Finite Group Databasebeta

← C127×#14534 #44578207

Subgroups — C127×#14534 #44578207

Order 32512.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C127C211yesmaximal, characteristic
2C2×#390×C127C211yesmaximal, characteristic, complemented
3C2×#390×C127C211yesmaximal, characteristic, complemented
4C2×#388×C127C211yesmaximal, characteristic, complemented
5C2×#386×C127C211yesmaximal, characteristic, complemented
6C2×#386×C127C211yesmaximal, characteristic, complemented
7C2×#385×C127C211yesmaximal, 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×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C23×D4×C127C2211yescharacteristic
18C23×D4×C127C2211yescharacteristic
19C24×C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊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×C22⋊C4×C127C2211yescharacteristic
37C22×C42×C127C2211yescharacteristic
38C22×C42×C127C2211yescharacteristic
39#392×C127C418yescomplemented
40#390×C127—24no—
41#390×C127—24no—
42#388×C127—24no—
43#386×C127—24no—
44#386×C127—24no—
45#385×C127—24no—
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C2×#95×C127C2211yescharacteristic
57C2×#95×C127C2211yescharacteristic
58C25×C127C2311yescharacteristic
59C25×C127C2311yescharacteristic
60C25×C127C2311yescharacteristic
61C22×D4×C127—22no—
62C22×D4×C127—22no—
63C22×D4×C127—22no—
64C22×D4×C127—22no—
65C22×D4×C127—22no—
66C22×D4×C127—22no—
67C22×D4×C127—22no—
68C22×D4×C127—22no—
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×C127—41no—
79C22×D4×C127C2×C414yes—
80C22×D4×C127C2×C414yes—
81C22×D4×C127C2×C414yescomplemented
82C23×C4×C127—22no—
83C23×C4×C127—22no—
84C23×C4×C127—22no—
85C23×C4×C127—41no—
86C23×C4×C127—41no—
87C23×C4×C127—41no—
88C23×C4×C127—41no—
89C23×C4×C127C2311yescharacteristic
90C23×C4×C127C2311yescharacteristic
91C23×C4×C127C2311yescharacteristic
92C23×C4×C127C2311yescharacteristic
93C23×C4×C127C2311yescharacteristic
94C23×C4×C127C2311yescharacteristic
95C23×C4×C127C2311yescharacteristic
96C23×C4×C127C2311yescharacteristic
97C23×C4×C127C2311yescharacteristic
98C23×C4×C127C2311yescharacteristic
99C23×C4×C127C2311yescharacteristic
100C23×C4×C127C2311yescharacteristic
101C2×C4⋊C4×C127—22no—
102C2×C4⋊C4×C127—22no—
103C2×C4⋊C4×C127—22no—
104C2×C4⋊C4×C127—22no—
105C2×C4⋊C4×C127—41no—
106C2×C4⋊C4×C127—41no—
107C2×C4⋊C4×C127—41no—
108C2×C4⋊C4×C127—41no—
109C2×C4⋊C4×C127D414yescomplemented
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—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×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×C127C2×C414yes—
149C2×C22⋊C4×C127C2×C414yescomplemented
150C2×C22⋊C4×C127C2×C414yescomplemented
151C2×C22⋊C4×C127D414yescomplemented
152C2×C42×C127—22no—
153C2×C42×C127—22no—
154C2×C42×C127—22no—
155C2×C42×C127—41no—
156C2×C42×C127—41no—
157C2×C42×C127—41no—
158#95×C127—22no—
159#95×C127—22no—
160#95×C127—22no—
161#95×C127—22no—
162#95×C127—22no—
163#95×C127—22no—
164#95×C127—22no—
165#95×C127—41no—
166#95×C127—41no—
167#95×C127—41no—
168#95×C127C2×C414yescomplemented
169#95×C127D414yescomplemented
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×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×C127C22×C412yes—
211C24×C127C22×C412yes—
212C24×C127C22×C412yes—
213C24×C127C2×D412yes—
214C24×C127#4112yes—
215C24×C127C2411yescharacteristic
216C2×D4×C127—28no—
217C2×D4×C127—28no—
218C2×D4×C127—28no—
219C2×D4×C127—28no—
220C2×D4×C127—44no—
221C2×D4×C127—44no—
222C2×D4×C127—44no—
223C2×D4×C127—44no—
224C2×D4×C127—44no—
225C2×D4×C127—44no—
226C2×D4×C127—44no—
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—
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×C127—21no—
303C22×C4×C127—21no—
304C22×C4×C127—21no—
305C22×C4×C127—21no—
306C22×C4×C127—21no—
307C22×C4×C127—44no—
308C22×C4×C127—44no—
309C22×C4×C127—44no—
310C22×C4×C127—44no—
311C22×C4×C127—44no—
312C22×C4×C127—44no—
313C22×C4×C127—44no—
314C22×C4×C127C22×C412yes—
315C22×C4×C127C22×C412yes—
316C22×C4×C127C22×C412yes—
317C22×C4×C127C22×C412yes—
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—
328C4⋊C4×C127—44no—
329C4⋊C4×C127—44no—
330C4⋊C4×C127—44no—
331C22⋊C4×C127—28no—
332C22⋊C4×C127—28no—
333C22⋊C4×C127—44no—
334C22⋊C4×C127—44no—
335C22⋊C4×C127—44no—
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—
345C42×C127—44no—
346C42×C127—44no—
347C23×C127—22no—
348C23×C127—22no—
349C23×C127—22no—
350C23×C127—22no—
351C23×C127—22no—
352C23×C127—22no—
353C23×C127—22no—
354C23×C127—22no—
355C23×C127—22no—
356C23×C127—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—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—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×C127C4×D414yes—
452C23×C127C23×C411yescharacteristic
453C23×C127C22×D411yescharacteristic
454C23×C127C22×D411yescharacteristic
455C23×C127C22×D411yescharacteristic
456C23×C127C2×#4111yescharacteristic
457C23×C127C2×#4111yescharacteristic
458C23×C127C2×#4111yescharacteristic
459C23×C127H(5,𝔽2)11yescharacteristic
460C23×C127H(5,𝔽2)11yescharacteristic
461C23×C127H(5,𝔽2)11yescharacteristic
462C23×C127H(5,𝔽2)11yescharacteristic
463C23×C127H(5,𝔽2)11yescharacteristic
464C23×C127H(5,𝔽2)11yescharacteristic
465C23×C127H(5,𝔽2)11yescharacteristic
466C23×C1272−1+411yescharacteristic
467D4×C127—416no—
468D4×C127—416no—
469D4×C127—416no—
470C2×C4×C127—22no—
471C2×C4×C127—22no—
472C2×C4×C127—22no—
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—416no—
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×C127C4×D414yes—
554C2×C4×C127C4×D414yes—
555C22×C127—24no—
556C22×C127—24no—
557C22×C127—24no—
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—42no—
579C22×C127—42no—
580C22×C127—42no—
581C22×C127—42no—
582C22×C127—42no—
583C22×C127—42no—
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×C127C2×C4×D411yescharacteristic
601C22×C127C2×C4×D411yescharacteristic
602C22×C127C2×C4×D411yescharacteristic
603C22×C127#51811yescharacteristic
604C22×C127#51811yescharacteristic
605C22×C127#51811yescharacteristic
606C22×C127#52011yescharacteristic
607C22×C127#53411yescharacteristic
608C22×C127#53411yescharacteristic
609C22×C127#53511yescharacteristic
610C22×C127#53511yescharacteristic
611C22×C127#53511yescharacteristic
612C22×C127#53711yescharacteristic
613C22×C127#53811yescharacteristic
614C22×C127#53811yescharacteristic
615C22×C127#53811yescharacteristic
616C22×C127#53811yescharacteristic
617C22×C127#54011yescharacteristic
618C22×C127#54211yescharacteristic
619C22×C127D4211yescharacteristic
620C22×C127D4211yescharacteristic
621C22×C127D4211yescharacteristic
622C22×C127#54611yescharacteristic
623C22×C127#54611yescharacteristic
624C22×C127#54711yescharacteristic
625C22×C127#54811yescharacteristic
626C22×C127#55011yescharacteristic
627C22×C127#55011yescharacteristic
628C22×C127#55111yescharacteristic
629C22×C127#55311yescharacteristic
630C22×C127#55911yescharacteristic
631C22×C127#56011yescharacteristic
632C22×C127#56011yescharacteristic
633C22×C127#56211yescharacteristic
634C22×C127#56211yescharacteristic
635C4×C127—24no—
636C4×C127—24no—
637C4×C127—42no—
638C4×C127—42no—
639C4×C127—42no—
640C4×C127—42no—
641C4×C127—42no—
642C4×C127—42no—
643C4×C127—42no—
644C4×C127—42no—
645C4×C127—81no—
646C4×C127—81no—
647#14534C12711yesmaximal, characteristic, direct product factor, Sylow
648C2×C127—44no—
649C2×C127—82no—
650C2×C127—82no—
651C2×C127#232111yescharacteristic
652C2×C127#232111yescharacteristic
653C2×C127#232411yescharacteristic
654C2×C127#235811yescharacteristic
655C2×C127#236111yescharacteristic
656C2×C127#236611yescharacteristic
657C2×C127#237711yescharacteristic
658C2×C127#266911yescharacteristic
659C2×C127#267311yescharacteristic
660C2×C127#267611yescharacteristic
661C2×C127#268211yescharacteristic
662C2×C127#271011yescharacteristic
663C2×C127#271411yescharacteristic
664C2×C127#273011yescharacteristic
665C2×C127#279711yescharacteristic
666C2×#392C2×C12711yescharacteristic
667C2×#390C2×C12711yescharacteristic, complemented
668C2×#390C2×C12711yescharacteristic, complemented
669C2×#388C2×C12711yescharacteristic, complemented
670C2×#386C2×C12711yescharacteristic, complemented
671C2×#386C2×C12711yescharacteristic, complemented
672C2×#385C2×C12711yescharacteristic, complemented
673#1440C2×C12711yescharacteristic, complemented
674#1439C2×C12711yescharacteristic, complemented
675#1439C2×C12711yescharacteristic, complemented
676#1438C2×C12711yescharacteristic, complemented
677#1438C2×C12711yescharacteristic, complemented
678#1437C2×C12711yescharacteristic, complemented
679#1436C2×C12711yescharacteristic, complemented
680#1436C2×C12711yescharacteristic, complemented
681C127#1453411yescharacteristic, direct product factor, Sylow
682C23×D4C22×C12711yescharacteristic
683C23×D4C22×C12711yescharacteristic
684C23×D4C22×C12711yescharacteristic
685C24×C4C22×C12711yescharacteristic
686C22×C4⋊C4C22×C12711yescharacteristic
687C22×C4⋊C4C22×C12711yescharacteristic
688C22×C4⋊C4C22×C12711yescharacteristic
689C22×C22⋊C4C22×C12711yescharacteristic
690C22×C22⋊C4C22×C12711yescharacteristic
691C22×C22⋊C4C22×C12711yescharacteristic
692C22×C22⋊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×C42C22×C12711yescharacteristic
704C22×C42C22×C12711yescharacteristic
705#392C4×C12718yescomplemented
706#390—24no—
707#390—24no—
708#388—24no—
709#386—24no—
710#386—24no—
711#385—24no—
712C2×#95C22×C12711yescharacteristic
713C2×#95C22×C12711yescharacteristic
714C2×#95C22×C12711yescharacteristic
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
724C25C23×C12711yescharacteristic
725C25C23×C12711yescharacteristic
726C25C23×C12711yescharacteristic
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C22×D4C2×C4×C12714yes—
746C22×D4C2×C4×C12714yes—
747C22×D4C2×C4×C12714yescomplemented
748C23×C4—22no—
749C23×C4—22no—
750C23×C4—22no—
751C23×C4—41no—
752C23×C4—41no—
753C23×C4—41no—
754C23×C4—41no—
755C23×C4C23×C12711yescharacteristic
756C23×C4C23×C12711yescharacteristic
757C23×C4C23×C12711yescharacteristic
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
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4—41no—
773C2×C4⋊C4—41no—
774C2×C4⋊C4—41no—
775C2×C4⋊C4D4×C12714yescomplemented
776C2×C22⋊C4—22no—
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—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
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⋊C4C2×C4×C12714yes—
815C2×C22⋊C4C2×C4×C12714yescomplemented
816C2×C22⋊C4C2×C4×C12714yescomplemented
817C2×C22⋊C4D4×C12714yescomplemented
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—41no—
822C2×C42—41no—
823C2×C42—41no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—41no—
832#95—41no—
833#95—41no—
834#95C2×C4×C12714yescomplemented
835#95D4×C12714yescomplemented
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
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—
876C24C22×C4×C12712yes—
877C24C22×C4×C12712yes—
878C24C22×C4×C12712yes—
879C24C2×D4×C12712yes—
880C24#41×C12712yes—
881C24C24×C12711yescharacteristic
882C2×D4—28no—
883C2×D4—28no—
884C2×D4—28no—
885C2×D4—28no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
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×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—44no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4C22×C4×C12712yes—
981C22×C4C22×C4×C12712yes—
982C22×C4C22×C4×C12712yes—
983C22×C4C22×C4×C12712yes—
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×C4#41×C12712yes—
993C22×C4#41×C12712yes—
994C4⋊C4—44no—
995C4⋊C4—44no—
996C4⋊C4—44no—
997C22⋊C4—28no—
998C22⋊C4—28no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
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—
1011C42—44no—
1012C42—44no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
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—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
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—
1117C23C4×D4×C12714yes—
1118C23C23×C4×C12711yescharacteristic
1119C23C22×D4×C12711yescharacteristic
1120C23C22×D4×C12711yescharacteristic
1121C23C22×D4×C12711yescharacteristic
1122C23C2×#41×C12711yescharacteristic
1123C23C2×#41×C12711yescharacteristic
1124C23C2×#41×C12711yescharacteristic
1125C23H(5,𝔽2)×C12711yescharacteristic
1126C23H(5,𝔽2)×C12711yescharacteristic
1127C23H(5,𝔽2)×C12711yescharacteristic
1128C23H(5,𝔽2)×C12711yescharacteristic
1129C23H(5,𝔽2)×C12711yescharacteristic
1130C23H(5,𝔽2)×C12711yescharacteristic
1131C23H(5,𝔽2)×C12711yescharacteristic
1132C232−1+4×C12711yescharacteristic
1133D4—416no—
1134D4—416no—
1135D4—416no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
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—416no—
1173C2×C4—41no—
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×C4C4×D4×C12714yes—
1220C2×C4C4×D4×C12714yes—
1221C22—24no—
1222C22—24no—
1223C22—24no—
1224C22—42no—
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—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
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—
1266C22C2×C4×D4×C12711yescharacteristic
1267C22C2×C4×D4×C12711yescharacteristic
1268C22C2×C4×D4×C12711yescharacteristic
1269C22#518×C12711yescharacteristic
1270C22#518×C12711yescharacteristic
1271C22#518×C12711yescharacteristic
1272C22#520×C12711yescharacteristic
1273C22#534×C12711yescharacteristic
1274C22#534×C12711yescharacteristic
1275C22#535×C12711yescharacteristic
1276C22#535×C12711yescharacteristic
1277C22#535×C12711yescharacteristic
1278C22#537×C12711yescharacteristic
1279C22#538×C12711yescharacteristic
1280C22#538×C12711yescharacteristic
1281C22#538×C12711yescharacteristic
1282C22#538×C12711yescharacteristic
1283C22#540×C12711yescharacteristic
1284C22#542×C12711yescharacteristic
1285C22D42×C12711yescharacteristic
1286C22D42×C12711yescharacteristic
1287C22D42×C12711yescharacteristic
1288C22#546×C12711yescharacteristic
1289C22#546×C12711yescharacteristic
1290C22#547×C12711yescharacteristic
1291C22#548×C12711yescharacteristic
1292C22#550×C12711yescharacteristic
1293C22#550×C12711yescharacteristic
1294C22#551×C12711yescharacteristic
1295C22#553×C12711yescharacteristic
1296C22#559×C12711yescharacteristic
1297C22#560×C12711yescharacteristic
1298C22#560×C12711yescharacteristic
1299C22#562×C12711yescharacteristic
1300C22#562×C12711yescharacteristic
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—81no—
1312C4—81no—
1313C2—44no—
1314C2—82no—
1315C2—82no—
1316C2C127×#232111yescharacteristic
1317C2C127×#232111yescharacteristic
1318C2C127×#232411yescharacteristic
1319C2C127×#235811yescharacteristic
1320C2C127×#236111yescharacteristic
1321C2C127×#236611yescharacteristic
1322C2C127×#237711yescharacteristic
1323C2C127×#266911yescharacteristic
1324C2C127×#267311yescharacteristic
1325C2C127×#267611yescharacteristic
1326C2C127×#268211yescharacteristic
1327C2C127×#271011yescharacteristic
1328C2C127×#271411yescharacteristic
1329C2C127×#273011yescharacteristic
1330C2C127×#279711yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#390×C127C2semidirect
3. C2×#390×C127C2semidirect
4. C2×#388×C127C2semidirect
5. C2×#386×C127C2semidirect
6. C2×#386×C127C2semidirect
7. C2×#385×C127C2semidirect
8. C127×#1440C2semidirect
9. C127×#1439C2semidirect
10. C127×#1439C2semidirect
11. C127×#1438C2semidirect
12. C127×#1438C2semidirect
13. C127×#1437C2semidirect
14. C127×#1436C2semidirect
15. C127×#1436C2semidirect
39. #392×C127C4semidirect
81. C22×D4×C127C2×C4semidirect
109. C2×C4⋊C4×C127D4semidirect
149. C2×C22⋊C4×C127C2×C4semidirect
150. C2×C22⋊C4×C127C2×C4semidirect
151. C2×C22⋊C4×C127D4semidirect
168. #95×C127C2×C4semidirect
169. #95×C127D4semidirect
647. #14534C127direct (N × H)
667. C2×#390C2×C127semidirect
668. C2×#390C2×C127semidirect
669. C2×#388C2×C127semidirect
670. C2×#386C2×C127semidirect
671. C2×#386C2×C127semidirect
672. C2×#385C2×C127semidirect
673. #1440C2×C127semidirect
674. #1439C2×C127semidirect
675. #1439C2×C127semidirect
676. #1438C2×C127semidirect
677. #1438C2×C127semidirect
678. #1437C2×C127semidirect
679. #1436C2×C127semidirect
680. #1436C2×C127semidirect
681. C127#14534direct (N × H)
705. #392C4×C127semidirect
747. C22×D4C2×C4×C127semidirect
775. C2×C4⋊C4D4×C127semidirect
815. C2×C22⋊C4C2×C4×C127semidirect
816. C2×C22⋊C4C2×C4×C127semidirect
817. C2×C22⋊C4D4×C127semidirect
834. #95C2×C4×C127semidirect
835. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#392×C1272
C2×#390×C1272
C2×#388×C1272
C2×#386×C1272
C2×#385×C1272
C127×#14402
C127×#14392
C127×#14382
C127×#14372
C127×#14362
#14534127