no—
442C2×C127C2×#39611yescharacteristic
443C2×C127#240811yescharacteristic
444C2×C127#241011yescharacteristic
445C2×C127#241111yescharacteristic
446C2×C127#242412yes—
447C2×C127#243712yes—
448C2×C127#243712yes—
449C2×C127#248012yes—
450C2×C127#253411yescharacteristic
451C2×C127#262611yescharacteristic
452C2×C127#284811yescharacteristic
453C23×C22⋊C4C2×C12711yescharacteristic
454C2×#396C2×C12712yescomplemented
455C2×#385C2×C12711yescharacteristic, complemented
456C2×#385C2×C12711yescharacteristic, complemented
457C2×#380C2×C12711yescharacteristic, complemented
458C2×#379C2×C12711yescharacteristic
459C2×#379C2×C12711yescharacteristic
460#1439C2×C12712yescomplemented
461#1439C2×C12712yescomplemented
462#1439C2×C12712yescomplemented
463C22⋊#95C2×C12711yescharacteristic, complemented
464C127#1472611yescharacteristic, direct product factor, Sylow
465C26C22×C12711yescharacteristic
466C24×C4C22×C12711yescharacteristic
467C24×C4C22×C12711yescharacteristic
468C22×C4⋊C4C22×C12711yescharacteristic, complemented
469C22×C4⋊C4C22×C12712yescomplemented
470C22×C4⋊C4C22×C12712yescomplemented
471C22×C4⋊C4C22×C12711yescharacteristic, complemented
472C22×C22⋊C4—24no—
473C22×C22⋊C4—28no—
474C22×C22⋊C4C22×C12712yes—
475C22×C22⋊C4C22×C12711yescharacteristic
476C22×C22⋊C4C22×C12711yescharacteristic
477C22×C22⋊C4C22×C12712yes—
478C22×C22⋊C4C22×C12712yes—
479C22×C22⋊C4C22×C12712yes—
480C22×C22⋊C4C22×C12712yes—
481C22×C22⋊C4C22×C12712yes—
482C22×C22⋊C4C22×C12711yescharacteristic
483C22×C22⋊C4C22×C12711yescharacteristic
484#396—28no—
485#385—24no—
486#385—24no—
487#380—24no—
488#379—24no—
489#379—24no—
490C2×#95C22×C12712yescomplemented
491C2×#95C22×C12712yescomplemented
492C2×#95C22×C12711yescharacteristic, complemented
493C2×#95C22×C12711yescharacteristic, complemented
494C2×#95C22×C12712yescomplemented
495C2×#95C22×C12712yescomplemented
496C25—24no—
497C25—22no—
498C25—24no—
499C25—22no—
500C25—22no—
501C25—22no—
502C25—22no—
503C25—22no—
504C25—42no—
505C25—42no—
506C25Q8×C12714yes—
507C25C23×C12712yes—
508C25C23×C12711yescharacteristic
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—24no—
513C23×C4—24no—
514C23×C4—22no—
515C23×C4—22no—
516C23×C4—42no—
517C23×C4—42no—
518C23×C4D4×C12714yes—
519C23×C4C23×C12711yescharacteristic
520C23×C4C23×C12712yes—
521C23×C4C23×C12711yescharacteristic
522C23×C4C23×C12711yescharacteristic
523C23×C4C23×C12712yes—
524C23×C4C23×C12711yescharacteristic
525C23×C4C23×C12711yescharacteristic
526C23×C4C23×C12712yes—
527C23×C4C23×C12711yescharacteristic
528C2×C4⋊C4—24no—
529C2×C4⋊C4—24no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—24no—
533C2×C4⋊C4—24no—
534C2×C4⋊C4—24no—
535C2×C4⋊C4—42no—
536C2×C4⋊C4—42no—
537C2×C4⋊C4—42no—
538C2×C22⋊C4—232no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4D4×C12718yes—
567C2×C22⋊C4D4×C12714yes—
568C2×C22⋊C4D4×C12714yes—
569#95—24no—
570#95—24no—
571#95—22no—
572#95—22no—
573#95—24no—
574#95—42no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—28no—
580C24—28no—
581C24—216no—
582C24—216no—
583C24—28no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—28no—
597C24—28no—
598C24—48no—
599C24—48no—
600C24—48no—
601C24—48no—
602C24—48no—
603C24—48no—
604C24—48no—
605C24—48no—
606C24—48no—
607C24—44no—
608C24—44no—
609C24—48no—
610C24—44no—
611C24—44no—
612C24—44no—
613C24—44no—
614C24C2×D4×C12714yes—
615C24C2×D4×C12712yes—
616C24C2×D4×C12712yes—
617C24C2×D4×C12712yes—
618C24C2×Q8×C12714yes—
619C24C2×Q8×C12712yes—
620C24#41×C12714yes—
621C24#41×C12712yes—
622C24#41×C12712yes—
623C24#41×C12712yes—
624C24C24×C12711yescharacteristic
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—28no—
629C22×C4—28no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—21no—
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—28no—
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—22no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—44no—
673C22×C4—48no—
674C22×C4—48no—
675C22×C4—48no—
676C22×C4—48no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4C2×D4×C12712yes—
680C22×C4C2×D4×C12714yes—
681C22×C4C2×D4×C12712yes—
682C22×C4C2×D4×C12714yes—
683C22×C4C2×D4×C12712yes—
684C22×C4C2×D4×C12712yes—
685C22×C4C2×D4×C12714yes—
686C4⋊C4—48no—
687C4⋊C4—48no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C22⋊C4—216no—
691C22⋊C4—28no—
692C22⋊C4—28no—
693C22⋊C4—216no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—48no—
697C22⋊C4—48no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—232no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—432no—
736C23—432no—
737C23—416no—
738C23—416no—
739C23—416no—
740C23—416no—
741C23—432no—
742C23—432no—
743C23—416no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—416no—
761C23#121×C12714yes—
762C23#121×C12714yes—
763C23#121×C12714yes—
764C23C22⋊Q8×C12718yes—
765C23C22⋊Q8×C12714yes—
766C23C22⋊Q8×C12714yes—
767C23C22⋊Q8×C12714yes—
768C23#126×C12714yes—
769C23C22×D4×C12711yescharacteristic
770C23C22×D4×C12712yes—
771C23C22×D4×C12711yescharacteristic
772C23C22×D4×C12711yescharacteristic
773C23C22×Q8×C12711yescharacteristic
774C23C2×#41×C12711yescharacteristic
775C23C2×#41×C12711yescharacteristic
776C23C2×#41×C12711yescharacteristic
777C23C2×#41×C12712yes—
778C23H(5,𝔽2)×C12712yes—
779C23H(5,𝔽2)×C12712yes—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—416no—
798C2×C4—416no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
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—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4#120×C12714yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—28no—
839C22—28no—
840C22—28no—
841C22—28no—
842C22—24no—
843C22—28no—
844C22—28no—
845C22—28no—
846C22—464no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22#396×C12718yescomplemented
860C22C2×#120×C12711yescharacteristic
861C22C2×#121×C12711yescharacteristic
862C22C2×#121×C12711yescharacteristic
863C22C2×#121×C12711yescharacteristic
864C22C2×C22⋊Q8×C12711yescharacteristic
865C22C2×C22⋊Q8×C12712yes—
866C22C2×C22⋊Q8×C12711yescharacteristic
867C22C2×C22⋊Q8×C12711yescharacteristic
868C22#525×C12711yescharacteristic
869C22#525×C12712yes—
870C22C2×#126×C12711yescharacteristic
871C22#534×C12711yescharacteristic
872C22#535×C12711yescharacteristic
873C22#538×C12712yes—
874C22#543×C12712yes—
875C22D42×C12712yes—
876C22D42×C12712yes—
877C22#546×C12712yes—
878C22#546×C12712yes—
879C22#546×C12712yes—
880C22#546×C12712yes—
881C22#551×C12712yes—
882C22#551×C12712yes—
883C4—24no—
884C4—44no—
885C4—42no—
886C4—42no—
887C4—44no—
888C4—42no—
889C4—81no—
890C4—81no—
891C4—82no—
892C2—28no—
893C2—48no—
894C2C2×#396×C12711yescharacteristic
895C2C127×#240811yescharacteristic
896C2C127×#241011yescharacteristic
897C2C127×#241111yescharacteristic
898C2C127×#242412yes—
899C2C127×#243712yes—
900C2C127×#243712yes—
901C2C127×#248012yes—
902C2C127×#253411yescharacteristic
903C2C127×#262611yescharacteristic
904C2C127×#284811yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#396×C127C2semidirect
3. C2×#385×C127C2semidirect
4. C2×#385×C127C2semidirect
5. C2×#380×C127C2semidirect
8. C127×#1439C2semidirect
9. C127×#1439C2semidirect
10. C127×#1439C2semidirect
11. C127×C22⋊#95C2semidirect
15. C22×C4⋊C4×C127C22semidirect
16. C22×C4⋊C4×C127C22semidirect
17. C22×C4⋊C4×C127C22semidirect
18. C22×C4⋊C4×C127C22semidirect
37. C2×#95×C127C22semidirect
38. C2×#95×C127C22semidirect
39. C2×#95×C127C22semidirect
40. C2×#95×C127C22semidirect
41. C2×#95×C127C22semidirect
42. C2×#95×C127C22semidirect
406. C22×C127#396semidirect
439. #14726C127direct (N × H)
454. C2×#396C2×C127semidirect
455. C2×#385C2×C127semidirect
456. C2×#385C2×C127semidirect
457. C2×#380C2×C127semidirect
460. #1439C2×C127semidirect
461. #1439C2×C127semidirect
462. #1439C2×C127semidirect
463. C22⋊#95C2×C127semidirect
464. C127#14726direct (N × H)
468. C22×C4⋊C4C22×C127semidirect
469. C22×C4⋊C4C22×C127semidirect
470. C22×C4⋊C4C22×C127semidirect
471. C22×C4⋊C4C22×C127semidirect
490. C2×#95C22×C127semidirect
491. C2×#95C22×C127semidirect
492. C2×#95C22×C127semidirect
493. C2×#95C22×C127semidirect
494. C2×#95C22×C127semidirect
495. C2×#95C22×C127semidirect
859. C22#396×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×#396×C1272
C2×#385×C1272
C2×#380×C1272
C2×#379×C1272
C127×#14392
C127×C22⋊#952
#14726127