Finite Group Databasebeta

← C127×#15501 #44579174

Subgroups — C127×#15501 #44579174

Order 32512.

2154 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C127C211yesmaximal, characteristic, complemented
2C2×#394×C127C211yesmaximal, characteristic, complemented
3C2×#392×C127C211yesmaximal, characteristic
4C2×#390×C127C211yesmaximal, characteristic, complemented
5C2×#386×C127C211yesmaximal, characteristic, complemented
6C2×#386×C127C211yesmaximal, characteristic, complemented
7C127×#1441C211yesmaximal, characteristic, complemented
8C127×#1440C211yesmaximal, characteristic, complemented
9C127×#1440C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1438C211yesmaximal, characteristic, complemented
12C127×#1438C211yesmaximal, characteristic, complemented
13C127×#1437C211yesmaximal, characteristic, complemented
14C127×#1434C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C24×C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊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×C42×C127C2211yescharacteristic
37#397×C127—24no—
38#394×C127—24no—
39#392×C127—24no—
40#390×C127—24no—
41#386×C127—24no—
42#386×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
59C25×C127C2311yescharacteristic
60C22×D4×C127—22no—
61C22×D4×C127—22no—
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—41no—
73C22×D4×C127—41no—
74C22×D4×C127—41no—
75C22×D4×C127—41no—
76C22×D4×C127—41no—
77C22×D4×C127—41no—
78C22×D4×C127—41no—
79C22×D4×C127—41no—
80C22×D4×C127D414yes—
81C23×C4×C127—22no—
82C23×C4×C127—22no—
83C23×C4×C127—22no—
84C23×C4×C127—41no—
85C23×C4×C127—41no—
86C23×C4×C127—41no—
87C23×C4×C127—41no—
88C23×C4×C127C2311yescharacteristic
89C23×C4×C127C2311yescharacteristic
90C23×C4×C127C2311yescharacteristic
91C23×C4×C127C2311yescharacteristic
92C23×C4×C127C2311yescharacteristic
93C23×C4×C127C2311yescharacteristic
94C23×C4×C127C2311yescharacteristic
95C23×C4×C127C2311yescharacteristic
96C23×C4×C127C2311yescharacteristic
97C23×C4×C127C2311yescharacteristic
98C23×C4×C127C2311yescharacteristic
99C23×C4×C127C2311yescharacteristic
100C2×C4⋊C4×C127—22no—
101C2×C4⋊C4×C127—22no—
102C2×C4⋊C4×C127—22no—
103C2×C4⋊C4×C127—22no—
104C2×C4⋊C4×C127—41no—
105C2×C4⋊C4×C127—41no—
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—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—41no—
132C2×C22⋊C4×C127—41no—
133C2×C22⋊C4×C127—41no—
134C2×C22⋊C4×C127—41no—
135C2×C22⋊C4×C127—41no—
136C2×C22⋊C4×C127—41no—
137C2×C22⋊C4×C127—41no—
138C2×C22⋊C4×C127—41no—
139C2×C22⋊C4×C127—41no—
140C2×C22⋊C4×C127—41no—
141C2×C22⋊C4×C127—41no—
142C2×C22⋊C4×C127—41no—
143C2×C22⋊C4×C127—41no—
144C2×C22⋊C4×C127—41no—
145C2×C22⋊C4×C127—41no—
146C2×C22⋊C4×C127—41no—
147C2×C22⋊C4×C127D414yescomplemented
148C2×C42×C127—22no—
149C2×C42×C127—22no—
150C2×C42×C127—41no—
151#95×C127—22no—
152#95×C127—22no—
153#95×C127—22no—
154#95×C127—22no—
155#95×C127—22no—
156#95×C127—22no—
157#95×C127—22no—
158#95×C127—22no—
159#95×C127—41no—
160#95×C127—41no—
161#95×C127—41no—
162#95×C127—41no—
163#95×C127—41no—
164#95×C127D414yescomplemented
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×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×C127C2×D412yes—
206C24×C127C2×D412yes—
207C24×C127C2×D412yes—
208C24×C127#4112yes—
209C24×C127#4112yes—
210C24×C127C2411yescharacteristic
211C2×D4×C127—28no—
212C2×D4×C127—28no—
213C2×D4×C127—28no—
214C2×D4×C127—44no—
215C2×D4×C127—44no—
216C2×D4×C127—44no—
217C2×D4×C127—44no—
218C2×D4×C127—44no—
219C2×D4×C127—44no—
220C2×D4×C127—44no—
221C2×D4×C127—44no—
222C2×D4×C127—44no—
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—
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×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—44no—
307C22×C4×C127—44no—
308C22×C4×C127—44no—
309C22×C4×C127—44no—
310C22×C4×C127—44no—
311C22×C4×C127—44no—
312C22×C4×C127—44no—
313C22×C4×C127C2×D412yes—
314C22×C4×C127C2×D412yes—
315C22×C4×C127C2×D412yes—
316C22×C4×C127C2×D412yes—
317C22×C4×C127C2×D412yes—
318C22×C4×C127C2×D412yes—
319C22×C4×C127#4112yes—
320C22×C4×C127#4112yes—
321C22×C4×C127#4112yes—
322C22×C4×C127#4112yes—
323C4⋊C4×C127—44no—
324C4⋊C4×C127—44no—
325C22⋊C4×C127—44no—
326C22⋊C4×C127—44no—
327C22⋊C4×C127—44no—
328C22⋊C4×C127—44no—
329C22⋊C4×C127—44no—
330C22⋊C4×C127—44no—
331C22⋊C4×C127—44no—
332C22⋊C4×C127—44no—
333C22⋊C4×C127—44no—
334C22⋊C4×C127—44no—
335C22⋊C4×C127—44no—
336C22⋊C4×C127—44no—
337C22⋊C4×C127—44no—
338C22⋊C4×C127—44no—
339C42×C127—44no—
340C23×C127—22no—
341C23×C127—22no—
342C23×C127—22no—
343C23×C127—22no—
344C23×C127—22no—
345C23×C127—22no—
346C23×C127—22no—
347C23×C127—22no—
348C23×C127—22no—
349C23×C127—22no—
350C23×C127—22no—
351C23×C127—22no—
352C23×C127—22no—
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—41no—
373C23×C127—41no—
374C23×C127—41no—
375C23×C127—41no—
376C23×C127—41no—
377C23×C127—41no—
378C23×C127—41no—
379C23×C127—41no—
380C23×C127—41no—
381C23×C127—41no—
382C23×C127—41no—
383C23×C127—41no—
384C23×C127—41no—
385C23×C127—41no—
386C23×C127—41no—
387C23×C127—41no—
388C23×C127—41no—
389C23×C127—41no—
390C23×C127—41no—
391C23×C127—41no—
392C23×C127—41no—
393C23×C127—41no—
394C23×C127—41no—
395C23×C127—41no—
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#12114yes—
445C23×C127C22×D411yescharacteristic
446C23×C127C22×D411yescharacteristic
447C23×C127C22×D411yescharacteristic
448C23×C127C2×#4111yescharacteristic
449C23×C127C2×#4111yescharacteristic
450C23×C127C2×#4111yescharacteristic
451C23×C127C2×#4111yescharacteristic
452C23×C127C2×#4111yescharacteristic
453C23×C127C2×#4111yescharacteristic
454C23×C127H(5,𝔽2)11yescharacteristic
455C23×C127H(5,𝔽2)11yescharacteristic
456C23×C127H(5,𝔽2)11yescharacteristic
457C23×C127H(5,𝔽2)11yescharacteristic
458C23×C127H(5,𝔽2)11yescharacteristic
459C23×C127H(5,𝔽2)11yescharacteristic
460D4×C127—416no—
461D4×C127—416no—
462D4×C127—416no—
463C2×C4×C127—22no—
464C2×C4×C127—22no—
465C2×C4×C127—22no—
466C2×C4×C127—22no—
467C2×C4×C127—22no—
468C2×C4×C127—22no—
469C2×C4×C127—22no—
470C2×C4×C127—22no—
471C2×C4×C127—22no—
472C2×C4×C127—22no—
473C2×C4×C127—22no—
474C2×C4×C127—22no—
475C2×C4×C127—22no—
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—416no—
491C2×C4×C127—41no—
492C2×C4×C127—41no—
493C2×C4×C127—41no—
494C2×C4×C127—41no—
495C2×C4×C127—41no—
496C2×C4×C127—41no—
497C2×C4×C127—41no—
498C2×C4×C127—41no—
499C2×C4×C127—41no—
500C2×C4×C127—41no—
501C2×C4×C127—41no—
502C2×C4×C127—41no—
503C2×C4×C127—41no—
504C2×C4×C127—41no—
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#12314yes—
548C22×C127—24no—
549C22×C127—24no—
550C22×C127—24no—
551C22×C127—42no—
552C22×C127—42no—
553C22×C127—42no—
554C22×C127—42no—
555C22×C127—42no—
556C22×C127—42no—
557C22×C127—42no—
558C22×C127—42no—
559C22×C127—42no—
560C22×C127—42no—
561C22×C127—42no—
562C22×C127—42no—
563C22×C127—42no—
564C22×C127—42no—
565C22×C127—42no—
566C22×C127—42no—
567C22×C127—42no—
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—81no—
578C22×C127—81no—
579C22×C127—81no—
580C22×C127—81no—
581C22×C127—81no—
582C22×C127—81no—
583C22×C127—81no—
584C22×C127—81no—
585C22×C127—81no—
586C22×C127—81no—
587C22×C127—81no—
588C22×C127—81no—
589C22×C127—81no—
590C22×C127—81no—
591C22×C127—81no—
592C22×C127—81no—
593C22×C127C2×#12111yescharacteristic
594C22×C127C2×#12311yescharacteristic
595C22×C127#52511yescharacteristic
596C22×C127#52911yescharacteristic
597C22×C127#53211yescharacteristic
598C22×C127#53211yescharacteristic
599C22×C127#53411yescharacteristic
600C22×C127#53411yescharacteristic
601C22×C127#53511yescharacteristic
602C22×C127#53811yescharacteristic
603C22×C127#53811yescharacteristic
604C22×C127#53811yescharacteristic
605C22×C127#53811yescharacteristic
606C22×C127#54011yescharacteristic
607C22×C127#54011yescharacteristic
608C22×C127D4211yescharacteristic
609C22×C127D4211yescharacteristic
610C22×C127#54611yescharacteristic
611C22×C127#54611yescharacteristic
612C22×C127#54611yescharacteristic
613C22×C127#54611yescharacteristic
614C22×C127#54611yescharacteristic
615C22×C127#54611yescharacteristic
616C22×C127#54611yescharacteristic
617C22×C127#55011yescharacteristic
618C22×C127#55111yescharacteristic
619C22×C127#55111yescharacteristic
620C22×C127#55111yescharacteristic
621C22×C127#55311yescharacteristic
622C22×C127#55311yescharacteristic
623C22×C127#55311yescharacteristic
624C22×C127#55511yescharacteristic
625C22×C127#55911yescharacteristic
626C22×C127#56011yescharacteristic
627C22×C127#56011yescharacteristic
628C4×C127—24no—
629C4×C127—42no—
630C4×C127—42no—
631C4×C127—42no—
632C4×C127—42no—
633C4×C127—42no—
634C4×C127—42no—
635C4×C127—42no—
636C4×C127—81no—
637C4×C127—81no—
638C4×C127—81no—
639C4×C127—81no—
640#15501C12711yesmaximal, characteristic, direct product factor, Sylow
641C2×C127—44no—
642C2×C127—82no—
643C2×C127—82no—
644C2×C127#241211yescharacteristic
645C2×C127#242011yescharacteristic
646C2×C127#242411yescharacteristic
647C2×C127#244511yescharacteristic
648C2×C127#246711yescharacteristic
649C2×C127#254311yescharacteristic
650C2×C127#255511yescharacteristic
651C2×C127#255711yescharacteristic
652C2×C127#260311yescharacteristic
653C2×C127#267311yescharacteristic
654C2×C127#267811yescharacteristic
655C2×C127#268811yescharacteristic
656C2×C127#269711yescharacteristic
657C2×C127#275611yescharacteristic
658C2×C127#279711yescharacteristic
659C2×#397C2×C12711yescharacteristic, complemented
660C2×#394C2×C12711yescharacteristic, complemented
661C2×#392C2×C12711yescharacteristic
662C2×#390C2×C12711yescharacteristic, complemented
663C2×#386C2×C12711yescharacteristic, complemented
664C2×#386C2×C12711yescharacteristic, complemented
665#1441C2×C12711yescharacteristic, complemented
666#1440C2×C12711yescharacteristic, complemented
667#1440C2×C12711yescharacteristic, complemented
668#1439C2×C12711yescharacteristic, complemented
669#1438C2×C12711yescharacteristic, complemented
670#1438C2×C12711yescharacteristic, complemented
671#1437C2×C12711yescharacteristic, complemented
672#1434C2×C12711yescharacteristic, complemented
673C22⋊#95C2×C12711yescharacteristic, complemented
674C127#1550111yescharacteristic, direct product factor, Sylow
675C23×D4C22×C12711yescharacteristic
676C23×D4C22×C12711yescharacteristic
677C23×D4C22×C12711yescharacteristic
678C24×C4C22×C12711yescharacteristic
679C22×C4⋊C4C22×C12711yescharacteristic
680C22×C4⋊C4C22×C12711yescharacteristic
681C22×C22⋊C4C22×C12711yescharacteristic
682C22×C22⋊C4C22×C12711yescharacteristic
683C22×C22⋊C4C22×C12711yescharacteristic
684C22×C22⋊C4C22×C12711yescharacteristic
685C22×C22⋊C4C22×C12711yescharacteristic
686C22×C22⋊C4C22×C12711yescharacteristic
687C22×C22⋊C4C22×C12711yescharacteristic
688C22×C22⋊C4C22×C12711yescharacteristic
689C22×C22⋊C4C22×C12711yescharacteristic
690C22×C22⋊C4C22×C12711yescharacteristic
691C22×C22⋊C4C22×C12711yescharacteristic
692C22×C22⋊C4C22×C12711yescharacteristic
693C22×C22⋊C4C22×C12711yescharacteristic
694C22×C22⋊C4C22×C12711yescharacteristic
695C22×C42C22×C12711yescharacteristic
696#397—24no—
697#394—24no—
698#392—24no—
699#390—24no—
700#386—24no—
701#386—24no—
702C2×#95C22×C12711yescharacteristic
703C2×#95C22×C12711yescharacteristic
704C2×#95C22×C12711yescharacteristic
705C2×#95C22×C12711yescharacteristic
706C2×#95C22×C12711yescharacteristic
707C2×#95C22×C12711yescharacteristic
708C2×#95C22×C12711yescharacteristic
709C2×#95C22×C12711yescharacteristic
710C2×#95C22×C12711yescharacteristic
711C2×#95C22×C12711yescharacteristic
712C2×#95C22×C12711yescharacteristic
713C2×#95C22×C12711yescharacteristic
714C2×#95C22×C12711yescharacteristic
715C2×#95C22×C12711yescharacteristic
716C25C23×C12711yescharacteristic
717C25C23×C12711yescharacteristic
718C25C23×C12711yescharacteristic
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4D4×C12714yes—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—22no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4—41no—
747C23×C4C23×C12711yescharacteristic
748C23×C4C23×C12711yescharacteristic
749C23×C4C23×C12711yescharacteristic
750C23×C4C23×C12711yescharacteristic
751C23×C4C23×C12711yescharacteristic
752C23×C4C23×C12711yescharacteristic
753C23×C4C23×C12711yescharacteristic
754C23×C4C23×C12711yescharacteristic
755C23×C4C23×C12711yescharacteristic
756C23×C4C23×C12711yescharacteristic
757C23×C4C23×C12711yescharacteristic
758C23×C4C23×C12711yescharacteristic
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4D4×C12714yescomplemented
807C2×C42—22no—
808C2×C42—22no—
809C2×C42—41no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—41no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823#95D4×C12714yescomplemented
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
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—
864C24C2×D4×C12712yes—
865C24C2×D4×C12712yes—
866C24C2×D4×C12712yes—
867C24#41×C12712yes—
868C24#41×C12712yes—
869C24C24×C12711yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—28no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
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—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4C2×D4×C12712yes—
973C22×C4C2×D4×C12712yes—
974C22×C4C2×D4×C12712yes—
975C22×C4C2×D4×C12712yes—
976C22×C4C2×D4×C12712yes—
977C22×C4C2×D4×C12712yes—
978C22×C4#41×C12712yes—
979C22×C4#41×C12712yes—
980C22×C4#41×C12712yes—
981C22×C4#41×C12712yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
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—
998C42—44no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
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#121×C12714yes—
1104C23C22×D4×C12711yescharacteristic
1105C23C22×D4×C12711yescharacteristic
1106C23C22×D4×C12711yescharacteristic
1107C23C2×#41×C12711yescharacteristic
1108C23C2×#41×C12711yescharacteristic
1109C23C2×#41×C12711yescharacteristic
1110C23C2×#41×C12711yescharacteristic
1111C23C2×#41×C12711yescharacteristic
1112C23C2×#41×C12711yescharacteristic
1113C23H(5,𝔽2)×C12711yescharacteristic
1114C23H(5,𝔽2)×C12711yescharacteristic
1115C23H(5,𝔽2)×C12711yescharacteristic
1116C23H(5,𝔽2)×C12711yescharacteristic
1117C23H(5,𝔽2)×C12711yescharacteristic
1118C23H(5,𝔽2)×C12711yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—416no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
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#123×C12714yes—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22C2×#121×C12711yescharacteristic
1253C22C2×#123×C12711yescharacteristic
1254C22#525×C12711yescharacteristic
1255C22#529×C12711yescharacteristic
1256C22#532×C12711yescharacteristic
1257C22#532×C12711yescharacteristic
1258C22#534×C12711yescharacteristic
1259C22#534×C12711yescharacteristic
1260C22#535×C12711yescharacteristic
1261C22#538×C12711yescharacteristic
1262C22#538×C12711yescharacteristic
1263C22#538×C12711yescharacteristic
1264C22#538×C12711yescharacteristic
1265C22#540×C12711yescharacteristic
1266C22#540×C12711yescharacteristic
1267C22D42×C12711yescharacteristic
1268C22D42×C12711yescharacteristic
1269C22#546×C12711yescharacteristic
1270C22#546×C12711yescharacteristic
1271C22#546×C12711yescharacteristic
1272C22#546×C12711yescharacteristic
1273C22#546×C12711yescharacteristic
1274C22#546×C12711yescharacteristic
1275C22#546×C12711yescharacteristic
1276C22#550×C12711yescharacteristic
1277C22#551×C12711yescharacteristic
1278C22#551×C12711yescharacteristic
1279C22#551×C12711yescharacteristic
1280C22#553×C12711yescharacteristic
1281C22#553×C12711yescharacteristic
1282C22#553×C12711yescharacteristic
1283C22#555×C12711yescharacteristic
1284C22#559×C12711yescharacteristic
1285C22#560×C12711yescharacteristic
1286C22#560×C12711yescharacteristic
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2C127×#241211yescharacteristic
1303C2C127×#242011yescharacteristic
1304C2C127×#242411yescharacteristic
1305C2C127×#244511yescharacteristic
1306C2C127×#246711yescharacteristic
1307C2C127×#254311yescharacteristic
1308C2C127×#255511yescharacteristic
1309C2C127×#255711yescharacteristic
1310C2C127×#260311yescharacteristic
1311C2C127×#267311yescharacteristic
1312C2C127×#267811yescharacteristic
1313C2C127×#268811yescharacteristic
1314C2C127×#269711yescharacteristic
1315C2C127×#275611yescharacteristic
1316C2C127×#279711yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C127C2semidirect
2. C2×#394×C127C2semidirect
4. C2×#390×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#386×C127C2semidirect
7. C127×#1441C2semidirect
8. C127×#1440C2semidirect
9. C127×#1440C2semidirect
10. C127×#1439C2semidirect
11. C127×#1438C2semidirect
12. C127×#1438C2semidirect
13. C127×#1437C2semidirect
14. C127×#1434C2semidirect
15. C127×C22⋊#95C2semidirect
147. C2×C22⋊C4×C127D4semidirect
164. #95×C127D4semidirect
640. #15501C127direct (N × H)
659. C2×#397C2×C127semidirect
660. C2×#394C2×C127semidirect
662. C2×#390C2×C127semidirect
663. C2×#386C2×C127semidirect
664. C2×#386C2×C127semidirect
665. #1441C2×C127semidirect
666. #1440C2×C127semidirect
667. #1440C2×C127semidirect
668. #1439C2×C127semidirect
669. #1438C2×C127semidirect
670. #1438C2×C127semidirect
671. #1437C2×C127semidirect
672. #1434C2×C127semidirect
673. C22⋊#95C2×C127semidirect
674. C127#15501direct (N × H)
806. C2×C22⋊C4D4×C127semidirect
823. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1272
C2×#394×C1272
C2×#392×C1272
C2×#390×C1272
C2×#386×C1272
C127×#14412
C127×#14402
C127×#14392
C127×#14382
C127×#14372
C127×#14342
C127×C22⋊#952
#15501127