Finite Group Databasebeta

← C127×#14566 #44578239

Subgroups — C127×#14566 #44578239

Order 32512.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C127C211yesmaximal, characteristic
2C2×#388×C127C211yesmaximal, characteristic, complemented
3C2×#388×C127C211yesmaximal, characteristic, complemented
4C127×#1443C211yesmaximal, characteristic, complemented
5C127×#1439C211yesmaximal, characteristic, complemented
6C127×#1439C211yesmaximal, characteristic, complemented
7C127×#1438C211yesmaximal, characteristic
8C127×#1438C211yesmaximal, characteristic
9C127×#1437C211yesmaximal, characteristic, complemented
10C127×#1437C211yesmaximal, characteristic, complemented
11C127×#1437C211yesmaximal, characteristic, complemented
12C127×#1437C211yesmaximal, characteristic, complemented
13C127×#1436C211yesmaximal, characteristic, complemented
14C127×#1436C211yesmaximal, characteristic, complemented
15C127×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2211yescharacteristic
23C22×C22⋊C4×C127C2211yescharacteristic
24C22×C22⋊C4×C127C2211yescharacteristic
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2211yescharacteristic
27C22×C22⋊C4×C127C2211yescharacteristic
28C22×C22⋊C4×C127C2211yescharacteristic
29C22×C22⋊C4×C127C2211yescharacteristic
30C22×C22⋊C4×C127C2211yescharacteristic
31C22×C22⋊C4×C127C2211yescharacteristic
32C22×C42×C127C2211yescharacteristic
33C22×C42×C127C2211yescharacteristic
34C22×C42×C127C2211yescharacteristic
35#394×C127C418yescomplemented
36#388×C127—24no—
37#388×C127—24no—
38C2×#95×C127C2211yescharacteristic
39C2×#95×C127C2211yescharacteristic
40C2×#95×C127C2211yescharacteristic
41C2×#95×C127C2211yescharacteristic
42C2×#95×C127C2211yescharacteristic
43C2×#95×C127C2211yescharacteristic
44C2×#95×C127C2211yescharacteristic
45C2×#95×C127C2211yescharacteristic
46C2×#95×C127C2211yescharacteristic
47C2×#95×C127C2211yescharacteristic
48C2×#95×C127C2211yescharacteristic
49C2×#95×C127C2211yescharacteristic
50C2×#95×C127C2211yescharacteristic
51C2×#95×C127C2211yescharacteristic
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C25×C127C2311yescharacteristic
55C25×C127C2311yescharacteristic
56C22×D4×C127—41no—
57C22×D4×C127—41no—
58C22×D4×C127—41no—
59C22×D4×C127—41no—
60C22×D4×C127—41no—
61C22×D4×C127—41no—
62C22×D4×C127C2×C414yes—
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C23×C4×C127C2311yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C23×C4×C127C2311yescharacteristic
70C23×C4×C127C2311yescharacteristic
71C23×C4×C127C2311yescharacteristic
72C23×C4×C127C2311yescharacteristic
73C23×C4×C127C2311yescharacteristic
74C23×C4×C127C2311yescharacteristic
75C23×C4×C127C2311yescharacteristic
76C2×C4⋊C4×C127—22no—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—41no—
81C2×C4⋊C4×C127—41no—
82C2×C4⋊C4×C127—41no—
83C2×C4⋊C4×C127—41no—
84C2×C4⋊C4×C127C2×C414yes—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—22no—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127—22no—
95C2×C22⋊C4×C127—22no—
96C2×C22⋊C4×C127—22no—
97C2×C22⋊C4×C127—22no—
98C2×C22⋊C4×C127—22no—
99C2×C22⋊C4×C127—22no—
100C2×C22⋊C4×C127—22no—
101C2×C22⋊C4×C127—41no—
102C2×C22⋊C4×C127—41no—
103C2×C22⋊C4×C127—41no—
104C2×C22⋊C4×C127—41no—
105C2×C22⋊C4×C127—41no—
106C2×C22⋊C4×C127—41no—
107C2×C22⋊C4×C127—41no—
108C2×C22⋊C4×C127—41no—
109C2×C22⋊C4×C127—41no—
110C2×C22⋊C4×C127—41no—
111C2×C22⋊C4×C127—41no—
112C2×C22⋊C4×C127—41no—
113C2×C22⋊C4×C127—41no—
114C2×C22⋊C4×C127—41no—
115C2×C22⋊C4×C127—41no—
116C2×C22⋊C4×C127—41no—
117C2×C22⋊C4×C127C2×C414yes—
118C2×C22⋊C4×C127C2×C414yes—
119C2×C22⋊C4×C127C2×C414yes—
120C2×C22⋊C4×C127C2×C414yes—
121C2×C42×C127—22no—
122C2×C42×C127—22no—
123C2×C42×C127—22no—
124C2×C42×C127—41no—
125C2×C42×C127—41no—
126C2×C42×C127—41no—
127C2×C42×C127—41no—
128C2×C42×C127—41no—
129C2×C42×C127—41no—
130#95×C127—22no—
131#95×C127—22no—
132#95×C127—22no—
133#95×C127—22no—
134#95×C127—41no—
135#95×C127—41no—
136#95×C127—41no—
137#95×C127—41no—
138#95×C127—41no—
139#95×C127—41no—
140#95×C127—41no—
141#95×C127—41no—
142#95×C127—41no—
143#95×C127—41no—
144#95×C127C2×C414yes—
145#95×C127D414yescomplemented
146C24×C127—21no—
147C24×C127—21no—
148C24×C127—21no—
149C24×C127—21no—
150C24×C127—21no—
151C24×C127—21no—
152C24×C127—21no—
153C24×C127—21no—
154C24×C127—21no—
155C24×C127—21no—
156C24×C127—21no—
157C24×C127—21no—
158C24×C127—21no—
159C24×C127—21no—
160C24×C127—21no—
161C24×C127—21no—
162C24×C127—21no—
163C24×C127—21no—
164C24×C127—21no—
165C24×C127—21no—
166C24×C127—21no—
167C24×C127—21no—
168C24×C127—21no—
169C24×C127—21no—
170C24×C127—21no—
171C24×C127—21no—
172C24×C127—21no—
173C24×C127—21no—
174C24×C127C22×C412yes—
175C24×C127C22×C412yes—
176C24×C127C2411yescharacteristic
177C2×D4×C127—44no—
178C2×D4×C127—44no—
179C2×D4×C127—44no—
180C2×D4×C127—44no—
181C2×D4×C127—44no—
182C2×D4×C127—44no—
183C2×D4×C127—44no—
184C22×C4×C127—21no—
185C22×C4×C127—21no—
186C22×C4×C127—21no—
187C22×C4×C127—21no—
188C22×C4×C127—21no—
189C22×C4×C127—21no—
190C22×C4×C127—21no—
191C22×C4×C127—21no—
192C22×C4×C127—21no—
193C22×C4×C127—21no—
194C22×C4×C127—21no—
195C22×C4×C127—21no—
196C22×C4×C127—21no—
197C22×C4×C127—21no—
198C22×C4×C127—21no—
199C22×C4×C127—21no—
200C22×C4×C127—21no—
201C22×C4×C127—21no—
202C22×C4×C127—21no—
203C22×C4×C127—21no—
204C22×C4×C127—21no—
205C22×C4×C127—21no—
206C22×C4×C127—21no—
207C22×C4×C127—21no—
208C22×C4×C127—21no—
209C22×C4×C127—21no—
210C22×C4×C127—21no—
211C22×C4×C127—21no—
212C22×C4×C127—21no—
213C22×C4×C127—21no—
214C22×C4×C127—21no—
215C22×C4×C127—21no—
216C22×C4×C127—21no—
217C22×C4×C127—21no—
218C22×C4×C127—21no—
219C22×C4×C127—21no—
220C22×C4×C127—21no—
221C22×C4×C127—21no—
222C22×C4×C127—21no—
223C22×C4×C127—21no—
224C22×C4×C127—21no—
225C22×C4×C127—21no—
226C22×C4×C127—21no—
227C22×C4×C127—21no—
228C22×C4×C127—21no—
229C22×C4×C127—21no—
230C22×C4×C127—21no—
231C22×C4×C127—21no—
232C22×C4×C127—21no—
233C22×C4×C127—21no—
234C22×C4×C127—21no—
235C22×C4×C127—21no—
236C22×C4×C127—21no—
237C22×C4×C127—21no—
238C22×C4×C127—21no—
239C22×C4×C127—21no—
240C22×C4×C127—21no—
241C22×C4×C127—21no—
242C22×C4×C127—21no—
243C22×C4×C127—21no—
244C22×C4×C127—21no—
245C22×C4×C127—21no—
246C22×C4×C127—21no—
247C22×C4×C127—21no—
248C22×C4×C127—21no—
249C22×C4×C127—21no—
250C22×C4×C127—21no—
251C22×C4×C127—21no—
252C22×C4×C127—21no—
253C22×C4×C127—21no—
254C22×C4×C127—21no—
255C22×C4×C127—21no—
256C22×C4×C127—21no—
257C22×C4×C127—21no—
258C22×C4×C127—21no—
259C22×C4×C127—21no—
260C22×C4×C127—21no—
261C22×C4×C127—21no—
262C22×C4×C127C22×C412yes—
263C22×C4×C127C22×C412yes—
264C22×C4×C127C22×C412yes—
265C22×C4×C127C22×C412yes—
266C22×C4×C127C22×C412yes—
267C22×C4×C127C2×D412yes—
268C22×C4×C127C2×D412yes—
269C22×C4×C127C2×D412yes—
270C22×C4×C127#4112yes—
271C22×C4×C127#4112yes—
272C22×C4×C127#4112yes—
273C22×C4×C127#4112yes—
274C22×C4×C127#4112yes—
275C4⋊C4×C127—44no—
276C4⋊C4×C127—44no—
277C4⋊C4×C127—44no—
278C22⋊C4×C127—28no—
279C22⋊C4×C127—28no—
280C22⋊C4×C127—44no—
281C22⋊C4×C127—44no—
282C22⋊C4×C127—44no—
283C22⋊C4×C127—44no—
284C22⋊C4×C127—44no—
285C22⋊C4×C127—44no—
286C22⋊C4×C127—44no—
287C22⋊C4×C127—44no—
288C22⋊C4×C127—44no—
289C22⋊C4×C127—44no—
290C42×C127—44no—
291C42×C127—44no—
292C42×C127—44no—
293C23×C127—22no—
294C23×C127—22no—
295C23×C127—22no—
296C23×C127—22no—
297C23×C127—22no—
298C23×C127—22no—
299C23×C127—22no—
300C23×C127—22no—
301C23×C127—22no—
302C23×C127—22no—
303C23×C127—22no—
304C23×C127—22no—
305C23×C127—22no—
306C23×C127—22no—
307C23×C127—41no—
308C23×C127—41no—
309C23×C127—41no—
310C23×C127—41no—
311C23×C127—41no—
312C23×C127—41no—
313C23×C127—41no—
314C23×C127—41no—
315C23×C127—41no—
316C23×C127—41no—
317C23×C127—41no—
318C23×C127—41no—
319C23×C127—41no—
320C23×C127—41no—
321C23×C127—41no—
322C23×C127—41no—
323C23×C127—41no—
324C23×C127—41no—
325C23×C127—41no—
326C23×C127—41no—
327C23×C127—41no—
328C23×C127—41no—
329C23×C127—41no—
330C23×C127—41no—
331C23×C127—41no—
332C23×C127—41no—
333C23×C127—41no—
334C23×C127—41no—
335C23×C127—41no—
336C23×C127—41no—
337C23×C127—41no—
338C23×C127—41no—
339C23×C127—41no—
340C23×C127—41no—
341C23×C127—41no—
342C23×C127—41no—
343C23×C127—41no—
344C23×C127—41no—
345C23×C127—41no—
346C23×C127—41no—
347C23×C127—41no—
348C23×C127—41no—
349C23×C127—41no—
350C23×C127—41no—
351C23×C127—41no—
352C23×C127—41no—
353C23×C127—41no—
354C23×C127—41no—
355C23×C127—41no—
356C23×C127—41no—
357C23×C127—41no—
358C23×C127—41no—
359C23×C127—41no—
360C23×C127—41no—
361C23×C127—41no—
362C23×C127—41no—
363C23×C127C23×C411yescharacteristic
364C23×C127C22×D411yescharacteristic
365C23×C127C2×#4111yescharacteristic
366C23×C127C2×#4111yescharacteristic
367C23×C127C2×#4111yescharacteristic
368C23×C127C2×#4111yescharacteristic
369C23×C127C2×#4111yescharacteristic
370C23×C127H(5,𝔽2)11yescharacteristic
371C23×C127H(5,𝔽2)11yescharacteristic
372C23×C127H(5,𝔽2)11yescharacteristic
373C23×C127H(5,𝔽2)11yescharacteristic
374C23×C127H(5,𝔽2)11yescharacteristic
375C23×C127H(5,𝔽2)11yescharacteristic
376C23×C127H(5,𝔽2)11yescharacteristic
377C23×C1272−1+411yescharacteristic
378D4×C127—416no—
379C2×C4×C127—22no—
380C2×C4×C127—22no—
381C2×C4×C127—22no—
382C2×C4×C127—22no—
383C2×C4×C127—22no—
384C2×C4×C127—22no—
385C2×C4×C127—22no—
386C2×C4×C127—22no—
387C2×C4×C127—22no—
388C2×C4×C127—22no—
389C2×C4×C127—22no—
390C2×C4×C127—22no—
391C2×C4×C127—22no—
392C2×C4×C127—22no—
393C2×C4×C127—22no—
394C2×C4×C127—22no—
395C2×C4×C127—22no—
396C2×C4×C127—22no—
397C2×C4×C127—22no—
398C2×C4×C127—22no—
399C2×C4×C127—22no—
400C2×C4×C127—22no—
401C2×C4×C127—22no—
402C2×C4×C127—22no—
403C2×C4×C127—22no—
404C2×C4×C127—22no—
405C2×C4×C127—22no—
406C2×C4×C127—22no—
407C2×C4×C127—22no—
408C2×C4×C127—22no—
409C2×C4×C127—22no—
410C2×C4×C127—22no—
411C2×C4×C127—22no—
412C2×C4×C127—22no—
413C2×C4×C127—22no—
414C2×C4×C127—22no—
415C2×C4×C127—41no—
416C2×C4×C127—41no—
417C2×C4×C127—41no—
418C2×C4×C127—41no—
419C2×C4×C127—41no—
420C2×C4×C127—41no—
421C2×C4×C127—41no—
422C2×C4×C127—41no—
423C2×C4×C127—41no—
424C2×C4×C127—41no—
425C2×C4×C127—41no—
426C2×C4×C127—41no—
427C2×C4×C127—41no—
428C2×C4×C127—41no—
429C2×C4×C127—41no—
430C2×C4×C127—41no—
431C2×C4×C127—41no—
432C2×C4×C127—41no—
433C2×C4×C127—41no—
434C2×C4×C127—41no—
435C2×C4×C127—41no—
436C2×C4×C127—41no—
437C2×C4×C127—41no—
438C2×C4×C127—41no—
439C2×C4×C127—41no—
440C2×C4×C127—41no—
441C2×C4×C127—41no—
442C2×C4×C127—41no—
443C2×C4×C127—41no—
444C2×C4×C127—41no—
445C2×C4×C127—41no—
446C2×C4×C127—41no—
447C2×C4×C127—41no—
448C2×C4×C127—41no—
449C2×C4×C127—41no—
450C2×C4×C127—41no—
451C2×C4×C127—41no—
452C2×C4×C127—41no—
453C2×C4×C127—41no—
454C2×C4×C127—41no—
455C2×C4×C127—41no—
456C2×C4×C127—41no—
457C2×C4×C127—41no—
458C2×C4×C127—41no—
459C2×C4×C127—41no—
460C2×C4×C127—41no—
461C2×C4×C127—41no—
462C2×C4×C127—41no—
463C2×C4×C127—41no—
464C2×C4×C127—41no—
465C2×C4×C127—41no—
466C2×C4×C127—41no—
467C2×C4×C127—41no—
468C2×C4×C127—41no—
469C2×C4×C127C4×D414yes—
470C22×C127—42no—
471C22×C127—42no—
472C22×C127—42no—
473C22×C127—42no—
474C22×C127—42no—
475C22×C127—42no—
476C22×C127—42no—
477C22×C127—42no—
478C22×C127—42no—
479C22×C127—42no—
480C22×C127—42no—
481C22×C127—42no—
482C22×C127—42no—
483C22×C127—42no—
484C22×C127—81no—
485C22×C127—81no—
486C22×C127—81no—
487C22×C127—81no—
488C22×C127—81no—
489C22×C127—81no—
490C22×C127—81no—
491C22×C127—81no—
492C22×C127—81no—
493C22×C127—81no—
494C22×C127—81no—
495C22×C127—81no—
496C22×C127—81no—
497C22×C127—81no—
498C22×C127—81no—
499C22×C127—81no—
500C22×C127C2×C4×D411yescharacteristic
501C22×C127C4×#4111yescharacteristic
502C22×C127C4×#4111yescharacteristic
503C22×C127#51811yescharacteristic
504C22×C127#51811yescharacteristic
505C22×C127#51811yescharacteristic
506C22×C127#52011yescharacteristic
507C22×C127#53511yescharacteristic
508C22×C127#53711yescharacteristic
509C22×C127#53811yescharacteristic
510C22×C127#53811yescharacteristic
511C22×C127#53811yescharacteristic
512C22×C127#53911yescharacteristic
513C22×C127#54011yescharacteristic
514C22×C127#54011yescharacteristic
515C22×C127#54211yescharacteristic
516C22×C127#54211yescharacteristic
517C22×C127#54211yescharacteristic
518C22×C127#54211yescharacteristic
519C22×C127#54611yescharacteristic
520C22×C127#54611yescharacteristic
521C22×C127#54611yescharacteristic
522C22×C127#55011yescharacteristic
523C22×C127#55111yescharacteristic
524C22×C127#55311yescharacteristic
525C22×C127#55311yescharacteristic
526C22×C127#55311yescharacteristic
527C22×C127#55311yescharacteristic
528C22×C127#55311yescharacteristic
529C22×C127#55511yescharacteristic
530C22×C127#55911yescharacteristic
531C22×C127#56011yescharacteristic
532C22×C127#56011yescharacteristic
533C22×C127#56011yescharacteristic
534C22×C127H(3,𝔽4)11yescharacteristic
535C4×C127—24no—
536C4×C127—42no—
537C4×C127—42no—
538C4×C127—42no—
539C4×C127—42no—
540C4×C127—42no—
541C4×C127—42no—
542C4×C127—42no—
543C4×C127—42no—
544C4×C127—42no—
545C4×C127—42no—
546C4×C127—81no—
547C4×C127—81no—
548#14566C12711yesmaximal, characteristic, direct product factor, Sylow
549C2×C127—82no—
550C2×C127—82no—
551C2×C127#232411yescharacteristic
552C2×C127#233511yescharacteristic
553C2×C127#233711yescharacteristic
554C2×C127#236311yescharacteristic
555C2×C127#236411yescharacteristic
556C2×C127#237411yescharacteristic
557C2×C127#237511yescharacteristic
558C2×C127#270311yescharacteristic
559C2×C127#270511yescharacteristic
560C2×C127#271211yescharacteristic
561C2×C127#271411yescharacteristic
562C2×C127#275311yescharacteristic
563C2×C127#279511yescharacteristic
564C2×C127#280111yescharacteristic
565C2×C127#280311yescharacteristic
566C2×#394C2×C12711yescharacteristic
567C2×#388C2×C12711yescharacteristic, complemented
568C2×#388C2×C12711yescharacteristic, complemented
569#1443C2×C12711yescharacteristic, complemented
570#1439C2×C12711yescharacteristic, complemented
571#1439C2×C12711yescharacteristic, complemented
572#1438C2×C12711yescharacteristic
573#1438C2×C12711yescharacteristic
574#1437C2×C12711yescharacteristic, complemented
575#1437C2×C12711yescharacteristic, complemented
576#1437C2×C12711yescharacteristic, complemented
577#1437C2×C12711yescharacteristic, complemented
578#1436C2×C12711yescharacteristic, complemented
579#1436C2×C12711yescharacteristic, complemented
580C4⋊#95C2×C12711yescharacteristic, complemented
581C127#1456611yescharacteristic, direct product factor, Sylow
582C23×D4C22×C12711yescharacteristic
583C22×C4⋊C4C22×C12711yescharacteristic
584C22×C4⋊C4C22×C12711yescharacteristic
585C22×C4⋊C4C22×C12711yescharacteristic
586C22×C22⋊C4C22×C12711yescharacteristic
587C22×C22⋊C4C22×C12711yescharacteristic
588C22×C22⋊C4C22×C12711yescharacteristic
589C22×C22⋊C4C22×C12711yescharacteristic
590C22×C22⋊C4C22×C12711yescharacteristic
591C22×C22⋊C4C22×C12711yescharacteristic
592C22×C22⋊C4C22×C12711yescharacteristic
593C22×C22⋊C4C22×C12711yescharacteristic
594C22×C22⋊C4C22×C12711yescharacteristic
595C22×C22⋊C4C22×C12711yescharacteristic
596C22×C22⋊C4C22×C12711yescharacteristic
597C22×C22⋊C4C22×C12711yescharacteristic
598C22×C42C22×C12711yescharacteristic
599C22×C42C22×C12711yescharacteristic
600C22×C42C22×C12711yescharacteristic
601#394C4×C12718yescomplemented
602#388—24no—
603#388—24no—
604C2×#95C22×C12711yescharacteristic
605C2×#95C22×C12711yescharacteristic
606C2×#95C22×C12711yescharacteristic
607C2×#95C22×C12711yescharacteristic
608C2×#95C22×C12711yescharacteristic
609C2×#95C22×C12711yescharacteristic
610C2×#95C22×C12711yescharacteristic
611C2×#95C22×C12711yescharacteristic
612C2×#95C22×C12711yescharacteristic
613C2×#95C22×C12711yescharacteristic
614C2×#95C22×C12711yescharacteristic
615C2×#95C22×C12711yescharacteristic
616C2×#95C22×C12711yescharacteristic
617C2×#95C22×C12711yescharacteristic
618C2×#95C22×C12711yescharacteristic
619C2×#95C22×C12711yescharacteristic
620C25C23×C12711yescharacteristic
621C25C23×C12711yescharacteristic
622C22×D4—41no—
623C22×D4—41no—
624C22×D4—41no—
625C22×D4—41no—
626C22×D4—41no—
627C22×D4—41no—
628C22×D4C2×C4×C12714yes—
629C23×C4C23×C12711yescharacteristic
630C23×C4C23×C12711yescharacteristic
631C23×C4C23×C12711yescharacteristic
632C23×C4C23×C12711yescharacteristic
633C23×C4C23×C12711yescharacteristic
634C23×C4C23×C12711yescharacteristic
635C23×C4C23×C12711yescharacteristic
636C23×C4C23×C12711yescharacteristic
637C23×C4C23×C12711yescharacteristic
638C23×C4C23×C12711yescharacteristic
639C23×C4C23×C12711yescharacteristic
640C23×C4C23×C12711yescharacteristic
641C23×C4C23×C12711yescharacteristic
642C2×C4⋊C4—22no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4C2×C4×C12714yes—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4—41no—
676C2×C22⋊C4—41no—
677C2×C22⋊C4—41no—
678C2×C22⋊C4—41no—
679C2×C22⋊C4—41no—
680C2×C22⋊C4—41no—
681C2×C22⋊C4—41no—
682C2×C22⋊C4—41no—
683C2×C22⋊C4C2×C4×C12714yes—
684C2×C22⋊C4C2×C4×C12714yes—
685C2×C22⋊C4C2×C4×C12714yes—
686C2×C22⋊C4C2×C4×C12714yes—
687C2×C42—22no—
688C2×C42—22no—
689C2×C42—22no—
690C2×C42—41no—
691C2×C42—41no—
692C2×C42—41no—
693C2×C42—41no—
694C2×C42—41no—
695C2×C42—41no—
696#95—22no—
697#95—22no—
698#95—22no—
699#95—22no—
700#95—41no—
701#95—41no—
702#95—41no—
703#95—41no—
704#95—41no—
705#95—41no—
706#95—41no—
707#95—41no—
708#95—41no—
709#95—41no—
710#95C2×C4×C12714yes—
711#95D4×C12714yescomplemented
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24C22×C4×C12712yes—
741C24C22×C4×C12712yes—
742C24C24×C12711yescharacteristic
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4C22×C4×C12712yes—
829C22×C4C22×C4×C12712yes—
830C22×C4C22×C4×C12712yes—
831C22×C4C22×C4×C12712yes—
832C22×C4C22×C4×C12712yes—
833C22×C4C2×D4×C12712yes—
834C22×C4C2×D4×C12712yes—
835C22×C4C2×D4×C12712yes—
836C22×C4#41×C12712yes—
837C22×C4#41×C12712yes—
838C22×C4#41×C12712yes—
839C22×C4#41×C12712yes—
840C22×C4#41×C12712yes—
841C4⋊C4—44no—
842C4⋊C4—44no—
843C4⋊C4—44no—
844C22⋊C4—28no—
845C22⋊C4—28no—
846C22⋊C4—44no—
847C22⋊C4—44no—
848C22⋊C4—44no—
849C22⋊C4—44no—
850C22⋊C4—44no—
851C22⋊C4—44no—
852C22⋊C4—44no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—44no—
856C42—44no—
857C42—44no—
858C42—44no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—41no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—41no—
879C23—41no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—41no—
886C23—41no—
887C23—41no—
888C23—41no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23C23×C4×C12711yescharacteristic
930C23C22×D4×C12711yescharacteristic
931C23C2×#41×C12711yescharacteristic
932C23C2×#41×C12711yescharacteristic
933C23C2×#41×C12711yescharacteristic
934C23C2×#41×C12711yescharacteristic
935C23C2×#41×C12711yescharacteristic
936C23H(5,𝔽2)×C12711yescharacteristic
937C23H(5,𝔽2)×C12711yescharacteristic
938C23H(5,𝔽2)×C12711yescharacteristic
939C23H(5,𝔽2)×C12711yescharacteristic
940C23H(5,𝔽2)×C12711yescharacteristic
941C23H(5,𝔽2)×C12711yescharacteristic
942C23H(5,𝔽2)×C12711yescharacteristic
943C232−1+4×C12711yescharacteristic
944D4—416no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4C4×D4×C12714yes—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22—81no—
1056C22—81no—
1057C22—81no—
1058C22—81no—
1059C22—81no—
1060C22—81no—
1061C22—81no—
1062C22—81no—
1063C22—81no—
1064C22—81no—
1065C22—81no—
1066C22C2×C4×D4×C12711yescharacteristic
1067C22C4×#41×C12711yescharacteristic
1068C22C4×#41×C12711yescharacteristic
1069C22#518×C12711yescharacteristic
1070C22#518×C12711yescharacteristic
1071C22#518×C12711yescharacteristic
1072C22#520×C12711yescharacteristic
1073C22#535×C12711yescharacteristic
1074C22#537×C12711yescharacteristic
1075C22#538×C12711yescharacteristic
1076C22#538×C12711yescharacteristic
1077C22#538×C12711yescharacteristic
1078C22#539×C12711yescharacteristic
1079C22#540×C12711yescharacteristic
1080C22#540×C12711yescharacteristic
1081C22#542×C12711yescharacteristic
1082C22#542×C12711yescharacteristic
1083C22#542×C12711yescharacteristic
1084C22#542×C12711yescharacteristic
1085C22#546×C12711yescharacteristic
1086C22#546×C12711yescharacteristic
1087C22#546×C12711yescharacteristic
1088C22#550×C12711yescharacteristic
1089C22#551×C12711yescharacteristic
1090C22#553×C12711yescharacteristic
1091C22#553×C12711yescharacteristic
1092C22#553×C12711yescharacteristic
1093C22#553×C12711yescharacteristic
1094C22#553×C12711yescharacteristic
1095C22#555×C12711yescharacteristic
1096C22#559×C12711yescharacteristic
1097C22#560×C12711yescharacteristic
1098C22#560×C12711yescharacteristic
1099C22#560×C12711yescharacteristic
1100C22H(3,𝔽4)×C12711yescharacteristic
1101C4—24no—
1102C4—42no—
1103C4—42no—
1104C4—42no—
1105C4—42no—
1106C4—42no—
1107C4—42no—
1108C4—42no—
1109C4—42no—
1110C4—42no—
1111C4—42no—
1112C4—81no—
1113C4—81no—
1114C2—82no—
1115C2—82no—
1116C2C127×#232411yescharacteristic
1117C2C127×#233511yescharacteristic
1118C2C127×#233711yescharacteristic
1119C2C127×#236311yescharacteristic
1120C2C127×#236411yescharacteristic
1121C2C127×#237411yescharacteristic
1122C2C127×#237511yescharacteristic
1123C2C127×#270311yescharacteristic
1124C2C127×#270511yescharacteristic
1125C2C127×#271211yescharacteristic
1126C2C127×#271411yescharacteristic
1127C2C127×#275311yescharacteristic
1128C2C127×#279511yescharacteristic
1129C2C127×#280111yescharacteristic
1130C2C127×#280311yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C127C2semidirect
3. C2×#388×C127C2semidirect
4. C127×#1443C2semidirect
5. C127×#1439C2semidirect
6. C127×#1439C2semidirect
9. C127×#1437C2semidirect
10. C127×#1437C2semidirect
11. C127×#1437C2semidirect
12. C127×#1437C2semidirect
13. C127×#1436C2semidirect
14. C127×#1436C2semidirect
15. C127×C4⋊#95C2semidirect
35. #394×C127C4semidirect
145. #95×C127D4semidirect
548. #14566C127direct (N × H)
567. C2×#388C2×C127semidirect
568. C2×#388C2×C127semidirect
569. #1443C2×C127semidirect
570. #1439C2×C127semidirect
571. #1439C2×C127semidirect
574. #1437C2×C127semidirect
575. #1437C2×C127semidirect
576. #1437C2×C127semidirect
577. #1437C2×C127semidirect
578. #1436C2×C127semidirect
579. #1436C2×C127semidirect
580. C4⋊#95C2×C127semidirect
581. C127#14566direct (N × H)
601. #394C4×C127semidirect
711. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#394×C1272
C2×#388×C1272
C127×#14432
C127×#14392
C127×#14382
C127×#14372
C127×#14362
C127×C4⋊#952
#14566127