Finite Group Databasebeta

← C127×#15913 #44579586

Subgroups — C127×#15913 #44579586

Order 32512.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C127C211yesmaximal, characteristic, complemented
2C2×#397×C127C211yesmaximal, characteristic, complemented
3C2×#396×C127C211yesmaximal, characteristic, complemented
4C2×#390×C127C211yesmaximal, characteristic
5C127×#1444C211yesmaximal, characteristic, complemented
6C127×#1440C211yesmaximal, characteristic, complemented
7C127×#1439C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1438C211yesmaximal, characteristic
11C127×#1438C211yesmaximal, characteristic
12C127×#1437C211yesmaximal, characteristic, complemented
13C127×#1436C211yesmaximal, characteristic, complemented
14C127×#1436C211yesmaximal, characteristic, complemented
15C127×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C2×#126×C127—24no—
18C2×#126×C127—24no—
19C2×#126×C127—24no—
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C22⋊C4×C127C2211yescharacteristic
32C22×C22⋊C4×C127C2211yescharacteristic
33C22×C22⋊C4×C127C2211yescharacteristic
34C22×C22⋊C4×C127C2211yescharacteristic
35C22×C22⋊C4×C127C2211yescharacteristic
36C22×C22⋊C4×C127C2211yescharacteristic
37C22×C22⋊C4×C127C2211yescharacteristic
38C22×C42×C127C2211yescharacteristic
39C22×C42×C127C2211yescharacteristic
40#397×C127—24no—
41#396×C127—24no—
42#390×C127—24no—
43C2×#95×C127C2211yescharacteristic
44C2×#95×C127C2211yescharacteristic
45C2×#95×C127C2211yescharacteristic
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C2×#95×C127C2211yescharacteristic
57C25×C127C2311yescharacteristic
58C25×C127C2311yescharacteristic
59C22×D4×C127—22no—
60C22×D4×C127—22no—
61C22×D4×C127—22no—
62C22×D4×C127—22no—
63C22×D4×C127—22no—
64C22×D4×C127—41no—
65C22×D4×C127—41no—
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2311yescharacteristic
78C23×C4×C127C2311yescharacteristic
79#126×C127—232no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—22no—
85C2×C4⋊C4×C127—22no—
86C2×C4⋊C4×C127—22no—
87C2×C4⋊C4×C127—22no—
88C2×C4⋊C4×C127—22no—
89C2×C4⋊C4×C127—22no—
90C2×C4⋊C4×C127—22no—
91C2×C4⋊C4×C127—22no—
92C2×C4⋊C4×C127—41no—
93C2×C4⋊C4×C127—41no—
94C2×C4⋊C4×C127—41no—
95C2×C4⋊C4×C127—41no—
96C2×C4⋊C4×C127D414yescomplemented
97C2×C4⋊C4×C127D414yescomplemented
98C2×C22⋊C4×C127—22no—
99C2×C22⋊C4×C127—22no—
100C2×C22⋊C4×C127—22no—
101C2×C22⋊C4×C127—22no—
102C2×C22⋊C4×C127—22no—
103C2×C22⋊C4×C127—22no—
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127—22no—
106C2×C22⋊C4×C127—22no—
107C2×C22⋊C4×C127—22no—
108C2×C22⋊C4×C127—22no—
109C2×C22⋊C4×C127—22no—
110C2×C22⋊C4×C127—22no—
111C2×C22⋊C4×C127—22no—
112C2×C22⋊C4×C127—22no—
113C2×C22⋊C4×C127—22no—
114C2×C22⋊C4×C127—22no—
115C2×C22⋊C4×C127—22no—
116C2×C22⋊C4×C127—22no—
117C2×C22⋊C4×C127—22no—
118C2×C22⋊C4×C127—22no—
119C2×C22⋊C4×C127—22no—
120C2×C22⋊C4×C127—22no—
121C2×C22⋊C4×C127—41no—
122C2×C22⋊C4×C127—41no—
123C2×C22⋊C4×C127—41no—
124C2×C22⋊C4×C127—41no—
125C2×C22⋊C4×C127—41no—
126C2×C22⋊C4×C127—41no—
127C2×C22⋊C4×C127—41no—
128C2×C22⋊C4×C127—41no—
129C2×C22⋊C4×C127—41no—
130C2×C22⋊C4×C127—41no—
131C2×C22⋊C4×C127—41no—
132C2×C22⋊C4×C127—41no—
133C2×C22⋊C4×C127D414yes—
134C2×C42×C127—22no—
135C2×C42×C127—22no—
136C2×C42×C127—22no—
137C2×C42×C127—22no—
138C2×C42×C127—22no—
139C2×C42×C127—41no—
140#95×C127—22no—
141#95×C127—22no—
142#95×C127—22no—
143#95×C127—22no—
144#95×C127—22no—
145#95×C127—22no—
146#95×C127—22no—
147#95×C127—22no—
148#95×C127—22no—
149#95×C127—41no—
150#95×C127—41no—
151#95×C127—41no—
152#95×C127—41no—
153#95×C127—41no—
154C24×C127—21no—
155C24×C127—21no—
156C24×C127—21no—
157C24×C127—21no—
158C24×C127—21no—
159C24×C127—21no—
160C24×C127—21no—
161C24×C127—21no—
162C24×C127—21no—
163C24×C127—21no—
164C24×C127—21no—
165C24×C127—21no—
166C24×C127—21no—
167C24×C127—21no—
168C24×C127—21no—
169C24×C127—21no—
170C24×C127—21no—
171C24×C127—21no—
172C24×C127—21no—
173C24×C127—21no—
174C24×C127—21no—
175C24×C127—21no—
176C24×C127—21no—
177C24×C127—21no—
178C24×C127—21no—
179C24×C127—21no—
180C24×C127—21no—
181C24×C127—21no—
182C24×C127C2×D412yes—
183C24×C127#4112yes—
184C24×C127C2411yescharacteristic
185C2×D4×C127—28no—
186C2×D4×C127—44no—
187C2×D4×C127—44no—
188C2×D4×C127—44no—
189C2×D4×C127—44no—
190C2×D4×C127—44no—
191C2×D4×C127—44no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—21no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—21no—
216C22×C4×C127—21no—
217C22×C4×C127—21no—
218C22×C4×C127—21no—
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—21no—
224C22×C4×C127—21no—
225C22×C4×C127—21no—
226C22×C4×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—21no—
248C22×C4×C127—21no—
249C22×C4×C127—21no—
250C22×C4×C127—21no—
251C22×C4×C127—21no—
252C22×C4×C127—21no—
253C22×C4×C127—21no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—21no—
260C22×C4×C127—21no—
261C22×C4×C127—21no—
262C22×C4×C127—21no—
263C22×C4×C127—21no—
264C22×C4×C127—21no—
265C22×C4×C127—21no—
266C22×C4×C127—21no—
267C22×C4×C127—21no—
268C22×C4×C127—21no—
269C22×C4×C127—21no—
270C22×C4×C127C2×D412yes—
271C22×C4×C127C2×D412yes—
272C22×C4×C127C2×D412yes—
273C22×C4×C127C2×D412yes—
274C22×C4×C127C2×D412yes—
275C22×C4×C127C2×D412yes—
276C22×C4×C127C2×D412yes—
277C22×C4×C127C2×D412yes—
278C22×C4×C127#4112yes—
279C22×C4×C127#4112yes—
280C22×C4×C127#4112yes—
281C22×C4×C127#4112yes—
282C22×C4×C127#4112yes—
283C4⋊C4×C127—28no—
284C4⋊C4×C127—28no—
285C4⋊C4×C127—28no—
286C4⋊C4×C127—44no—
287C4⋊C4×C127—44no—
288C4⋊C4×C127—44no—
289C22⋊C4×C127—28no—
290C22⋊C4×C127—28no—
291C22⋊C4×C127—28no—
292C22⋊C4×C127—44no—
293C22⋊C4×C127—44no—
294C22⋊C4×C127—44no—
295C22⋊C4×C127—44no—
296C22⋊C4×C127—44no—
297C22⋊C4×C127—44no—
298C22⋊C4×C127—44no—
299C22⋊C4×C127—44no—
300C22⋊C4×C127—44no—
301C42×C127—28no—
302C42×C127—44no—
303C23×C127—22no—
304C23×C127—22no—
305C23×C127—22no—
306C23×C127—22no—
307C23×C127—22no—
308C23×C127—22no—
309C23×C127—22no—
310C23×C127—22no—
311C23×C127—22no—
312C23×C127—22no—
313C23×C127—22no—
314C23×C127—22no—
315C23×C127—22no—
316C23×C127—22no—
317C23×C127—41no—
318C23×C127—41no—
319C23×C127—41no—
320C23×C127—41no—
321C23×C127—41no—
322C23×C127—41no—
323C23×C127—41no—
324C23×C127—41no—
325C23×C127—41no—
326C23×C127—41no—
327C23×C127—41no—
328C23×C127—41no—
329C23×C127—41no—
330C23×C127—41no—
331C23×C127—41no—
332C23×C127—41no—
333C23×C127—41no—
334C23×C127—41no—
335C23×C127—41no—
336C23×C127—41no—
337C23×C127—41no—
338C23×C127—41no—
339C23×C127—41no—
340C23×C127—41no—
341C23×C127—41no—
342C23×C127—41no—
343C23×C127—41no—
344C23×C127—41no—
345C23×C127—41no—
346C23×C127—41no—
347C23×C127—41no—
348C23×C127—41no—
349C23×C127—41no—
350C23×C127—41no—
351C23×C127—41no—
352C23×C127—41no—
353C23×C127—41no—
354C23×C127—41no—
355C23×C127—41no—
356C23×C127—41no—
357C23×C127—41no—
358C23×C127—41no—
359C23×C127—41no—
360C23×C127—41no—
361C23×C127—41no—
362C23×C127—41no—
363C23×C127—41no—
364C23×C127—41no—
365C23×C127—41no—
366C23×C127—41no—
367C23×C127—41no—
368C23×C127—41no—
369C23×C127—41no—
370C23×C127—41no—
371C23×C127—41no—
372C23×C127—41no—
373C23×C127C22×D411yescharacteristic
374C23×C127C22×D411yescharacteristic
375C23×C127C22×D411yescharacteristic
376C23×C127C2×#4111yescharacteristic
377C23×C127C2×#4111yescharacteristic
378C23×C127C2×#4111yescharacteristic
379C23×C127C2×#4111yescharacteristic
380C23×C127C2×#4111yescharacteristic
381C23×C127C2×#4111yescharacteristic
382C23×C127H(5,𝔽2)11yescharacteristic
383C23×C127H(5,𝔽2)11yescharacteristic
384C23×C127H(5,𝔽2)11yescharacteristic
385C23×C127H(5,𝔽2)11yescharacteristic
386C23×C1272−1+411yescharacteristic
387C23×C1272−1+411yescharacteristic
388D4×C127—416no—
389C2×C4×C127—22no—
390C2×C4×C127—22no—
391C2×C4×C127—22no—
392C2×C4×C127—22no—
393C2×C4×C127—22no—
394C2×C4×C127—22no—
395C2×C4×C127—22no—
396C2×C4×C127—22no—
397C2×C4×C127—22no—
398C2×C4×C127—22no—
399C2×C4×C127—22no—
400C2×C4×C127—22no—
401C2×C4×C127—22no—
402C2×C4×C127—22no—
403C2×C4×C127—22no—
404C2×C4×C127—22no—
405C2×C4×C127—22no—
406C2×C4×C127—22no—
407C2×C4×C127—22no—
408C2×C4×C127—22no—
409C2×C4×C127—22no—
410C2×C4×C127—22no—
411C2×C4×C127—22no—
412C2×C4×C127—22no—
413C2×C4×C127—22no—
414C2×C4×C127—22no—
415C2×C4×C127—22no—
416C2×C4×C127—22no—
417C2×C4×C127—22no—
418C2×C4×C127—22no—
419C2×C4×C127—22no—
420C2×C4×C127—22no—
421C2×C4×C127—22no—
422C2×C4×C127—41no—
423C2×C4×C127—41no—
424C2×C4×C127—41no—
425C2×C4×C127—41no—
426C2×C4×C127—41no—
427C2×C4×C127—41no—
428C2×C4×C127—41no—
429C2×C4×C127—41no—
430C2×C4×C127—41no—
431C2×C4×C127—41no—
432C2×C4×C127—41no—
433C2×C4×C127—41no—
434C2×C4×C127—41no—
435C2×C4×C127—41no—
436C2×C4×C127—41no—
437C2×C4×C127—41no—
438C2×C4×C127—41no—
439C2×C4×C127—41no—
440C2×C4×C127—41no—
441C2×C4×C127—41no—
442C2×C4×C127—41no—
443C2×C4×C127—41no—
444C2×C4×C127—41no—
445C2×C4×C127—41no—
446C2×C4×C127—41no—
447C2×C4×C127—41no—
448C2×C4×C127—41no—
449C2×C4×C127—41no—
450C2×C4×C127—41no—
451C2×C4×C127—41no—
452C2×C4×C127—41no—
453C2×C4×C127—41no—
454C2×C4×C127—41no—
455C2×C4×C127—41no—
456C2×C4×C127—41no—
457C2×C4×C127—41no—
458C2×C4×C127—41no—
459C2×C4×C127—41no—
460C2×C4×C127—41no—
461C2×C4×C127—41no—
462C2×C4×C127—41no—
463C2×C4×C127—41no—
464C2×C4×C127—41no—
465C2×C4×C127—41no—
466C2×C4×C127—41no—
467C2×C4×C127—41no—
468C2×C4×C127—41no—
469C2×C4×C127—41no—
470C2×C4×C127—41no—
471C2×C4×C127—41no—
472C2×C4×C127—41no—
473C2×C4×C127—41no—
474C2×C4×C127—41no—
475C2×C4×C127—41no—
476C2×C4×C127—41no—
477C2×C4×C127—41no—
478C2×C4×C127#12014yes—
479C2×C4×C127#12614yescomplemented
480C22×C127—42no—
481C22×C127—42no—
482C22×C127—42no—
483C22×C127—42no—
484C22×C127—42no—
485C22×C127—42no—
486C22×C127—42no—
487C22×C127—42no—
488C22×C127—42no—
489C22×C127—42no—
490C22×C127—42no—
491C22×C127—42no—
492C22×C127—42no—
493C22×C127—42no—
494C22×C127—81no—
495C22×C127—81no—
496C22×C127—81no—
497C22×C127—81no—
498C22×C127—81no—
499C22×C127—81no—
500C22×C127—81no—
501C22×C127—81no—
502C22×C127—81no—
503C22×C127—81no—
504C22×C127—81no—
505C22×C127—81no—
506C22×C127—81no—
507C22×C127—81no—
508C22×C127—81no—
509C22×C127—81no—
510C22×C127C2×#12011yescharacteristic
511C22×C127#52511yescharacteristic
512C22×C127C2×#12611yescharacteristic
513C22×C127#52911yescharacteristic
514C22×C127#53211yescharacteristic
515C22×C127#53211yescharacteristic
516C22×C127#53511yescharacteristic
517C22×C127#53711yescharacteristic
518C22×C127#53711yescharacteristic
519C22×C127#53811yescharacteristic
520C22×C127#53811yescharacteristic
521C22×C127#53911yescharacteristic
522C22×C127#53911yescharacteristic
523C22×C127#54211yescharacteristic
524C22×C127#54211yescharacteristic
525C22×C127#54611yescharacteristic
526C22×C127#54611yescharacteristic
527C22×C127#54611yescharacteristic
528C22×C127#54611yescharacteristic
529C22×C127#54611yescharacteristic
530C22×C127#54711yescharacteristic
531C22×C127#54711yescharacteristic
532C22×C127#54711yescharacteristic
533C22×C127#54811yescharacteristic
534C22×C127#55011yescharacteristic
535C22×C127#55011yescharacteristic
536C22×C127#55011yescharacteristic
537C22×C127#55111yescharacteristic
538C22×C127#55111yescharacteristic
539C22×C127#55311yescharacteristic
540C22×C127#55311yescharacteristic
541C22×C127#55611yescharacteristic
542C22×C127#55611yescharacteristic
543C22×C127#56011yescharacteristic
544C22×C127#56311yescharacteristic
545C4×C127—24no—
546C4×C127—24no—
547C4×C127—42no—
548C4×C127—42no—
549C4×C127—42no—
550C4×C127—42no—
551C4×C127—42no—
552C4×C127—42no—
553C4×C127—42no—
554C4×C127—81no—
555C4×C127—81no—
556C4×C127—81no—
557C4×C127—81no—
558#15913C12711yesmaximal, characteristic, direct product factor, Sylow
559C2×C127—82no—
560C2×C127—82no—
561C2×C127#240711yescharacteristic
562C2×C127#243011yescharacteristic
563C2×C127#243111yescharacteristic
564C2×C127#246611yescharacteristic
565C2×C127#248011yescharacteristic
566C2×C127#251211yescharacteristic
567C2×C127#251211yescharacteristic
568C2×C127#255411yescharacteristic
569C2×C127#256011yescharacteristic
570C2×C127#269111yescharacteristic
571C2×C127#270511yescharacteristic
572C2×C127#271411yescharacteristic
573C2×C127#271511yescharacteristic
574C2×C127#272311yescharacteristic
575C2×C127#272711yescharacteristic
576C22×#126C2×C12711yescharacteristic, complemented
577C2×#397C2×C12711yescharacteristic, complemented
578C2×#396C2×C12711yescharacteristic, complemented
579C2×#390C2×C12711yescharacteristic
580#1444C2×C12711yescharacteristic, complemented
581#1440C2×C12711yescharacteristic, complemented
582#1439C2×C12711yescharacteristic, complemented
583#1439C2×C12711yescharacteristic, complemented
584#1439C2×C12711yescharacteristic, complemented
585#1438C2×C12711yescharacteristic
586#1438C2×C12711yescharacteristic
587#1437C2×C12711yescharacteristic, complemented
588#1436C2×C12711yescharacteristic, complemented
589#1436C2×C12711yescharacteristic, complemented
590C4⋊#95C2×C12711yescharacteristic, complemented
591C127#1591311yescharacteristic, direct product factor, Sylow
592C23×D4C22×C12711yescharacteristic
593C2×#126—24no—
594C2×#126—24no—
595C2×#126—24no—
596C22×C4⋊C4C22×C12711yescharacteristic
597C22×C4⋊C4C22×C12711yescharacteristic
598C22×C4⋊C4C22×C12711yescharacteristic
599C22×C4⋊C4C22×C12711yescharacteristic
600C22×C4⋊C4C22×C12711yescharacteristic
601C22×C4⋊C4C22×C12711yescharacteristic
602C22×C22⋊C4C22×C12711yescharacteristic
603C22×C22⋊C4C22×C12711yescharacteristic
604C22×C22⋊C4C22×C12711yescharacteristic
605C22×C22⋊C4C22×C12711yescharacteristic
606C22×C22⋊C4C22×C12711yescharacteristic
607C22×C22⋊C4C22×C12711yescharacteristic
608C22×C22⋊C4C22×C12711yescharacteristic
609C22×C22⋊C4C22×C12711yescharacteristic
610C22×C22⋊C4C22×C12711yescharacteristic
611C22×C22⋊C4C22×C12711yescharacteristic
612C22×C22⋊C4C22×C12711yescharacteristic
613C22×C22⋊C4C22×C12711yescharacteristic
614C22×C42C22×C12711yescharacteristic
615C22×C42C22×C12711yescharacteristic
616#397—24no—
617#396—24no—
618#390—24no—
619C2×#95C22×C12711yescharacteristic
620C2×#95C22×C12711yescharacteristic
621C2×#95C22×C12711yescharacteristic
622C2×#95C22×C12711yescharacteristic
623C2×#95C22×C12711yescharacteristic
624C2×#95C22×C12711yescharacteristic
625C2×#95C22×C12711yescharacteristic
626C2×#95C22×C12711yescharacteristic
627C2×#95C22×C12711yescharacteristic
628C2×#95C22×C12711yescharacteristic
629C2×#95C22×C12711yescharacteristic
630C2×#95C22×C12711yescharacteristic
631C2×#95C22×C12711yescharacteristic
632C2×#95C22×C12711yescharacteristic
633C25C23×C12711yescharacteristic
634C25C23×C12711yescharacteristic
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—41no—
641C22×D4—41no—
642C23×C4C23×C12711yescharacteristic
643C23×C4C23×C12711yescharacteristic
644C23×C4C23×C12711yescharacteristic
645C23×C4C23×C12711yescharacteristic
646C23×C4C23×C12711yescharacteristic
647C23×C4C23×C12711yescharacteristic
648C23×C4C23×C12711yescharacteristic
649C23×C4C23×C12711yescharacteristic
650C23×C4C23×C12711yescharacteristic
651C23×C4C23×C12711yescharacteristic
652C23×C4C23×C12711yescharacteristic
653C23×C4C23×C12711yescharacteristic
654C23×C4C23×C12711yescharacteristic
655#126—232no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4D4×C12714yescomplemented
673C2×C4⋊C4D4×C12714yescomplemented
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4D4×C12714yes—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—41no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95—41no—
729#95—41no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24C2×D4×C12712yes—
759C24#41×C12712yes—
760C24C24×C12711yescharacteristic
761C2×D4—28no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4C2×D4×C12712yes—
847C22×C4C2×D4×C12712yes—
848C22×C4C2×D4×C12712yes—
849C22×C4C2×D4×C12712yes—
850C22×C4C2×D4×C12712yes—
851C22×C4C2×D4×C12712yes—
852C22×C4C2×D4×C12712yes—
853C22×C4C2×D4×C12712yes—
854C22×C4#41×C12712yes—
855C22×C4#41×C12712yes—
856C22×C4#41×C12712yes—
857C22×C4#41×C12712yes—
858C22×C4#41×C12712yes—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C42—28no—
878C42—44no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23C22×D4×C12711yescharacteristic
950C23C22×D4×C12711yescharacteristic
951C23C22×D4×C12711yescharacteristic
952C23C2×#41×C12711yescharacteristic
953C23C2×#41×C12711yescharacteristic
954C23C2×#41×C12711yescharacteristic
955C23C2×#41×C12711yescharacteristic
956C23C2×#41×C12711yescharacteristic
957C23C2×#41×C12711yescharacteristic
958C23H(5,𝔽2)×C12711yescharacteristic
959C23H(5,𝔽2)×C12711yescharacteristic
960C23H(5,𝔽2)×C12711yescharacteristic
961C23H(5,𝔽2)×C12711yescharacteristic
962C232−1+4×C12711yescharacteristic
963C232−1+4×C12711yescharacteristic
964D4—416no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4#120×C12714yes—
1055C2×C4#126×C12714yescomplemented
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22C2×#120×C12711yescharacteristic
1087C22#525×C12711yescharacteristic
1088C22C2×#126×C12711yescharacteristic
1089C22#529×C12711yescharacteristic
1090C22#532×C12711yescharacteristic
1091C22#532×C12711yescharacteristic
1092C22#535×C12711yescharacteristic
1093C22#537×C12711yescharacteristic
1094C22#537×C12711yescharacteristic
1095C22#538×C12711yescharacteristic
1096C22#538×C12711yescharacteristic
1097C22#539×C12711yescharacteristic
1098C22#539×C12711yescharacteristic
1099C22#542×C12711yescharacteristic
1100C22#542×C12711yescharacteristic
1101C22#546×C12711yescharacteristic
1102C22#546×C12711yescharacteristic
1103C22#546×C12711yescharacteristic
1104C22#546×C12711yescharacteristic
1105C22#546×C12711yescharacteristic
1106C22#547×C12711yescharacteristic
1107C22#547×C12711yescharacteristic
1108C22#547×C12711yescharacteristic
1109C22#548×C12711yescharacteristic
1110C22#550×C12711yescharacteristic
1111C22#550×C12711yescharacteristic
1112C22#550×C12711yescharacteristic
1113C22#551×C12711yescharacteristic
1114C22#551×C12711yescharacteristic
1115C22#553×C12711yescharacteristic
1116C22#553×C12711yescharacteristic
1117C22#556×C12711yescharacteristic
1118C22#556×C12711yescharacteristic
1119C22#560×C12711yescharacteristic
1120C22#563×C12711yescharacteristic
1121C4—24no—
1122C4—24no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C2—82no—
1135C2—82no—
1136C2C127×#240711yescharacteristic
1137C2C127×#243011yescharacteristic
1138C2C127×#243111yescharacteristic
1139C2C127×#246611yescharacteristic
1140C2C127×#248011yescharacteristic
1141C2C127×#251211yescharacteristic
1142C2C127×#251211yescharacteristic
1143C2C127×#255411yescharacteristic
1144C2C127×#256011yescharacteristic
1145C2C127×#269111yescharacteristic
1146C2C127×#270511yescharacteristic
1147C2C127×#271411yescharacteristic
1148C2C127×#271511yescharacteristic
1149C2C127×#272311yescharacteristic
1150C2C127×#272711yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#126×C127C2semidirect
2. C2×#397×C127C2semidirect
3. C2×#396×C127C2semidirect
5. C127×#1444C2semidirect
6. C127×#1440C2semidirect
7. C127×#1439C2semidirect
8. C127×#1439C2semidirect
9. C127×#1439C2semidirect
12. C127×#1437C2semidirect
13. C127×#1436C2semidirect
14. C127×#1436C2semidirect
15. C127×C4⋊#95C2semidirect
96. C2×C4⋊C4×C127D4semidirect
97. C2×C4⋊C4×C127D4semidirect
479. C2×C4×C127#126semidirect
558. #15913C127direct (N × H)
576. C22×#126C2×C127semidirect
577. C2×#397C2×C127semidirect
578. C2×#396C2×C127semidirect
580. #1444C2×C127semidirect
581. #1440C2×C127semidirect
582. #1439C2×C127semidirect
583. #1439C2×C127semidirect
584. #1439C2×C127semidirect
587. #1437C2×C127semidirect
588. #1436C2×C127semidirect
589. #1436C2×C127semidirect
590. C4⋊#95C2×C127semidirect
591. C127#15913direct (N × H)
672. C2×C4⋊C4D4×C127semidirect
673. C2×C4⋊C4D4×C127semidirect
1055. C2×C4#126×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C1272
C2×#397×C1272
C2×#396×C1272
C2×#390×C1272
C127×#14442
C127×#14402
C127×#14392
C127×#14382
C127×#14372
C127×#14362
C127×C4⋊#952
#15913127