Finite Group Databasebeta

← C127×#16530 #44580203

Subgroups — C127×#16530 #44580203

Order 32512.

1914 conjugacy classes of subgroups.

The subgroup lattice has 1292 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
5C127×#1442C211yesmaximal, characteristic, complemented
6C127×#1440C211yesmaximal, characteristic, complemented
7C127×#1440C211yesmaximal, characteristic, complemented
8C127×#1440C211yesmaximal, characteristic, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1438C211yesmaximal, characteristic, complemented
11C127×#1438C211yesmaximal, characteristic, complemented
12C127×#1438C211yesmaximal, characteristic, complemented
13C127×#1438C211yesmaximal, characteristic, complemented
14C127×#1437C211yesmaximal, characteristic, complemented
15C127×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊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×C42×C127C2211yescharacteristic
37#397×C127—24no—
38#394×C127—24no—
39#392×C127—24no—
40#390×C127—24no—
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
55C25×C127C2311yescharacteristic
56C25×C127C2311yescharacteristic
57C25×C127C2311yescharacteristic
58C22×D4×C127—22no—
59C22×D4×C127—22no—
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—41no—
67C22×D4×C127—41no—
68C22×D4×C127—41no—
69C22×D4×C127—41no—
70C22×D4×C127—41no—
71C22×D4×C127—41no—
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×C127D414yes—
79C23×C4×C127C2311yescharacteristic
80C23×C4×C127C2311yescharacteristic
81C23×C4×C127C2311yescharacteristic
82C23×C4×C127C2311yescharacteristic
83C23×C4×C127C2311yescharacteristic
84C23×C4×C127C2311yescharacteristic
85C23×C4×C127C2311yescharacteristic
86C23×C4×C127C2311yescharacteristic
87C23×C4×C127C2311yescharacteristic
88C23×C4×C127C2311yescharacteristic
89C23×C4×C127C2311yescharacteristic
90C23×C4×C127C2311yescharacteristic
91C2×C4⋊C4×C127—22no—
92C2×C4⋊C4×C127—41no—
93C2×C4⋊C4×C127—41no—
94C2×C4⋊C4×C127—41no—
95C2×C4⋊C4×C127—41no—
96C2×C4⋊C4×C127D414yescomplemented
97C2×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—41no—
119C2×C22⋊C4×C127—41no—
120C2×C22⋊C4×C127—41no—
121C2×C22⋊C4×C127—41no—
122C2×C22⋊C4×C127—41no—
123C2×C22⋊C4×C127—41no—
124C2×C22⋊C4×C127—41no—
125C2×C22⋊C4×C127—41no—
126C2×C22⋊C4×C127—41no—
127C2×C22⋊C4×C127—41no—
128C2×C22⋊C4×C127—41no—
129C2×C22⋊C4×C127—41no—
130C2×C22⋊C4×C127—41no—
131C2×C22⋊C4×C127—41no—
132C2×C22⋊C4×C127—41no—
133C2×C22⋊C4×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×C42×C127—22no—
143C2×C42×C127—41no—
144C2×C42×C127—41no—
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×C127—41no—
156#95×C127—41no—
157#95×C127—41no—
158#95×C127—41no—
159C24×C127—21no—
160C24×C127—21no—
161C24×C127—21no—
162C24×C127—21no—
163C24×C127—21no—
164C24×C127—21no—
165C24×C127—21no—
166C24×C127—21no—
167C24×C127—21no—
168C24×C127—21no—
169C24×C127—21no—
170C24×C127—21no—
171C24×C127—21no—
172C24×C127—21no—
173C24×C127—21no—
174C24×C127—21no—
175C24×C127—21no—
176C24×C127—21no—
177C24×C127—21no—
178C24×C127—21no—
179C24×C127—21no—
180C24×C127—21no—
181C24×C127—21no—
182C24×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×C127C2×D412yes—
202C24×C127C2×D412yes—
203C24×C127#4112yes—
204C24×C127C2411yescharacteristic
205C2×D4×C127—28no—
206C2×D4×C127—44no—
207C2×D4×C127—44no—
208C2×D4×C127—44no—
209C2×D4×C127—44no—
210C2×D4×C127—44no—
211C2×D4×C127—44no—
212C2×D4×C127—44no—
213C2×D4×C127—44no—
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—
226C22×C4×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—21no—
248C22×C4×C127—21no—
249C22×C4×C127—21no—
250C22×C4×C127—21no—
251C22×C4×C127—21no—
252C22×C4×C127—21no—
253C22×C4×C127—21no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—21no—
260C22×C4×C127—21no—
261C22×C4×C127—21no—
262C22×C4×C127—21no—
263C22×C4×C127—21no—
264C22×C4×C127—21no—
265C22×C4×C127—21no—
266C22×C4×C127—21no—
267C22×C4×C127—21no—
268C22×C4×C127—21no—
269C22×C4×C127—21no—
270C22×C4×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×C127C2×D412yes—
303C22×C4×C127C2×D412yes—
304C22×C4×C127C2×D412yes—
305C22×C4×C127C2×D412yes—
306C22×C4×C127#4112yes—
307C22×C4×C127#4112yes—
308C22×C4×C127#4112yes—
309C22×C4×C127#4112yes—
310C4⋊C4×C127—44no—
311C4⋊C4×C127—44no—
312C22⋊C4×C127—44no—
313C22⋊C4×C127—44no—
314C22⋊C4×C127—44no—
315C22⋊C4×C127—44no—
316C22⋊C4×C127—44no—
317C22⋊C4×C127—44no—
318C22⋊C4×C127—44no—
319C22⋊C4×C127—44no—
320C22⋊C4×C127—44no—
321C22⋊C4×C127—44no—
322C22⋊C4×C127—44no—
323C22⋊C4×C127—44no—
324C22⋊C4×C127—44no—
325C22⋊C4×C127—44no—
326C22⋊C4×C127—44no—
327C42×C127—44no—
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—41no—
350C23×C127—41no—
351C23×C127—41no—
352C23×C127—41no—
353C23×C127—41no—
354C23×C127—41no—
355C23×C127—41no—
356C23×C127—41no—
357C23×C127—41no—
358C23×C127—41no—
359C23×C127—41no—
360C23×C127—41no—
361C23×C127—41no—
362C23×C127—41no—
363C23×C127—41no—
364C23×C127—41no—
365C23×C127—41no—
366C23×C127—41no—
367C23×C127—41no—
368C23×C127—41no—
369C23×C127—41no—
370C23×C127—41no—
371C23×C127—41no—
372C23×C127—41no—
373C23×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×C127C22×D411yescharacteristic
434C23×C127C22×D411yescharacteristic
435C23×C127C2×#4111yescharacteristic
436C23×C127C2×#4111yescharacteristic
437C23×C127C2×#4111yescharacteristic
438C23×C127C2×#4111yescharacteristic
439C23×C127C2×#4111yescharacteristic
440C23×C127H(5,𝔽2)11yescharacteristic
441C23×C127H(5,𝔽2)11yescharacteristic
442C23×C127H(5,𝔽2)11yescharacteristic
443C23×C127H(5,𝔽2)11yescharacteristic
444C23×C127H(5,𝔽2)11yescharacteristic
445C23×C127H(5,𝔽2)11yescharacteristic
446C23×C127H(5,𝔽2)11yescharacteristic
447C23×C127H(5,𝔽2)11yescharacteristic
448D4×C127—416no—
449D4×C127—416no—
450D4×C127—416no—
451C2×C4×C127—22no—
452C2×C4×C127—22no—
453C2×C4×C127—22no—
454C2×C4×C127—22no—
455C2×C4×C127—22no—
456C2×C4×C127—22no—
457C2×C4×C127—22no—
458C2×C4×C127—22no—
459C2×C4×C127—22no—
460C2×C4×C127—22no—
461C2×C4×C127—22no—
462C2×C4×C127—22no—
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—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×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#12314yes—
535C22×C127—42no—
536C22×C127—42no—
537C22×C127—42no—
538C22×C127—42no—
539C22×C127—42no—
540C22×C127—42no—
541C22×C127—42no—
542C22×C127—42no—
543C22×C127—42no—
544C22×C127—42no—
545C22×C127—42no—
546C22×C127—42no—
547C22×C127—42no—
548C22×C127—42no—
549C22×C127—42no—
550C22×C127—42no—
551C22×C127—42no—
552C22×C127—42no—
553C22×C127—42no—
554C22×C127—42no—
555C22×C127—42no—
556C22×C127—81no—
557C22×C127—81no—
558C22×C127—81no—
559C22×C127—81no—
560C22×C127—81no—
561C22×C127—81no—
562C22×C127—81no—
563C22×C127—81no—
564C22×C127—81no—
565C22×C127—81no—
566C22×C127—81no—
567C22×C127—81no—
568C22×C127—81no—
569C22×C127—81no—
570C22×C127—81no—
571C22×C127—81no—
572C22×C127—81no—
573C22×C127—81no—
574C22×C127—81no—
575C22×C127—81no—
576C22×C127—81no—
577C22×C127—81no—
578C22×C127—81no—
579C22×C127—81no—
580C22×C127C2×#12311yescharacteristic
581C22×C127#52911yescharacteristic
582C22×C127#53211yescharacteristic
583C22×C127#53411yescharacteristic
584C22×C127#53411yescharacteristic
585C22×C127#53411yescharacteristic
586C22×C127#53511yescharacteristic
587C22×C127#53811yescharacteristic
588C22×C127#53811yescharacteristic
589C22×C127#53811yescharacteristic
590C22×C127#53811yescharacteristic
591C22×C127#53811yescharacteristic
592C22×C127#53811yescharacteristic
593C22×C127#53811yescharacteristic
594C22×C127#53811yescharacteristic
595C22×C127#54011yescharacteristic
596C22×C127#54011yescharacteristic
597C22×C127#54011yescharacteristic
598C22×C127#54011yescharacteristic
599C22×C127D4211yescharacteristic
600C22×C127#54611yescharacteristic
601C22×C127#54611yescharacteristic
602C22×C127#54611yescharacteristic
603C22×C127#54611yescharacteristic
604C22×C127#55011yescharacteristic
605C22×C127#55011yescharacteristic
606C22×C127#55111yescharacteristic
607C22×C127#55311yescharacteristic
608C22×C127#55311yescharacteristic
609C22×C127#55511yescharacteristic
610C22×C127#55911yescharacteristic
611C22×C127#56011yescharacteristic
612C22×C127#56011yescharacteristic
613C22×C127#56011yescharacteristic
614C22×C127H(3,𝔽4)11yescharacteristic
615C4×C127—24no—
616C4×C127—42no—
617C4×C127—42no—
618C4×C127—42no—
619C4×C127—42no—
620C4×C127—42no—
621C4×C127—81no—
622C4×C127—81no—
623C4×C127—81no—
624C4×C127—81no—
625C4×C127—81no—
626C4×C127—81no—
627#16530C12711yesmaximal, characteristic, direct product factor, Sylow
628C2×C127—82no—
629C2×C127—82no—
630C2×C127—82no—
631C2×C127#242011yescharacteristic
632C2×C127#244511yescharacteristic
633C2×C127#255411yescharacteristic
634C2×C127#262211yescharacteristic
635C2×C127#264811yescharacteristic
636C2×C127#266111yescharacteristic
637C2×C127#266811yescharacteristic
638C2×C127#267311yescharacteristic
639C2×C127#268411yescharacteristic
640C2×C127#268811yescharacteristic
641C2×C127#271411yescharacteristic
642C2×C127#273311yescharacteristic
643C2×C127#279711yescharacteristic
644C2×C127#280311yescharacteristic
645C2×C127#282811yescharacteristic
646C2×#397C2×C12711yescharacteristic, complemented
647C2×#394C2×C12711yescharacteristic, complemented
648C2×#392C2×C12711yescharacteristic
649C2×#390C2×C12711yescharacteristic, complemented
650#1442C2×C12711yescharacteristic, complemented
651#1440C2×C12711yescharacteristic, complemented
652#1440C2×C12711yescharacteristic, complemented
653#1440C2×C12711yescharacteristic, complemented
654#1439C2×C12711yescharacteristic, complemented
655#1438C2×C12711yescharacteristic, complemented
656#1438C2×C12711yescharacteristic, complemented
657#1438C2×C12711yescharacteristic, complemented
658#1438C2×C12711yescharacteristic, complemented
659#1437C2×C12711yescharacteristic, complemented
660#1436C2×C12711yescharacteristic, complemented
661C127#1653011yescharacteristic, direct product factor, Sylow
662C23×D4C22×C12711yescharacteristic
663C23×D4C22×C12711yescharacteristic
664C23×D4C22×C12711yescharacteristic
665C22×C4⋊C4C22×C12711yescharacteristic
666C22×C4⋊C4C22×C12711yescharacteristic
667C22×C22⋊C4C22×C12711yescharacteristic
668C22×C22⋊C4C22×C12711yescharacteristic
669C22×C22⋊C4C22×C12711yescharacteristic
670C22×C22⋊C4C22×C12711yescharacteristic
671C22×C22⋊C4C22×C12711yescharacteristic
672C22×C22⋊C4C22×C12711yescharacteristic
673C22×C22⋊C4C22×C12711yescharacteristic
674C22×C22⋊C4C22×C12711yescharacteristic
675C22×C22⋊C4C22×C12711yescharacteristic
676C22×C22⋊C4C22×C12711yescharacteristic
677C22×C22⋊C4C22×C12711yescharacteristic
678C22×C22⋊C4C22×C12711yescharacteristic
679C22×C22⋊C4C22×C12711yescharacteristic
680C22×C22⋊C4C22×C12711yescharacteristic
681C22×C22⋊C4C22×C12711yescharacteristic
682C22×C42C22×C12711yescharacteristic
683#397—24no—
684#394—24no—
685#392—24no—
686#390—24no—
687C2×#95C22×C12711yescharacteristic
688C2×#95C22×C12711yescharacteristic
689C2×#95C22×C12711yescharacteristic
690C2×#95C22×C12711yescharacteristic
691C2×#95C22×C12711yescharacteristic
692C2×#95C22×C12711yescharacteristic
693C2×#95C22×C12711yescharacteristic
694C2×#95C22×C12711yescharacteristic
695C2×#95C22×C12711yescharacteristic
696C2×#95C22×C12711yescharacteristic
697C2×#95C22×C12711yescharacteristic
698C2×#95C22×C12711yescharacteristic
699C2×#95C22×C12711yescharacteristic
700C2×#95C22×C12711yescharacteristic
701C25C23×C12711yescharacteristic
702C25C23×C12711yescharacteristic
703C25C23×C12711yescharacteristic
704C22×D4—22no—
705C22×D4—22no—
706C22×D4—22no—
707C22×D4—22no—
708C22×D4—22no—
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—41no—
713C22×D4—41no—
714C22×D4—41no—
715C22×D4—41no—
716C22×D4—41no—
717C22×D4—41no—
718C22×D4—41no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4D4×C12714yes—
725C23×C4C23×C12711yescharacteristic
726C23×C4C23×C12711yescharacteristic
727C23×C4C23×C12711yescharacteristic
728C23×C4C23×C12711yescharacteristic
729C23×C4C23×C12711yescharacteristic
730C23×C4C23×C12711yescharacteristic
731C23×C4C23×C12711yescharacteristic
732C23×C4C23×C12711yescharacteristic
733C23×C4C23×C12711yescharacteristic
734C23×C4C23×C12711yescharacteristic
735C23×C4C23×C12711yescharacteristic
736C23×C4C23×C12711yescharacteristic
737C2×C4⋊C4—22no—
738C2×C4⋊C4—41no—
739C2×C4⋊C4—41no—
740C2×C4⋊C4—41no—
741C2×C4⋊C4—41no—
742C2×C4⋊C4D4×C12714yescomplemented
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—41no—
765C2×C22⋊C4—41no—
766C2×C22⋊C4—41no—
767C2×C22⋊C4—41no—
768C2×C22⋊C4—41no—
769C2×C22⋊C4—41no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C42—22no—
789C2×C42—41no—
790C2×C42—41no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—41no—
800#95—41no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95—41no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
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—
847C24C2×D4×C12712yes—
848C24C2×D4×C12712yes—
849C24#41×C12712yes—
850C24C24×C12711yescharacteristic
851C2×D4—28no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
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×C4C2×D4×C12712yes—
949C22×C4C2×D4×C12712yes—
950C22×C4C2×D4×C12712yes—
951C22×C4C2×D4×C12712yes—
952C22×C4#41×C12712yes—
953C22×C4#41×C12712yes—
954C22×C4#41×C12712yes—
955C22×C4#41×C12712yes—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C42—44no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
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—
1079C23C22×D4×C12711yescharacteristic
1080C23C22×D4×C12711yescharacteristic
1081C23C2×#41×C12711yescharacteristic
1082C23C2×#41×C12711yescharacteristic
1083C23C2×#41×C12711yescharacteristic
1084C23C2×#41×C12711yescharacteristic
1085C23C2×#41×C12711yescharacteristic
1086C23H(5,𝔽2)×C12711yescharacteristic
1087C23H(5,𝔽2)×C12711yescharacteristic
1088C23H(5,𝔽2)×C12711yescharacteristic
1089C23H(5,𝔽2)×C12711yescharacteristic
1090C23H(5,𝔽2)×C12711yescharacteristic
1091C23H(5,𝔽2)×C12711yescharacteristic
1092C23H(5,𝔽2)×C12711yescharacteristic
1093C23H(5,𝔽2)×C12711yescharacteristic
1094D4—416no—
1095D4—416no—
1096D4—416no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
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#123×C12714yes—
1181C22—42no—
1182C22—42no—
1183C22—42no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—42no—
1188C22—42no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22C2×#123×C12711yescharacteristic
1227C22#529×C12711yescharacteristic
1228C22#532×C12711yescharacteristic
1229C22#534×C12711yescharacteristic
1230C22#534×C12711yescharacteristic
1231C22#534×C12711yescharacteristic
1232C22#535×C12711yescharacteristic
1233C22#538×C12711yescharacteristic
1234C22#538×C12711yescharacteristic
1235C22#538×C12711yescharacteristic
1236C22#538×C12711yescharacteristic
1237C22#538×C12711yescharacteristic
1238C22#538×C12711yescharacteristic
1239C22#538×C12711yescharacteristic
1240C22#538×C12711yescharacteristic
1241C22#540×C12711yescharacteristic
1242C22#540×C12711yescharacteristic
1243C22#540×C12711yescharacteristic
1244C22#540×C12711yescharacteristic
1245C22D42×C12711yescharacteristic
1246C22#546×C12711yescharacteristic
1247C22#546×C12711yescharacteristic
1248C22#546×C12711yescharacteristic
1249C22#546×C12711yescharacteristic
1250C22#550×C12711yescharacteristic
1251C22#550×C12711yescharacteristic
1252C22#551×C12711yescharacteristic
1253C22#553×C12711yescharacteristic
1254C22#553×C12711yescharacteristic
1255C22#555×C12711yescharacteristic
1256C22#559×C12711yescharacteristic
1257C22#560×C12711yescharacteristic
1258C22#560×C12711yescharacteristic
1259C22#560×C12711yescharacteristic
1260C22H(3,𝔽4)×C12711yescharacteristic
1261C4—24no—
1262C4—42no—
1263C4—42no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C2—82no—
1274C2—82no—
1275C2—82no—
1276C2C127×#242011yescharacteristic
1277C2C127×#244511yescharacteristic
1278C2C127×#255411yescharacteristic
1279C2C127×#262211yescharacteristic
1280C2C127×#264811yescharacteristic
1281C2C127×#266111yescharacteristic
1282C2C127×#266811yescharacteristic
1283C2C127×#267311yescharacteristic
1284C2C127×#268411yescharacteristic
1285C2C127×#268811yescharacteristic
1286C2C127×#271411yescharacteristic
1287C2C127×#273311yescharacteristic
1288C2C127×#279711yescharacteristic
1289C2C127×#280311yescharacteristic
1290C2C127×#282811yescharacteristic
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. C127×#1442C2semidirect
6. C127×#1440C2semidirect
7. C127×#1440C2semidirect
8. C127×#1440C2semidirect
9. C127×#1439C2semidirect
10. C127×#1438C2semidirect
11. C127×#1438C2semidirect
12. C127×#1438C2semidirect
13. C127×#1438C2semidirect
14. C127×#1437C2semidirect
15. C127×#1436C2semidirect
96. C2×C4⋊C4×C127D4semidirect
627. #16530C127direct (N × H)
646. C2×#397C2×C127semidirect
647. C2×#394C2×C127semidirect
649. C2×#390C2×C127semidirect
650. #1442C2×C127semidirect
651. #1440C2×C127semidirect
652. #1440C2×C127semidirect
653. #1440C2×C127semidirect
654. #1439C2×C127semidirect
655. #1438C2×C127semidirect
656. #1438C2×C127semidirect
657. #1438C2×C127semidirect
658. #1438C2×C127semidirect
659. #1437C2×C127semidirect
660. #1436C2×C127semidirect
661. C127#16530direct (N × H)
742. C2×C4⋊C4D4×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
C127×#14422
C127×#14402
C127×#14392
C127×#14382
C127×#14372
C127×#14362
#16530127