Finite Group Databasebeta

← C127×#15317 #44578990

Subgroups — C127×#15317 #44578990

Order 32512.

2306 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C127C211yesmaximal, characteristic, complemented
2C2×#394×C127C211yesmaximal, characteristic, complemented
3C2×#393×C127C211yesmaximal, characteristic, complemented
4C2×#392×C127C211yesmaximal, characteristic
5C2×#391×C127C211yesmaximal, characteristic, complemented
6C2×#390×C127C211yesmaximal, characteristic, complemented
7C127×#1440C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1438C211yesmaximal, characteristic, complemented
11C127×#1438C211yesmaximal, characteristic, complemented
12C127×#1438C211yesmaximal, characteristic, complemented
13C127×#1437C211yesmaximal, characteristic, complemented
14C127×#1437C211yesmaximal, characteristic, complemented
15C127×#1436C211yesmaximal, characteristic, complemented
16C23×Q8×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C23×D4×C127C2211yescharacteristic
20C2×#124×C127—24no—
21C2×#124×C127—24no—
22C2×#124×C127—24no—
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊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×C22⋊C4×C127C2211yescharacteristic
39C22×C22⋊C4×C127C2211yescharacteristic
40C22×C42×C127C2211yescharacteristic
41C22×C42×C127C2211yescharacteristic
42#394×C127—24no—
43#393×C127—24no—
44#392×C127—24no—
45#391×C127—24no—
46#390×C127—24no—
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
61C25×C127C2311yescharacteristic
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×Q8×C127D414yescomplemented
69C22×D4×C127—22no—
70C22×D4×C127—22no—
71C22×D4×C127—22no—
72C22×D4×C127—22no—
73C22×D4×C127—22no—
74C22×D4×C127—22no—
75C22×D4×C127—22no—
76C22×D4×C127—22no—
77C22×D4×C127—22no—
78C22×D4×C127—22no—
79C22×D4×C127—22no—
80C22×D4×C127—22no—
81C22×D4×C127—22no—
82C22×D4×C127—41no—
83C22×D4×C127—41no—
84C22×D4×C127—41no—
85C22×D4×C127—41no—
86C22×D4×C127—41no—
87C22×D4×C127—41no—
88C22×D4×C127—41no—
89C22×D4×C127—41no—
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
101C23×C4×C127C2311yescharacteristic
102#124×C127—232no—
103C2×C4⋊C4×C127—22no—
104C2×C4⋊C4×C127—22no—
105C2×C4⋊C4×C127—22no—
106C2×C4⋊C4×C127—22no—
107C2×C4⋊C4×C127—41no—
108C2×C4⋊C4×C127—41no—
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—22no—
134C2×C22⋊C4×C127—22no—
135C2×C22⋊C4×C127—22no—
136C2×C22⋊C4×C127—22no—
137C2×C22⋊C4×C127—22no—
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×C127—41no—
148C2×C22⋊C4×C127—41no—
149C2×C22⋊C4×C127—41no—
150C2×C22⋊C4×C127—41no—
151C2×C22⋊C4×C127—41no—
152C2×C22⋊C4×C127D414yescomplemented
153C2×C22⋊C4×C127D414yescomplemented
154C2×C42×C127—22no—
155C2×C42×C127—22no—
156C2×C42×C127—22no—
157C2×C42×C127—22no—
158C2×C42×C127—22no—
159C2×C42×C127—41no—
160#95×C127—22no—
161#95×C127—22no—
162#95×C127—22no—
163#95×C127—22no—
164#95×C127—22no—
165#95×C127—22no—
166#95×C127—22no—
167#95×C127—22no—
168#95×C127—41no—
169#95×C127—41no—
170#95×C127—41no—
171#95×C127D414yes—
172C24×C127—21no—
173C24×C127—21no—
174C24×C127—21no—
175C24×C127—21no—
176C24×C127—21no—
177C24×C127—21no—
178C24×C127—21no—
179C24×C127—21no—
180C24×C127—21no—
181C24×C127—21no—
182C24×C127—21no—
183C24×C127—21no—
184C24×C127—21no—
185C24×C127—21no—
186C24×C127—21no—
187C24×C127—21no—
188C24×C127—21no—
189C24×C127—21no—
190C24×C127—21no—
191C24×C127—21no—
192C24×C127—21no—
193C24×C127—21no—
194C24×C127—21no—
195C24×C127—21no—
196C24×C127—21no—
197C24×C127—21no—
198C24×C127—21no—
199C24×C127—21no—
200C24×C127—21no—
201C24×C127—21no—
202C24×C127—21no—
203C24×C127—21no—
204C24×C127—21no—
205C24×C127—21no—
206C24×C127—21no—
207C24×C127—21no—
208C24×C127—21no—
209C24×C127—21no—
210C24×C127—21no—
211C24×C127—21no—
212C24×C127—21no—
213C24×C127—21no—
214C24×C127C2×D412yes—
215C24×C127C2×D412yes—
216C24×C127#4112yes—
217C24×C127C2411yescharacteristic
218C2×Q8×C127—28no—
219C2×Q8×C127—28no—
220C2×Q8×C127—44no—
221C2×Q8×C127—44no—
222C2×Q8×C127—44no—
223C2×Q8×C127—44no—
224C2×Q8×C127—44no—
225C2×D4×C127—28no—
226C2×D4×C127—28no—
227C2×D4×C127—44no—
228C2×D4×C127—44no—
229C2×D4×C127—44no—
230C2×D4×C127—44no—
231C2×D4×C127—44no—
232C2×D4×C127—44no—
233C2×D4×C127—44no—
234C2×D4×C127—44no—
235C2×D4×C127—44no—
236C2×D4×C127—44no—
237C2×D4×C127—44no—
238C2×D4×C127—44no—
239C2×D4×C127—44no—
240C2×D4×C127—44no—
241C2×D4×C127—44no—
242C2×D4×C127—44no—
243C2×D4×C127—44no—
244C2×D4×C127—44no—
245C2×D4×C127—44no—
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×C127C2×D412yes—
317C22×C4×C127C2×D412yes—
318C22×C4×C127C2×D412yes—
319C22×C4×C127C2×D412yes—
320C22×C4×C127C2×D412yes—
321C22×C4×C127C2×D412yes—
322C22×C4×C127C2×D412yes—
323C22×C4×C127C2×D412yes—
324C22×C4×C127C2×D412yes—
325C22×C4×C127C2×D412yes—
326C22×C4×C127#4112yes—
327C22×C4×C127#4112yes—
328C22×C4×C127#4112yes—
329C22×C4×C127#4112yes—
330C4⋊C4×C127—44no—
331C4⋊C4×C127—44no—
332C22⋊C4×C127—28no—
333C22⋊C4×C127—28no—
334C22⋊C4×C127—28no—
335C22⋊C4×C127—28no—
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—
347C42×C127—28no—
348C42×C127—44no—
349C23×C127—22no—
350C23×C127—22no—
351C23×C127—22no—
352C23×C127—22no—
353C23×C127—22no—
354C23×C127—22no—
355C23×C127—22no—
356C23×C127—22no—
357C23×C127—22no—
358C23×C127—22no—
359C23×C127—22no—
360C23×C127—22no—
361C23×C127—22no—
362C23×C127—22no—
363C23×C127—22no—
364C23×C127—22no—
365C23×C127—22no—
366C23×C127—22no—
367C23×C127—22no—
368C23×C127—22no—
369C23×C127—22no—
370C23×C127—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×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×C127C22×D411yescharacteristic
455C23×C127C22×D411yescharacteristic
456C23×C127C22×D411yescharacteristic
457C23×C127C22×D411yescharacteristic
458C23×C127C2×#4111yescharacteristic
459C23×C127C2×#4111yescharacteristic
460C23×C127C2×#4111yescharacteristic
461C23×C127C2×#4111yescharacteristic
462C23×C127C2×#4111yescharacteristic
463C23×C127H(5,𝔽2)11yescharacteristic
464C23×C127H(5,𝔽2)11yescharacteristic
465C23×C127H(5,𝔽2)11yescharacteristic
466C23×C127H(5,𝔽2)11yescharacteristic
467C23×C127H(5,𝔽2)11yescharacteristic
468C23×C1272−1+411yescharacteristic
469Q8×C127—416no—
470D4×C127—416no—
471D4×C127—416no—
472D4×C127—416no—
473C2×C4×C127—22no—
474C2×C4×C127—22no—
475C2×C4×C127—22no—
476C2×C4×C127—22no—
477C2×C4×C127—22no—
478C2×C4×C127—22no—
479C2×C4×C127—22no—
480C2×C4×C127—22no—
481C2×C4×C127—22no—
482C2×C4×C127—22no—
483C2×C4×C127—22no—
484C2×C4×C127—22no—
485C2×C4×C127—22no—
486C2×C4×C127—22no—
487C2×C4×C127—22no—
488C2×C4×C127—22no—
489C2×C4×C127—22no—
490C2×C4×C127—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—22no—
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#12014yes—
555C2×C4×C127#12114yes—
556C2×C4×C127#12414yescomplemented
557C22×C127—42no—
558C22×C127—42no—
559C22×C127—42no—
560C22×C127—42no—
561C22×C127—42no—
562C22×C127—42no—
563C22×C127—42no—
564C22×C127—42no—
565C22×C127—42no—
566C22×C127—42no—
567C22×C127—42no—
568C22×C127—42no—
569C22×C127—42no—
570C22×C127—42no—
571C22×C127—42no—
572C22×C127—42no—
573C22×C127—42no—
574C22×C127—42no—
575C22×C127—42no—
576C22×C127—42no—
577C22×C127—42no—
578C22×C127—81no—
579C22×C127—81no—
580C22×C127—81no—
581C22×C127—81no—
582C22×C127—81no—
583C22×C127—81no—
584C22×C127—81no—
585C22×C127—81no—
586C22×C127—81no—
587C22×C127—81no—
588C22×C127—81no—
589C22×C127—81no—
590C22×C127—81no—
591C22×C127—81no—
592C22×C127—81no—
593C22×C127—81no—
594C22×C127—81no—
595C22×C127—81no—
596C22×C127—81no—
597C22×C127—81no—
598C22×C127—81no—
599C22×C127—81no—
600C22×C127—81no—
601C22×C127—81no—
602C22×C127C2×#12011yescharacteristic
603C22×C127C2×#12111yescharacteristic
604C22×C127#52511yescharacteristic
605C22×C127C2×#12411yescharacteristic
606C22×C127#52911yescharacteristic
607C22×C127#53211yescharacteristic
608C22×C127#53411yescharacteristic
609C22×C127#53511yescharacteristic
610C22×C127#53511yescharacteristic
611C22×C127#53711yescharacteristic
612C22×C127#53811yescharacteristic
613C22×C127#53811yescharacteristic
614C22×C127#53811yescharacteristic
615C22×C127#54211yescharacteristic
616C22×C127#54211yescharacteristic
617C22×C127D4211yescharacteristic
618C22×C127D4211yescharacteristic
619C22×C127#54611yescharacteristic
620C22×C127#54611yescharacteristic
621C22×C127#54611yescharacteristic
622C22×C127#54611yescharacteristic
623C22×C127#54611yescharacteristic
624C22×C127#54611yescharacteristic
625C22×C127#54711yescharacteristic
626C22×C127#54811yescharacteristic
627C22×C127#54811yescharacteristic
628C22×C127#55011yescharacteristic
629C22×C127#55011yescharacteristic
630C22×C127#55011yescharacteristic
631C22×C127#55111yescharacteristic
632C22×C127#55511yescharacteristic
633C22×C127#55911yescharacteristic
634C22×C127#55911yescharacteristic
635C22×C127H(3,𝔽4)11yescharacteristic
636C22×C127#56211yescharacteristic
637C4×C127—24no—
638C4×C127—24no—
639C4×C127—24no—
640C4×C127—42no—
641C4×C127—42no—
642C4×C127—42no—
643C4×C127—42no—
644C4×C127—42no—
645C4×C127—81no—
646C4×C127—81no—
647C4×C127—81no—
648C4×C127—81no—
649#15317C12711yesmaximal, characteristic, direct product factor, Sylow
650C2×C127—82no—
651C2×C127—82no—
652C2×C127—82no—
653C2×C127#240711yescharacteristic
654C2×C127#241011yescharacteristic
655C2×C127#242611yescharacteristic
656C2×C127#243111yescharacteristic
657C2×C127#245911yescharacteristic
658C2×C127#247211yescharacteristic
659C2×C127#249111yescharacteristic
660C2×C127#254811yescharacteristic
661C2×C127#255711yescharacteristic
662C2×C127#267011yescharacteristic
663C2×C127#267611yescharacteristic
664C2×C127#271011yescharacteristic
665C2×C127#271211yescharacteristic
666C2×C127#273011yescharacteristic
667C2×C127#273311yescharacteristic
668C22×#124C2×C12711yescharacteristic, complemented
669C2×#394C2×C12711yescharacteristic, complemented
670C2×#393C2×C12711yescharacteristic, complemented
671C2×#392C2×C12711yescharacteristic
672C2×#391C2×C12711yescharacteristic, complemented
673C2×#390C2×C12711yescharacteristic, complemented
674#1440C2×C12711yescharacteristic, complemented
675#1439C2×C12711yescharacteristic, complemented
676#1439C2×C12711yescharacteristic, complemented
677#1438C2×C12711yescharacteristic, complemented
678#1438C2×C12711yescharacteristic, complemented
679#1438C2×C12711yescharacteristic, complemented
680#1437C2×C12711yescharacteristic, complemented
681#1437C2×C12711yescharacteristic, complemented
682#1436C2×C12711yescharacteristic, complemented
683C127#1531711yescharacteristic, direct product factor, Sylow
684C23×Q8C22×C12711yescharacteristic
685C23×D4C22×C12711yescharacteristic
686C23×D4C22×C12711yescharacteristic
687C23×D4C22×C12711yescharacteristic
688C2×#124—24no—
689C2×#124—24no—
690C2×#124—24no—
691C22×C4⋊C4C22×C12711yescharacteristic
692C22×C4⋊C4C22×C12711yescharacteristic
693C22×C22⋊C4C22×C12711yescharacteristic
694C22×C22⋊C4C22×C12711yescharacteristic
695C22×C22⋊C4C22×C12711yescharacteristic
696C22×C22⋊C4C22×C12711yescharacteristic
697C22×C22⋊C4C22×C12711yescharacteristic
698C22×C22⋊C4C22×C12711yescharacteristic
699C22×C22⋊C4C22×C12711yescharacteristic
700C22×C22⋊C4C22×C12711yescharacteristic
701C22×C22⋊C4C22×C12711yescharacteristic
702C22×C22⋊C4C22×C12711yescharacteristic
703C22×C22⋊C4C22×C12711yescharacteristic
704C22×C22⋊C4C22×C12711yescharacteristic
705C22×C22⋊C4C22×C12711yescharacteristic
706C22×C22⋊C4C22×C12711yescharacteristic
707C22×C22⋊C4C22×C12711yescharacteristic
708C22×C42C22×C12711yescharacteristic
709C22×C42C22×C12711yescharacteristic
710#394—24no—
711#393—24no—
712#392—24no—
713#391—24no—
714#390—24no—
715C2×#95C22×C12711yescharacteristic
716C2×#95C22×C12711yescharacteristic
717C2×#95C22×C12711yescharacteristic
718C2×#95C22×C12711yescharacteristic
719C2×#95C22×C12711yescharacteristic
720C2×#95C22×C12711yescharacteristic
721C2×#95C22×C12711yescharacteristic
722C2×#95C22×C12711yescharacteristic
723C2×#95C22×C12711yescharacteristic
724C2×#95C22×C12711yescharacteristic
725C2×#95C22×C12711yescharacteristic
726C2×#95C22×C12711yescharacteristic
727C25C23×C12711yescharacteristic
728C25C23×C12711yescharacteristic
729C25C23×C12711yescharacteristic
730C22×Q8—22no—
731C22×Q8—22no—
732C22×Q8—22no—
733C22×Q8—22no—
734C22×Q8—41no—
735C22×Q8—41no—
736C22×Q8D4×C12714yescomplemented
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—41no—
751C22×D4—41no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
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
770#124—232no—
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×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—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—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
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⋊C4D4×C12714yescomplemented
821C2×C22⋊C4D4×C12714yescomplemented
822C2×C42—22no—
823C2×C42—22no—
824C2×C42—22no—
825C2×C42—22no—
826C2×C42—22no—
827C2×C42—41no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95—41no—
838#95—41no—
839#95D4×C12714yes—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
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—
882C24C2×D4×C12712yes—
883C24C2×D4×C12712yes—
884C24#41×C12712yes—
885C24C24×C12711yescharacteristic
886C2×Q8—28no—
887C2×Q8—28no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—44no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—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×C4C2×D4×C12712yes—
985C22×C4C2×D4×C12712yes—
986C22×C4C2×D4×C12712yes—
987C22×C4C2×D4×C12712yes—
988C22×C4C2×D4×C12712yes—
989C22×C4C2×D4×C12712yes—
990C22×C4C2×D4×C12712yes—
991C22×C4C2×D4×C12712yes—
992C22×C4C2×D4×C12712yes—
993C22×C4C2×D4×C12712yes—
994C22×C4#41×C12712yes—
995C22×C4#41×C12712yes—
996C22×C4#41×C12712yes—
997C22×C4#41×C12712yes—
998C4⋊C4—44no—
999C4⋊C4—44no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C42—28no—
1016C42—44no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
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—
1122C23C22×D4×C12711yescharacteristic
1123C23C22×D4×C12711yescharacteristic
1124C23C22×D4×C12711yescharacteristic
1125C23C22×D4×C12711yescharacteristic
1126C23C2×#41×C12711yescharacteristic
1127C23C2×#41×C12711yescharacteristic
1128C23C2×#41×C12711yescharacteristic
1129C23C2×#41×C12711yescharacteristic
1130C23C2×#41×C12711yescharacteristic
1131C23H(5,𝔽2)×C12711yescharacteristic
1132C23H(5,𝔽2)×C12711yescharacteristic
1133C23H(5,𝔽2)×C12711yescharacteristic
1134C23H(5,𝔽2)×C12711yescharacteristic
1135C23H(5,𝔽2)×C12711yescharacteristic
1136C232−1+4×C12711yescharacteristic
1137Q8—416no—
1138D4—416no—
1139D4—416no—
1140D4—416no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—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#120×C12714yes—
1223C2×C4#121×C12714yes—
1224C2×C4#124×C12714yescomplemented
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C2×#120×C12711yescharacteristic
1271C22C2×#121×C12711yescharacteristic
1272C22#525×C12711yescharacteristic
1273C22C2×#124×C12711yescharacteristic
1274C22#529×C12711yescharacteristic
1275C22#532×C12711yescharacteristic
1276C22#534×C12711yescharacteristic
1277C22#535×C12711yescharacteristic
1278C22#535×C12711yescharacteristic
1279C22#537×C12711yescharacteristic
1280C22#538×C12711yescharacteristic
1281C22#538×C12711yescharacteristic
1282C22#538×C12711yescharacteristic
1283C22#542×C12711yescharacteristic
1284C22#542×C12711yescharacteristic
1285C22D42×C12711yescharacteristic
1286C22D42×C12711yescharacteristic
1287C22#546×C12711yescharacteristic
1288C22#546×C12711yescharacteristic
1289C22#546×C12711yescharacteristic
1290C22#546×C12711yescharacteristic
1291C22#546×C12711yescharacteristic
1292C22#546×C12711yescharacteristic
1293C22#547×C12711yescharacteristic
1294C22#548×C12711yescharacteristic
1295C22#548×C12711yescharacteristic
1296C22#550×C12711yescharacteristic
1297C22#550×C12711yescharacteristic
1298C22#550×C12711yescharacteristic
1299C22#551×C12711yescharacteristic
1300C22#555×C12711yescharacteristic
1301C22#559×C12711yescharacteristic
1302C22#559×C12711yescharacteristic
1303C22H(3,𝔽4)×C12711yescharacteristic
1304C22#562×C12711yescharacteristic
1305C4—24no—
1306C4—24no—
1307C4—24no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C2—82no—
1318C2—82no—
1319C2—82no—
1320C2C127×#240711yescharacteristic
1321C2C127×#241011yescharacteristic
1322C2C127×#242611yescharacteristic
1323C2C127×#243111yescharacteristic
1324C2C127×#245911yescharacteristic
1325C2C127×#247211yescharacteristic
1326C2C127×#249111yescharacteristic
1327C2C127×#254811yescharacteristic
1328C2C127×#255711yescharacteristic
1329C2C127×#267011yescharacteristic
1330C2C127×#267611yescharacteristic
1331C2C127×#271011yescharacteristic
1332C2C127×#271211yescharacteristic
1333C2C127×#273011yescharacteristic
1334C2C127×#273311yescharacteristic
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. C22×#124×C127C2semidirect
2. C2×#394×C127C2semidirect
3. C2×#393×C127C2semidirect
5. C2×#391×C127C2semidirect
6. C2×#390×C127C2semidirect
7. C127×#1440C2semidirect
8. C127×#1439C2semidirect
9. C127×#1439C2semidirect
10. C127×#1438C2semidirect
11. C127×#1438C2semidirect
12. C127×#1438C2semidirect
13. C127×#1437C2semidirect
14. C127×#1437C2semidirect
15. C127×#1436C2semidirect
68. C22×Q8×C127D4semidirect
152. C2×C22⋊C4×C127D4semidirect
153. C2×C22⋊C4×C127D4semidirect
556. C2×C4×C127#124semidirect
649. #15317C127direct (N × H)
668. C22×#124C2×C127semidirect
669. C2×#394C2×C127semidirect
670. C2×#393C2×C127semidirect
672. C2×#391C2×C127semidirect
673. C2×#390C2×C127semidirect
674. #1440C2×C127semidirect
675. #1439C2×C127semidirect
676. #1439C2×C127semidirect
677. #1438C2×C127semidirect
678. #1438C2×C127semidirect
679. #1438C2×C127semidirect
680. #1437C2×C127semidirect
681. #1437C2×C127semidirect
682. #1436C2×C127semidirect
683. C127#15317direct (N × H)
736. C22×Q8D4×C127semidirect
820. C2×C22⋊C4D4×C127semidirect
821. C2×C22⋊C4D4×C127semidirect
1224. 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×#394×C1272
C2×#393×C1272
C2×#392×C1272
C2×#391×C1272
C2×#390×C1272
C127×#14402
C127×#14392
C127×#14382
C127×#14372
C127×#14362
#15317127