Finite Group Databasebeta

← C127×#15311 #44578984

Subgroups — C127×#15311 #44578984

Order 32512.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C127C211yesmaximal, characteristic
2C2×#397×C127C211yesmaximal, characteristic, complemented
3C2×#395×C127C211yesmaximal, characteristic, complemented
4C2×#394×C127C211yesmaximal, characteristic
5C2×#386×C127C211yesmaximal, characteristic
6C2×#380×C127C211yesmaximal, characteristic, complemented
7C127×#1446C211yesmaximal, characteristic, complemented
8C127×#1440C211yesmaximal, characteristic, complemented
9C127×#1440C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1439C211yesmaximal, characteristic, complemented
12C127×#1439C211yesmaximal, characteristic, complemented
13C127×#1436C211yesmaximal, characteristic, complemented
14C127×#1436C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C24×C4×C127C2211yescharacteristic
19C2×#124×C127—24no—
20C2×#124×C127—24no—
21C2×#124×C127—24no—
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊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×C42×C127C2211yescharacteristic
38#397×C127—24no—
39#395×C127—24no—
40#394×C127—24no—
41#386×C127—24no—
42#380×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
57C2×#95×C127C2211yescharacteristic
58C2×#95×C127C2211yescharacteristic
59C25×C127C2311yescharacteristic
60C25×C127C2311yescharacteristic
61C22×Q8×C127—22no—
62C22×Q8×C127—22no—
63C22×Q8×C127—22no—
64C22×Q8×C127—22no—
65C22×Q8×C127—22no—
66C22×Q8×C127—41no—
67C22×Q8×C127—41no—
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×C127D414yes—
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×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
91C23×C4×C127C2311yescharacteristic
92C23×C4×C127C2311yescharacteristic
93C23×C4×C127C2311yescharacteristic
94C23×C4×C127C2311yescharacteristic
95#124×C127—232no—
96C2×C4⋊C4×C127—22no—
97C2×C4⋊C4×C127—22no—
98C2×C4⋊C4×C127—22no—
99C2×C4⋊C4×C127—22no—
100C2×C4⋊C4×C127—22no—
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×C4⋊C4×C127—41no—
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—22no—
132C2×C22⋊C4×C127—22no—
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×C127D414yes—
140C2×C22⋊C4×C127D414yes—
141C2×C42×C127—22no—
142C2×C42×C127—22no—
143C2×C42×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—22no—
154#95×C127—22no—
155#95×C127—22no—
156#95×C127—41no—
157#95×C127—41no—
158#95×C127—41no—
159#95×C127D414yes—
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×C127C2×D412yes—
187C24×C127C2×D412yes—
188C24×C127C2×D412yes—
189C24×C127C2×D412yes—
190C24×C127C2411yescharacteristic
191C2×Q8×C127—28no—
192C2×Q8×C127—44no—
193C2×Q8×C127—44no—
194C2×Q8×C127—44no—
195C2×Q8×C127—44no—
196C2×Q8×C127—44no—
197C2×Q8×C127—44no—
198C2×D4×C127—28no—
199C2×D4×C127—28no—
200C2×D4×C127—44no—
201C2×D4×C127—44no—
202C2×D4×C127—44no—
203C2×D4×C127—44no—
204C2×D4×C127—44no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
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—28no—
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—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—44no—
285C22×C4×C127—44no—
286C22×C4×C127—44no—
287C22×C4×C127—44no—
288C22×C4×C127—44no—
289C22×C4×C127—44no—
290C22×C4×C127C2×D412yes—
291C22×C4×C127C2×D412yes—
292C22×C4×C127C2×D412yes—
293C22×C4×C127C2×D412yes—
294C22×C4×C127C2×D412yes—
295C22×C4×C127C2×D412yes—
296C22×C4×C127C2×D412yes—
297C22×C4×C127C2×D412yes—
298C22×C4×C127#4112yes—
299C22×C4×C127#4112yes—
300C22×C4×C127#4112yes—
301C22×C4×C127#4112yes—
302C22×C4×C127#4112yes—
303C4⋊C4×C127—44no—
304C4⋊C4×C127—44no—
305C4⋊C4×C127—44no—
306C4⋊C4×C127—44no—
307C22⋊C4×C127—28no—
308C22⋊C4×C127—28no—
309C22⋊C4×C127—28no—
310C22⋊C4×C127—28no—
311C22⋊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—
318C42×C127—28no—
319C23×C127—22no—
320C23×C127—22no—
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—41no—
345C23×C127—41no—
346C23×C127—41no—
347C23×C127—41no—
348C23×C127—41no—
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#12014yes—
389C23×C127C22×D411yescharacteristic
390C23×C127C22×D411yescharacteristic
391C23×C127C22×D411yescharacteristic
392C23×C127C22×D411yescharacteristic
393C23×C127C2×#4111yescharacteristic
394C23×C127C2×#4111yescharacteristic
395C23×C127C2×#4111yescharacteristic
396C23×C127C2×#4111yescharacteristic
397C23×C127C2×#4111yescharacteristic
398C23×C127H(5,𝔽2)11yescharacteristic
399C23×C127H(5,𝔽2)11yescharacteristic
400C23×C127H(5,𝔽2)11yescharacteristic
401C23×C1272−1+411yescharacteristic
402C23×C1272−1+411yescharacteristic
403C23×C1272−1+411yescharacteristic
404Q8×C127—416no—
405D4×C127—416no—
406C2×C4×C127—22no—
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—416no—
440C2×C4×C127—41no—
441C2×C4×C127—41no—
442C2×C4×C127—41no—
443C2×C4×C127—41no—
444C2×C4×C127—41no—
445C2×C4×C127—41no—
446C2×C4×C127—41no—
447C2×C4×C127—41no—
448C2×C4×C127—41no—
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#12114yes—
497C2×C4×C127#12414yescomplemented
498C22×C127—24no—
499C22×C127—24no—
500C22×C127—24no—
501C22×C127—42no—
502C22×C127—42no—
503C22×C127—42no—
504C22×C127—42no—
505C22×C127—42no—
506C22×C127—42no—
507C22×C127—42no—
508C22×C127—42no—
509C22×C127—42no—
510C22×C127—42no—
511C22×C127—42no—
512C22×C127—42no—
513C22×C127—42no—
514C22×C127—42no—
515C22×C127—42no—
516C22×C127—42no—
517C22×C127—42no—
518C22×C127—42no—
519C22×C127—42no—
520C22×C127—81no—
521C22×C127—81no—
522C22×C127—81no—
523C22×C127—81no—
524C22×C127—81no—
525C22×C127—81no—
526C22×C127—81no—
527C22×C127—81no—
528C22×C127C2×#12011yescharacteristic
529C22×C127C2×#12111yescharacteristic
530C22×C127#52511yescharacteristic
531C22×C127C2×#12411yescharacteristic
532C22×C127#52911yescharacteristic
533C22×C127#53211yescharacteristic
534C22×C127#53411yescharacteristic
535C22×C127#53611yescharacteristic
536C22×C127#53611yescharacteristic
537C22×C127#53711yescharacteristic
538C22×C127#53811yescharacteristic
539C22×C127#54211yescharacteristic
540C22×C127#54211yescharacteristic
541C22×C127#54211yescharacteristic
542C22×C127#54211yescharacteristic
543C22×C127D4211yescharacteristic
544C22×C127D4211yescharacteristic
545C22×C127#54611yescharacteristic
546C22×C127#54611yescharacteristic
547C22×C127#54611yescharacteristic
548C22×C127#54611yescharacteristic
549C22×C127#54611yescharacteristic
550C22×C127#54711yescharacteristic
551C22×C127#54711yescharacteristic
552C22×C127#54711yescharacteristic
553C22×C127#54711yescharacteristic
554C22×C127#54711yescharacteristic
555C22×C127#54711yescharacteristic
556C22×C127#54811yescharacteristic
557C22×C127#55111yescharacteristic
558C22×C127#55511yescharacteristic
559C22×C127#55611yescharacteristic
560C22×C127#55611yescharacteristic
561C22×C127#56211yescharacteristic
562C22×C127#56311yescharacteristic
563C4×C127—24no—
564C4×C127—24no—
565C4×C127—42no—
566C4×C127—42no—
567C4×C127—42no—
568C4×C127—42no—
569C4×C127—42no—
570C4×C127—42no—
571C4×C127—42no—
572C4×C127—81no—
573C4×C127—81no—
574C4×C127—81no—
575C4×C127—81no—
576#15311C12711yesmaximal, characteristic, direct product factor, Sylow
577C2×C127—44no—
578C2×C127—82no—
579C2×C127#240611yescharacteristic
580C2×C127#241011yescharacteristic
581C2×C127#242711yescharacteristic
582C2×C127#243011yescharacteristic
583C2×C127#247211yescharacteristic
584C2×C127#247411yescharacteristic
585C2×C127#249111yescharacteristic
586C2×C127#252111yescharacteristic
587C2×C127#254711yescharacteristic
588C2×C127#267211yescharacteristic
589C2×C127#267411yescharacteristic
590C2×C127#268611yescharacteristic
591C2×C127#270011yescharacteristic
592C2×C127#271511yescharacteristic
593C2×C127#271711yescharacteristic
594C22×#124C2×C12711yescharacteristic
595C2×#397C2×C12711yescharacteristic, complemented
596C2×#395C2×C12711yescharacteristic, complemented
597C2×#394C2×C12711yescharacteristic
598C2×#386C2×C12711yescharacteristic
599C2×#380C2×C12711yescharacteristic, complemented
600#1446C2×C12711yescharacteristic, complemented
601#1440C2×C12711yescharacteristic, complemented
602#1440C2×C12711yescharacteristic, complemented
603#1439C2×C12711yescharacteristic, complemented
604#1439C2×C12711yescharacteristic, complemented
605#1439C2×C12711yescharacteristic, complemented
606#1436C2×C12711yescharacteristic, complemented
607#1436C2×C12711yescharacteristic, complemented
608C22⋊#95C2×C12711yescharacteristic, complemented
609C127#1531111yescharacteristic, direct product factor, Sylow
610C23×Q8C22×C12711yescharacteristic
611C23×D4C22×C12711yescharacteristic
612C24×C4C22×C12711yescharacteristic
613C2×#124—24no—
614C2×#124—24no—
615C2×#124—24no—
616C22×C4⋊C4C22×C12711yescharacteristic
617C22×C4⋊C4C22×C12711yescharacteristic
618C22×C4⋊C4C22×C12711yescharacteristic
619C22×C4⋊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×C22⋊C4C22×C12711yescharacteristic
629C22×C22⋊C4C22×C12711yescharacteristic
630C22×C22⋊C4C22×C12711yescharacteristic
631C22×C42C22×C12711yescharacteristic
632#397—24no—
633#395—24no—
634#394—24no—
635#386—24no—
636#380—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
653C25C23×C12711yescharacteristic
654C25C23×C12711yescharacteristic
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—22no—
658C22×Q8—22no—
659C22×Q8—22no—
660C22×Q8—41no—
661C22×Q8—41no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—22no—
665C22×D4—22no—
666C22×D4—41no—
667C22×D4—41no—
668C22×D4D4×C12714yes—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—41no—
675C23×C4—41no—
676C23×C4C23×C12711yescharacteristic
677C23×C4C23×C12711yescharacteristic
678C23×C4C23×C12711yescharacteristic
679C23×C4C23×C12711yescharacteristic
680C23×C4C23×C12711yescharacteristic
681C23×C4C23×C12711yescharacteristic
682C23×C4C23×C12711yescharacteristic
683C23×C4C23×C12711yescharacteristic
684C23×C4C23×C12711yescharacteristic
685C23×C4C23×C12711yescharacteristic
686C23×C4C23×C12711yescharacteristic
687C23×C4C23×C12711yescharacteristic
688C23×C4C23×C12711yescharacteristic
689#124—232no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—41no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4—41no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
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—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4D4×C12714yes—
734C2×C22⋊C4D4×C12714yes—
735C2×C42—22no—
736C2×C42—22no—
737C2×C42—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#95—41no—
753#95D4×C12714yes—
754C24—21no—
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—
777C24—21no—
778C24—21no—
779C24—21no—
780C24C2×D4×C12712yes—
781C24C2×D4×C12712yes—
782C24C2×D4×C12712yes—
783C24C2×D4×C12712yes—
784C24C24×C12711yescharacteristic
785C2×Q8—28no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—28no—
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—21no—
859C22×C4—21no—
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—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4C2×D4×C12712yes—
885C22×C4C2×D4×C12712yes—
886C22×C4C2×D4×C12712yes—
887C22×C4C2×D4×C12712yes—
888C22×C4C2×D4×C12712yes—
889C22×C4C2×D4×C12712yes—
890C22×C4C2×D4×C12712yes—
891C22×C4C2×D4×C12712yes—
892C22×C4#41×C12712yes—
893C22×C4#41×C12712yes—
894C22×C4#41×C12712yes—
895C22×C4#41×C12712yes—
896C22×C4#41×C12712yes—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C42—28no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
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—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
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—41no—
982C23#120×C12714yes—
983C23C22×D4×C12711yescharacteristic
984C23C22×D4×C12711yescharacteristic
985C23C22×D4×C12711yescharacteristic
986C23C22×D4×C12711yescharacteristic
987C23C2×#41×C12711yescharacteristic
988C23C2×#41×C12711yescharacteristic
989C23C2×#41×C12711yescharacteristic
990C23C2×#41×C12711yescharacteristic
991C23C2×#41×C12711yescharacteristic
992C23H(5,𝔽2)×C12711yescharacteristic
993C23H(5,𝔽2)×C12711yescharacteristic
994C23H(5,𝔽2)×C12711yescharacteristic
995C232−1+4×C12711yescharacteristic
996C232−1+4×C12711yescharacteristic
997C232−1+4×C12711yescharacteristic
998Q8—416no—
999D4—416no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
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—416no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
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#121×C12714yes—
1091C2×C4#124×C12714yescomplemented
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22C2×#120×C12711yescharacteristic
1123C22C2×#121×C12711yescharacteristic
1124C22#525×C12711yescharacteristic
1125C22C2×#124×C12711yescharacteristic
1126C22#529×C12711yescharacteristic
1127C22#532×C12711yescharacteristic
1128C22#534×C12711yescharacteristic
1129C22#536×C12711yescharacteristic
1130C22#536×C12711yescharacteristic
1131C22#537×C12711yescharacteristic
1132C22#538×C12711yescharacteristic
1133C22#542×C12711yescharacteristic
1134C22#542×C12711yescharacteristic
1135C22#542×C12711yescharacteristic
1136C22#542×C12711yescharacteristic
1137C22D42×C12711yescharacteristic
1138C22D42×C12711yescharacteristic
1139C22#546×C12711yescharacteristic
1140C22#546×C12711yescharacteristic
1141C22#546×C12711yescharacteristic
1142C22#546×C12711yescharacteristic
1143C22#546×C12711yescharacteristic
1144C22#547×C12711yescharacteristic
1145C22#547×C12711yescharacteristic
1146C22#547×C12711yescharacteristic
1147C22#547×C12711yescharacteristic
1148C22#547×C12711yescharacteristic
1149C22#547×C12711yescharacteristic
1150C22#548×C12711yescharacteristic
1151C22#551×C12711yescharacteristic
1152C22#555×C12711yescharacteristic
1153C22#556×C12711yescharacteristic
1154C22#556×C12711yescharacteristic
1155C22#562×C12711yescharacteristic
1156C22#563×C12711yescharacteristic
1157C4—24no—
1158C4—24no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—82no—
1172C2C127×#240611yescharacteristic
1173C2C127×#241011yescharacteristic
1174C2C127×#242711yescharacteristic
1175C2C127×#243011yescharacteristic
1176C2C127×#247211yescharacteristic
1177C2C127×#247411yescharacteristic
1178C2C127×#249111yescharacteristic
1179C2C127×#252111yescharacteristic
1180C2C127×#254711yescharacteristic
1181C2C127×#267211yescharacteristic
1182C2C127×#267411yescharacteristic
1183C2C127×#268611yescharacteristic
1184C2C127×#270011yescharacteristic
1185C2C127×#271511yescharacteristic
1186C2C127×#271711yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#397×C127C2semidirect
3. C2×#395×C127C2semidirect
6. C2×#380×C127C2semidirect
7. C127×#1446C2semidirect
8. C127×#1440C2semidirect
9. C127×#1440C2semidirect
10. C127×#1439C2semidirect
11. C127×#1439C2semidirect
12. C127×#1439C2semidirect
13. C127×#1436C2semidirect
14. C127×#1436C2semidirect
15. C127×C22⋊#95C2semidirect
497. C2×C4×C127#124semidirect
576. #15311C127direct (N × H)
595. C2×#397C2×C127semidirect
596. C2×#395C2×C127semidirect
599. C2×#380C2×C127semidirect
600. #1446C2×C127semidirect
601. #1440C2×C127semidirect
602. #1440C2×C127semidirect
603. #1439C2×C127semidirect
604. #1439C2×C127semidirect
605. #1439C2×C127semidirect
606. #1436C2×C127semidirect
607. #1436C2×C127semidirect
608. C22⋊#95C2×C127semidirect
609. C127#15311direct (N × H)
1091. C2×C4#124×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1272
C2×#397×C1272
C2×#395×C1272
C2×#394×C1272
C2×#386×C1272
C2×#380×C1272
C127×#14462
C127×#14402
C127×#14392
C127×#14362
C127×C22⋊#952
#15311127