Finite Group Databasebeta

← C127×#14563 #44578236

Subgroups — C127×#14563 #44578236

Order 32512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#394×C127C211yesmaximal, characteristic
2C2×#390×C127C211yesmaximal, characteristic
3C2×#389×C127C211yesmaximal, characteristic, complemented
4C2×#388×C127C211yesmaximal, characteristic, complemented
5C2×#388×C127C211yesmaximal, characteristic, complemented
6C127×#1439C211yesmaximal, characteristic, complemented
7C127×#1439C211yesmaximal, characteristic, complemented
8C127×#1439C211yesmaximal, characteristic, complemented
9C127×#1439C211yesmaximal, characteristic, complemented
10C127×#1438C211yesmaximal, characteristic
11C127×#1437C211yesmaximal, characteristic, complemented
12C127×#1437C211yesmaximal, characteristic, complemented
13C127×#1436C211yesmaximal, characteristic, complemented
14C127×#1436C211yesmaximal, characteristic, complemented
15C127×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊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×C22⋊C4×C127C2211yescharacteristic
33C22×C22⋊C4×C127C2211yescharacteristic
34C22×C42×C127C2211yescharacteristic
35C22×C42×C127C2211yescharacteristic
36C22×C42×C127C2211yescharacteristic
37#394×C127C418yescomplemented
38#390×C127—24no—
39#389×C127—24no—
40#388×C127—24no—
41#388×C127—24no—
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
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C25×C127C2311yescharacteristic
57C25×C127C2311yescharacteristic
58C22×D4×C127—22no—
59C22×D4×C127—22no—
60C22×D4×C127—41no—
61C22×D4×C127—41no—
62C22×D4×C127—41no—
63C22×D4×C127—41no—
64C22×D4×C127C2×C414yes—
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
76C23×C4×C127C2311yescharacteristic
77C23×C4×C127C2311yescharacteristic
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—22no—
85C2×C4⋊C4×C127—41no—
86C2×C4⋊C4×C127—41no—
87C2×C4⋊C4×C127—41no—
88C2×C4⋊C4×C127—41no—
89C2×C4⋊C4×C127—41no—
90C2×C4⋊C4×C127—41no—
91C2×C4⋊C4×C127C2×C414yes—
92C2×C4⋊C4×C127D414yes—
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—22no—
102C2×C22⋊C4×C127—22no—
103C2×C22⋊C4×C127—22no—
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127—22no—
106C2×C22⋊C4×C127—22no—
107C2×C22⋊C4×C127—22no—
108C2×C22⋊C4×C127—22no—
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×C127—41no—
118C2×C22⋊C4×C127—41no—
119C2×C22⋊C4×C127—41no—
120C2×C22⋊C4×C127—41no—
121C2×C22⋊C4×C127—41no—
122C2×C22⋊C4×C127—41no—
123C2×C22⋊C4×C127—41no—
124C2×C22⋊C4×C127—41no—
125C2×C22⋊C4×C127C2×C414yes—
126C2×C22⋊C4×C127C2×C414yes—
127C2×C22⋊C4×C127C2×C414yes—
128C2×C22⋊C4×C127C2×C414yes—
129C2×C42×C127—22no—
130C2×C42×C127—22no—
131C2×C42×C127—22no—
132C2×C42×C127—22no—
133C2×C42×C127—41no—
134C2×C42×C127—41no—
135C2×C42×C127—41no—
136C2×C42×C127—41no—
137C2×C42×C127—41no—
138#95×C127—22no—
139#95×C127—22no—
140#95×C127—22no—
141#95×C127—22no—
142#95×C127—22no—
143#95×C127—22no—
144#95×C127—22no—
145#95×C127—41no—
146#95×C127—41no—
147#95×C127—41no—
148#95×C127—41no—
149#95×C127—41no—
150#95×C127C2×C414yes—
151#95×C127D414yescomplemented
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×C127—21no—
175C24×C127—21no—
176C24×C127—21no—
177C24×C127—21no—
178C24×C127—21no—
179C24×C127—21no—
180C24×C127C22×C412yes—
181C24×C127C22×C412yes—
182C24×C127C2411yescharacteristic
183C2×D4×C127—28no—
184C2×D4×C127—44no—
185C2×D4×C127—44no—
186C2×D4×C127—44no—
187C2×D4×C127—44no—
188C2×D4×C127—44no—
189C2×D4×C127—44no—
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×C127—21no—
263C22×C4×C127—21no—
264C22×C4×C127—21no—
265C22×C4×C127—21no—
266C22×C4×C127C22×C412yes—
267C22×C4×C127C22×C412yes—
268C22×C4×C127C22×C412yes—
269C22×C4×C127C22×C412yes—
270C22×C4×C127C22×C412yes—
271C22×C4×C127C2×D412yes—
272C22×C4×C127C2×D412yes—
273C22×C4×C127C2×D412yes—
274C22×C4×C127C2×D412yes—
275C22×C4×C127C2×D412yes—
276C22×C4×C127C2×D412yes—
277C22×C4×C127#4112yes—
278C22×C4×C127#4112yes—
279C22×C4×C127#4112yes—
280C22×C4×C127#4112yes—
281C4⋊C4×C127—28no—
282C4⋊C4×C127—44no—
283C4⋊C4×C127—44no—
284C4⋊C4×C127—44no—
285C4⋊C4×C127—44no—
286C22⋊C4×C127—28no—
287C22⋊C4×C127—28no—
288C22⋊C4×C127—44no—
289C22⋊C4×C127—44no—
290C22⋊C4×C127—44no—
291C22⋊C4×C127—44no—
292C22⋊C4×C127—44no—
293C22⋊C4×C127—44no—
294C22⋊C4×C127—44no—
295C22⋊C4×C127—44no—
296C22⋊C4×C127—44no—
297C22⋊C4×C127—44no—
298C42×C127—44no—
299C42×C127—44no—
300C42×C127—44no—
301C23×C127—22no—
302C23×C127—22no—
303C23×C127—22no—
304C23×C127—22no—
305C23×C127—22no—
306C23×C127—22no—
307C23×C127—22no—
308C23×C127—22no—
309C23×C127—22no—
310C23×C127—22no—
311C23×C127—22no—
312C23×C127—22no—
313C23×C127—22no—
314C23×C127—22no—
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×C127—41no—
364C23×C127—41no—
365C23×C127—41no—
366C23×C127—41no—
367C23×C127—41no—
368C23×C127—41no—
369C23×C127—41no—
370C23×C127—41no—
371C23×C127C23×C411yescharacteristic
372C23×C127C22×D411yescharacteristic
373C23×C127C22×D411yescharacteristic
374C23×C127C2×#4111yescharacteristic
375C23×C127C2×#4111yescharacteristic
376C23×C127C2×#4111yescharacteristic
377C23×C127C2×#4111yescharacteristic
378C23×C127H(5,𝔽2)11yescharacteristic
379C23×C127H(5,𝔽2)11yescharacteristic
380C23×C127H(5,𝔽2)11yescharacteristic
381C23×C127H(5,𝔽2)11yescharacteristic
382C23×C127H(5,𝔽2)11yescharacteristic
383C23×C127H(5,𝔽2)11yescharacteristic
384C23×C1272−1+411yescharacteristic
385C23×C1272−1+411yescharacteristic
386D4×C127—416no—
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—22no—
416C2×C4×C127—22no—
417C2×C4×C127—22no—
418C2×C4×C127—22no—
419C2×C4×C127—22no—
420C2×C4×C127—22no—
421C2×C4×C127—22no—
422C2×C4×C127—22no—
423C2×C4×C127—22no—
424C2×C4×C127—22no—
425C2×C4×C127—22no—
426C2×C4×C127—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×C127—41no—
470C2×C4×C127—41no—
471C2×C4×C127—41no—
472C2×C4×C127—41no—
473C2×C4×C127—41no—
474C2×C4×C127—41no—
475C2×C4×C127—41no—
476C2×C4×C127C4×D414yes—
477C2×C4×C127C4×D414yes—
478C22×C127—42no—
479C22×C127—42no—
480C22×C127—42no—
481C22×C127—42no—
482C22×C127—42no—
483C22×C127—42no—
484C22×C127—42no—
485C22×C127—42no—
486C22×C127—42no—
487C22×C127—42no—
488C22×C127—42no—
489C22×C127—42no—
490C22×C127—42no—
491C22×C127—42no—
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×C127—81no—
501C22×C127—81no—
502C22×C127—81no—
503C22×C127—81no—
504C22×C127—81no—
505C22×C127—81no—
506C22×C127—81no—
507C22×C127—81no—
508C22×C127C2×C4×D411yescharacteristic
509C22×C127C2×C4×D411yescharacteristic
510C22×C127C4×#4111yescharacteristic
511C22×C127#51811yescharacteristic
512C22×C127#51811yescharacteristic
513C22×C127#52011yescharacteristic
514C22×C127#52011yescharacteristic
515C22×C127#53411yescharacteristic
516C22×C127#53511yescharacteristic
517C22×C127#53511yescharacteristic
518C22×C127#53711yescharacteristic
519C22×C127#53811yescharacteristic
520C22×C127#53811yescharacteristic
521C22×C127#53811yescharacteristic
522C22×C127#53911yescharacteristic
523C22×C127#54011yescharacteristic
524C22×C127#54011yescharacteristic
525C22×C127#54211yescharacteristic
526C22×C127#54211yescharacteristic
527C22×C127D4211yescharacteristic
528C22×C127#54611yescharacteristic
529C22×C127#54611yescharacteristic
530C22×C127#54711yescharacteristic
531C22×C127#54811yescharacteristic
532C22×C127#54811yescharacteristic
533C22×C127#55011yescharacteristic
534C22×C127#55311yescharacteristic
535C22×C127#55311yescharacteristic
536C22×C127#55511yescharacteristic
537C22×C127#55611yescharacteristic
538C22×C127#55911yescharacteristic
539C22×C127#56011yescharacteristic
540C22×C127#56211yescharacteristic
541C22×C127#56211yescharacteristic
542C22×C127#56311yescharacteristic
543C4×C127—24no—
544C4×C127—24no—
545C4×C127—42no—
546C4×C127—42no—
547C4×C127—42no—
548C4×C127—42no—
549C4×C127—42no—
550C4×C127—42no—
551C4×C127—42no—
552C4×C127—42no—
553C4×C127—42no—
554C4×C127—81no—
555C4×C127—81no—
556#14563C12711yesmaximal, characteristic, direct product factor, Sylow
557C2×C127—82no—
558C2×C127—82no—
559C2×C127#232111yescharacteristic
560C2×C127#232411yescharacteristic
561C2×C127#233511yescharacteristic
562C2×C127#236111yescharacteristic
563C2×C127#236311yescharacteristic
564C2×C127#236711yescharacteristic
565C2×C127#237611yescharacteristic
566C2×C127#267311yescharacteristic
567C2×C127#267611yescharacteristic
568C2×C127#271011yescharacteristic
569C2×C127#271111yescharacteristic
570C2×C127#272711yescharacteristic
571C2×C127#273111yescharacteristic
572C2×C127#280011yescharacteristic
573C2×C127#280311yescharacteristic
574C2×#394C2×C12711yescharacteristic
575C2×#390C2×C12711yescharacteristic
576C2×#389C2×C12711yescharacteristic, complemented
577C2×#388C2×C12711yescharacteristic, complemented
578C2×#388C2×C12711yescharacteristic, complemented
579#1439C2×C12711yescharacteristic, complemented
580#1439C2×C12711yescharacteristic, complemented
581#1439C2×C12711yescharacteristic, complemented
582#1439C2×C12711yescharacteristic, complemented
583#1438C2×C12711yescharacteristic
584#1437C2×C12711yescharacteristic, complemented
585#1437C2×C12711yescharacteristic, complemented
586#1436C2×C12711yescharacteristic, complemented
587#1436C2×C12711yescharacteristic, complemented
588#1436C2×C12711yescharacteristic, complemented
589C127#1456311yescharacteristic, direct product factor, Sylow
590C23×D4C22×C12711yescharacteristic
591C22×C4⋊C4C22×C12711yescharacteristic
592C22×C4⋊C4C22×C12711yescharacteristic
593C22×C4⋊C4C22×C12711yescharacteristic
594C22×C4⋊C4C22×C12711yescharacteristic
595C22×C4⋊C4C22×C12711yescharacteristic
596C22×C22⋊C4C22×C12711yescharacteristic
597C22×C22⋊C4C22×C12711yescharacteristic
598C22×C22⋊C4C22×C12711yescharacteristic
599C22×C22⋊C4C22×C12711yescharacteristic
600C22×C22⋊C4C22×C12711yescharacteristic
601C22×C22⋊C4C22×C12711yescharacteristic
602C22×C22⋊C4C22×C12711yescharacteristic
603C22×C22⋊C4C22×C12711yescharacteristic
604C22×C22⋊C4C22×C12711yescharacteristic
605C22×C22⋊C4C22×C12711yescharacteristic
606C22×C22⋊C4C22×C12711yescharacteristic
607C22×C22⋊C4C22×C12711yescharacteristic
608C22×C42C22×C12711yescharacteristic
609C22×C42C22×C12711yescharacteristic
610C22×C42C22×C12711yescharacteristic
611#394C4×C12718yescomplemented
612#390—24no—
613#389—24no—
614#388—24no—
615#388—24no—
616C2×#95C22×C12711yescharacteristic
617C2×#95C22×C12711yescharacteristic
618C2×#95C22×C12711yescharacteristic
619C2×#95C22×C12711yescharacteristic
620C2×#95C22×C12711yescharacteristic
621C2×#95C22×C12711yescharacteristic
622C2×#95C22×C12711yescharacteristic
623C2×#95C22×C12711yescharacteristic
624C2×#95C22×C12711yescharacteristic
625C2×#95C22×C12711yescharacteristic
626C2×#95C22×C12711yescharacteristic
627C2×#95C22×C12711yescharacteristic
628C2×#95C22×C12711yescharacteristic
629C2×#95C22×C12711yescharacteristic
630C25C23×C12711yescharacteristic
631C25C23×C12711yescharacteristic
632C22×D4—22no—
633C22×D4—22no—
634C22×D4—41no—
635C22×D4—41no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4C2×C4×C12714yes—
639C23×C4C23×C12711yescharacteristic
640C23×C4C23×C12711yescharacteristic
641C23×C4C23×C12711yescharacteristic
642C23×C4C23×C12711yescharacteristic
643C23×C4C23×C12711yescharacteristic
644C23×C4C23×C12711yescharacteristic
645C23×C4C23×C12711yescharacteristic
646C23×C4C23×C12711yescharacteristic
647C23×C4C23×C12711yescharacteristic
648C23×C4C23×C12711yescharacteristic
649C23×C4C23×C12711yescharacteristic
650C23×C4C23×C12711yescharacteristic
651C23×C4C23×C12711yescharacteristic
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4C2×C4×C12714yes—
666C2×C4⋊C4D4×C12714yes—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—41no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4C2×C4×C12714yes—
700C2×C22⋊C4C2×C4×C12714yes—
701C2×C22⋊C4C2×C4×C12714yes—
702C2×C22⋊C4C2×C4×C12714yes—
703C2×C42—22no—
704C2×C42—22no—
705C2×C42—22no—
706C2×C42—22no—
707C2×C42—41no—
708C2×C42—41no—
709C2×C42—41no—
710C2×C42—41no—
711C2×C42—41no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—22no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—41no—
720#95—41no—
721#95—41no—
722#95—41no—
723#95—41no—
724#95C2×C4×C12714yes—
725#95D4×C12714yescomplemented
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—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24C22×C4×C12712yes—
755C24C22×C4×C12712yes—
756C24C24×C12711yescharacteristic
757C2×D4—28no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
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×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4C22×C4×C12712yes—
841C22×C4C22×C4×C12712yes—
842C22×C4C22×C4×C12712yes—
843C22×C4C22×C4×C12712yes—
844C22×C4C22×C4×C12712yes—
845C22×C4C2×D4×C12712yes—
846C22×C4C2×D4×C12712yes—
847C22×C4C2×D4×C12712yes—
848C22×C4C2×D4×C12712yes—
849C22×C4C2×D4×C12712yes—
850C22×C4C2×D4×C12712yes—
851C22×C4#41×C12712yes—
852C22×C4#41×C12712yes—
853C22×C4#41×C12712yes—
854C22×C4#41×C12712yes—
855C4⋊C4—28no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C22⋊C4—28no—
861C22⋊C4—28no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C42—44no—
873C42—44no—
874C42—44no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
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—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23C23×C4×C12711yescharacteristic
946C23C22×D4×C12711yescharacteristic
947C23C22×D4×C12711yescharacteristic
948C23C2×#41×C12711yescharacteristic
949C23C2×#41×C12711yescharacteristic
950C23C2×#41×C12711yescharacteristic
951C23C2×#41×C12711yescharacteristic
952C23H(5,𝔽2)×C12711yescharacteristic
953C23H(5,𝔽2)×C12711yescharacteristic
954C23H(5,𝔽2)×C12711yescharacteristic
955C23H(5,𝔽2)×C12711yescharacteristic
956C23H(5,𝔽2)×C12711yescharacteristic
957C23H(5,𝔽2)×C12711yescharacteristic
958C232−1+4×C12711yescharacteristic
959C232−1+4×C12711yescharacteristic
960D4—416no—
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—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
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×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4C4×D4×C12714yes—
1051C2×C4C4×D4×C12714yes—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—81no—
1067C22—81no—
1068C22—81no—
1069C22—81no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22C2×C4×D4×C12711yescharacteristic
1083C22C2×C4×D4×C12711yescharacteristic
1084C22C4×#41×C12711yescharacteristic
1085C22#518×C12711yescharacteristic
1086C22#518×C12711yescharacteristic
1087C22#520×C12711yescharacteristic
1088C22#520×C12711yescharacteristic
1089C22#534×C12711yescharacteristic
1090C22#535×C12711yescharacteristic
1091C22#535×C12711yescharacteristic
1092C22#537×C12711yescharacteristic
1093C22#538×C12711yescharacteristic
1094C22#538×C12711yescharacteristic
1095C22#538×C12711yescharacteristic
1096C22#539×C12711yescharacteristic
1097C22#540×C12711yescharacteristic
1098C22#540×C12711yescharacteristic
1099C22#542×C12711yescharacteristic
1100C22#542×C12711yescharacteristic
1101C22D42×C12711yescharacteristic
1102C22#546×C12711yescharacteristic
1103C22#546×C12711yescharacteristic
1104C22#547×C12711yescharacteristic
1105C22#548×C12711yescharacteristic
1106C22#548×C12711yescharacteristic
1107C22#550×C12711yescharacteristic
1108C22#553×C12711yescharacteristic
1109C22#553×C12711yescharacteristic
1110C22#555×C12711yescharacteristic
1111C22#556×C12711yescharacteristic
1112C22#559×C12711yescharacteristic
1113C22#560×C12711yescharacteristic
1114C22#562×C12711yescharacteristic
1115C22#562×C12711yescharacteristic
1116C22#563×C12711yescharacteristic
1117C4—24no—
1118C4—24no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—81no—
1129C4—81no—
1130C2—82no—
1131C2—82no—
1132C2C127×#232111yescharacteristic
1133C2C127×#232411yescharacteristic
1134C2C127×#233511yescharacteristic
1135C2C127×#236111yescharacteristic
1136C2C127×#236311yescharacteristic
1137C2C127×#236711yescharacteristic
1138C2C127×#237611yescharacteristic
1139C2C127×#267311yescharacteristic
1140C2C127×#267611yescharacteristic
1141C2C127×#271011yescharacteristic
1142C2C127×#271111yescharacteristic
1143C2C127×#272711yescharacteristic
1144C2C127×#273111yescharacteristic
1145C2C127×#280011yescharacteristic
1146C2C127×#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
3. C2×#389×C127C2semidirect
4. C2×#388×C127C2semidirect
5. C2×#388×C127C2semidirect
6. C127×#1439C2semidirect
7. C127×#1439C2semidirect
8. C127×#1439C2semidirect
9. C127×#1439C2semidirect
11. C127×#1437C2semidirect
12. C127×#1437C2semidirect
13. C127×#1436C2semidirect
14. C127×#1436C2semidirect
15. C127×#1436C2semidirect
37. #394×C127C4semidirect
151. #95×C127D4semidirect
556. #14563C127direct (N × H)
576. C2×#389C2×C127semidirect
577. C2×#388C2×C127semidirect
578. C2×#388C2×C127semidirect
579. #1439C2×C127semidirect
580. #1439C2×C127semidirect
581. #1439C2×C127semidirect
582. #1439C2×C127semidirect
584. #1437C2×C127semidirect
585. #1437C2×C127semidirect
586. #1436C2×C127semidirect
587. #1436C2×C127semidirect
588. #1436C2×C127semidirect
589. C127#14563direct (N × H)
611. #394C4×C127semidirect
725. #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×#390×C1272
C2×#389×C1272
C2×#388×C1272
C127×#14392
C127×#14382
C127×#14372
C127×#14362
#14563127