Finite Group Databasebeta

← C127×#13999 #44577672

Subgroups — C127×#13999 #44577672

Order 32512.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C127C211yesmaximal, characteristic, complemented
2C2×#386×C127C211yesmaximal, characteristic
3C2×#386×C127C211yesmaximal, characteristic
4C2×#386×C127C211yesmaximal, characteristic
5C2×#380×C127C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
7C22×#95×C127C211yesmaximal, characteristic, complemented
8C127×#1443C211yesmaximal, characteristic, complemented
9C127×#1442C211yesmaximal, characteristic, complemented
10C127×#1440C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1437C211yesmaximal, characteristic, complemented
13C127×#1436C211yesmaximal, characteristic, complemented
14C127×#1434C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C24×C4×C127C2211yescharacteristic
18C24×C4×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×C42×C127C2211yescharacteristic
32C22×C42×C127C2211yescharacteristic
33#388×C127—24no—
34#386×C127—24no—
35#386×C127—24no—
36#386×C127C418yescomplemented
37#380×C127—24no—
38C4×C22⋊C4×C127—24no—
39C2×#95×C127—24no—
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
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
57C2×#95×C127C2211yescharacteristic
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×C127C2×C414yes—
67C23×C4×C127—22no—
68C23×C4×C127—22no—
69C23×C4×C127—22no—
70C23×C4×C127—22no—
71C23×C4×C127—22no—
72C23×C4×C127—22no—
73C23×C4×C127—22no—
74C23×C4×C127—22no—
75C23×C4×C127—22no—
76C23×C4×C127—22no—
77C23×C4×C127—22no—
78C23×C4×C127—22no—
79C23×C4×C127—22no—
80C23×C4×C127—41no—
81C23×C4×C127—41no—
82C23×C4×C127—41no—
83C23×C4×C127—41no—
84C23×C4×C127—41no—
85C23×C4×C127—41no—
86C23×C4×C127C2×C414yes—
87C23×C4×C127D414yes—
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
100C23×C4×C127C2311yescharacteristic
101C2×C4⋊C4×C127—22no—
102C2×C4⋊C4×C127—22no—
103C2×C4⋊C4×C127—22no—
104C2×C4⋊C4×C127—22no—
105C2×C4⋊C4×C127—41no—
106C2×C4⋊C4×C127—41no—
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—41no—
125C2×C22⋊C4×C127—41no—
126C2×C22⋊C4×C127—41no—
127C2×C22⋊C4×C127—41no—
128C2×C22⋊C4×C127—41no—
129C2×C22⋊C4×C127—41no—
130C2×C22⋊C4×C127C2×C414yes—
131C2×C22⋊C4×C127C2×C414yescomplemented
132C2×C22⋊C4×C127C2×C414yescomplemented
133C2×C22⋊C4×C127D414yes—
134C2×C42×C127—22no—
135C2×C42×C127—22no—
136C2×C42×C127—22no—
137C2×C42×C127—22no—
138C2×C42×C127—41no—
139C2×C42×C127—41no—
140#95×C127—22no—
141#95×C127—22no—
142#95×C127—22no—
143#95×C127—22no—
144#95×C127—22no—
145#95×C127—22no—
146#95×C127—22no—
147#95×C127—22no—
148#95×C127—22no—
149#95×C127—22no—
150#95×C127—22no—
151#95×C127—22no—
152#95×C127—22no—
153#95×C127—41no—
154#95×C127—41no—
155#95×C127C2×C414yescomplemented
156#95×C127C2×C414yescomplemented
157#95×C127D414yescomplemented
158C24×C127—21no—
159C24×C127—21no—
160C24×C127—21no—
161C24×C127—21no—
162C24×C127—21no—
163C24×C127—21no—
164C24×C127—21no—
165C24×C127—21no—
166C24×C127—21no—
167C24×C127—21no—
168C24×C127—21no—
169C24×C127—21no—
170C24×C127—21no—
171C24×C127—21no—
172C24×C127—21no—
173C24×C127—21no—
174C24×C127—21no—
175C24×C127—21no—
176C24×C127—21no—
177C24×C127—21no—
178C24×C127—21no—
179C24×C127—21no—
180C24×C127C22×C412yes—
181C24×C127C22×C412yes—
182C24×C127C2×D412yes—
183C24×C127C2×D412yes—
184C24×C127#4112yes—
185C24×C127#4112yes—
186C24×C127#4112yes—
187C24×C127#4112yes—
188C24×C127C2411yescharacteristic
189C2×D4×C127—28no—
190C2×D4×C127—28no—
191C2×D4×C127—28no—
192C2×D4×C127—44no—
193C2×D4×C127—44no—
194C2×D4×C127—44no—
195C2×D4×C127—44no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—28no—
205C22×C4×C127—28no—
206C22×C4×C127—28no—
207C22×C4×C127—21no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—21no—
216C22×C4×C127—21no—
217C22×C4×C127—21no—
218C22×C4×C127—21no—
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—21no—
224C22×C4×C127—21no—
225C22×C4×C127—21no—
226C22×C4×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—21no—
248C22×C4×C127—21no—
249C22×C4×C127—21no—
250C22×C4×C127—21no—
251C22×C4×C127—21no—
252C22×C4×C127—21no—
253C22×C4×C127—21no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—21no—
260C22×C4×C127—21no—
261C22×C4×C127—28no—
262C22×C4×C127—28no—
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—44no—
278C22×C4×C127—44no—
279C22×C4×C127—44no—
280C22×C4×C127—44no—
281C22×C4×C127—44no—
282C22×C4×C127—44no—
283C22×C4×C127—44no—
284C22×C4×C127—44no—
285C22×C4×C127—44no—
286C22×C4×C127—44no—
287C22×C4×C127—44no—
288C22×C4×C127—44no—
289C22×C4×C127—44no—
290C22×C4×C127—44no—
291C22×C4×C127—44no—
292C22×C4×C127—44no—
293C22×C4×C127C22×C412yes—
294C22×C4×C127C22×C412yes—
295C22×C4×C127C22×C412yes—
296C22×C4×C127C22×C412yes—
297C22×C4×C127C22×C412yes—
298C22×C4×C127C2×D412yes—
299C22×C4×C127C2×D412yes—
300C22×C4×C127C2×D412yes—
301C22×C4×C127C2×D412yes—
302C22×C4×C127C2×D412yes—
303C22×C4×C127C2×D412yes—
304C22×C4×C127C2×D412yes—
305C22×C4×C127#4112yes—
306C22×C4×C127#4112yes—
307C22×C4×C127#4112yes—
308C4⋊C4×C127—44no—
309C4⋊C4×C127—44no—
310C22⋊C4×C127—28no—
311C22⋊C4×C127—28no—
312C22⋊C4×C127—28no—
313C22⋊C4×C127—44no—
314C22⋊C4×C127—44no—
315C22⋊C4×C127—44no—
316C22⋊C4×C127—44no—
317C22⋊C4×C127—44no—
318C22⋊C4×C127—44no—
319C42×C127—44no—
320C42×C127—44no—
321C23×C127—22no—
322C23×C127—22no—
323C23×C127—22no—
324C23×C127—22no—
325C23×C127—22no—
326C23×C127—22no—
327C23×C127—22no—
328C23×C127—22no—
329C23×C127—22no—
330C23×C127—22no—
331C23×C127—22no—
332C23×C127—22no—
333C23×C127—22no—
334C23×C127—22no—
335C23×C127—22no—
336C23×C127—22no—
337C23×C127—22no—
338C23×C127—22no—
339C23×C127—22no—
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—41no—
357C23×C127—41no—
358C23×C127—41no—
359C23×C127—41no—
360C23×C127—41no—
361C23×C127—41no—
362C23×C127—41no—
363C23×C127—41no—
364C23×C127—41no—
365C23×C127—41no—
366C23×C127—41no—
367C23×C127—41no—
368C23×C127—41no—
369C23×C127—41no—
370C23×C127—41no—
371C23×C127—41no—
372C23×C127—41no—
373C23×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#11714yes—
385C23×C127C4×D414yes—
386C23×C127C4×D414yes—
387C23×C127#12114yes—
388C23×C127#12314yes—
389C23×C127#12414yes—
390C23×C127#12614yes—
391C23×C127C23×C411yescharacteristic
392C23×C127C22×D411yescharacteristic
393C23×C127C22×D411yescharacteristic
394C23×C127C22×D411yescharacteristic
395C23×C127C2×#4111yescharacteristic
396C23×C127C2×#4111yescharacteristic
397C23×C127C2×#4111yescharacteristic
398C23×C127C2×#4111yescharacteristic
399C23×C127C2×#4111yescharacteristic
400C23×C127C2×#4111yescharacteristic
401C23×C127C2×#4111yescharacteristic
402C23×C127H(5,𝔽2)11yescharacteristic
403C23×C127H(5,𝔽2)11yescharacteristic
404C23×C127H(5,𝔽2)11yescharacteristic
405C23×C1272−1+411yescharacteristic
406D4×C127—416no—
407C2×C4×C127—22no—
408C2×C4×C127—22no—
409C2×C4×C127—22no—
410C2×C4×C127—22no—
411C2×C4×C127—22no—
412C2×C4×C127—22no—
413C2×C4×C127—22no—
414C2×C4×C127—22no—
415C2×C4×C127—22no—
416C2×C4×C127—22no—
417C2×C4×C127—22no—
418C2×C4×C127—22no—
419C2×C4×C127—22no—
420C2×C4×C127—22no—
421C2×C4×C127—22no—
422C2×C4×C127—22no—
423C2×C4×C127—22no—
424C2×C4×C127—22no—
425C2×C4×C127—22no—
426C2×C4×C127—22no—
427C2×C4×C127—22no—
428C2×C4×C127—22no—
429C2×C4×C127—22no—
430C2×C4×C127—22no—
431C2×C4×C127—22no—
432C2×C4×C127—22no—
433C2×C4×C127—22no—
434C2×C4×C127—22no—
435C2×C4×C127—22no—
436C2×C4×C127—22no—
437C2×C4×C127—22no—
438C2×C4×C127—22no—
439C2×C4×C127—22no—
440C2×C4×C127—22no—
441C2×C4×C127—22no—
442C2×C4×C127—22no—
443C2×C4×C127—22no—
444C2×C4×C127—22no—
445C2×C4×C127—22no—
446C2×C4×C127—416no—
447C2×C4×C127—416no—
448C2×C4×C127—416no—
449C2×C4×C127—41no—
450C2×C4×C127—41no—
451C2×C4×C127—41no—
452C2×C4×C127—41no—
453C2×C4×C127—41no—
454C2×C4×C127—41no—
455C2×C4×C127—41no—
456C2×C4×C127—41no—
457C2×C4×C127—41no—
458C2×C4×C127—41no—
459C2×C4×C127—41no—
460C2×C4×C127—41no—
461C2×C4×C127—41no—
462C2×C4×C127—41no—
463C2×C4×C127—41no—
464C2×C4×C127—41no—
465C2×C4×C127—41no—
466C2×C4×C127—41no—
467C2×C4×C127—41no—
468C2×C4×C127—41no—
469C2×C4×C127—41no—
470C2×C4×C127—41no—
471C2×C4×C127—41no—
472C2×C4×C127—41no—
473C2×C4×C127—41no—
474C2×C4×C127—41no—
475C2×C4×C127—41no—
476C2×C4×C127—41no—
477C2×C4×C127—41no—
478C2×C4×C127—41no—
479C2×C4×C127—41no—
480C2×C4×C127—41no—
481C2×C4×C127—41no—
482C2×C4×C127—41no—
483C2×C4×C127—41no—
484C2×C4×C127—41no—
485C2×C4×C127—41no—
486C2×C4×C127—41no—
487C2×C4×C127—41no—
488C2×C4×C127—41no—
489C2×C4×C127—41no—
490C2×C4×C127—41no—
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×C127C4×D414yes—
500C2×C4×C127#12114yes—
501C22×C127—24no—
502C22×C127—24no—
503C22×C127—24no—
504C22×C127—24no—
505C22×C127—24no—
506C22×C127—24no—
507C22×C127—24no—
508C22×C127—24no—
509C22×C127—24no—
510C22×C127—24no—
511C22×C127—24no—
512C22×C127—24no—
513C22×C127—24no—
514C22×C127—24no—
515C22×C127—42no—
516C22×C127—42no—
517C22×C127—42no—
518C22×C127—42no—
519C22×C127—42no—
520C22×C127—42no—
521C22×C127—42no—
522C22×C127—81no—
523C22×C127—81no—
524C22×C127—81no—
525C22×C127—81no—
526C22×C127—81no—
527C22×C127—81no—
528C22×C127—81no—
529C22×C127—81no—
530C22×C127#38818yescomplemented
531C22×C127C2×#11711yescharacteristic
532C22×C127C2×C4×D411yescharacteristic
533C22×C127C2×C4×D411yescharacteristic
534C22×C127C2×C4×D411yescharacteristic
535C22×C127C4×#4111yescharacteristic
536C22×C127#51811yescharacteristic
537C22×C127#52011yescharacteristic
538C22×C127C2×#12111yescharacteristic
539C22×C127C2×#12111yescharacteristic
540C22×C127C2×#12311yescharacteristic
541C22×C127#52511yescharacteristic
542C22×C127C2×#12411yescharacteristic
543C22×C127C2×#12611yescharacteristic
544C22×C127#52911yescharacteristic
545C22×C127#53211yescharacteristic
546C22×C127#53411yescharacteristic
547C22×C127#53711yescharacteristic
548C22×C127#53811yescharacteristic
549C22×C127#53911yescharacteristic
550C22×C127D4211yescharacteristic
551C22×C127#54611yescharacteristic
552C22×C127#54611yescharacteristic
553C22×C127#54611yescharacteristic
554C22×C127#54611yescharacteristic
555C22×C127#54711yescharacteristic
556C22×C127#54811yescharacteristic
557C22×C127#55111yescharacteristic
558C22×C127#55111yescharacteristic
559C22×C127#55111yescharacteristic
560C22×C127#55111yescharacteristic
561C22×C127#55211yescharacteristic
562C22×C127#55211yescharacteristic
563C22×C127#55311yescharacteristic
564C22×C127#55311yescharacteristic
565C22×C127#55311yescharacteristic
566C4×C127—24no—
567C4×C127—24no—
568C4×C127—42no—
569C4×C127—42no—
570C4×C127—42no—
571C4×C127—42no—
572C4×C127—42no—
573C4×C127—42no—
574C4×C127—42no—
575C4×C127—42no—
576C4×C127—42no—
577C4×C127—81no—
578C4×C127—81no—
579#13999C12711yesmaximal, characteristic, direct product factor, Sylow
580C2×C127—28no—
581C2×C127—82no—
582C2×C127C2×#38811yescharacteristic
583C2×C127C4×#12111yescharacteristic
584C2×C127#232511yescharacteristic
585C2×C127#235211yescharacteristic
586C2×C127#235311yescharacteristic
587C2×C127#235811yescharacteristic
588C2×C127#235911yescharacteristic
589C2×C127#241211yescharacteristic
590C2×C127#241611yescharacteristic
591C2×C127#247211yescharacteristic
592C2×C127#248111yescharacteristic
593C2×C127#248811yescharacteristic
594C2×C127#249811yescharacteristic
595C2×C127#251011yescharacteristic
596C2×C127#254311yescharacteristic
597C2×#388C2×C12711yescharacteristic, complemented
598C2×#386C2×C12711yescharacteristic
599C2×#386C2×C12711yescharacteristic
600C2×#386C2×C12711yescharacteristic
601C2×#380C2×C12711yescharacteristic, complemented
602C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
603C22×#95C2×C12711yescharacteristic, complemented
604#1443C2×C12711yescharacteristic, complemented
605#1442C2×C12711yescharacteristic, complemented
606#1440C2×C12711yescharacteristic, complemented
607#1439C2×C12711yescharacteristic, complemented
608#1437C2×C12711yescharacteristic, complemented
609#1436C2×C12711yescharacteristic, complemented
610#1434C2×C12711yescharacteristic, complemented
611C22⋊#95C2×C12711yescharacteristic, complemented
612C127#1399911yescharacteristic, direct product factor, Sylow
613C23×D4C22×C12711yescharacteristic
614C24×C4C22×C12711yescharacteristic
615C24×C4C22×C12711yescharacteristic
616C24×C4C22×C12711yescharacteristic
617C22×C4⋊C4C22×C12711yescharacteristic
618C22×C4⋊C4C22×C12711yescharacteristic
619C22×C22⋊C4C22×C12711yescharacteristic
620C22×C22⋊C4C22×C12711yescharacteristic
621C22×C22⋊C4C22×C12711yescharacteristic
622C22×C22⋊C4C22×C12711yescharacteristic
623C22×C22⋊C4C22×C12711yescharacteristic
624C22×C22⋊C4C22×C12711yescharacteristic
625C22×C22⋊C4C22×C12711yescharacteristic
626C22×C22⋊C4C22×C12711yescharacteristic
627C22×C22⋊C4C22×C12711yescharacteristic
628C22×C42C22×C12711yescharacteristic
629C22×C42C22×C12711yescharacteristic
630#388—24no—
631#386—24no—
632#386—24no—
633#386C4×C12718yescomplemented
634#380—24no—
635C4×C22⋊C4—24no—
636C2×#95—24no—
637C2×#95C22×C12711yescharacteristic
638C2×#95C22×C12711yescharacteristic
639C2×#95C22×C12711yescharacteristic
640C2×#95C22×C12711yescharacteristic
641C2×#95C22×C12711yescharacteristic
642C2×#95C22×C12711yescharacteristic
643C2×#95C22×C12711yescharacteristic
644C2×#95C22×C12711yescharacteristic
645C2×#95C22×C12711yescharacteristic
646C2×#95C22×C12711yescharacteristic
647C2×#95C22×C12711yescharacteristic
648C2×#95C22×C12711yescharacteristic
649C2×#95C22×C12711yescharacteristic
650C2×#95C22×C12711yescharacteristic
651C2×#95C22×C12711yescharacteristic
652C2×#95C22×C12711yescharacteristic
653C2×#95C22×C12711yescharacteristic
654C2×#95C22×C12711yescharacteristic
655C25C23×C12711yescharacteristic
656C25C23×C12711yescharacteristic
657C22×D4—22no—
658C22×D4—22no—
659C22×D4—22no—
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4C2×C4×C12714yes—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—41no—
678C23×C4—41no—
679C23×C4—41no—
680C23×C4—41no—
681C23×C4—41no—
682C23×C4—41no—
683C23×C4C2×C4×C12714yes—
684C23×C4D4×C12714yes—
685C23×C4C23×C12711yescharacteristic
686C23×C4C23×C12711yescharacteristic
687C23×C4C23×C12711yescharacteristic
688C23×C4C23×C12711yescharacteristic
689C23×C4C23×C12711yescharacteristic
690C23×C4C23×C12711yescharacteristic
691C23×C4C23×C12711yescharacteristic
692C23×C4C23×C12711yescharacteristic
693C23×C4C23×C12711yescharacteristic
694C23×C4C23×C12711yescharacteristic
695C23×C4C23×C12711yescharacteristic
696C23×C4C23×C12711yescharacteristic
697C23×C4C23×C12711yescharacteristic
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—41no—
703C2×C4⋊C4—41no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4C2×C4×C12714yes—
728C2×C22⋊C4C2×C4×C12714yescomplemented
729C2×C22⋊C4C2×C4×C12714yescomplemented
730C2×C22⋊C4D4×C12714yes—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—22no—
735C2×C42—41no—
736C2×C42—41no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—22no—
749#95—22no—
750#95—41no—
751#95—41no—
752#95C2×C4×C12714yescomplemented
753#95C2×C4×C12714yescomplemented
754#95D4×C12714yescomplemented
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24C22×C4×C12712yes—
778C24C22×C4×C12712yes—
779C24C2×D4×C12712yes—
780C24C2×D4×C12712yes—
781C24#41×C12712yes—
782C24#41×C12712yes—
783C24#41×C12712yes—
784C24#41×C12712yes—
785C24C24×C12711yescharacteristic
786C2×D4—28no—
787C2×D4—28no—
788C2×D4—28no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—28no—
803C22×C4—28no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—28no—
859C22×C4—28no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4C22×C4×C12712yes—
891C22×C4C22×C4×C12712yes—
892C22×C4C22×C4×C12712yes—
893C22×C4C22×C4×C12712yes—
894C22×C4C22×C4×C12712yes—
895C22×C4C2×D4×C12712yes—
896C22×C4C2×D4×C12712yes—
897C22×C4C2×D4×C12712yes—
898C22×C4C2×D4×C12712yes—
899C22×C4C2×D4×C12712yes—
900C22×C4C2×D4×C12712yes—
901C22×C4C2×D4×C12712yes—
902C22×C4#41×C12712yes—
903C22×C4#41×C12712yes—
904C22×C4#41×C12712yes—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C22⋊C4—28no—
908C22⋊C4—28no—
909C22⋊C4—28no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C42—44no—
917C42—44no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23#117×C12714yes—
982C23C4×D4×C12714yes—
983C23C4×D4×C12714yes—
984C23#121×C12714yes—
985C23#123×C12714yes—
986C23#124×C12714yes—
987C23#126×C12714yes—
988C23C23×C4×C12711yescharacteristic
989C23C22×D4×C12711yescharacteristic
990C23C22×D4×C12711yescharacteristic
991C23C22×D4×C12711yescharacteristic
992C23C2×#41×C12711yescharacteristic
993C23C2×#41×C12711yescharacteristic
994C23C2×#41×C12711yescharacteristic
995C23C2×#41×C12711yescharacteristic
996C23C2×#41×C12711yescharacteristic
997C23C2×#41×C12711yescharacteristic
998C23C2×#41×C12711yescharacteristic
999C23H(5,𝔽2)×C12711yescharacteristic
1000C23H(5,𝔽2)×C12711yescharacteristic
1001C23H(5,𝔽2)×C12711yescharacteristic
1002C232−1+4×C12711yescharacteristic
1003D4—416no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—416no—
1044C2×C4—416no—
1045C2×C4—416no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4C4×D4×C12714yes—
1097C2×C4#121×C12714yes—
1098C22—24no—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—24no—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—24no—
1111C22—24no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22—81no—
1124C22—81no—
1125C22—81no—
1126C22—81no—
1127C22#388×C12718yescomplemented
1128C22C2×#117×C12711yescharacteristic
1129C22C2×C4×D4×C12711yescharacteristic
1130C22C2×C4×D4×C12711yescharacteristic
1131C22C2×C4×D4×C12711yescharacteristic
1132C22C4×#41×C12711yescharacteristic
1133C22#518×C12711yescharacteristic
1134C22#520×C12711yescharacteristic
1135C22C2×#121×C12711yescharacteristic
1136C22C2×#121×C12711yescharacteristic
1137C22C2×#123×C12711yescharacteristic
1138C22#525×C12711yescharacteristic
1139C22C2×#124×C12711yescharacteristic
1140C22C2×#126×C12711yescharacteristic
1141C22#529×C12711yescharacteristic
1142C22#532×C12711yescharacteristic
1143C22#534×C12711yescharacteristic
1144C22#537×C12711yescharacteristic
1145C22#538×C12711yescharacteristic
1146C22#539×C12711yescharacteristic
1147C22D42×C12711yescharacteristic
1148C22#546×C12711yescharacteristic
1149C22#546×C12711yescharacteristic
1150C22#546×C12711yescharacteristic
1151C22#546×C12711yescharacteristic
1152C22#547×C12711yescharacteristic
1153C22#548×C12711yescharacteristic
1154C22#551×C12711yescharacteristic
1155C22#551×C12711yescharacteristic
1156C22#551×C12711yescharacteristic
1157C22#551×C12711yescharacteristic
1158C22#552×C12711yescharacteristic
1159C22#552×C12711yescharacteristic
1160C22#553×C12711yescharacteristic
1161C22#553×C12711yescharacteristic
1162C22#553×C12711yescharacteristic
1163C4—24no—
1164C4—24no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—42no—
1171C4—42no—
1172C4—42no—
1173C4—42no—
1174C4—81no—
1175C4—81no—
1176C2—28no—
1177C2—82no—
1178C2C2×#388×C12711yescharacteristic
1179C2C4×#121×C12711yescharacteristic
1180C2C127×#232511yescharacteristic
1181C2C127×#235211yescharacteristic
1182C2C127×#235311yescharacteristic
1183C2C127×#235811yescharacteristic
1184C2C127×#235911yescharacteristic
1185C2C127×#241211yescharacteristic
1186C2C127×#241611yescharacteristic
1187C2C127×#247211yescharacteristic
1188C2C127×#248111yescharacteristic
1189C2C127×#248811yescharacteristic
1190C2C127×#249811yescharacteristic
1191C2C127×#251011yescharacteristic
1192C2C127×#254311yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#388×C127C2semidirect
5. C2×#380×C127C2semidirect
6. C2×C4×C22⋊C4×C127C2semidirect
7. C22×#95×C127C2semidirect
8. C127×#1443C2semidirect
9. C127×#1442C2semidirect
10. C127×#1440C2semidirect
11. C127×#1439C2semidirect
12. C127×#1437C2semidirect
13. C127×#1436C2semidirect
14. C127×#1434C2semidirect
15. C127×C22⋊#95C2semidirect
36. #386×C127C4semidirect
131. C2×C22⋊C4×C127C2×C4semidirect
132. C2×C22⋊C4×C127C2×C4semidirect
155. #95×C127C2×C4semidirect
156. #95×C127C2×C4semidirect
157. #95×C127D4semidirect
530. C22×C127#388semidirect
579. #13999C127direct (N × H)
597. C2×#388C2×C127semidirect
601. C2×#380C2×C127semidirect
602. C2×C4×C22⋊C4C2×C127semidirect
603. C22×#95C2×C127semidirect
604. #1443C2×C127semidirect
605. #1442C2×C127semidirect
606. #1440C2×C127semidirect
607. #1439C2×C127semidirect
608. #1437C2×C127semidirect
609. #1436C2×C127semidirect
610. #1434C2×C127semidirect
611. C22⋊#95C2×C127semidirect
612. C127#13999direct (N × H)
633. #386C4×C127semidirect
728. C2×C22⋊C4C2×C4×C127semidirect
729. C2×C22⋊C4C2×C4×C127semidirect
752. #95C2×C4×C127semidirect
753. #95C2×C4×C127semidirect
754. #95D4×C127semidirect
1127. C22#388×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1272
C2×#386×C1272
C2×#380×C1272
C2×C4×C22⋊C4×C1272
C22×#95×C1272
C127×#14432
C127×#14422
C127×#14402
C127×#14392
C127×#14372
C127×#14362
C127×#14342
C127×C22⋊#952
#13999127