Finite Group Databasebeta

← C127×#15297 #44578970

Subgroups — C127×#15297 #44578970

Order 32512.

2826 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C127C211yesmaximal, characteristic, complemented
2C2×#396×C127C211yesmaximal, characteristic, complemented
3C2×#388×C127C211yesmaximal, characteristic, complemented
4C2×#379×C127C211yesmaximal, characteristic
5C2×#379×C127C211yesmaximal, characteristic
6C2×#379×C127C211yesmaximal, characteristic
7C127×#1440C211yesmaximal, characteristic, complemented
8C127×#1440C211yesmaximal, characteristic, complemented
9C127×#1440C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1439C211yesmaximal, characteristic, complemented
13C127×#1439C211yesmaximal, characteristic, complemented
14C127×#1437C211yesmaximal, characteristic, complemented
15C127×#1437C211yesmaximal, characteristic, complemented
16C26×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic, complemented
18C22×C4⋊C4×C127C2211yescharacteristic, complemented
19C22×C4⋊C4×C127C2211yescharacteristic, complemented
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊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×C22⋊C4×C127C2211yescharacteristic
37C22×C22⋊C4×C127C2211yescharacteristic
38C22×C42×C127C2211yescharacteristic, complemented
39#397×C127—24no—
40#396×C127—24no—
41#388×C127—24no—
42#379×C127—24no—
43#379×C127—24no—
44#379×C127—24no—
45C2×#95×C127C2211yescharacteristic, complemented
46C2×#95×C127C2211yescharacteristic, complemented
47C2×#95×C127C2211yescharacteristic, complemented
48C2×#95×C127C2211yescharacteristic, complemented
49C2×#95×C127C2211yescharacteristic, complemented
50C2×#95×C127C2211yescharacteristic, complemented
51C2×#95×C127C2211yescharacteristic, complemented
52C2×#95×C127C2211yescharacteristic, complemented
53C2×#95×C127C2211yescharacteristic, complemented
54C2×#95×C127C2211yescharacteristic, complemented
55C2×#95×C127C2211yescharacteristic, complemented
56C2×#95×C127C2211yescharacteristic, complemented
57C25×C127—22no—
58C25×C127—22no—
59C25×C127—22no—
60C25×C127—22no—
61C25×C127—22no—
62C25×C127—22no—
63C25×C127—22no—
64C25×C127—22no—
65C25×C127—22no—
66C25×C127—41no—
67C25×C127—41no—
68C25×C127—41no—
69C25×C127—41no—
70C25×C127—41no—
71C25×C127—41no—
72C25×C127C2311yescharacteristic
73C25×C127C2311yescharacteristic
74C25×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2311yescharacteristic
78C23×C4×C127C2311yescharacteristic
79C23×C4×C127C2311yescharacteristic
80C23×C4×C127C2311yescharacteristic
81C23×C4×C127C2311yescharacteristic
82C23×C4×C127C2311yescharacteristic
83C23×C4×C127C2311yescharacteristic
84C23×C4×C127C2311yescharacteristic
85C23×C4×C127C2311yescharacteristic
86C23×C4×C127C2311yescharacteristic
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×C22⋊C4×C127—22no—
97C2×C22⋊C4×C127—22no—
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—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—41no—
130C2×C22⋊C4×C127—41no—
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×C127D414yes—
148C2×C22⋊C4×C127D414yes—
149C2×C22⋊C4×C127D414yes—
150C2×C42×C127—22no—
151C2×C42×C127—41no—
152C2×C42×C127—41no—
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×C127—41no—
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—28no—
202C24×C127—28no—
203C24×C127—28no—
204C24×C127—44no—
205C24×C127—44no—
206C24×C127—44no—
207C24×C127—44no—
208C24×C127—44no—
209C24×C127—44no—
210C24×C127—44no—
211C24×C127—44no—
212C24×C127—44no—
213C24×C127—44no—
214C24×C127—44no—
215C24×C127—44no—
216C24×C127—44no—
217C24×C127—44no—
218C24×C127—44no—
219C24×C127—44no—
220C24×C127—44no—
221C24×C127—44no—
222C24×C127—44no—
223C24×C127—44no—
224C24×C127—44no—
225C24×C127—44no—
226C24×C127—44no—
227C24×C127—44no—
228C24×C127—44no—
229C24×C127—44no—
230C24×C127—44no—
231C24×C127—44no—
232C24×C127—44no—
233C24×C127—44no—
234C24×C127—44no—
235C24×C127—44no—
236C24×C127C2×D412yes—
237C24×C127C2×D412yes—
238C24×C127C2×D412yes—
239C24×C127#4112yes—
240C24×C127#4112yes—
241C24×C127#4112yes—
242C24×C127#4112yes—
243C24×C127#4112yes—
244C24×C127#4112yes—
245C24×C127C2411yescharacteristic
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—21no—
315C22×C4×C127—21no—
316C22×C4×C127—21no—
317C22×C4×C127—21no—
318C22×C4×C127—21no—
319C22×C4×C127—21no—
320C22×C4×C127—21no—
321C22×C4×C127—21no—
322C22×C4×C127—21no—
323C22×C4×C127—21no—
324C22×C4×C127C2×D412yes—
325C22×C4×C127C2×D412yes—
326C22×C4×C127C2×D412yes—
327C22×C4×C127C2×D412yes—
328C22×C4×C127C2×D412yes—
329C22×C4×C127C2×D412yes—
330C4⋊C4×C127—44no—
331C4⋊C4×C127—44no—
332C4⋊C4×C127—44no—
333C22⋊C4×C127—28no—
334C22⋊C4×C127—44no—
335C22⋊C4×C127—44no—
336C22⋊C4×C127—44no—
337C22⋊C4×C127—44no—
338C22⋊C4×C127—44no—
339C22⋊C4×C127—44no—
340C22⋊C4×C127—44no—
341C22⋊C4×C127—44no—
342C22⋊C4×C127—44no—
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—
351C42×C127—44no—
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—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—22no—
397C23×C127—22no—
398C23×C127—22no—
399C23×C127—22no—
400C23×C127—22no—
401C23×C127—22no—
402C23×C127—22no—
403C23×C127—22no—
404C23×C127—22no—
405C23×C127—22no—
406C23×C127—416no—
407C23×C127—416no—
408C23×C127—416no—
409C23×C127—416no—
410C23×C127—416no—
411C23×C127—416no—
412C23×C127—416no—
413C23×C127—416no—
414C23×C127—416no—
415C23×C127—416no—
416C23×C127—416no—
417C23×C127—416no—
418C23×C127—416no—
419C23×C127—416no—
420C23×C127—416no—
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—41no—
457C23×C127—41no—
458C23×C127—41no—
459C23×C127—41no—
460C23×C127—41no—
461C23×C127—41no—
462C23×C127—41no—
463C23×C127—41no—
464C23×C127—41no—
465C23×C127—41no—
466C23×C127—41no—
467C23×C127—41no—
468C23×C127—41no—
469C23×C127#12114yes—
470C23×C127#12414yes—
471C23×C127#12614yes—
472C23×C127C22×D411yescharacteristic
473C23×C127C22×D411yescharacteristic
474C23×C127C22×D411yescharacteristic
475C23×C127C2×#4111yescharacteristic
476C23×C127C2×#4111yescharacteristic
477C23×C127C2×#4111yescharacteristic
478C23×C127C2×#4111yescharacteristic
479C23×C127C2×#4111yescharacteristic
480C23×C127C2×#4111yescharacteristic
481C23×C127H(5,𝔽2)11yescharacteristic
482C23×C127H(5,𝔽2)11yescharacteristic
483C23×C127H(5,𝔽2)11yescharacteristic
484C23×C127H(5,𝔽2)11yescharacteristic
485C23×C127H(5,𝔽2)11yescharacteristic
486C23×C127H(5,𝔽2)11yescharacteristic
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—22no—
504C2×C4×C127—22no—
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—41no—
562C2×C4×C127—41no—
563C2×C4×C127—41no—
564C2×C4×C127—41no—
565C2×C4×C127—41no—
566C2×C4×C127—41no—
567C2×C4×C127—41no—
568C2×C4×C127—41no—
569C2×C4×C127—41no—
570C2×C4×C127—41no—
571C22×C127—24no—
572C22×C127—24no—
573C22×C127—24no—
574C22×C127—24no—
575C22×C127—24no—
576C22×C127—24no—
577C22×C127—24no—
578C22×C127—24no—
579C22×C127—24no—
580C22×C127—464no—
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—42no—
600C22×C127—42no—
601C22×C127—42no—
602C22×C127—42no—
603C22×C127—42no—
604C22×C127—42no—
605C22×C127—42no—
606C22×C127—42no—
607C22×C127—42no—
608C22×C127—42no—
609C22×C127—42no—
610C22×C127—42no—
611C22×C127—42no—
612C22×C127—42no—
613C22×C127—42no—
614C22×C127—42no—
615C22×C127—42no—
616C22×C127—42no—
617C22×C127C2×#12111yescharacteristic
618C22×C127#52511yescharacteristic
619C22×C127#52511yescharacteristic
620C22×C127#52511yescharacteristic
621C22×C127C2×#12411yescharacteristic
622C22×C127C2×#12611yescharacteristic
623C22×C127#53411yescharacteristic
624C22×C127#53411yescharacteristic
625C22×C127#53511yescharacteristic
626C22×C127#53811yescharacteristic
627C22×C127#53811yescharacteristic
628C22×C127#53811yescharacteristic
629C22×C127#53811yescharacteristic
630C22×C127#53811yescharacteristic
631C22×C127#53811yescharacteristic
632C22×C127D4211yescharacteristic
633C22×C127D4211yescharacteristic
634C22×C127#54611yescharacteristic
635C22×C127#54611yescharacteristic
636C22×C127#54611yescharacteristic
637C22×C127#54611yescharacteristic
638C22×C127#54611yescharacteristic
639C22×C127#54611yescharacteristic
640C22×C127#54611yescharacteristic
641C22×C127#54611yescharacteristic
642C22×C127#55111yescharacteristic
643C22×C127#55111yescharacteristic
644C22×C127#55111yescharacteristic
645C22×C127#55111yescharacteristic
646C22×C127#55111yescharacteristic
647C22×C127#55111yescharacteristic
648C22×C127#55111yescharacteristic
649C22×C127#55111yescharacteristic
650C22×C127#56011yescharacteristic
651C22×C127#56011yescharacteristic
652C4×C127—42no—
653C4×C127—42no—
654C4×C127—42no—
655C4×C127—42no—
656C4×C127—42no—
657C4×C127—42no—
658C4×C127—81no—
659C4×C127—81no—
660C4×C127—81no—
661C4×C127—81no—
662C4×C127—81no—
663C4×C127—81no—
664#15297C12711yesmaximal, characteristic, direct product factor, Sylow
665C2×C127—44no—
666C2×C127—44no—
667C2×C127—44no—
668C2×C127#241111yescharacteristic
669C2×C127#242411yescharacteristic
670C2×C127#247211yescharacteristic
671C2×C127#247211yescharacteristic
672C2×C127#248011yescharacteristic
673C2×C127#248011yescharacteristic
674C2×C127#248011yescharacteristic
675C2×C127#253411yescharacteristic
676C2×C127#256111yescharacteristic
677C2×C127#266811yescharacteristic
678C2×C127#267811yescharacteristic
679C2×C127#268511yescharacteristic
680C2×C127#269711yescharacteristic
681C2×C127#273511yescharacteristic
682C2×C127#273511yescharacteristic
683C2×#397C2×C12711yescharacteristic, complemented
684C2×#396C2×C12711yescharacteristic, complemented
685C2×#388C2×C12711yescharacteristic, complemented
686C2×#379C2×C12711yescharacteristic
687C2×#379C2×C12711yescharacteristic
688C2×#379C2×C12711yescharacteristic
689#1440C2×C12711yescharacteristic, complemented
690#1440C2×C12711yescharacteristic, complemented
691#1440C2×C12711yescharacteristic, complemented
692#1439C2×C12711yescharacteristic, complemented
693#1439C2×C12711yescharacteristic, complemented
694#1439C2×C12711yescharacteristic, complemented
695#1439C2×C12711yescharacteristic, complemented
696#1437C2×C12711yescharacteristic, complemented
697#1437C2×C12711yescharacteristic, complemented
698C127#1529711yescharacteristic, direct product factor, Sylow
699C26C22×C12711yescharacteristic
700C22×C4⋊C4C22×C12711yescharacteristic, complemented
701C22×C4⋊C4C22×C12711yescharacteristic, complemented
702C22×C4⋊C4C22×C12711yescharacteristic, complemented
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
713C22×C22⋊C4C22×C12711yescharacteristic
714C22×C22⋊C4C22×C12711yescharacteristic
715C22×C22⋊C4C22×C12711yescharacteristic
716C22×C22⋊C4C22×C12711yescharacteristic
717C22×C22⋊C4C22×C12711yescharacteristic
718C22×C22⋊C4C22×C12711yescharacteristic
719C22×C22⋊C4C22×C12711yescharacteristic
720C22×C22⋊C4C22×C12711yescharacteristic
721C22×C42C22×C12711yescharacteristic, complemented
722#397—24no—
723#396—24no—
724#388—24no—
725#379—24no—
726#379—24no—
727#379—24no—
728C2×#95C22×C12711yescharacteristic, complemented
729C2×#95C22×C12711yescharacteristic, complemented
730C2×#95C22×C12711yescharacteristic, complemented
731C2×#95C22×C12711yescharacteristic, complemented
732C2×#95C22×C12711yescharacteristic, complemented
733C2×#95C22×C12711yescharacteristic, complemented
734C2×#95C22×C12711yescharacteristic, complemented
735C2×#95C22×C12711yescharacteristic, complemented
736C2×#95C22×C12711yescharacteristic, complemented
737C2×#95C22×C12711yescharacteristic, complemented
738C2×#95C22×C12711yescharacteristic, complemented
739C2×#95C22×C12711yescharacteristic, complemented
740C25—22no—
741C25—22no—
742C25—22no—
743C25—22no—
744C25—22no—
745C25—22no—
746C25—22no—
747C25—22no—
748C25—22no—
749C25—41no—
750C25—41no—
751C25—41no—
752C25—41no—
753C25—41no—
754C25—41no—
755C25C23×C12711yescharacteristic
756C25C23×C12711yescharacteristic
757C25C23×C12711yescharacteristic
758C23×C4C23×C12711yescharacteristic
759C23×C4C23×C12711yescharacteristic
760C23×C4C23×C12711yescharacteristic
761C23×C4C23×C12711yescharacteristic
762C23×C4C23×C12711yescharacteristic
763C23×C4C23×C12711yescharacteristic
764C23×C4C23×C12711yescharacteristic
765C23×C4C23×C12711yescharacteristic
766C23×C4C23×C12711yescharacteristic
767C23×C4C23×C12711yescharacteristic
768C23×C4C23×C12711yescharacteristic
769C23×C4C23×C12711yescharacteristic
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—41no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4—41no—
778C2×C4⋊C4—41no—
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—22no—
791C2×C22⋊C4—22no—
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—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
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—
831C2×C22⋊C4D4×C12714yes—
832C2×C22⋊C4D4×C12714yes—
833C2×C42—22no—
834C2×C42—41no—
835C2×C42—41no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—22no—
842#95—41no—
843#95—41no—
844#95—41no—
845#95—41no—
846#95—41no—
847#95—41no—
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—
883C24—21no—
884C24—28no—
885C24—28no—
886C24—28no—
887C24—44no—
888C24—44no—
889C24—44no—
890C24—44no—
891C24—44no—
892C24—44no—
893C24—44no—
894C24—44no—
895C24—44no—
896C24—44no—
897C24—44no—
898C24—44no—
899C24—44no—
900C24—44no—
901C24—44no—
902C24—44no—
903C24—44no—
904C24—44no—
905C24—44no—
906C24—44no—
907C24—44no—
908C24—44no—
909C24—44no—
910C24—44no—
911C24—44no—
912C24—44no—
913C24—44no—
914C24—44no—
915C24—44no—
916C24—44no—
917C24—44no—
918C24—44no—
919C24C2×D4×C12712yes—
920C24C2×D4×C12712yes—
921C24C2×D4×C12712yes—
922C24#41×C12712yes—
923C24#41×C12712yes—
924C24#41×C12712yes—
925C24#41×C12712yes—
926C24#41×C12712yes—
927C24#41×C12712yes—
928C24C24×C12711yescharacteristic
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—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4C2×D4×C12712yes—
1008C22×C4C2×D4×C12712yes—
1009C22×C4C2×D4×C12712yes—
1010C22×C4C2×D4×C12712yes—
1011C22×C4C2×D4×C12712yes—
1012C22×C4C2×D4×C12712yes—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C22⋊C4—28no—
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—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C42—44no—
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—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—416no—
1090C23—416no—
1091C23—416no—
1092C23—416no—
1093C23—416no—
1094C23—416no—
1095C23—416no—
1096C23—416no—
1097C23—416no—
1098C23—416no—
1099C23—416no—
1100C23—416no—
1101C23—416no—
1102C23—416no—
1103C23—416no—
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—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23#121×C12714yes—
1153C23#124×C12714yes—
1154C23#126×C12714yes—
1155C23C22×D4×C12711yescharacteristic
1156C23C22×D4×C12711yescharacteristic
1157C23C22×D4×C12711yescharacteristic
1158C23C2×#41×C12711yescharacteristic
1159C23C2×#41×C12711yescharacteristic
1160C23C2×#41×C12711yescharacteristic
1161C23C2×#41×C12711yescharacteristic
1162C23C2×#41×C12711yescharacteristic
1163C23C2×#41×C12711yescharacteristic
1164C23H(5,𝔽2)×C12711yescharacteristic
1165C23H(5,𝔽2)×C12711yescharacteristic
1166C23H(5,𝔽2)×C12711yescharacteristic
1167C23H(5,𝔽2)×C12711yescharacteristic
1168C23H(5,𝔽2)×C12711yescharacteristic
1169C23H(5,𝔽2)×C12711yescharacteristic
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
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—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—464no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22C2×#121×C12711yescharacteristic
1301C22#525×C12711yescharacteristic
1302C22#525×C12711yescharacteristic
1303C22#525×C12711yescharacteristic
1304C22C2×#124×C12711yescharacteristic
1305C22C2×#126×C12711yescharacteristic
1306C22#534×C12711yescharacteristic
1307C22#534×C12711yescharacteristic
1308C22#535×C12711yescharacteristic
1309C22#538×C12711yescharacteristic
1310C22#538×C12711yescharacteristic
1311C22#538×C12711yescharacteristic
1312C22#538×C12711yescharacteristic
1313C22#538×C12711yescharacteristic
1314C22#538×C12711yescharacteristic
1315C22D42×C12711yescharacteristic
1316C22D42×C12711yescharacteristic
1317C22#546×C12711yescharacteristic
1318C22#546×C12711yescharacteristic
1319C22#546×C12711yescharacteristic
1320C22#546×C12711yescharacteristic
1321C22#546×C12711yescharacteristic
1322C22#546×C12711yescharacteristic
1323C22#546×C12711yescharacteristic
1324C22#546×C12711yescharacteristic
1325C22#551×C12711yescharacteristic
1326C22#551×C12711yescharacteristic
1327C22#551×C12711yescharacteristic
1328C22#551×C12711yescharacteristic
1329C22#551×C12711yescharacteristic
1330C22#551×C12711yescharacteristic
1331C22#551×C12711yescharacteristic
1332C22#551×C12711yescharacteristic
1333C22#560×C12711yescharacteristic
1334C22#560×C12711yescharacteristic
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C2—44no—
1348C2—44no—
1349C2—44no—
1350C2C127×#241111yescharacteristic
1351C2C127×#242411yescharacteristic
1352C2C127×#247211yescharacteristic
1353C2C127×#247211yescharacteristic
1354C2C127×#248011yescharacteristic
1355C2C127×#248011yescharacteristic
1356C2C127×#248011yescharacteristic
1357C2C127×#253411yescharacteristic
1358C2C127×#256111yescharacteristic
1359C2C127×#266811yescharacteristic
1360C2C127×#267811yescharacteristic
1361C2C127×#268511yescharacteristic
1362C2C127×#269711yescharacteristic
1363C2C127×#273511yescharacteristic
1364C2C127×#273511yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#397×C127C2semidirect
2. C2×#396×C127C2semidirect
3. C2×#388×C127C2semidirect
7. C127×#1440C2semidirect
8. C127×#1440C2semidirect
9. C127×#1440C2semidirect
10. C127×#1439C2semidirect
11. C127×#1439C2semidirect
12. C127×#1439C2semidirect
13. C127×#1439C2semidirect
14. C127×#1437C2semidirect
15. C127×#1437C2semidirect
17. C22×C4⋊C4×C127C22semidirect
18. C22×C4⋊C4×C127C22semidirect
19. C22×C4⋊C4×C127C22semidirect
38. C22×C42×C127C22semidirect
45. C2×#95×C127C22semidirect
46. C2×#95×C127C22semidirect
47. C2×#95×C127C22semidirect
48. C2×#95×C127C22semidirect
49. C2×#95×C127C22semidirect
50. C2×#95×C127C22semidirect
51. C2×#95×C127C22semidirect
52. C2×#95×C127C22semidirect
53. C2×#95×C127C22semidirect
54. C2×#95×C127C22semidirect
55. C2×#95×C127C22semidirect
56. C2×#95×C127C22semidirect
664. #15297C127direct (N × H)
683. C2×#397C2×C127semidirect
684. C2×#396C2×C127semidirect
685. C2×#388C2×C127semidirect
689. #1440C2×C127semidirect
690. #1440C2×C127semidirect
691. #1440C2×C127semidirect
692. #1439C2×C127semidirect
693. #1439C2×C127semidirect
694. #1439C2×C127semidirect
695. #1439C2×C127semidirect
696. #1437C2×C127semidirect
697. #1437C2×C127semidirect
698. C127#15297direct (N × H)
700. C22×C4⋊C4C22×C127semidirect
701. C22×C4⋊C4C22×C127semidirect
702. C22×C4⋊C4C22×C127semidirect
721. C22×C42C22×C127semidirect
728. C2×#95C22×C127semidirect
729. C2×#95C22×C127semidirect
730. C2×#95C22×C127semidirect
731. C2×#95C22×C127semidirect
732. C2×#95C22×C127semidirect
733. C2×#95C22×C127semidirect
734. C2×#95C22×C127semidirect
735. C2×#95C22×C127semidirect
736. C2×#95C22×C127semidirect
737. C2×#95C22×C127semidirect
738. C2×#95C22×C127semidirect
739. C2×#95C22×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×#396×C1272
C2×#388×C1272
C2×#379×C1272
C127×#14402
C127×#14392
C127×#14372
#15297127