Finite Group Databasebeta

← C127×#15277 #44578950

Subgroups — C127×#15277 #44578950

Order 32512.

2466 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic
2C2×#397×C127C211yesmaximal, characteristic, complemented
3C2×#394×C127C211yesmaximal, characteristic, complemented
4C2×#386×C127C211yesmaximal, characteristic, complemented
5C2×#386×C127C211yesmaximal, characteristic, complemented
6C2×#385×C127C211yesmaximal, characteristic, complemented
7C127×#1442C211yesmaximal, characteristic, complemented
8C127×#1441C211yesmaximal, characteristic, complemented
9C127×#1440C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1438C211yesmaximal, characteristic, complemented
12C127×#1438C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic, complemented
14C127×C22⋊#95C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C24×C4×C127C2211yescharacteristic
20C24×C4×C127C2211yescharacteristic
21C2×#121×C127—24no—
22C2×#121×C127—24no—
23C2×#121×C127—24no—
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2211yescharacteristic
26C22×C4⋊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×C22⋊C4×C127C2211yescharacteristic
39C22×C22⋊C4×C127C2211yescharacteristic
40#397×C127—24no—
41#394×C127—24no—
42#386×C127—24no—
43#386×C127—24no—
44#385×C127—24no—
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
57C2×#95×C127C2211yescharacteristic
58C2×#95×C127C2211yescharacteristic
59C25×C127C2311yescharacteristic
60C25×C127C2311yescharacteristic
61C25×C127C2311yescharacteristic
62C22×D4×C127—22no—
63C22×D4×C127—22no—
64C22×D4×C127—22no—
65C22×D4×C127—22no—
66C22×D4×C127—22no—
67C22×D4×C127—22no—
68C22×D4×C127—22no—
69C22×D4×C127—22no—
70C22×D4×C127—22no—
71C22×D4×C127—22no—
72C22×D4×C127—22no—
73C22×D4×C127—22no—
74C22×D4×C127—22no—
75C22×D4×C127—41no—
76C22×D4×C127—41no—
77C22×D4×C127—41no—
78C22×D4×C127—41no—
79C22×D4×C127—41no—
80C22×D4×C127—41no—
81C22×D4×C127D414yes—
82C22×D4×C127D414yes—
83C23×C4×C127—22no—
84C23×C4×C127—22no—
85C23×C4×C127—22no—
86C23×C4×C127—22no—
87C23×C4×C127—22no—
88C23×C4×C127—22no—
89C23×C4×C127—22no—
90C23×C4×C127—22no—
91C23×C4×C127—41no—
92C23×C4×C127—41no—
93C23×C4×C127—41no—
94C23×C4×C127—41no—
95C23×C4×C127—41no—
96C23×C4×C127—41no—
97C23×C4×C127C2311yescharacteristic
98C23×C4×C127C2311yescharacteristic
99C23×C4×C127C2311yescharacteristic
100C23×C4×C127C2311yescharacteristic
101C23×C4×C127C2311yescharacteristic
102C23×C4×C127C2311yescharacteristic
103C23×C4×C127C2311yescharacteristic
104C23×C4×C127C2311yescharacteristic
105C23×C4×C127C2311yescharacteristic
106C23×C4×C127C2311yescharacteristic
107C23×C4×C127C2311yescharacteristic
108C23×C4×C127C2311yescharacteristic
109#121×C127—232no—
110C2×C4⋊C4×C127—22no—
111C2×C4⋊C4×C127—22no—
112C2×C4⋊C4×C127—22no—
113C2×C4⋊C4×C127—22no—
114C2×C4⋊C4×C127—22no—
115C2×C4⋊C4×C127—22no—
116C2×C4⋊C4×C127—22no—
117C2×C4⋊C4×C127—22no—
118C2×C4⋊C4×C127—41no—
119C2×C22⋊C4×C127—22no—
120C2×C22⋊C4×C127—22no—
121C2×C22⋊C4×C127—22no—
122C2×C22⋊C4×C127—22no—
123C2×C22⋊C4×C127—22no—
124C2×C22⋊C4×C127—22no—
125C2×C22⋊C4×C127—22no—
126C2×C22⋊C4×C127—22no—
127C2×C22⋊C4×C127—22no—
128C2×C22⋊C4×C127—22no—
129C2×C22⋊C4×C127—22no—
130C2×C22⋊C4×C127—22no—
131C2×C22⋊C4×C127—22no—
132C2×C22⋊C4×C127—22no—
133C2×C22⋊C4×C127—22no—
134C2×C22⋊C4×C127—22no—
135C2×C22⋊C4×C127—22no—
136C2×C22⋊C4×C127—22no—
137C2×C22⋊C4×C127—22no—
138C2×C22⋊C4×C127—22no—
139C2×C22⋊C4×C127—22no—
140C2×C22⋊C4×C127—22no—
141C2×C22⋊C4×C127—22no—
142C2×C22⋊C4×C127—22no—
143C2×C22⋊C4×C127—22no—
144C2×C22⋊C4×C127—22no—
145C2×C22⋊C4×C127—41no—
146C2×C22⋊C4×C127—41no—
147C2×C22⋊C4×C127—41no—
148C2×C22⋊C4×C127—41no—
149C2×C22⋊C4×C127—41no—
150C2×C22⋊C4×C127—41no—
151C2×C22⋊C4×C127—41no—
152C2×C22⋊C4×C127—41no—
153C2×C22⋊C4×C127—41no—
154C2×C22⋊C4×C127—41no—
155C2×C22⋊C4×C127—41no—
156C2×C22⋊C4×C127—41no—
157C2×C22⋊C4×C127D414yes—
158#95×C127—22no—
159#95×C127—22no—
160#95×C127—22no—
161#95×C127—22no—
162#95×C127—22no—
163#95×C127—22no—
164#95×C127—22no—
165#95×C127—22no—
166#95×C127—41no—
167#95×C127—41no—
168#95×C127—41no—
169#95×C127—41no—
170#95×C127—41no—
171#95×C127D414yescomplemented
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×C127—21no—
183C24×C127—21no—
184C24×C127—21no—
185C24×C127—21no—
186C24×C127—21no—
187C24×C127—21no—
188C24×C127—21no—
189C24×C127—21no—
190C24×C127—21no—
191C24×C127—21no—
192C24×C127—21no—
193C24×C127—21no—
194C24×C127—21no—
195C24×C127—21no—
196C24×C127—21no—
197C24×C127—21no—
198C24×C127—21no—
199C24×C127—21no—
200C24×C127—21no—
201C24×C127—21no—
202C24×C127—21no—
203C24×C127—21no—
204C24×C127—21no—
205C24×C127—21no—
206C24×C127—21no—
207C24×C127—21no—
208C24×C127—21no—
209C24×C127—21no—
210C24×C127C2×D412yes—
211C24×C127C2×D412yes—
212C24×C127C2×D412yes—
213C24×C127C2×D412yes—
214C24×C127C2×D412yes—
215C24×C127#4112yes—
216C24×C127#4112yes—
217C24×C127C2411yescharacteristic
218C2×D4×C127—28no—
219C2×D4×C127—28no—
220C2×D4×C127—28no—
221C2×D4×C127—28no—
222C2×D4×C127—28no—
223C2×D4×C127—44no—
224C2×D4×C127—44no—
225C2×D4×C127—44no—
226C2×D4×C127—44no—
227C2×D4×C127—44no—
228C2×D4×C127—44no—
229C2×D4×C127—44no—
230C2×D4×C127—44no—
231C2×D4×C127—44no—
232C2×D4×C127—44no—
233C2×D4×C127—44no—
234C2×D4×C127—44no—
235C2×D4×C127—44no—
236C2×D4×C127—44no—
237C2×D4×C127—44no—
238C2×D4×C127—44no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—28no—
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×C127—21no—
271C22×C4×C127—21no—
272C22×C4×C127—21no—
273C22×C4×C127—21no—
274C22×C4×C127—21no—
275C22×C4×C127—21no—
276C22×C4×C127—21no—
277C22×C4×C127—21no—
278C22×C4×C127—21no—
279C22×C4×C127—21no—
280C22×C4×C127—21no—
281C22×C4×C127—21no—
282C22×C4×C127—21no—
283C22×C4×C127—21no—
284C22×C4×C127—21no—
285C22×C4×C127—21no—
286C22×C4×C127—21no—
287C22×C4×C127—21no—
288C22×C4×C127—21no—
289C22×C4×C127—21no—
290C22×C4×C127—21no—
291C22×C4×C127—21no—
292C22×C4×C127—21no—
293C22×C4×C127—21no—
294C22×C4×C127—21no—
295C22×C4×C127—21no—
296C22×C4×C127—21no—
297C22×C4×C127—21no—
298C22×C4×C127—21no—
299C22×C4×C127—21no—
300C22×C4×C127—21no—
301C22×C4×C127—21no—
302C22×C4×C127—21no—
303C22×C4×C127—21no—
304C22×C4×C127—21no—
305C22×C4×C127—21no—
306C22×C4×C127—21no—
307C22×C4×C127—21no—
308C22×C4×C127—21no—
309C22×C4×C127—21no—
310C22×C4×C127—21no—
311C22×C4×C127—21no—
312C22×C4×C127—21no—
313C22×C4×C127—21no—
314C22×C4×C127—44no—
315C22×C4×C127—44no—
316C22×C4×C127—44no—
317C22×C4×C127—44no—
318C22×C4×C127—44no—
319C22×C4×C127—44no—
320C22×C4×C127—44no—
321C22×C4×C127—44no—
322C22×C4×C127—44no—
323C22×C4×C127—44no—
324C22×C4×C127—44no—
325C22×C4×C127—44no—
326C22×C4×C127—44no—
327C22×C4×C127C2×D412yes—
328C22×C4×C127C2×D412yes—
329C22×C4×C127C2×D412yes—
330C22×C4×C127C2×D412yes—
331C22×C4×C127C2×D412yes—
332C22×C4×C127C2×D412yes—
333C22×C4×C127C2×D412yes—
334C22×C4×C127#4112yes—
335C22×C4×C127#4112yes—
336C22×C4×C127#4112yes—
337C4⋊C4×C127—28no—
338C4⋊C4×C127—44no—
339C4⋊C4×C127—44no—
340C22⋊C4×C127—28no—
341C22⋊C4×C127—28no—
342C22⋊C4×C127—28no—
343C22⋊C4×C127—44no—
344C22⋊C4×C127—44no—
345C22⋊C4×C127—44no—
346C22⋊C4×C127—44no—
347C22⋊C4×C127—44no—
348C22⋊C4×C127—44no—
349C22⋊C4×C127—44no—
350C22⋊C4×C127—44no—
351C22⋊C4×C127—44no—
352C22⋊C4×C127—44no—
353C23×C127—22no—
354C23×C127—22no—
355C23×C127—22no—
356C23×C127—22no—
357C23×C127—22no—
358C23×C127—22no—
359C23×C127—22no—
360C23×C127—22no—
361C23×C127—22no—
362C23×C127—22no—
363C23×C127—22no—
364C23×C127—22no—
365C23×C127—22no—
366C23×C127—22no—
367C23×C127—22no—
368C23×C127—22no—
369C23×C127—22no—
370C23×C127—22no—
371C23×C127—22no—
372C23×C127—22no—
373C23×C127—22no—
374C23×C127—22no—
375C23×C127—22no—
376C23×C127—22no—
377C23×C127—22no—
378C23×C127—22no—
379C23×C127—22no—
380C23×C127—22no—
381C23×C127—22no—
382C23×C127—22no—
383C23×C127—22no—
384C23×C127—22no—
385C23×C127—22no—
386C23×C127—22no—
387C23×C127—22no—
388C23×C127—22no—
389C23×C127—22no—
390C23×C127—22no—
391C23×C127—22no—
392C23×C127—22no—
393C23×C127—22no—
394C23×C127—22no—
395C23×C127—22no—
396C23×C127—41no—
397C23×C127—41no—
398C23×C127—41no—
399C23×C127—41no—
400C23×C127—41no—
401C23×C127—41no—
402C23×C127—41no—
403C23×C127—41no—
404C23×C127—41no—
405C23×C127—41no—
406C23×C127—41no—
407C23×C127—41no—
408C23×C127—41no—
409C23×C127—41no—
410C23×C127—41no—
411C23×C127—41no—
412C23×C127—41no—
413C23×C127—41no—
414C23×C127—41no—
415C23×C127—41no—
416C23×C127—41no—
417C23×C127—41no—
418C23×C127—41no—
419C23×C127—41no—
420C23×C127—41no—
421C23×C127—41no—
422C23×C127—41no—
423C23×C127—41no—
424C23×C127—41no—
425C23×C127—41no—
426C23×C127—41no—
427C23×C127—41no—
428C23×C127—41no—
429C23×C127—41no—
430C23×C127—41no—
431C23×C127—41no—
432C23×C127—41no—
433C23×C127—41no—
434C23×C127—41no—
435C23×C127—41no—
436C23×C127—41no—
437C23×C127—41no—
438C23×C127—41no—
439C23×C127—41no—
440C23×C127—41no—
441C23×C127—41no—
442C23×C127—41no—
443C23×C127—41no—
444C23×C127—41no—
445C23×C127—41no—
446C23×C127—41no—
447C23×C127—41no—
448C23×C127—41no—
449C23×C127—41no—
450C23×C127—41no—
451C23×C127—41no—
452C23×C127—41no—
453C23×C127—41no—
454C23×C127—41no—
455C23×C127—41no—
456C23×C127#12014yes—
457C23×C127#12314yes—
458C23×C127C22×D411yescharacteristic
459C23×C127C22×D411yescharacteristic
460C23×C127C22×D411yescharacteristic
461C23×C127C22×D411yescharacteristic
462C23×C127C2×#4111yescharacteristic
463C23×C127C2×#4111yescharacteristic
464C23×C127C2×#4111yescharacteristic
465C23×C127C2×#4111yescharacteristic
466C23×C127C2×#4111yescharacteristic
467C23×C127H(5,𝔽2)11yescharacteristic
468C23×C127H(5,𝔽2)11yescharacteristic
469C23×C127H(5,𝔽2)11yescharacteristic
470C23×C127H(5,𝔽2)11yescharacteristic
471C23×C127H(5,𝔽2)11yescharacteristic
472C23×C1272−1+411yescharacteristic
473D4×C127—416no—
474D4×C127—416no—
475D4×C127—416no—
476C2×C4×C127—22no—
477C2×C4×C127—22no—
478C2×C4×C127—22no—
479C2×C4×C127—22no—
480C2×C4×C127—22no—
481C2×C4×C127—22no—
482C2×C4×C127—22no—
483C2×C4×C127—22no—
484C2×C4×C127—22no—
485C2×C4×C127—22no—
486C2×C4×C127—22no—
487C2×C4×C127—22no—
488C2×C4×C127—22no—
489C2×C4×C127—22no—
490C2×C4×C127—22no—
491C2×C4×C127—22no—
492C2×C4×C127—22no—
493C2×C4×C127—22no—
494C2×C4×C127—22no—
495C2×C4×C127—22no—
496C2×C4×C127—22no—
497C2×C4×C127—22no—
498C2×C4×C127—22no—
499C2×C4×C127—22no—
500C2×C4×C127—22no—
501C2×C4×C127—22no—
502C2×C4×C127—22no—
503C2×C4×C127—416no—
504C2×C4×C127—416no—
505C2×C4×C127—41no—
506C2×C4×C127—41no—
507C2×C4×C127—41no—
508C2×C4×C127—41no—
509C2×C4×C127—41no—
510C2×C4×C127—41no—
511C2×C4×C127—41no—
512C2×C4×C127—41no—
513C2×C4×C127—41no—
514C2×C4×C127—41no—
515C2×C4×C127—41no—
516C2×C4×C127—41no—
517C2×C4×C127—41no—
518C2×C4×C127—41no—
519C2×C4×C127—41no—
520C2×C4×C127—41no—
521C2×C4×C127—41no—
522C2×C4×C127—41no—
523C2×C4×C127—41no—
524C2×C4×C127—41no—
525C2×C4×C127—41no—
526C2×C4×C127—41no—
527C2×C4×C127—41no—
528C2×C4×C127—41no—
529C2×C4×C127—41no—
530C2×C4×C127—41no—
531C2×C4×C127—41no—
532C2×C4×C127—41no—
533C2×C4×C127—41no—
534C2×C4×C127—41no—
535C2×C4×C127—41no—
536C2×C4×C127—41no—
537C2×C4×C127—41no—
538C2×C4×C127—41no—
539C2×C4×C127—41no—
540C2×C4×C127—41no—
541C2×C4×C127—41no—
542C2×C4×C127—41no—
543C2×C4×C127—41no—
544C2×C4×C127—41no—
545C2×C4×C127—41no—
546C2×C4×C127—41no—
547C2×C4×C127—41no—
548C2×C4×C127—41no—
549C2×C4×C127—41no—
550C2×C4×C127—41no—
551C2×C4×C127—41no—
552C2×C4×C127—41no—
553C2×C4×C127—41no—
554C2×C4×C127—41no—
555C2×C4×C127—41no—
556C2×C4×C127—41no—
557C2×C4×C127—41no—
558C2×C4×C127—41no—
559C2×C4×C127—41no—
560C2×C4×C127—41no—
561C2×C4×C127#12114yes—
562C22×C127—24no—
563C22×C127—24no—
564C22×C127—24no—
565C22×C127—24no—
566C22×C127—24no—
567C22×C127—24no—
568C22×C127—42no—
569C22×C127—42no—
570C22×C127—42no—
571C22×C127—42no—
572C22×C127—42no—
573C22×C127—42no—
574C22×C127—42no—
575C22×C127—42no—
576C22×C127—42no—
577C22×C127—42no—
578C22×C127—42no—
579C22×C127—42no—
580C22×C127—42no—
581C22×C127—42no—
582C22×C127—42no—
583C22×C127—42no—
584C22×C127—42no—
585C22×C127—42no—
586C22×C127—42no—
587C22×C127—42no—
588C22×C127—42no—
589C22×C127—42no—
590C22×C127—42no—
591C22×C127—42no—
592C22×C127—42no—
593C22×C127—42no—
594C22×C127—42no—
595C22×C127—42no—
596C22×C127—42no—
597C22×C127—42no—
598C22×C127—42no—
599C22×C127—81no—
600C22×C127—81no—
601C22×C127—81no—
602C22×C127—81no—
603C22×C127—81no—
604C22×C127—81no—
605C22×C127—81no—
606C22×C127—81no—
607C22×C127C2×#12011yescharacteristic
608C22×C127C2×#12111yescharacteristic
609C22×C127C2×#12311yescharacteristic
610C22×C127#52511yescharacteristic
611C22×C127#52911yescharacteristic
612C22×C127#53211yescharacteristic
613C22×C127#53411yescharacteristic
614C22×C127#53411yescharacteristic
615C22×C127#53511yescharacteristic
616C22×C127#53711yescharacteristic
617C22×C127#53811yescharacteristic
618C22×C127#53811yescharacteristic
619C22×C127#53911yescharacteristic
620C22×C127#54011yescharacteristic
621C22×C127#54211yescharacteristic
622C22×C127D4211yescharacteristic
623C22×C127D4211yescharacteristic
624C22×C127#54611yescharacteristic
625C22×C127#54611yescharacteristic
626C22×C127#54611yescharacteristic
627C22×C127#54611yescharacteristic
628C22×C127#54611yescharacteristic
629C22×C127#54611yescharacteristic
630C22×C127#54611yescharacteristic
631C22×C127#54611yescharacteristic
632C22×C127#54611yescharacteristic
633C22×C127#54711yescharacteristic
634C22×C127#54711yescharacteristic
635C22×C127#54811yescharacteristic
636C22×C127#55311yescharacteristic
637C22×C127#55311yescharacteristic
638C22×C127#55311yescharacteristic
639C22×C127#55311yescharacteristic
640C22×C127#56011yescharacteristic
641C22×C127#56211yescharacteristic
642C4×C127—24no—
643C4×C127—42no—
644C4×C127—42no—
645C4×C127—42no—
646C4×C127—42no—
647C4×C127—42no—
648C4×C127—42no—
649C4×C127—42no—
650C4×C127—81no—
651C4×C127—81no—
652C4×C127—81no—
653C4×C127—81no—
654#15277C12711yesmaximal, characteristic, direct product factor, Sylow
655C2×C127—44no—
656C2×C127—44no—
657C2×C127—82no—
658C2×C127#240511yescharacteristic
659C2×C127#241011yescharacteristic
660C2×C127#242711yescharacteristic
661C2×C127#243011yescharacteristic
662C2×C127#244311yescharacteristic
663C2×C127#244411yescharacteristic
664C2×C127#246411yescharacteristic
665C2×C127#253511yescharacteristic
666C2×C127#255911yescharacteristic
667C2×C127#267611yescharacteristic
668C2×C127#267811yescharacteristic
669C2×C127#268811yescharacteristic
670C2×C127#269111yescharacteristic
671C2×C127#270111yescharacteristic
672C2×C127#270811yescharacteristic
673C22×#121C2×C12711yescharacteristic
674C2×#397C2×C12711yescharacteristic, complemented
675C2×#394C2×C12711yescharacteristic, complemented
676C2×#386C2×C12711yescharacteristic, complemented
677C2×#386C2×C12711yescharacteristic, complemented
678C2×#385C2×C12711yescharacteristic, complemented
679#1442C2×C12711yescharacteristic, complemented
680#1441C2×C12711yescharacteristic, complemented
681#1440C2×C12711yescharacteristic, complemented
682#1439C2×C12711yescharacteristic, complemented
683#1438C2×C12711yescharacteristic, complemented
684#1438C2×C12711yescharacteristic, complemented
685#1438C2×C12711yescharacteristic, complemented
686C22⋊#95C2×C12711yescharacteristic, complemented
687C22⋊#95C2×C12711yescharacteristic, complemented
688C127#1527711yescharacteristic, direct product factor, Sylow
689C23×D4C22×C12711yescharacteristic
690C23×D4C22×C12711yescharacteristic
691C23×D4C22×C12711yescharacteristic
692C24×C4C22×C12711yescharacteristic
693C24×C4C22×C12711yescharacteristic
694C2×#121—24no—
695C2×#121—24no—
696C2×#121—24no—
697C22×C4⋊C4C22×C12711yescharacteristic
698C22×C4⋊C4C22×C12711yescharacteristic
699C22×C4⋊C4C22×C12711yescharacteristic
700C22×C22⋊C4C22×C12711yescharacteristic
701C22×C22⋊C4C22×C12711yescharacteristic
702C22×C22⋊C4C22×C12711yescharacteristic
703C22×C22⋊C4C22×C12711yescharacteristic
704C22×C22⋊C4C22×C12711yescharacteristic
705C22×C22⋊C4C22×C12711yescharacteristic
706C22×C22⋊C4C22×C12711yescharacteristic
707C22×C22⋊C4C22×C12711yescharacteristic
708C22×C22⋊C4C22×C12711yescharacteristic
709C22×C22⋊C4C22×C12711yescharacteristic
710C22×C22⋊C4C22×C12711yescharacteristic
711C22×C22⋊C4C22×C12711yescharacteristic
712C22×C22⋊C4C22×C12711yescharacteristic
713#397—24no—
714#394—24no—
715#386—24no—
716#386—24no—
717#385—24no—
718C2×#95C22×C12711yescharacteristic
719C2×#95C22×C12711yescharacteristic
720C2×#95C22×C12711yescharacteristic
721C2×#95C22×C12711yescharacteristic
722C2×#95C22×C12711yescharacteristic
723C2×#95C22×C12711yescharacteristic
724C2×#95C22×C12711yescharacteristic
725C2×#95C22×C12711yescharacteristic
726C2×#95C22×C12711yescharacteristic
727C2×#95C22×C12711yescharacteristic
728C2×#95C22×C12711yescharacteristic
729C2×#95C22×C12711yescharacteristic
730C2×#95C22×C12711yescharacteristic
731C2×#95C22×C12711yescharacteristic
732C25C23×C12711yescharacteristic
733C25C23×C12711yescharacteristic
734C25C23×C12711yescharacteristic
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4—41no—
751C22×D4—41no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4D4×C12714yes—
755C22×D4D4×C12714yes—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4—41no—
769C23×C4—41no—
770C23×C4C23×C12711yescharacteristic
771C23×C4C23×C12711yescharacteristic
772C23×C4C23×C12711yescharacteristic
773C23×C4C23×C12711yescharacteristic
774C23×C4C23×C12711yescharacteristic
775C23×C4C23×C12711yescharacteristic
776C23×C4C23×C12711yescharacteristic
777C23×C4C23×C12711yescharacteristic
778C23×C4C23×C12711yescharacteristic
779C23×C4C23×C12711yescharacteristic
780C23×C4C23×C12711yescharacteristic
781C23×C4C23×C12711yescharacteristic
782#121—232no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—22no—
789C2×C4⋊C4—22no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—41no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4—41no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4D4×C12714yes—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—41no—
840#95—41no—
841#95—41no—
842#95—41no—
843#95—41no—
844#95D4×C12714yescomplemented
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24C2×D4×C12712yes—
884C24C2×D4×C12712yes—
885C24C2×D4×C12712yes—
886C24C2×D4×C12712yes—
887C24C2×D4×C12712yes—
888C24#41×C12712yes—
889C24#41×C12712yes—
890C24C24×C12711yescharacteristic
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—28no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4C2×D4×C12712yes—
1001C22×C4C2×D4×C12712yes—
1002C22×C4C2×D4×C12712yes—
1003C22×C4C2×D4×C12712yes—
1004C22×C4C2×D4×C12712yes—
1005C22×C4C2×D4×C12712yes—
1006C22×C4C2×D4×C12712yes—
1007C22×C4#41×C12712yes—
1008C22×C4#41×C12712yes—
1009C22×C4#41×C12712yes—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23#120×C12714yes—
1130C23#123×C12714yes—
1131C23C22×D4×C12711yescharacteristic
1132C23C22×D4×C12711yescharacteristic
1133C23C22×D4×C12711yescharacteristic
1134C23C22×D4×C12711yescharacteristic
1135C23C2×#41×C12711yescharacteristic
1136C23C2×#41×C12711yescharacteristic
1137C23C2×#41×C12711yescharacteristic
1138C23C2×#41×C12711yescharacteristic
1139C23C2×#41×C12711yescharacteristic
1140C23H(5,𝔽2)×C12711yescharacteristic
1141C23H(5,𝔽2)×C12711yescharacteristic
1142C23H(5,𝔽2)×C12711yescharacteristic
1143C23H(5,𝔽2)×C12711yescharacteristic
1144C23H(5,𝔽2)×C12711yescharacteristic
1145C232−1+4×C12711yescharacteristic
1146D4—416no—
1147D4—416no—
1148D4—416no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—416no—
1177C2×C4—416no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4#121×C12714yes—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×#120×C12711yescharacteristic
1281C22C2×#121×C12711yescharacteristic
1282C22C2×#123×C12711yescharacteristic
1283C22#525×C12711yescharacteristic
1284C22#529×C12711yescharacteristic
1285C22#532×C12711yescharacteristic
1286C22#534×C12711yescharacteristic
1287C22#534×C12711yescharacteristic
1288C22#535×C12711yescharacteristic
1289C22#537×C12711yescharacteristic
1290C22#538×C12711yescharacteristic
1291C22#538×C12711yescharacteristic
1292C22#539×C12711yescharacteristic
1293C22#540×C12711yescharacteristic
1294C22#542×C12711yescharacteristic
1295C22D42×C12711yescharacteristic
1296C22D42×C12711yescharacteristic
1297C22#546×C12711yescharacteristic
1298C22#546×C12711yescharacteristic
1299C22#546×C12711yescharacteristic
1300C22#546×C12711yescharacteristic
1301C22#546×C12711yescharacteristic
1302C22#546×C12711yescharacteristic
1303C22#546×C12711yescharacteristic
1304C22#546×C12711yescharacteristic
1305C22#546×C12711yescharacteristic
1306C22#547×C12711yescharacteristic
1307C22#547×C12711yescharacteristic
1308C22#548×C12711yescharacteristic
1309C22#553×C12711yescharacteristic
1310C22#553×C12711yescharacteristic
1311C22#553×C12711yescharacteristic
1312C22#553×C12711yescharacteristic
1313C22#560×C12711yescharacteristic
1314C22#562×C12711yescharacteristic
1315C4—24no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C2—44no—
1328C2—44no—
1329C2—82no—
1330C2C127×#240511yescharacteristic
1331C2C127×#241011yescharacteristic
1332C2C127×#242711yescharacteristic
1333C2C127×#243011yescharacteristic
1334C2C127×#244311yescharacteristic
1335C2C127×#244411yescharacteristic
1336C2C127×#246411yescharacteristic
1337C2C127×#253511yescharacteristic
1338C2C127×#255911yescharacteristic
1339C2C127×#267611yescharacteristic
1340C2C127×#267811yescharacteristic
1341C2C127×#268811yescharacteristic
1342C2C127×#269111yescharacteristic
1343C2C127×#270111yescharacteristic
1344C2C127×#270811yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC22×#121×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#397×C127C2semidirect
3. C2×#394×C127C2semidirect
4. C2×#386×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#385×C127C2semidirect
7. C127×#1442C2semidirect
8. C127×#1441C2semidirect
9. C127×#1440C2semidirect
10. C127×#1439C2semidirect
11. C127×#1438C2semidirect
12. C127×#1438C2semidirect
13. C127×#1438C2semidirect
14. C127×C22⋊#95C2semidirect
15. C127×C22⋊#95C2semidirect
171. #95×C127D4semidirect
654. #15277C127direct (N × H)
674. C2×#397C2×C127semidirect
675. C2×#394C2×C127semidirect
676. C2×#386C2×C127semidirect
677. C2×#386C2×C127semidirect
678. C2×#385C2×C127semidirect
679. #1442C2×C127semidirect
680. #1441C2×C127semidirect
681. #1440C2×C127semidirect
682. #1439C2×C127semidirect
683. #1438C2×C127semidirect
684. #1438C2×C127semidirect
685. #1438C2×C127semidirect
686. C22⋊#95C2×C127semidirect
687. C22⋊#95C2×C127semidirect
688. C127#15277direct (N × H)
844. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1272
C2×#397×C1272
C2×#394×C1272
C2×#386×C1272
C2×#385×C1272
C127×#14422
C127×#14412
C127×#14402
C127×#14392
C127×#14382
C127×C22⋊#952
#15277127