Finite Group Databasebeta

← C127×#13980 #44577653

Subgroups — C127×#13980 #44577653

Order 32512.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#387×C127C211yesmaximal, characteristic, complemented
2C2×#385×C127C211yesmaximal, characteristic
3C2×#380×C127C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C127C211yesmaximal, characteristic
5C22×#95×C127C211yesmaximal, characteristic
6C127×#1445C211yesmaximal, characteristic, complemented
7C127×#1443C211yesmaximal, characteristic, complemented
8C127×#1442C211yesmaximal, characteristic, complemented
9C127×#1441C211yesmaximal, characteristic, complemented
10C127×#1436C211yesmaximal, characteristic, complemented
11C127×#1436C211yesmaximal, characteristic, complemented
12C127×#1434C211yesmaximal, characteristic, complemented
13C127×C22⋊#95C211yesmaximal, characteristic
14C127×C22⋊#95C211yesmaximal, characteristic
15C127×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C127C2211yescharacteristic
17C24×C4×C127C2211yescharacteristic
18C24×C4×C127C2211yescharacteristic
19C22×C4⋊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×C42×C127C2211yescharacteristic
28C22×C42×C127C2211yescharacteristic
29#387×C127—24no—
30#385×C127C418yescomplemented
31#380×C127—24no—
32C4×C22⋊C4×C127—24no—
33C2×#95×C127—24no—
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2211yescharacteristic
37C2×#95×C127C2211yescharacteristic
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
54C2×#95×C127C2211yescharacteristic
55C2×#95×C127C2211yescharacteristic
56C25×C127C2311yescharacteristic
57C23×C4×C127—22no—
58C23×C4×C127—22no—
59C23×C4×C127—22no—
60C23×C4×C127—22no—
61C23×C4×C127—22no—
62C23×C4×C127—22no—
63C23×C4×C127—22no—
64C23×C4×C127—22no—
65C23×C4×C127—22no—
66C23×C4×C127—22no—
67C23×C4×C127—22no—
68C23×C4×C127—22no—
69C23×C4×C127—22no—
70C23×C4×C127—41no—
71C23×C4×C127—41no—
72C23×C4×C127—41no—
73C23×C4×C127—41no—
74C23×C4×C127—41no—
75C23×C4×C127—41no—
76C23×C4×C127C2×C414yes—
77C23×C4×C127Q814yes—
78C23×C4×C127C2311yescharacteristic
79C23×C4×C127C2311yescharacteristic
80C23×C4×C127C2311yescharacteristic
81C23×C4×C127C2311yescharacteristic
82C23×C4×C127C2311yescharacteristic
83C23×C4×C127C2311yescharacteristic
84C23×C4×C127C2311yescharacteristic
85C23×C4×C127C2311yescharacteristic
86C23×C4×C127C2311yescharacteristic
87C23×C4×C127C2311yescharacteristic
88C23×C4×C127C2311yescharacteristic
89C23×C4×C127C2311yescharacteristic
90C23×C4×C127C2311yescharacteristic
91C23×C4×C127C2311yescharacteristic
92C2×C4⋊C4×C127—22no—
93C2×C4⋊C4×C127—22no—
94C2×C4⋊C4×C127—22no—
95C2×C4⋊C4×C127—22no—
96C2×C4⋊C4×C127—22no—
97C2×C4⋊C4×C127—22no—
98C2×C4⋊C4×C127—41no—
99C2×C4⋊C4×C127—41no—
100C2×C4⋊C4×C127—41no—
101C2×C4⋊C4×C127—41no—
102C2×C4⋊C4×C127C2×C414yescomplemented
103C2×C4⋊C4×C127C2×C414yescomplemented
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—22no—
110C2×C22⋊C4×C127—22no—
111C2×C22⋊C4×C127—22no—
112C2×C22⋊C4×C127—22no—
113C2×C22⋊C4×C127C2×C414yes—
114C2×C22⋊C4×C127C2×C414yes—
115C2×C22⋊C4×C127D414yes—
116C2×C42×C127—22no—
117C2×C42×C127—22no—
118C2×C42×C127—22no—
119C2×C42×C127—22no—
120C2×C42×C127—41no—
121C2×C42×C127—41no—
122#95×C127—22no—
123#95×C127—22no—
124#95×C127—22no—
125#95×C127—22no—
126#95×C127—22no—
127#95×C127—22no—
128#95×C127—22no—
129#95×C127—22no—
130#95×C127—22no—
131#95×C127—22no—
132#95×C127—22no—
133#95×C127—22no—
134#95×C127—22no—
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×C127C2×C414yescomplemented
142#95×C127C2×C414yescomplemented
143#95×C127D414yes—
144C24×C127—21no—
145C24×C127—21no—
146C24×C127—21no—
147C24×C127—21no—
148C24×C127—21no—
149C24×C127—21no—
150C24×C127—21no—
151C24×C127—21no—
152C24×C127C22×C412yes—
153C24×C127C2×D412yes—
154C24×C127C2×Q812yes—
155C24×C127#4112yes—
156C24×C127#4112yes—
157C24×C127#4112yes—
158C24×C127#4112yes—
159C24×C127C2411yescharacteristic
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—21no—
165C22×C4×C127—21no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—28no—
169C22×C4×C127—28no—
170C22×C4×C127—28no—
171C22×C4×C127—21no—
172C22×C4×C127—21no—
173C22×C4×C127—21no—
174C22×C4×C127—21no—
175C22×C4×C127—21no—
176C22×C4×C127—21no—
177C22×C4×C127—21no—
178C22×C4×C127—21no—
179C22×C4×C127—21no—
180C22×C4×C127—21no—
181C22×C4×C127—21no—
182C22×C4×C127—21no—
183C22×C4×C127—21no—
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—28no—
232C22×C4×C127—28no—
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—44no—
248C22×C4×C127—44no—
249C22×C4×C127—44no—
250C22×C4×C127—44no—
251C22×C4×C127—44no—
252C22×C4×C127—44no—
253C22×C4×C127—44no—
254C22×C4×C127—44no—
255C22×C4×C127—44no—
256C22×C4×C127—44no—
257C22×C4×C127—44no—
258C22×C4×C127—44no—
259C22×C4×C127—44no—
260C22×C4×C127—44no—
261C22×C4×C127—44no—
262C22×C4×C127—44no—
263C22×C4×C127C22×C412yes—
264C22×C4×C127C22×C412yes—
265C22×C4×C127C22×C412yes—
266C22×C4×C127C22×C412yes—
267C22×C4×C127C22×C412yes—
268C22×C4×C127C22×C412yes—
269C22×C4×C127C2×D412yes—
270C22×C4×C127C2×D412yes—
271C22×C4×C127C2×D412yes—
272C22×C4×C127C2×D412yes—
273C22×C4×C127C2×D412yes—
274C22×C4×C127C2×Q812yes—
275C22×C4×C127C2×Q812yes—
276C22×C4×C127#4112yes—
277C22×C4×C127#4112yes—
278C22×C4×C127#4112yes—
279C4⋊C4×C127—28no—
280C4⋊C4×C127—44no—
281C4⋊C4×C127—44no—
282C4⋊C4×C127—44no—
283C22⋊C4×C127—28no—
284C22⋊C4×C127—28no—
285C22⋊C4×C127—28no—
286C22⋊C4×C127—44no—
287C42×C127—44no—
288C42×C127—44no—
289C23×C127—22no—
290C23×C127—22no—
291C23×C127—22no—
292C23×C127—22no—
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—22no—
308C23×C127—22no—
309C23×C127—22no—
310C23×C127—22no—
311C23×C127—22no—
312C23×C127—22no—
313C23×C127—22no—
314C23×C127—22no—
315C23×C127—22no—
316C23×C127—22no—
317C23×C127#11714yes—
318C23×C127C4×D414yes—
319C23×C127C4×Q814yes—
320C23×C127C22⋊Q814yes—
321C23×C127#12314yes—
322C23×C127#12514yes—
323C23×C127#12614yes—
324C23×C127C23×C411yescharacteristic
325C23×C127C22×D411yescharacteristic
326C23×C127C22×D411yescharacteristic
327C23×C127C22×Q811yescharacteristic
328C23×C127C2×#4111yescharacteristic
329C23×C127C2×#4111yescharacteristic
330C23×C127C2×#4111yescharacteristic
331C23×C127C2×#4111yescharacteristic
332C23×C127C2×#4111yescharacteristic
333C23×C127C2×#4111yescharacteristic
334C23×C127C2×#4111yescharacteristic
335C23×C127H(5,𝔽2)11yescharacteristic
336C23×C127H(5,𝔽2)11yescharacteristic
337C23×C127H(5,𝔽2)11yescharacteristic
338C23×C1272−1+411yescharacteristic
339C2×C4×C127—22no—
340C2×C4×C127—22no—
341C2×C4×C127—22no—
342C2×C4×C127—22no—
343C2×C4×C127—22no—
344C2×C4×C127—22no—
345C2×C4×C127—22no—
346C2×C4×C127—22no—
347C2×C4×C127—22no—
348C2×C4×C127—22no—
349C2×C4×C127—22no—
350C2×C4×C127—22no—
351C2×C4×C127—22no—
352C2×C4×C127—22no—
353C2×C4×C127—22no—
354C2×C4×C127—22no—
355C2×C4×C127—22no—
356C2×C4×C127—22no—
357C2×C4×C127—22no—
358C2×C4×C127—22no—
359C2×C4×C127—22no—
360C2×C4×C127—22no—
361C2×C4×C127—22no—
362C2×C4×C127—22no—
363C2×C4×C127—22no—
364C2×C4×C127—22no—
365C2×C4×C127—22no—
366C2×C4×C127—22no—
367C2×C4×C127—22no—
368C2×C4×C127—22no—
369C2×C4×C127—22no—
370C2×C4×C127—22no—
371C2×C4×C127—22no—
372C2×C4×C127—22no—
373C2×C4×C127—22no—
374C2×C4×C127—22no—
375C2×C4×C127—22no—
376C2×C4×C127—22no—
377C2×C4×C127—22no—
378C2×C4×C127—22no—
379C2×C4×C127—22no—
380C2×C4×C127—22no—
381C2×C4×C127—416no—
382C2×C4×C127—416no—
383C2×C4×C127—416no—
384C2×C4×C127—41no—
385C2×C4×C127—41no—
386C2×C4×C127—41no—
387C2×C4×C127—41no—
388C2×C4×C127—41no—
389C2×C4×C127—41no—
390C2×C4×C127—41no—
391C2×C4×C127—41no—
392C2×C4×C127—41no—
393C2×C4×C127—41no—
394C2×C4×C127—41no—
395C2×C4×C127—41no—
396C2×C4×C127—41no—
397C2×C4×C127—41no—
398C2×C4×C127—41no—
399C2×C4×C127—41no—
400C2×C4×C127—41no—
401C2×C4×C127—41no—
402C2×C4×C127—41no—
403C2×C4×C127—41no—
404C2×C4×C127—41no—
405C2×C4×C127—41no—
406C2×C4×C127—41no—
407C2×C4×C127—41no—
408C2×C4×C127—41no—
409C2×C4×C127—41no—
410C2×C4×C127—41no—
411C2×C4×C127—41no—
412C2×C4×C127—41no—
413C2×C4×C127—41no—
414C2×C4×C127—41no—
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×C127C4×D414yes—
439C2×C4×C127C22⋊Q814yes—
440C22×C127—24no—
441C22×C127—24no—
442C22×C127—24no—
443C22×C127—24no—
444C22×C127—24no—
445C22×C127—24no—
446C22×C127—24no—
447C22×C127—24no—
448C22×C127—24no—
449C22×C127—24no—
450C22×C127—24no—
451C22×C127—24no—
452C22×C127—24no—
453C22×C127—24no—
454C22×C127#38718yescomplemented
455C22×C127C2×#11711yescharacteristic
456C22×C127C2×C4×D411yescharacteristic
457C22×C127C2×C4×D411yescharacteristic
458C22×C127C2×C4×Q811yescharacteristic
459C22×C127C4×#4111yescharacteristic
460C22×C127#51811yescharacteristic
461C22×C127#52011yescharacteristic
462C22×C127C2×C22⋊Q811yescharacteristic
463C22×C127C2×C22⋊Q811yescharacteristic
464C22×C127C2×#12311yescharacteristic
465C22×C127#52511yescharacteristic
466C22×C127C2×#12511yescharacteristic
467C22×C127C2×#12611yescharacteristic
468C22×C127#52911yescharacteristic
469C22×C127#53311yescharacteristic
470C22×C127#53811yescharacteristic
471C22×C127#53911yescharacteristic
472C22×C127#54311yescharacteristic
473C22×C127#54411yescharacteristic
474C22×C127D4211yescharacteristic
475C22×C127#54611yescharacteristic
476C22×C127#54611yescharacteristic
477C22×C127#54611yescharacteristic
478C22×C127#54611yescharacteristic
479C22×C127#54711yescharacteristic
480C22×C127#54811yescharacteristic
481C22×C127#55111yescharacteristic
482C22×C127#55111yescharacteristic
483C22×C127#55111yescharacteristic
484C22×C127#55111yescharacteristic
485C22×C127#55211yescharacteristic
486C22×C127#55211yescharacteristic
487C22×C127#55311yescharacteristic
488C22×C127#55311yescharacteristic
489C22×C127#55311yescharacteristic
490C4×C127—24no—
491C4×C127—24no—
492C4×C127—42no—
493C4×C127—42no—
494C4×C127—42no—
495C4×C127—42no—
496C4×C127—42no—
497C4×C127—42no—
498C4×C127—42no—
499C4×C127—42no—
500C4×C127—42no—
501C4×C127—42no—
502C4×C127—81no—
503C4×C127—81no—
504#13980C12711yesmaximal, characteristic, direct product factor, Sylow
505C2×C127—28no—
506C2×C127C2×#38711yescharacteristic
507C2×C127C4×C22⋊Q811yescharacteristic
508C2×C127#232911yescharacteristic
509C2×C127#235211yescharacteristic
510C2×C127#235311yescharacteristic
511C2×C127#235811yescharacteristic
512C2×C127#235911yescharacteristic
513C2×C127#243711yescharacteristic
514C2×C127#243811yescharacteristic
515C2×C127#244211yescharacteristic
516C2×C127#244311yescharacteristic
517C2×C127#244411yescharacteristic
518C2×C127#248011yescharacteristic
519C2×C127#249311yescharacteristic
520C2×C127#256911yescharacteristic
521C2×#387C2×C12711yescharacteristic, complemented
522C2×#385C2×C12711yescharacteristic
523C2×#380C2×C12711yescharacteristic
524C2×C4×C22⋊C4C2×C12711yescharacteristic
525C22×#95C2×C12711yescharacteristic
526#1445C2×C12711yescharacteristic, complemented
527#1443C2×C12711yescharacteristic, complemented
528#1442C2×C12711yescharacteristic, complemented
529#1441C2×C12711yescharacteristic, complemented
530#1436C2×C12711yescharacteristic, complemented
531#1436C2×C12711yescharacteristic, complemented
532#1434C2×C12711yescharacteristic, complemented
533C22⋊#95C2×C12711yescharacteristic
534C22⋊#95C2×C12711yescharacteristic
535C22⋊#95C2×C12711yescharacteristic
536C127#1398011yescharacteristic, direct product factor, Sylow
537C24×C4C22×C12711yescharacteristic
538C24×C4C22×C12711yescharacteristic
539C24×C4C22×C12711yescharacteristic
540C22×C4⋊C4C22×C12711yescharacteristic
541C22×C4⋊C4C22×C12711yescharacteristic
542C22×C4⋊C4C22×C12711yescharacteristic
543C22×C4⋊C4C22×C12711yescharacteristic
544C22×C22⋊C4C22×C12711yescharacteristic
545C22×C22⋊C4C22×C12711yescharacteristic
546C22×C22⋊C4C22×C12711yescharacteristic
547C22×C22⋊C4C22×C12711yescharacteristic
548C22×C42C22×C12711yescharacteristic
549C22×C42C22×C12711yescharacteristic
550#387—24no—
551#385C4×C12718yescomplemented
552#380—24no—
553C4×C22⋊C4—24no—
554C2×#95—24no—
555C2×#95C22×C12711yescharacteristic
556C2×#95C22×C12711yescharacteristic
557C2×#95C22×C12711yescharacteristic
558C2×#95C22×C12711yescharacteristic
559C2×#95C22×C12711yescharacteristic
560C2×#95C22×C12711yescharacteristic
561C2×#95C22×C12711yescharacteristic
562C2×#95C22×C12711yescharacteristic
563C2×#95C22×C12711yescharacteristic
564C2×#95C22×C12711yescharacteristic
565C2×#95C22×C12711yescharacteristic
566C2×#95C22×C12711yescharacteristic
567C2×#95C22×C12711yescharacteristic
568C2×#95C22×C12711yescharacteristic
569C2×#95C22×C12711yescharacteristic
570C2×#95C22×C12711yescharacteristic
571C2×#95C22×C12711yescharacteristic
572C2×#95C22×C12711yescharacteristic
573C2×#95C22×C12711yescharacteristic
574C2×#95C22×C12711yescharacteristic
575C2×#95C22×C12711yescharacteristic
576C2×#95C22×C12711yescharacteristic
577C25C23×C12711yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—22no—
584C23×C4—22no—
585C23×C4—22no—
586C23×C4—22no—
587C23×C4—22no—
588C23×C4—22no—
589C23×C4—22no—
590C23×C4—22no—
591C23×C4—41no—
592C23×C4—41no—
593C23×C4—41no—
594C23×C4—41no—
595C23×C4—41no—
596C23×C4—41no—
597C23×C4C2×C4×C12714yes—
598C23×C4Q8×C12714yes—
599C23×C4C23×C12711yescharacteristic
600C23×C4C23×C12711yescharacteristic
601C23×C4C23×C12711yescharacteristic
602C23×C4C23×C12711yescharacteristic
603C23×C4C23×C12711yescharacteristic
604C23×C4C23×C12711yescharacteristic
605C23×C4C23×C12711yescharacteristic
606C23×C4C23×C12711yescharacteristic
607C23×C4C23×C12711yescharacteristic
608C23×C4C23×C12711yescharacteristic
609C23×C4C23×C12711yescharacteristic
610C23×C4C23×C12711yescharacteristic
611C23×C4C23×C12711yescharacteristic
612C23×C4C23×C12711yescharacteristic
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4C2×C4×C12714yescomplemented
624C2×C4⋊C4C2×C4×C12714yescomplemented
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4C2×C4×C12714yes—
635C2×C22⋊C4C2×C4×C12714yes—
636C2×C22⋊C4D4×C12714yes—
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—22no—
640C2×C42—22no—
641C2×C42—41no—
642C2×C42—41no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—41no—
657#95—41no—
658#95—41no—
659#95—41no—
660#95—41no—
661#95—41no—
662#95C2×C4×C12714yescomplemented
663#95C2×C4×C12714yescomplemented
664#95D4×C12714yes—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24C22×C4×C12712yes—
674C24C2×D4×C12712yes—
675C24C2×Q8×C12712yes—
676C24#41×C12712yes—
677C24#41×C12712yes—
678C24#41×C12712yes—
679C24#41×C12712yes—
680C24C24×C12711yescharacteristic
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—28no—
690C22×C4—28no—
691C22×C4—28no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—28no—
753C22×C4—28no—
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—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4C22×C4×C12712yes—
785C22×C4C22×C4×C12712yes—
786C22×C4C22×C4×C12712yes—
787C22×C4C22×C4×C12712yes—
788C22×C4C22×C4×C12712yes—
789C22×C4C22×C4×C12712yes—
790C22×C4C2×D4×C12712yes—
791C22×C4C2×D4×C12712yes—
792C22×C4C2×D4×C12712yes—
793C22×C4C2×D4×C12712yes—
794C22×C4C2×D4×C12712yes—
795C22×C4C2×Q8×C12712yes—
796C22×C4C2×Q8×C12712yes—
797C22×C4#41×C12712yes—
798C22×C4#41×C12712yes—
799C22×C4#41×C12712yes—
800C4⋊C4—28no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—44no—
808C42—44no—
809C42—44no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23#117×C12714yes—
839C23C4×D4×C12714yes—
840C23C4×Q8×C12714yes—
841C23C22⋊Q8×C12714yes—
842C23#123×C12714yes—
843C23#125×C12714yes—
844C23#126×C12714yes—
845C23C23×C4×C12711yescharacteristic
846C23C22×D4×C12711yescharacteristic
847C23C22×D4×C12711yescharacteristic
848C23C22×Q8×C12711yescharacteristic
849C23C2×#41×C12711yescharacteristic
850C23C2×#41×C12711yescharacteristic
851C23C2×#41×C12711yescharacteristic
852C23C2×#41×C12711yescharacteristic
853C23C2×#41×C12711yescharacteristic
854C23C2×#41×C12711yescharacteristic
855C23C2×#41×C12711yescharacteristic
856C23H(5,𝔽2)×C12711yescharacteristic
857C23H(5,𝔽2)×C12711yescharacteristic
858C23H(5,𝔽2)×C12711yescharacteristic
859C232−1+4×C12711yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—416no—
903C2×C4—416no—
904C2×C4—416no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4C4×D4×C12714yes—
960C2×C4C22⋊Q8×C12714yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22#387×C12718yescomplemented
976C22C2×#117×C12711yescharacteristic
977C22C2×C4×D4×C12711yescharacteristic
978C22C2×C4×D4×C12711yescharacteristic
979C22C2×C4×Q8×C12711yescharacteristic
980C22C4×#41×C12711yescharacteristic
981C22#518×C12711yescharacteristic
982C22#520×C12711yescharacteristic
983C22C2×C22⋊Q8×C12711yescharacteristic
984C22C2×C22⋊Q8×C12711yescharacteristic
985C22C2×#123×C12711yescharacteristic
986C22#525×C12711yescharacteristic
987C22C2×#125×C12711yescharacteristic
988C22C2×#126×C12711yescharacteristic
989C22#529×C12711yescharacteristic
990C22#533×C12711yescharacteristic
991C22#538×C12711yescharacteristic
992C22#539×C12711yescharacteristic
993C22#543×C12711yescharacteristic
994C22#544×C12711yescharacteristic
995C22D42×C12711yescharacteristic
996C22#546×C12711yescharacteristic
997C22#546×C12711yescharacteristic
998C22#546×C12711yescharacteristic
999C22#546×C12711yescharacteristic
1000C22#547×C12711yescharacteristic
1001C22#548×C12711yescharacteristic
1002C22#551×C12711yescharacteristic
1003C22#551×C12711yescharacteristic
1004C22#551×C12711yescharacteristic
1005C22#551×C12711yescharacteristic
1006C22#552×C12711yescharacteristic
1007C22#552×C12711yescharacteristic
1008C22#553×C12711yescharacteristic
1009C22#553×C12711yescharacteristic
1010C22#553×C12711yescharacteristic
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—81no—
1024C4—81no—
1025C2—28no—
1026C2C2×#387×C12711yescharacteristic
1027C2C4×C22⋊Q8×C12711yescharacteristic
1028C2C127×#232911yescharacteristic
1029C2C127×#235211yescharacteristic
1030C2C127×#235311yescharacteristic
1031C2C127×#235811yescharacteristic
1032C2C127×#235911yescharacteristic
1033C2C127×#243711yescharacteristic
1034C2C127×#243811yescharacteristic
1035C2C127×#244211yescharacteristic
1036C2C127×#244311yescharacteristic
1037C2C127×#244411yescharacteristic
1038C2C127×#248011yescharacteristic
1039C2C127×#249311yescharacteristic
1040C2C127×#256911yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#387×C127C2semidirect
6. C127×#1445C2semidirect
7. C127×#1443C2semidirect
8. C127×#1442C2semidirect
9. C127×#1441C2semidirect
10. C127×#1436C2semidirect
11. C127×#1436C2semidirect
12. C127×#1434C2semidirect
30. #385×C127C4semidirect
102. C2×C4⋊C4×C127C2×C4semidirect
103. C2×C4⋊C4×C127C2×C4semidirect
141. #95×C127C2×C4semidirect
142. #95×C127C2×C4semidirect
454. C22×C127#387semidirect
504. #13980C127direct (N × H)
521. C2×#387C2×C127semidirect
526. #1445C2×C127semidirect
527. #1443C2×C127semidirect
528. #1442C2×C127semidirect
529. #1441C2×C127semidirect
530. #1436C2×C127semidirect
531. #1436C2×C127semidirect
532. #1434C2×C127semidirect
536. C127#13980direct (N × H)
551. #385C4×C127semidirect
623. C2×C4⋊C4C2×C4×C127semidirect
624. C2×C4⋊C4C2×C4×C127semidirect
662. #95C2×C4×C127semidirect
663. #95C2×C4×C127semidirect
975. C22#387×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#387×C1272
C2×#385×C1272
C2×#380×C1272
C2×C4×C22⋊C4×C1272
C22×#95×C1272
C127×#14452
C127×#14432
C127×#14422
C127×#14412
C127×#14362
C127×#14342
C127×C22⋊#952
#13980127