Finite Group Databasebeta

← C127×#14721 #44578394

Subgroups — C127×#14721 #44578394

Order 32512.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C211yesmaximal, characteristic, complemented
2C22×C4×D4×C127C211yesmaximal, characteristic, complemented
3C2×#394×C127C211yesmaximal, characteristic, complemented
4C2×#392×C127C211yesmaximal, characteristic
5C2×#386×C127C211yesmaximal, characteristic, complemented
6C2×#385×C127C211yesmaximal, characteristic, complemented
7C127×#1444C211yesmaximal, characteristic, complemented
8C127×#1440C211yesmaximal, characteristic, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1439C211yesmaximal, characteristic, complemented
11C127×#1438C211yesmaximal, characteristic, complemented
12C127×#1438C211yesmaximal, characteristic, complemented
13C127×#1437C211yesmaximal, characteristic, complemented
14C127×#1436C211yesmaximal, characteristic, complemented
15C127×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C24×C4×C127C2211yescharacteristic
20C24×C4×C127C2211yescharacteristic
21C2×#123×C127—24no—
22C2×#123×C127—24no—
23C2×#123×C127—24no—
24C2×C4×D4×C127—24no—
25C2×C4×D4×C127—24no—
26C2×C4×D4×C127—24no—
27C22×C4⋊C4×C127C2211yescharacteristic
28C22×C4⋊C4×C127C2211yescharacteristic
29C22×C4⋊C4×C127C2211yescharacteristic
30C22×C4⋊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×C22⋊C4×C127C2211yescharacteristic
41C22×C22⋊C4×C127C2211yescharacteristic
42C22×C22⋊C4×C127C2211yescharacteristic
43C22×C22⋊C4×C127C2211yescharacteristic
44C22×C42×C127C2211yescharacteristic
45#394×C127—24no—
46#392×C127—24no—
47#386×C127—24no—
48#385×C127—24no—
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
59C2×#95×C127C2211yescharacteristic
60C2×#95×C127C2211yescharacteristic
61C25×C127C2311yescharacteristic
62C25×C127C2311yescharacteristic
63C25×C127C2311yescharacteristic
64C22×D4×C127—22no—
65C22×D4×C127—22no—
66C22×D4×C127—22no—
67C22×D4×C127—22no—
68C22×D4×C127—22no—
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—41no—
81C22×D4×C127—41no—
82C22×D4×C127—41no—
83C22×D4×C127—41no—
84C22×D4×C127D414yes—
85C23×C4×C127—22no—
86C23×C4×C127—22no—
87C23×C4×C127—22no—
88C23×C4×C127—22no—
89C23×C4×C127—22no—
90C23×C4×C127—22no—
91C23×C4×C127—22no—
92C23×C4×C127—22no—
93C23×C4×C127—22no—
94C23×C4×C127—41no—
95C23×C4×C127—41no—
96C23×C4×C127—41no—
97C23×C4×C127—41no—
98C23×C4×C127D414yescomplemented
99C23×C4×C127C2311yescharacteristic
100C23×C4×C127C2311yescharacteristic
101C23×C4×C127C2311yescharacteristic
102C23×C4×C127C2311yescharacteristic
103C23×C4×C127C2311yescharacteristic
104C23×C4×C127C2311yescharacteristic
105C23×C4×C127C2311yescharacteristic
106C23×C4×C127C2311yescharacteristic
107C23×C4×C127C2311yescharacteristic
108C23×C4×C127C2311yescharacteristic
109C23×C4×C127C2311yescharacteristic
110C23×C4×C127C2311yescharacteristic
111#123×C127—232no—
112C4×D4×C127—232no—
113C2×C4⋊C4×C127—22no—
114C2×C4⋊C4×C127—22no—
115C2×C4⋊C4×C127—22no—
116C2×C4⋊C4×C127—22no—
117C2×C4⋊C4×C127—22no—
118C2×C4⋊C4×C127—22no—
119C2×C4⋊C4×C127—22no—
120C2×C4⋊C4×C127—22no—
121C2×C4⋊C4×C127—22no—
122C2×C4⋊C4×C127—22no—
123C2×C4⋊C4×C127—41no—
124C2×C4⋊C4×C127D414yescomplemented
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—22no—
139C2×C22⋊C4×C127—22no—
140C2×C22⋊C4×C127—22no—
141C2×C22⋊C4×C127—22no—
142C2×C22⋊C4×C127—22no—
143C2×C22⋊C4×C127—22no—
144C2×C22⋊C4×C127—22no—
145C2×C22⋊C4×C127—22no—
146C2×C22⋊C4×C127—22no—
147C2×C22⋊C4×C127—22no—
148C2×C22⋊C4×C127—22no—
149C2×C22⋊C4×C127—22no—
150C2×C22⋊C4×C127—22no—
151C2×C22⋊C4×C127—22no—
152C2×C22⋊C4×C127—22no—
153C2×C22⋊C4×C127—22no—
154C2×C22⋊C4×C127—22no—
155C2×C22⋊C4×C127—22no—
156C2×C22⋊C4×C127—41no—
157C2×C22⋊C4×C127—41no—
158C2×C22⋊C4×C127—41no—
159C2×C22⋊C4×C127—41no—
160C2×C22⋊C4×C127—41no—
161C2×C22⋊C4×C127—41no—
162C2×C22⋊C4×C127D414yescomplemented
163C2×C22⋊C4×C127D414yescomplemented
164C2×C42×C127—22no—
165C2×C42×C127—22no—
166C2×C42×C127—22no—
167#95×C127—22no—
168#95×C127—22no—
169#95×C127—22no—
170#95×C127—22no—
171#95×C127—22no—
172#95×C127—22no—
173#95×C127—22no—
174#95×C127—22no—
175#95×C127—22no—
176#95×C127—41no—
177#95×C127—41no—
178#95×C127—41no—
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×C127—21no—
215C24×C127—21no—
216C24×C127—21no—
217C24×C127C2×D412yes—
218C24×C127C2×D412yes—
219C24×C127C2×D412yes—
220C24×C127C2×D412yes—
221C24×C127C2×D412yes—
222C24×C127#4112yes—
223C24×C127#4112yes—
224C24×C127C2411yescharacteristic
225C2×D4×C127—28no—
226C2×D4×C127—28no—
227C2×D4×C127—28no—
228C2×D4×C127—28no—
229C2×D4×C127—28no—
230C2×D4×C127—28no—
231C2×D4×C127—28no—
232C2×D4×C127—28no—
233C2×D4×C127—28no—
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—28no—
255C22×C4×C127—28no—
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—28no—
305C22×C4×C127—21no—
306C22×C4×C127—21no—
307C22×C4×C127—21no—
308C22×C4×C127—21no—
309C22×C4×C127—21no—
310C22×C4×C127—21no—
311C22×C4×C127—21no—
312C22×C4×C127—21no—
313C22×C4×C127—21no—
314C22×C4×C127—21no—
315C22×C4×C127—21no—
316C22×C4×C127—21no—
317C22×C4×C127—21no—
318C22×C4×C127—21no—
319C22×C4×C127—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—
327C22×C4×C127—44no—
328C22×C4×C127—44no—
329C22×C4×C127—44no—
330C22×C4×C127C2×D412yes—
331C22×C4×C127C2×D412yes—
332C22×C4×C127C2×D412yes—
333C22×C4×C127C2×D412yes—
334C22×C4×C127C2×D412yes—
335C22×C4×C127C2×D412yes—
336C22×C4×C127C2×D412yes—
337C22×C4×C127C2×D412yes—
338C22×C4×C127C2×D412yes—
339C22×C4×C127C2×D412yes—
340C22×C4×C127#4112yes—
341C22×C4×C127#4112yes—
342C22×C4×C127#4112yes—
343C22×C4×C127#4112yes—
344C4⋊C4×C127—28no—
345C4⋊C4×C127—28no—
346C4⋊C4×C127—28no—
347C4⋊C4×C127—44no—
348C22⋊C4×C127—28no—
349C22⋊C4×C127—28no—
350C22⋊C4×C127—28no—
351C22⋊C4×C127—28no—
352C22⋊C4×C127—28no—
353C22⋊C4×C127—28no—
354C22⋊C4×C127—44no—
355C22⋊C4×C127—44no—
356C22⋊C4×C127—44no—
357C22⋊C4×C127—44no—
358C22⋊C4×C127—44no—
359C22⋊C4×C127—44no—
360C22⋊C4×C127—44no—
361C42×C127—28no—
362C23×C127—22no—
363C23×C127—22no—
364C23×C127—22no—
365C23×C127—22no—
366C23×C127—22no—
367C23×C127—22no—
368C23×C127—22no—
369C23×C127—22no—
370C23×C127—22no—
371C23×C127—22no—
372C23×C127—22no—
373C23×C127—22no—
374C23×C127—22no—
375C23×C127—22no—
376C23×C127—22no—
377C23×C127—22no—
378C23×C127—22no—
379C23×C127—22no—
380C23×C127—22no—
381C23×C127—22no—
382C23×C127—22no—
383C23×C127—22no—
384C23×C127—22no—
385C23×C127—22no—
386C23×C127—22no—
387C23×C127—22no—
388C23×C127—22no—
389C23×C127—22no—
390C23×C127—22no—
391C23×C127—22no—
392C23×C127—22no—
393C23×C127—22no—
394C23×C127—22no—
395C23×C127—22no—
396C23×C127—22no—
397C23×C127—22no—
398C23×C127—22no—
399C23×C127—22no—
400C23×C127—22no—
401C23×C127—22no—
402C23×C127—22no—
403C23×C127—22no—
404C23×C127—22no—
405C23×C127—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×C127—41no—
455C23×C127—41no—
456C23×C127—41no—
457C23×C127—41no—
458C23×C127—41no—
459C23×C127—41no—
460C23×C127—41no—
461C23×C127—41no—
462C23×C127—41no—
463C23×C127—41no—
464C23×C127—41no—
465C23×C127#12014yes—
466C23×C127#12314yescomplemented
467C23×C127C22×D411yescharacteristic
468C23×C127C22×D411yescharacteristic
469C23×C127C22×D411yescharacteristic
470C23×C127C22×D411yescharacteristic
471C23×C127C22×D411yescharacteristic
472C23×C127C2×#4111yescharacteristic
473C23×C127C2×#4111yescharacteristic
474C23×C127C2×#4111yescharacteristic
475C23×C127C2×#4111yescharacteristic
476C23×C127C2×#4111yescharacteristic
477C23×C127C2×#4111yescharacteristic
478C23×C127H(5,𝔽2)11yescharacteristic
479C23×C127H(5,𝔽2)11yescharacteristic
480C23×C127H(5,𝔽2)11yescharacteristic
481C23×C1272−1+411yescharacteristic
482D4×C127—232no—
483D4×C127—416no—
484D4×C127—416no—
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—22no—
507C2×C4×C127—22no—
508C2×C4×C127—22no—
509C2×C4×C127—22no—
510C2×C4×C127—22no—
511C2×C4×C127—22no—
512C2×C4×C127—22no—
513C2×C4×C127—22no—
514C2×C4×C127—22no—
515C2×C4×C127—22no—
516C2×C4×C127—22no—
517C2×C4×C127—22no—
518C2×C4×C127—22no—
519C2×C4×C127—22no—
520C2×C4×C127—22no—
521C2×C4×C127—416no—
522C2×C4×C127—416no—
523C2×C4×C127—41no—
524C2×C4×C127—41no—
525C2×C4×C127—41no—
526C2×C4×C127—41no—
527C2×C4×C127—41no—
528C2×C4×C127—41no—
529C2×C4×C127—41no—
530C2×C4×C127—41no—
531C2×C4×C127—41no—
532C2×C4×C127—41no—
533C2×C4×C127—41no—
534C2×C4×C127—41no—
535C2×C4×C127—41no—
536C2×C4×C127—41no—
537C2×C4×C127—41no—
538C2×C4×C127—41no—
539C2×C4×C127—41no—
540C2×C4×C127—41no—
541C2×C4×C127—41no—
542C2×C4×C127—41no—
543C2×C4×C127—41no—
544C2×C4×C127—41no—
545C2×C4×C127—41no—
546C2×C4×C127—41no—
547C2×C4×C127—41no—
548C2×C4×C127—41no—
549C2×C4×C127—41no—
550C2×C4×C127—41no—
551C2×C4×C127—41no—
552C2×C4×C127—41no—
553C2×C4×C127—41no—
554C2×C4×C127—41no—
555C2×C4×C127—41no—
556C2×C4×C127—41no—
557C2×C4×C127—41no—
558C2×C4×C127—41no—
559C2×C4×C127—41no—
560C2×C4×C127—41no—
561C2×C4×C127—41no—
562C2×C4×C127—41no—
563C2×C4×C127—41no—
564C2×C4×C127—41no—
565C2×C4×C127—41no—
566C2×C4×C127—41no—
567C2×C4×C127—41no—
568C2×C4×C127—41no—
569C2×C4×C127#12014yes—
570C2×C4×C127#12314yescomplemented
571C22×C127—24no—
572C22×C127—24no—
573C22×C127—24no—
574C22×C127—24no—
575C22×C127—24no—
576C22×C127—24no—
577C22×C127—42no—
578C22×C127—42no—
579C22×C127—42no—
580C22×C127—42no—
581C22×C127—42no—
582C22×C127—42no—
583C22×C127—42no—
584C22×C127—42no—
585C22×C127—42no—
586C22×C127—42no—
587C22×C127—42no—
588C22×C127—42no—
589C22×C127—42no—
590C22×C127—42no—
591C22×C127—42no—
592C22×C127—42no—
593C22×C127—42no—
594C22×C127—42no—
595C22×C127—42no—
596C22×C127—42no—
597C22×C127—42no—
598C22×C127—42no—
599C22×C127—42no—
600C22×C127—42no—
601C22×C127—42no—
602C22×C127—42no—
603C22×C127—42no—
604C22×C127—42no—
605C22×C127—42no—
606C22×C127—42no—
607C22×C127—42no—
608C22×C127—81no—
609C22×C127—81no—
610C22×C127—81no—
611C22×C127—81no—
612C22×C127—81no—
613C22×C127—81no—
614C22×C127—81no—
615C22×C127—81no—
616C22×C127C2×#12011yescharacteristic
617C22×C127C2×#12011yescharacteristic
618C22×C127C2×#12311yescharacteristic
619C22×C127C2×#12311yescharacteristic
620C22×C127#52511yescharacteristic
621C22×C127#52511yescharacteristic
622C22×C127#52511yescharacteristic
623C22×C127#52511yescharacteristic
624C22×C127#52511yescharacteristic
625C22×C127#52511yescharacteristic
626C22×C127#53211yescharacteristic
627C22×C127#53211yescharacteristic
628C22×C127#53211yescharacteristic
629C22×C127#53411yescharacteristic
630C22×C127#53711yescharacteristic
631C22×C127#53811yescharacteristic
632C22×C127#53911yescharacteristic
633C22×C127#54011yescharacteristic
634C22×C127#54211yescharacteristic
635C22×C127D4211yescharacteristic
636C22×C127D4211yescharacteristic
637C22×C127D4211yescharacteristic
638C22×C127D4211yescharacteristic
639C22×C127#54611yescharacteristic
640C22×C127#54611yescharacteristic
641C22×C127#54611yescharacteristic
642C22×C127#54711yescharacteristic
643C22×C127#54711yescharacteristic
644C22×C127#54711yescharacteristic
645C22×C127#54811yescharacteristic
646C22×C127#55011yescharacteristic
647C22×C127#55111yescharacteristic
648C22×C127#55311yescharacteristic
649C22×C127#55311yescharacteristic
650C22×C127#55911yescharacteristic
651C4×C127—24no—
652C4×C127—24no—
653C4×C127—42no—
654C4×C127—42no—
655C4×C127—42no—
656C4×C127—42no—
657C4×C127—42no—
658C4×C127—42no—
659C4×C127—42no—
660C4×C127—42no—
661C4×C127—81no—
662C4×C127—81no—
663#14721C12711yesmaximal, characteristic, direct product factor, Sylow
664C2×C127—44no—
665C2×C127—44no—
666C2×C127—82no—
667C2×C127#238811yescharacteristic
668C2×C127#240311yescharacteristic
669C2×C127#240711yescharacteristic
670C2×C127#241811yescharacteristic
671C2×C127#242211yescharacteristic
672C2×C127#243011yescharacteristic
673C2×C127#244311yescharacteristic
674C2×C127#244511yescharacteristic
675C2×C127#245511yescharacteristic
676C2×C127#245611yescharacteristic
677C2×C127#246111yescharacteristic
678C2×C127#246411yescharacteristic
679C2×C127#260211yescharacteristic
680C2×C127#263011yescharacteristic
681C2×C127#284911yescharacteristic
682C22×#123C2×C12711yescharacteristic, complemented
683C22×C4×D4C2×C12711yescharacteristic, complemented
684C2×#394C2×C12711yescharacteristic, complemented
685C2×#392C2×C12711yescharacteristic
686C2×#386C2×C12711yescharacteristic, complemented
687C2×#385C2×C12711yescharacteristic, complemented
688#1444C2×C12711yescharacteristic, complemented
689#1440C2×C12711yescharacteristic, complemented
690#1439C2×C12711yescharacteristic, complemented
691#1439C2×C12711yescharacteristic, complemented
692#1438C2×C12711yescharacteristic, complemented
693#1438C2×C12711yescharacteristic, complemented
694#1437C2×C12711yescharacteristic, complemented
695#1436C2×C12711yescharacteristic, complemented
696C22⋊#95C2×C12711yescharacteristic, complemented
697C127#1472111yescharacteristic, direct product factor, Sylow
698C23×D4C22×C12711yescharacteristic
699C23×D4C22×C12711yescharacteristic
700C23×D4C22×C12711yescharacteristic
701C24×C4C22×C12711yescharacteristic
702C24×C4C22×C12711yescharacteristic
703C2×#123—24no—
704C2×#123—24no—
705C2×#123—24no—
706C2×C4×D4—24no—
707C2×C4×D4—24no—
708C2×C4×D4—24no—
709C22×C4⋊C4C22×C12711yescharacteristic
710C22×C4⋊C4C22×C12711yescharacteristic
711C22×C4⋊C4C22×C12711yescharacteristic
712C22×C4⋊C4C22×C12711yescharacteristic
713C22×C22⋊C4C22×C12711yescharacteristic
714C22×C22⋊C4C22×C12711yescharacteristic
715C22×C22⋊C4C22×C12711yescharacteristic
716C22×C22⋊C4C22×C12711yescharacteristic
717C22×C22⋊C4C22×C12711yescharacteristic
718C22×C22⋊C4C22×C12711yescharacteristic
719C22×C22⋊C4C22×C12711yescharacteristic
720C22×C22⋊C4C22×C12711yescharacteristic
721C22×C22⋊C4C22×C12711yescharacteristic
722C22×C22⋊C4C22×C12711yescharacteristic
723C22×C22⋊C4C22×C12711yescharacteristic
724C22×C22⋊C4C22×C12711yescharacteristic
725C22×C22⋊C4C22×C12711yescharacteristic
726C22×C42C22×C12711yescharacteristic
727#394—24no—
728#392—24no—
729#386—24no—
730#385—24no—
731C2×#95C22×C12711yescharacteristic
732C2×#95C22×C12711yescharacteristic
733C2×#95C22×C12711yescharacteristic
734C2×#95C22×C12711yescharacteristic
735C2×#95C22×C12711yescharacteristic
736C2×#95C22×C12711yescharacteristic
737C2×#95C22×C12711yescharacteristic
738C2×#95C22×C12711yescharacteristic
739C2×#95C22×C12711yescharacteristic
740C2×#95C22×C12711yescharacteristic
741C2×#95C22×C12711yescharacteristic
742C2×#95C22×C12711yescharacteristic
743C25C23×C12711yescharacteristic
744C25C23×C12711yescharacteristic
745C25C23×C12711yescharacteristic
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—22no—
755C22×D4—22no—
756C22×D4—22no—
757C22×D4—22no—
758C22×D4—22no—
759C22×D4—22no—
760C22×D4—22no—
761C22×D4—22no—
762C22×D4—41no—
763C22×D4—41no—
764C22×D4—41no—
765C22×D4—41no—
766C22×D4D4×C12714yes—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—22no—
771C23×C4—22no—
772C23×C4—22no—
773C23×C4—22no—
774C23×C4—22no—
775C23×C4—22no—
776C23×C4—41no—
777C23×C4—41no—
778C23×C4—41no—
779C23×C4—41no—
780C23×C4D4×C12714yescomplemented
781C23×C4C23×C12711yescharacteristic
782C23×C4C23×C12711yescharacteristic
783C23×C4C23×C12711yescharacteristic
784C23×C4C23×C12711yescharacteristic
785C23×C4C23×C12711yescharacteristic
786C23×C4C23×C12711yescharacteristic
787C23×C4C23×C12711yescharacteristic
788C23×C4C23×C12711yescharacteristic
789C23×C4C23×C12711yescharacteristic
790C23×C4C23×C12711yescharacteristic
791C23×C4C23×C12711yescharacteristic
792C23×C4C23×C12711yescharacteristic
793#123—232no—
794C4×D4—232no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—22no—
799C2×C4⋊C4—22no—
800C2×C4⋊C4—22no—
801C2×C4⋊C4—22no—
802C2×C4⋊C4—22no—
803C2×C4⋊C4—22no—
804C2×C4⋊C4—22no—
805C2×C4⋊C4—41no—
806C2×C4⋊C4D4×C12714yescomplemented
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
828C2×C22⋊C4—22no—
829C2×C22⋊C4—22no—
830C2×C22⋊C4—22no—
831C2×C22⋊C4—22no—
832C2×C22⋊C4—22no—
833C2×C22⋊C4—22no—
834C2×C22⋊C4—22no—
835C2×C22⋊C4—22no—
836C2×C22⋊C4—22no—
837C2×C22⋊C4—22no—
838C2×C22⋊C4—41no—
839C2×C22⋊C4—41no—
840C2×C22⋊C4—41no—
841C2×C22⋊C4—41no—
842C2×C22⋊C4—41no—
843C2×C22⋊C4—41no—
844C2×C22⋊C4D4×C12714yescomplemented
845C2×C22⋊C4D4×C12714yescomplemented
846C2×C42—22no—
847C2×C42—22no—
848C2×C42—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—22no—
857#95—22no—
858#95—41no—
859#95—41no—
860#95—41no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24—21no—
896C24—21no—
897C24—21no—
898C24—21no—
899C24C2×D4×C12712yes—
900C24C2×D4×C12712yes—
901C24C2×D4×C12712yes—
902C24C2×D4×C12712yes—
903C24C2×D4×C12712yes—
904C24#41×C12712yes—
905C24#41×C12712yes—
906C24C24×C12711yescharacteristic
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—28no—
910C2×D4—28no—
911C2×D4—28no—
912C2×D4—28no—
913C2×D4—28no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
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—28no—
937C22×C4—28no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—28no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
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×C4C2×D4×C12712yes—
1013C22×C4C2×D4×C12712yes—
1014C22×C4C2×D4×C12712yes—
1015C22×C4C2×D4×C12712yes—
1016C22×C4C2×D4×C12712yes—
1017C22×C4C2×D4×C12712yes—
1018C22×C4C2×D4×C12712yes—
1019C22×C4C2×D4×C12712yes—
1020C22×C4C2×D4×C12712yes—
1021C22×C4C2×D4×C12712yes—
1022C22×C4#41×C12712yes—
1023C22×C4#41×C12712yes—
1024C22×C4#41×C12712yes—
1025C22×C4#41×C12712yes—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—44no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—28no—
1034C22⋊C4—28no—
1035C22⋊C4—28no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4—44no—
1039C22⋊C4—44no—
1040C22⋊C4—44no—
1041C22⋊C4—44no—
1042C22⋊C4—44no—
1043C42—28no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—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—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23#120×C12714yes—
1148C23#123×C12714yescomplemented
1149C23C22×D4×C12711yescharacteristic
1150C23C22×D4×C12711yescharacteristic
1151C23C22×D4×C12711yescharacteristic
1152C23C22×D4×C12711yescharacteristic
1153C23C22×D4×C12711yescharacteristic
1154C23C2×#41×C12711yescharacteristic
1155C23C2×#41×C12711yescharacteristic
1156C23C2×#41×C12711yescharacteristic
1157C23C2×#41×C12711yescharacteristic
1158C23C2×#41×C12711yescharacteristic
1159C23C2×#41×C12711yescharacteristic
1160C23H(5,𝔽2)×C12711yescharacteristic
1161C23H(5,𝔽2)×C12711yescharacteristic
1162C23H(5,𝔽2)×C12711yescharacteristic
1163C232−1+4×C12711yescharacteristic
1164D4—232no—
1165D4—416no—
1166D4—416no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—416no—
1204C2×C4—416no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4#120×C12714yes—
1252C2×C4#123×C12714yescomplemented
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22C2×#120×C12711yescharacteristic
1299C22C2×#120×C12711yescharacteristic
1300C22C2×#123×C12711yescharacteristic
1301C22C2×#123×C12711yescharacteristic
1302C22#525×C12711yescharacteristic
1303C22#525×C12711yescharacteristic
1304C22#525×C12711yescharacteristic
1305C22#525×C12711yescharacteristic
1306C22#525×C12711yescharacteristic
1307C22#525×C12711yescharacteristic
1308C22#532×C12711yescharacteristic
1309C22#532×C12711yescharacteristic
1310C22#532×C12711yescharacteristic
1311C22#534×C12711yescharacteristic
1312C22#537×C12711yescharacteristic
1313C22#538×C12711yescharacteristic
1314C22#539×C12711yescharacteristic
1315C22#540×C12711yescharacteristic
1316C22#542×C12711yescharacteristic
1317C22D42×C12711yescharacteristic
1318C22D42×C12711yescharacteristic
1319C22D42×C12711yescharacteristic
1320C22D42×C12711yescharacteristic
1321C22#546×C12711yescharacteristic
1322C22#546×C12711yescharacteristic
1323C22#546×C12711yescharacteristic
1324C22#547×C12711yescharacteristic
1325C22#547×C12711yescharacteristic
1326C22#547×C12711yescharacteristic
1327C22#548×C12711yescharacteristic
1328C22#550×C12711yescharacteristic
1329C22#551×C12711yescharacteristic
1330C22#553×C12711yescharacteristic
1331C22#553×C12711yescharacteristic
1332C22#559×C12711yescharacteristic
1333C4—24no—
1334C4—24no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—42no—
1343C4—81no—
1344C4—81no—
1345C2—44no—
1346C2—44no—
1347C2—82no—
1348C2C127×#238811yescharacteristic
1349C2C127×#240311yescharacteristic
1350C2C127×#240711yescharacteristic
1351C2C127×#241811yescharacteristic
1352C2C127×#242211yescharacteristic
1353C2C127×#243011yescharacteristic
1354C2C127×#244311yescharacteristic
1355C2C127×#244511yescharacteristic
1356C2C127×#245511yescharacteristic
1357C2C127×#245611yescharacteristic
1358C2C127×#246111yescharacteristic
1359C2C127×#246411yescharacteristic
1360C2C127×#260211yescharacteristic
1361C2C127×#263011yescharacteristic
1362C2C127×#284911yescharacteristic
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×#123×C127C2semidirect
2. C22×C4×D4×C127C2semidirect
3. C2×#394×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#385×C127C2semidirect
7. C127×#1444C2semidirect
8. C127×#1440C2semidirect
9. C127×#1439C2semidirect
10. C127×#1439C2semidirect
11. C127×#1438C2semidirect
12. C127×#1438C2semidirect
13. C127×#1437C2semidirect
14. C127×#1436C2semidirect
15. C127×C22⋊#95C2semidirect
98. C23×C4×C127D4semidirect
124. C2×C4⋊C4×C127D4semidirect
162. C2×C22⋊C4×C127D4semidirect
163. C2×C22⋊C4×C127D4semidirect
466. C23×C127#123semidirect
570. C2×C4×C127#123semidirect
663. #14721C127direct (N × H)
682. C22×#123C2×C127semidirect
683. C22×C4×D4C2×C127semidirect
684. C2×#394C2×C127semidirect
686. C2×#386C2×C127semidirect
687. C2×#385C2×C127semidirect
688. #1444C2×C127semidirect
689. #1440C2×C127semidirect
690. #1439C2×C127semidirect
691. #1439C2×C127semidirect
692. #1438C2×C127semidirect
693. #1438C2×C127semidirect
694. #1437C2×C127semidirect
695. #1436C2×C127semidirect
696. C22⋊#95C2×C127semidirect
697. C127#14721direct (N × H)
780. C23×C4D4×C127semidirect
806. C2×C4⋊C4D4×C127semidirect
844. C2×C22⋊C4D4×C127semidirect
845. C2×C22⋊C4D4×C127semidirect
1148. C23#123×C127semidirect
1252. C2×C4#123×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C22×C4×D4×C1272
C2×#394×C1272
C2×#392×C1272
C2×#386×C1272
C2×#385×C1272
C127×#14442
C127×#14402
C127×#14392
C127×#14382
C127×#14372
C127×#14362
C127×C22⋊#952
#14721127