Finite Group Databasebeta

← C127×#21562 #44585235

Subgroups — C127×#21562 #44585235

Order 32512.

930 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#435×C127C211yesmaximal, characteristic
2C2×C4×M16×C127C211yesmaximal, characteristic, complemented
3C4×#123×C127C211yesmaximal, characteristic
4C127×#1924C211yesmaximal, characteristic, complemented
5C127×#1923C211yesmaximal, characteristic, complemented
6C127×#1917C211yesmaximal, characteristic, complemented
7C127×#1916C211yesmaximal, characteristic, complemented
8C127×#1870C211yesmaximal, characteristic
9C127×#1851C211yesmaximal, characteristic, complemented
10C127×#1817C211yesmaximal, characteristic, complemented
11C127×#1771C211yesmaximal, characteristic, complemented
12C127×#1770C211yesmaximal, characteristic, complemented
13C127×#1753C211yesmaximal, characteristic, complemented
14C127×#1752C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C127C211yesmaximal, characteristic, complemented
16C22×M16×C127C2211yescharacteristic
17C22×M16×C127C2211yescharacteristic
18C23×C8×C127C2211yescharacteristic
19C2×#123×C127C411yescharacteristic
20C2×C4×D4×C127C2211yescharacteristic
21C22×C42×C127C2211yescharacteristic
22#435×C127—24no—
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×C4⋊C8×C127C2211yescharacteristic
25C2×C4⋊C8×C127C2211yescharacteristic
26C2×C22⋊C8×C127C2211yescharacteristic
27C2×C22⋊C8×C127C2211yescharacteristic
28C2×C22⋊C8×C127C2211yescharacteristic
29C2×C22⋊C8×C127C2211yescharacteristic
30C2×C22⋊C8×C127C2211yescharacteristic
31C4×M16×C127—24no—
32C2×#97×C127C2211yescharacteristic
33C2×#97×C127C2211yescharacteristic
34C2×#97×C127C2211yescharacteristic
35C2×#97×C127C2211yescharacteristic
36C2×C4×C8×C127C2211yescharacteristic
37C2×C4×C8×C127C2211yescharacteristic
38C2×C4×C8×C127C2211yescharacteristic
39#388×C127C411yescharacteristic
40#388×C127C411yescharacteristic
41#387×C127C411yescharacteristic
42#387×C127C411yescharacteristic
43#386×C127C411yescharacteristic
44#385×C127C411yescharacteristic
45#381×C127C411yescharacteristic
46C4×C4⋊C4×C127C2211yescharacteristic
47C4×C4⋊C4×C127C2211yescharacteristic
48C4×C22⋊C4×C127C2211yescharacteristic
49C4×C22⋊C4×C127C2211yescharacteristic
50C4×C22⋊C4×C127C2211yescharacteristic
51#336×C127C2211yescharacteristic
52#336×C127C2211yescharacteristic
53#336×C127C2211yescharacteristic
54#336×C127C2211yescharacteristic
55#336×C127C2211yescharacteristic
56#336×C127C2211yescharacteristic
57#336×C127C2211yescharacteristic
58#336×C127C2211yescharacteristic
59#336×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61C22×D4×C127C2×C411yescharacteristic
62C23×C4×C127C2×C411yescharacteristic
63C23×C4×C127C2×C411yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C2×M16×C127—22no—
67C2×M16×C127—22no—
68C2×M16×C127—22no—
69C2×M16×C127—22no—
70C2×M16×C127—22no—
71C2×M16×C127D414yes—
72C22×C8×C127—22no—
73C22×C8×C127—22no—
74C22×C8×C127—22no—
75C22×C8×C127C2311yescharacteristic
76C22×C8×C127C2311yescharacteristic
77C22×C8×C127C2311yescharacteristic
78C22×C8×C127C2311yescharacteristic
79C22×C8×C127C2311yescharacteristic
80C22×C8×C127C2311yescharacteristic
81C22×C8×C127C2311yescharacteristic
82C22×C8×C127C2311yescharacteristic
83#123×C127—24no—
84C4×D4×C127—22no—
85C4×D4×C127—22no—
86C2×C4⋊C4×C127C2×C411yescharacteristic
87C2×C4⋊C4×C127C2×C411yescharacteristic
88C2×C4⋊C4×C127C2×C411yescharacteristic
89C2×C4⋊C4×C127C2×C411yescharacteristic
90C2×C4⋊C4×C127C2×C411yescharacteristic
91C2×C22⋊C4×C127C2×C411yescharacteristic
92C2×C22⋊C4×C127C2×C411yescharacteristic
93C2×C22⋊C4×C127C2×C411yescharacteristic
94C2×C22⋊C4×C127C2×C411yescharacteristic
95C2×C22⋊C4×C127C2×C411yescharacteristic
96C2×C22⋊C4×C127C2×C411yescharacteristic
97C2×C22⋊C4×C127C2×C411yescharacteristic
98C2×C22⋊C4×C127C2×C411yescharacteristic
99C2×C42×C127—22no—
100C2×C42×C127—22no—
101C2×C42×C127C2×C411yescharacteristic
102C2×C42×C127C2×C411yescharacteristic
103C2×C42×C127C2311yescharacteristic
104C2×C42×C127C2311yescharacteristic
105C2×C42×C127C2311yescharacteristic
106C2×C42×C127C2311yescharacteristic
107C2×C42×C127C2311yescharacteristic
108C4⋊C8×C127—22no—
109C4⋊C8×C127—22no—
110C4⋊C8×C127—22no—
111C22⋊C8×C127—22no—
112C22⋊C8×C127—22no—
113C22⋊C8×C127—22no—
114C22⋊C8×C127—22no—
115C22⋊C8×C127—22no—
116#97×C127—22no—
117#97×C127—22no—
118#97×C127—22no—
119#97×C127—22no—
120C4×C8×C127—22no—
121C4×C8×C127—22no—
122C4×C8×C127—22no—
123#95×C127C2×C411yescharacteristic
124#95×C127C2×C411yescharacteristic
125#95×C127C2×C411yescharacteristic
126#95×C127C2×C411yescharacteristic
127#95×C127C2×C411yescharacteristic
128#95×C127C2×C411yescharacteristic
129#95×C127C2×C411yescharacteristic
130#95×C127C2×C411yescharacteristic
131#95×C127C2×C411yescharacteristic
132#95×C127C2×C411yescharacteristic
133C24×C127C22×C411yescharacteristic
134C24×C127C22×C411yescharacteristic
135C2×D4×C127—22no—
136C2×D4×C127—22no—
137C2×D4×C127—41no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—21no—
141C22×C4×C127—21no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—21no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—41no—
153C22×C4×C127—41no—
154C22×C4×C127C22×C411yescharacteristic
155C22×C4×C127C22×C411yescharacteristic
156C22×C4×C127C22×C411yescharacteristic
157C22×C4×C127C22×C411yescharacteristic
158C22×C4×C127C22×C411yescharacteristic
159C22×C4×C127C22×C411yescharacteristic
160C22×C4×C127C22×C411yescharacteristic
161C22×C4×C127C22×C411yescharacteristic
162C22×C4×C127C22×C411yescharacteristic
163C22×C4×C127C22×C411yescharacteristic
164C22×C4×C127C22×C411yescharacteristic
165C22×C4×C127C22×C411yescharacteristic
166C22×C4×C127C2×D412yes—
167C22×C4×C127#4112yes—
168C22×C4×C127C2411yescharacteristic
169M16×C127—28no—
170M16×C127—28no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—21no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—21no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—21no—
182C2×C8×C127—21no—
183C2×C8×C127—21no—
184C2×C8×C127—21no—
185C2×C8×C127—21no—
186C2×C8×C127—21no—
187C2×C8×C127—21no—
188C2×C8×C127—21no—
189C2×C8×C127—44no—
190C2×C8×C127C2×D412yes—
191C2×C8×C127C2×D412yes—
192C2×C8×C127#4112yes—
193C2×C8×C127#4112yes—
194C2×C8×C127#4112yes—
195C2×C8×C127#4112yes—
196C4⋊C4×C127—22no—
197C4⋊C4×C127—22no—
198C4⋊C4×C127—22no—
199C4⋊C4×C127—22no—
200C4⋊C4×C127—41no—
201C22⋊C4×C127—22no—
202C22⋊C4×C127—22no—
203C22⋊C4×C127—22no—
204C22⋊C4×C127—22no—
205C22⋊C4×C127—22no—
206C22⋊C4×C127—41no—
207C22⋊C4×C127—41no—
208C22⋊C4×C127M1614yescomplemented
209C42×C127—22no—
210C42×C127—22no—
211C42×C127—21no—
212C42×C127—21no—
213C42×C127—21no—
214C42×C127—21no—
215C42×C127—21no—
216C42×C127—21no—
217C42×C127—21no—
218C42×C127—21no—
219C42×C127—21no—
220C42×C127—21no—
221C23×C127—21no—
222C23×C127—21no—
223C23×C127—21no—
224C23×C127—21no—
225C23×C127—21no—
226C23×C127—21no—
227C23×C127—21no—
228C23×C127—21no—
229C23×C127—21no—
230C23×C127—21no—
231C23×C127—21no—
232C23×C127—21no—
233C23×C127C4×D412yes—
234C23×C127C2×M1612yes—
235C23×C127C23×C411yescharacteristic
236D4×C127—44no—
237C2×C4×C127—21no—
238C2×C4×C127—21no—
239C2×C4×C127—21no—
240C2×C4×C127—21no—
241C2×C4×C127—21no—
242C2×C4×C127—21no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—22no—
246C2×C4×C127—22no—
247C2×C4×C127—22no—
248C2×C4×C127—22no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—21no—
253C2×C4×C127—21no—
254C2×C4×C127—21no—
255C2×C4×C127—21no—
256C2×C4×C127—21no—
257C2×C4×C127—21no—
258C2×C4×C127—21no—
259C2×C4×C127—21no—
260C2×C4×C127—21no—
261C2×C4×C127—21no—
262C2×C4×C127—21no—
263C2×C4×C127—21no—
264C2×C4×C127—21no—
265C2×C4×C127—21no—
266C2×C4×C127—21no—
267C2×C4×C127—21no—
268C2×C4×C127—21no—
269C2×C4×C127—21no—
270C2×C4×C127—21no—
271C2×C4×C127—21no—
272C2×C4×C127—21no—
273C2×C4×C127—44no—
274C2×C4×C127—44no—
275C2×C4×C127—41no—
276C2×C4×C127—41no—
277C2×C4×C127—41no—
278C2×C4×C127—41no—
279C2×C4×C127C4×D412yes—
280C2×C4×C127C2×M1612yes—
281C2×C4×C127C2×M1612yes—
282C2×C4×C127#13112yes—
283C2×C4×C127C22×D411yescharacteristic
284C2×C4×C127C2×#4111yescharacteristic
285C2×C4×C127C2×#4111yescharacteristic
286C2×C4×C127C2×#4111yescharacteristic
287C2×C4×C127C2×#4111yescharacteristic
288C2×C4×C127C2×#4111yescharacteristic
289C8×C127—22no—
290C8×C127—22no—
291C8×C127—22no—
292C8×C127—41no—
293C8×C127—41no—
294C8×C127—41no—
295C8×C127—41no—
296C8×C127#12314yescomplemented
297C22×C127—22no—
298C22×C127—22no—
299C22×C127—22no—
300C22×C127—22no—
301C22×C127—22no—
302C22×C127—22no—
303C22×C127—41no—
304C22×C127—41no—
305C22×C127—41no—
306C22×C127—41no—
307C22×C127—41no—
308C22×C127—41no—
309C22×C127—41no—
310C22×C127—41no—
311C22×C127C2×C4×D411yescharacteristic
312C22×C127C4×#4111yescharacteristic
313C22×C127C4×#4111yescharacteristic
314C22×C127C22×M1611yescharacteristic
315C22×C127C2×#13111yescharacteristic
316C22×C127#56811yescharacteristic
317C22×C127#56811yescharacteristic
318C4×C127—22no—
319C4×C127—22no—
320C4×C127—22no—
321C4×C127—22no—
322C4×C127—41no—
323C4×C127—41no—
324C4×C127—41no—
325C4×C127—41no—
326C4×C127—41no—
327C4×C127—41no—
328C4×C127—41no—
329C4×C127—41no—
330C4×C127C2×#12311yescharacteristic
331C4×C127#52511yescharacteristic
332C4×C127#52911yescharacteristic
333C4×C127#52911yescharacteristic
334#21562C12711yesmaximal, characteristic, direct product factor, Sylow
335C2×C127—42no—
336C2×C127—42no—
337C2×C127C4×#12311yescharacteristic
338C2×C127#293311yescharacteristic
339C2×C127D4×M1611yescharacteristic
340C2×C127#296511yescharacteristic
341C2×C127#296711yescharacteristic
342C2×C127#296911yescharacteristic
343C2×C127#297011yescharacteristic
344C2×#435C2×C12711yescharacteristic
345C2×C4×M16C2×C12711yescharacteristic, complemented
346C4×#123C2×C12711yescharacteristic
347#1924C2×C12711yescharacteristic, complemented
348#1923C2×C12711yescharacteristic, complemented
349#1917C2×C12711yescharacteristic, complemented
350#1916C2×C12711yescharacteristic, complemented
351#1870C2×C12711yescharacteristic
352#1851C2×C12711yescharacteristic, complemented
353#1817C2×C12711yescharacteristic, complemented
354#1771C2×C12711yescharacteristic, complemented
355#1770C2×C12711yescharacteristic, complemented
356#1753C2×C12711yescharacteristic, complemented
357#1752C2×C12711yescharacteristic, complemented
358C8×C22⋊C4C2×C12711yescharacteristic, complemented
359C127#2156211yescharacteristic, direct product factor, Sylow
360C22×M16C22×C12711yescharacteristic
361C22×M16C22×C12711yescharacteristic
362C23×C8C22×C12711yescharacteristic
363C2×#123C4×C12711yescharacteristic
364C2×C4×D4C22×C12711yescharacteristic
365C22×C42C22×C12711yescharacteristic
366#435—24no—
367C2×C4⋊C8C22×C12711yescharacteristic
368C2×C4⋊C8C22×C12711yescharacteristic
369C2×C4⋊C8C22×C12711yescharacteristic
370C2×C22⋊C8C22×C12711yescharacteristic
371C2×C22⋊C8C22×C12711yescharacteristic
372C2×C22⋊C8C22×C12711yescharacteristic
373C2×C22⋊C8C22×C12711yescharacteristic
374C2×C22⋊C8C22×C12711yescharacteristic
375C4×M16—24no—
376C2×#97C22×C12711yescharacteristic
377C2×#97C22×C12711yescharacteristic
378C2×#97C22×C12711yescharacteristic
379C2×#97C22×C12711yescharacteristic
380C2×C4×C8C22×C12711yescharacteristic
381C2×C4×C8C22×C12711yescharacteristic
382C2×C4×C8C22×C12711yescharacteristic
383#388C4×C12711yescharacteristic
384#388C4×C12711yescharacteristic
385#387C4×C12711yescharacteristic
386#387C4×C12711yescharacteristic
387#386C4×C12711yescharacteristic
388#385C4×C12711yescharacteristic
389#381C4×C12711yescharacteristic
390C4×C4⋊C4C22×C12711yescharacteristic
391C4×C4⋊C4C22×C12711yescharacteristic
392C4×C22⋊C4C22×C12711yescharacteristic
393C4×C22⋊C4C22×C12711yescharacteristic
394C4×C22⋊C4C22×C12711yescharacteristic
395#336C22×C12711yescharacteristic
396#336C22×C12711yescharacteristic
397#336C22×C12711yescharacteristic
398#336C22×C12711yescharacteristic
399#336C22×C12711yescharacteristic
400#336C22×C12711yescharacteristic
401#336C22×C12711yescharacteristic
402#336C22×C12711yescharacteristic
403#336C22×C12711yescharacteristic
404#336C22×C12711yescharacteristic
405C22×D4C2×C4×C12711yescharacteristic
406C23×C4C2×C4×C12711yescharacteristic
407C23×C4C2×C4×C12711yescharacteristic
408C23×C4C23×C12711yescharacteristic
409C23×C4C23×C12711yescharacteristic
410C2×M16—22no—
411C2×M16—22no—
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—22no—
415C2×M16D4×C12714yes—
416C22×C8—22no—
417C22×C8—22no—
418C22×C8—22no—
419C22×C8C23×C12711yescharacteristic
420C22×C8C23×C12711yescharacteristic
421C22×C8C23×C12711yescharacteristic
422C22×C8C23×C12711yescharacteristic
423C22×C8C23×C12711yescharacteristic
424C22×C8C23×C12711yescharacteristic
425C22×C8C23×C12711yescharacteristic
426C22×C8C23×C12711yescharacteristic
427#123—24no—
428C4×D4—22no—
429C4×D4—22no—
430C2×C4⋊C4C2×C4×C12711yescharacteristic
431C2×C4⋊C4C2×C4×C12711yescharacteristic
432C2×C4⋊C4C2×C4×C12711yescharacteristic
433C2×C4⋊C4C2×C4×C12711yescharacteristic
434C2×C4⋊C4C2×C4×C12711yescharacteristic
435C2×C22⋊C4C2×C4×C12711yescharacteristic
436C2×C22⋊C4C2×C4×C12711yescharacteristic
437C2×C22⋊C4C2×C4×C12711yescharacteristic
438C2×C22⋊C4C2×C4×C12711yescharacteristic
439C2×C22⋊C4C2×C4×C12711yescharacteristic
440C2×C22⋊C4C2×C4×C12711yescharacteristic
441C2×C22⋊C4C2×C4×C12711yescharacteristic
442C2×C22⋊C4C2×C4×C12711yescharacteristic
443C2×C42—22no—
444C2×C42—22no—
445C2×C42C2×C4×C12711yescharacteristic
446C2×C42C2×C4×C12711yescharacteristic
447C2×C42C23×C12711yescharacteristic
448C2×C42C23×C12711yescharacteristic
449C2×C42C23×C12711yescharacteristic
450C2×C42C23×C12711yescharacteristic
451C2×C42C23×C12711yescharacteristic
452C4⋊C8—22no—
453C4⋊C8—22no—
454C4⋊C8—22no—
455C22⋊C8—22no—
456C22⋊C8—22no—
457C22⋊C8—22no—
458C22⋊C8—22no—
459C22⋊C8—22no—
460#97—22no—
461#97—22no—
462#97—22no—
463#97—22no—
464C4×C8—22no—
465C4×C8—22no—
466C4×C8—22no—
467#95C2×C4×C12711yescharacteristic
468#95C2×C4×C12711yescharacteristic
469#95C2×C4×C12711yescharacteristic
470#95C2×C4×C12711yescharacteristic
471#95C2×C4×C12711yescharacteristic
472#95C2×C4×C12711yescharacteristic
473#95C2×C4×C12711yescharacteristic
474#95C2×C4×C12711yescharacteristic
475#95C2×C4×C12711yescharacteristic
476#95C2×C4×C12711yescharacteristic
477C24C22×C4×C12711yescharacteristic
478C24C22×C4×C12711yescharacteristic
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—41no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4C22×C4×C12711yescharacteristic
499C22×C4C22×C4×C12711yescharacteristic
500C22×C4C22×C4×C12711yescharacteristic
501C22×C4C22×C4×C12711yescharacteristic
502C22×C4C22×C4×C12711yescharacteristic
503C22×C4C22×C4×C12711yescharacteristic
504C22×C4C22×C4×C12711yescharacteristic
505C22×C4C22×C4×C12711yescharacteristic
506C22×C4C22×C4×C12711yescharacteristic
507C22×C4C22×C4×C12711yescharacteristic
508C22×C4C22×C4×C12711yescharacteristic
509C22×C4C22×C4×C12711yescharacteristic
510C22×C4C2×D4×C12712yes—
511C22×C4#41×C12712yes—
512C22×C4C24×C12711yescharacteristic
513M16—28no—
514M16—28no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—44no—
534C2×C8C2×D4×C12712yes—
535C2×C8C2×D4×C12712yes—
536C2×C8#41×C12712yes—
537C2×C8#41×C12712yes—
538C2×C8#41×C12712yes—
539C2×C8#41×C12712yes—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—41no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4M16×C12714yescomplemented
553C42—22no—
554C42—22no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23C4×D4×C12712yes—
578C23C2×M16×C12712yes—
579C23C23×C4×C12711yescharacteristic
580D4—44no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4C4×D4×C12712yes—
624C2×C4C2×M16×C12712yes—
625C2×C4C2×M16×C12712yes—
626C2×C4#131×C12712yes—
627C2×C4C22×D4×C12711yescharacteristic
628C2×C4C2×#41×C12711yescharacteristic
629C2×C4C2×#41×C12711yescharacteristic
630C2×C4C2×#41×C12711yescharacteristic
631C2×C4C2×#41×C12711yescharacteristic
632C2×C4C2×#41×C12711yescharacteristic
633C8—22no—
634C8—22no—
635C8—22no—
636C8—41no—
637C8—41no—
638C8—41no—
639C8—41no—
640C8#123×C12714yescomplemented
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22C2×C4×D4×C12711yescharacteristic
656C22C4×#41×C12711yescharacteristic
657C22C4×#41×C12711yescharacteristic
658C22C22×M16×C12711yescharacteristic
659C22C2×#131×C12711yescharacteristic
660C22#568×C12711yescharacteristic
661C22#568×C12711yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4C2×#123×C12711yescharacteristic
675C4#525×C12711yescharacteristic
676C4#529×C12711yescharacteristic
677C4#529×C12711yescharacteristic
678C2—42no—
679C2—42no—
680C2C4×#123×C12711yescharacteristic
681C2C127×#293311yescharacteristic
682C2D4×M16×C12711yescharacteristic
683C2C127×#296511yescharacteristic
684C2C127×#296711yescharacteristic
685C2C127×#296911yescharacteristic
686C2C127×#297011yescharacteristic
subgroupG/H
centerC22×C4×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radicalC22×D4×C127C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×M16×C127C2semidirect
4. C127×#1924C2semidirect
5. C127×#1923C2semidirect
6. C127×#1917C2semidirect
7. C127×#1916C2semidirect
9. C127×#1851C2semidirect
10. C127×#1817C2semidirect
11. C127×#1771C2semidirect
12. C127×#1770C2semidirect
13. C127×#1753C2semidirect
14. C127×#1752C2semidirect
15. C8×C22⋊C4×C127C2semidirect
208. C22⋊C4×C127M16semidirect
296. C8×C127#123semidirect
334. #21562C127direct (N × H)
345. C2×C4×M16C2×C127semidirect
347. #1924C2×C127semidirect
348. #1923C2×C127semidirect
349. #1917C2×C127semidirect
350. #1916C2×C127semidirect
352. #1851C2×C127semidirect
353. #1817C2×C127semidirect
354. #1771C2×C127semidirect
355. #1770C2×C127semidirect
356. #1753C2×C127semidirect
357. #1752C2×C127semidirect
358. C8×C22⋊C4C2×C127semidirect
359. C127#21562direct (N × H)
552. C22⋊C4M16×C127semidirect
640. C8#123×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#435×C1272
C2×C4×M16×C1272
C4×#123×C1272
C127×#19242
C127×#19232
C127×#19172
C127×#19162
C127×#18702
C127×#18512
C127×#18172
C127×#17712
C127×#17702
C127×#17532
C127×#17522
C8×C22⋊C4×C1272
#21562127