Finite Group Databasebeta

← C127×#14251 #44577924

Subgroups — C127×#14251 #44577924

Order 32512.

1158 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#401×C127C211yesmaximal, characteristic
2C127×#1443C211yesmaximal, characteristic
3C127×#1443C211yesmaximal, characteristic
4C127×#1442C211yesmaximal, characteristic
5C127×#1436C211yesmaximal, characteristic
6C127×#1436C211yesmaximal, characteristic
7C127×#1436C211yesmaximal, characteristic
8C127×#1436C211yesmaximal, characteristic
9C127×#1436C211yesmaximal, characteristic
10C127×#1434C211yesmaximal, characteristic
11C127×#1434C211yesmaximal, characteristic
12C127×#1434C211yesmaximal, characteristic
13C127×#1434C211yesmaximal, characteristic
14C4×#95×C127C211yesmaximal, characteristic
15C4×#95×C127C211yesmaximal, characteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C42×C127C2211yescharacteristic
19C22×C42×C127C2211yescharacteristic
20C22×C42×C127C2211yescharacteristic
21C22×C42×C127C2211yescharacteristic
22C22×C42×C127C2211yescharacteristic
23#401×C127C418yescomplemented
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2211yescharacteristic
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2211yescharacteristic
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
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C23×C4×C127C2311yescharacteristic
56C23×C4×C127C2311yescharacteristic
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2311yescharacteristic
59C23×C4×C127C2311yescharacteristic
60C23×C4×C127C2311yescharacteristic
61C23×C4×C127C2311yescharacteristic
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2311yescharacteristic
65C23×C4×C127C2311yescharacteristic
66C23×C4×C127C2311yescharacteristic
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127—22no—
72C2×C4⋊C4×C127—41no—
73C2×C42×C127—22no—
74C2×C42×C127—22no—
75C2×C42×C127—22no—
76C2×C42×C127—22no—
77C2×C42×C127—22no—
78C2×C42×C127—22no—
79C2×C42×C127—22no—
80C2×C42×C127—22no—
81C2×C42×C127—22no—
82C2×C42×C127—22no—
83C2×C42×C127—41no—
84C2×C42×C127—41no—
85C2×C42×C127—41no—
86C2×C42×C127—41no—
87C2×C42×C127—41no—
88#95×C127—22no—
89#95×C127—22no—
90#95×C127—22no—
91#95×C127—22no—
92#95×C127—22no—
93#95×C127—22no—
94#95×C127—22no—
95#95×C127—22no—
96#95×C127—22no—
97#95×C127—22no—
98#95×C127—22no—
99#95×C127—22no—
100#95×C127—22no—
101#95×C127—22no—
102#95×C127—22no—
103#95×C127—41no—
104#95×C127—41no—
105#95×C127—41no—
106#95×C127—41no—
107#95×C127—41no—
108#95×C127—41no—
109#95×C127C2×C414yes—
110#95×C127C2×C414yes—
111#95×C127C2×C414yes—
112#95×C127C2×C414yes—
113#95×C127C2×C414yes—
114#95×C127C2×C414yes—
115#95×C127C2×C414yes—
116C24×C127C2411yescharacteristic
117C22×C4×C127—21no—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—21no—
130C22×C4×C127—21no—
131C22×C4×C127—21no—
132C22×C4×C127—21no—
133C22×C4×C127—21no—
134C22×C4×C127—21no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—21no—
141C22×C4×C127—21no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—21no—
151C22×C4×C127—21no—
152C22×C4×C127—21no—
153C22×C4×C127—21no—
154C22×C4×C127—21no—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
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—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
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×C127C22×C412yes—
206C22×C4×C127C22×C412yes—
207C22×C4×C127C22×C412yes—
208C22×C4×C127C22×C412yes—
209C22×C4×C127C22×C412yes—
210C22×C4×C127C22×C412yes—
211C22×C4×C127C22×C412yes—
212C22×C4×C127#4112yes—
213C22×C4×C127#4112yes—
214C22×C4×C127#4112yes—
215C22×C4×C127#4112yes—
216C22×C4×C127#4112yes—
217C22×C4×C127#4112yes—
218C22×C4×C127#4112yes—
219C22×C4×C127#4112yes—
220C22×C4×C127#4112yes—
221C22×C4×C127#4112yes—
222C4⋊C4×C127—44no—
223C4⋊C4×C127—44no—
224C42×C127—44no—
225C42×C127—44no—
226C42×C127—44no—
227C42×C127—44no—
228C42×C127—44no—
229C23×C127C23×C411yescharacteristic
230C23×C127C2×#4111yescharacteristic
231C23×C127C2×#4111yescharacteristic
232C23×C127C2×#4111yescharacteristic
233C23×C127C2×#4111yescharacteristic
234C23×C127C2×#4111yescharacteristic
235C23×C127C2×#4111yescharacteristic
236C23×C127C2×#4111yescharacteristic
237C23×C127C2×#4111yescharacteristic
238C23×C127C2×#4111yescharacteristic
239C23×C127C2×#4111yescharacteristic
240C23×C127H(5,𝔽2)11yescharacteristic
241C23×C127H(5,𝔽2)11yescharacteristic
242C23×C1272−1+411yescharacteristic
243C23×C1272−1+411yescharacteristic
244C2×C4×C127—22no—
245C2×C4×C127—22no—
246C2×C4×C127—22no—
247C2×C4×C127—22no—
248C2×C4×C127—22no—
249C2×C4×C127—22no—
250C2×C4×C127—22no—
251C2×C4×C127—22no—
252C2×C4×C127—22no—
253C2×C4×C127—22no—
254C2×C4×C127—22no—
255C2×C4×C127—22no—
256C2×C4×C127—22no—
257C2×C4×C127—22no—
258C2×C4×C127—22no—
259C2×C4×C127—22no—
260C2×C4×C127—22no—
261C2×C4×C127—22no—
262C2×C4×C127—22no—
263C2×C4×C127—22no—
264C2×C4×C127—22no—
265C2×C4×C127—22no—
266C2×C4×C127—22no—
267C2×C4×C127—22no—
268C2×C4×C127—22no—
269C2×C4×C127—22no—
270C2×C4×C127—22no—
271C2×C4×C127—22no—
272C2×C4×C127—22no—
273C2×C4×C127—22no—
274C2×C4×C127—22no—
275C2×C4×C127—22no—
276C2×C4×C127—22no—
277C2×C4×C127—22no—
278C2×C4×C127—22no—
279C2×C4×C127—22no—
280C2×C4×C127—22no—
281C2×C4×C127—22no—
282C2×C4×C127—22no—
283C2×C4×C127—22no—
284C2×C4×C127—22no—
285C2×C4×C127—22no—
286C2×C4×C127—22no—
287C2×C4×C127—22no—
288C2×C4×C127—22no—
289C2×C4×C127—41no—
290C2×C4×C127—41no—
291C2×C4×C127—41no—
292C2×C4×C127—41no—
293C2×C4×C127—41no—
294C2×C4×C127—41no—
295C2×C4×C127—41no—
296C2×C4×C127—41no—
297C2×C4×C127—41no—
298C2×C4×C127—41no—
299C2×C4×C127—41no—
300C2×C4×C127—41no—
301C2×C4×C127—41no—
302C2×C4×C127—41no—
303C2×C4×C127—41no—
304C2×C4×C127—41no—
305C2×C4×C127—41no—
306C2×C4×C127—41no—
307C2×C4×C127—41no—
308C2×C4×C127—41no—
309C2×C4×C127—41no—
310C2×C4×C127—41no—
311C2×C4×C127—41no—
312C2×C4×C127—41no—
313C2×C4×C127—41no—
314C2×C4×C127—41no—
315C2×C4×C127—41no—
316C2×C4×C127—41no—
317C2×C4×C127—41no—
318C2×C4×C127—41no—
319C2×C4×C127—41no—
320C2×C4×C127—41no—
321C2×C4×C127—41no—
322C2×C4×C127—41no—
323C2×C4×C127—41no—
324C2×C4×C127—41no—
325C2×C4×C127—41no—
326C2×C4×C127—41no—
327C2×C4×C127—41no—
328C2×C4×C127—41no—
329C2×C4×C127—41no—
330C2×C4×C127—41no—
331C2×C4×C127—41no—
332C2×C4×C127—41no—
333C2×C4×C127—41no—
334C2×C4×C127—41no—
335C2×C4×C127—41no—
336C2×C4×C127—41no—
337C2×C4×C127—41no—
338C2×C4×C127—41no—
339C2×C4×C127—41no—
340C2×C4×C127—41no—
341C2×C4×C127—41no—
342C2×C4×C127—41no—
343C2×C4×C127—41no—
344C2×C4×C127—41no—
345C2×C4×C127—41no—
346C2×C4×C127—41no—
347C2×C4×C127#12614yes—
348C2×C4×C127#12614yes—
349C22×C127C4×#4111yescharacteristic
350C22×C127C4×#4111yescharacteristic
351C22×C127C4×#4111yescharacteristic
352C22×C127C4×#4111yescharacteristic
353C22×C127C4×#4111yescharacteristic
354C22×C127#52011yescharacteristic
355C22×C127#52011yescharacteristic
356C22×C127C2×#12611yescharacteristic
357C22×C127C2×#12611yescharacteristic
358C22×C127#52911yescharacteristic
359C22×C127#52911yescharacteristic
360C22×C127#52911yescharacteristic
361C22×C127#52911yescharacteristic
362C22×C127#52911yescharacteristic
363C22×C127#52911yescharacteristic
364C22×C127#53811yescharacteristic
365C22×C127#53911yescharacteristic
366C22×C127#54111yescharacteristic
367C22×C127#54211yescharacteristic
368C22×C127#55111yescharacteristic
369C22×C127#55111yescharacteristic
370C22×C127#55111yescharacteristic
371C22×C127#55111yescharacteristic
372C22×C127#55211yescharacteristic
373C22×C127#55211yescharacteristic
374C22×C127#55211yescharacteristic
375C22×C127#55211yescharacteristic
376C22×C127#55311yescharacteristic
377C22×C127#55311yescharacteristic
378C22×C127#55311yescharacteristic
379C22×C127#55311yescharacteristic
380C22×C127#55611yescharacteristic
381C22×C127#55611yescharacteristic
382C22×C127#55611yescharacteristic
383C22×C127#55611yescharacteristic
384C4×C127—24no—
385C4×C127—24no—
386C4×C127—42no—
387C4×C127—42no—
388C4×C127—42no—
389C4×C127—42no—
390C4×C127—42no—
391C4×C127—42no—
392C4×C127—42no—
393C4×C127—42no—
394C4×C127—42no—
395C4×C127—42no—
396C4×C127—42no—
397C4×C127—81no—
398C4×C127—81no—
399#14251C12711yesmaximal, characteristic, direct product factor, Sylow
400C2×C127C4×#12611yescharacteristic
401C2×C127C4×#12611yescharacteristic
402C2×C127#233411yescharacteristic
403C2×C127#237311yescharacteristic
404C2×C127#237311yescharacteristic
405C2×C127#237311yescharacteristic
406C2×C127#237311yescharacteristic
407C2×C127#249311yescharacteristic
408C2×C127#249411yescharacteristic
409C2×C127#251011yescharacteristic
410C2×C127#251411yescharacteristic
411C2×C127#252711yescharacteristic
412C2×C127#252811yescharacteristic
413C2×C127#257611yescharacteristic
414C2×C127#259411yescharacteristic
415C2×#401C2×C12711yescharacteristic
416#1443C2×C12711yescharacteristic
417#1443C2×C12711yescharacteristic
418#1442C2×C12711yescharacteristic
419#1436C2×C12711yescharacteristic
420#1436C2×C12711yescharacteristic
421#1436C2×C12711yescharacteristic
422#1436C2×C12711yescharacteristic
423#1436C2×C12711yescharacteristic
424#1434C2×C12711yescharacteristic
425#1434C2×C12711yescharacteristic
426#1434C2×C12711yescharacteristic
427#1434C2×C12711yescharacteristic
428C4×#95C2×C12711yescharacteristic
429C4×#95C2×C12711yescharacteristic
430C127#1425111yescharacteristic, direct product factor, Sylow
431C22×C4⋊C4C22×C12711yescharacteristic
432C22×C4⋊C4C22×C12711yescharacteristic
433C22×C42C22×C12711yescharacteristic
434C22×C42C22×C12711yescharacteristic
435C22×C42C22×C12711yescharacteristic
436C22×C42C22×C12711yescharacteristic
437C22×C42C22×C12711yescharacteristic
438#401C4×C12718yescomplemented
439C2×#95C22×C12711yescharacteristic
440C2×#95C22×C12711yescharacteristic
441C2×#95C22×C12711yescharacteristic
442C2×#95C22×C12711yescharacteristic
443C2×#95C22×C12711yescharacteristic
444C2×#95C22×C12711yescharacteristic
445C2×#95C22×C12711yescharacteristic
446C2×#95C22×C12711yescharacteristic
447C2×#95C22×C12711yescharacteristic
448C2×#95C22×C12711yescharacteristic
449C2×#95C22×C12711yescharacteristic
450C2×#95C22×C12711yescharacteristic
451C2×#95C22×C12711yescharacteristic
452C2×#95C22×C12711yescharacteristic
453C2×#95C22×C12711yescharacteristic
454C2×#95C22×C12711yescharacteristic
455C2×#95C22×C12711yescharacteristic
456C2×#95C22×C12711yescharacteristic
457C2×#95C22×C12711yescharacteristic
458C2×#95C22×C12711yescharacteristic
459C2×#95C22×C12711yescharacteristic
460C2×#95C22×C12711yescharacteristic
461C2×#95C22×C12711yescharacteristic
462C2×#95C22×C12711yescharacteristic
463C2×#95C22×C12711yescharacteristic
464C2×#95C22×C12711yescharacteristic
465C2×#95C22×C12711yescharacteristic
466C2×#95C22×C12711yescharacteristic
467C23×C4C23×C12711yescharacteristic
468C23×C4C23×C12711yescharacteristic
469C23×C4C23×C12711yescharacteristic
470C23×C4C23×C12711yescharacteristic
471C23×C4C23×C12711yescharacteristic
472C23×C4C23×C12711yescharacteristic
473C23×C4C23×C12711yescharacteristic
474C23×C4C23×C12711yescharacteristic
475C23×C4C23×C12711yescharacteristic
476C23×C4C23×C12711yescharacteristic
477C23×C4C23×C12711yescharacteristic
478C23×C4C23×C12711yescharacteristic
479C23×C4C23×C12711yescharacteristic
480C23×C4C23×C12711yescharacteristic
481C23×C4C23×C12711yescharacteristic
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—41no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—41no—
499C2×C42—41no—
500C2×C42—41no—
501C2×C42—41no—
502C2×C42—41no—
503#95—22no—
504#95—22no—
505#95—22no—
506#95—22no—
507#95—22no—
508#95—22no—
509#95—22no—
510#95—22no—
511#95—22no—
512#95—22no—
513#95—22no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—41no—
519#95—41no—
520#95—41no—
521#95—41no—
522#95—41no—
523#95—41no—
524#95C2×C4×C12714yes—
525#95C2×C4×C12714yes—
526#95C2×C4×C12714yes—
527#95C2×C4×C12714yes—
528#95C2×C4×C12714yes—
529#95C2×C4×C12714yes—
530#95C2×C4×C12714yes—
531C24C24×C12711yescharacteristic
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4C22×C4×C12712yes—
621C22×C4C22×C4×C12712yes—
622C22×C4C22×C4×C12712yes—
623C22×C4C22×C4×C12712yes—
624C22×C4C22×C4×C12712yes—
625C22×C4C22×C4×C12712yes—
626C22×C4C22×C4×C12712yes—
627C22×C4#41×C12712yes—
628C22×C4#41×C12712yes—
629C22×C4#41×C12712yes—
630C22×C4#41×C12712yes—
631C22×C4#41×C12712yes—
632C22×C4#41×C12712yes—
633C22×C4#41×C12712yes—
634C22×C4#41×C12712yes—
635C22×C4#41×C12712yes—
636C22×C4#41×C12712yes—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C42—44no—
640C42—44no—
641C42—44no—
642C42—44no—
643C42—44no—
644C23C23×C4×C12711yescharacteristic
645C23C2×#41×C12711yescharacteristic
646C23C2×#41×C12711yescharacteristic
647C23C2×#41×C12711yescharacteristic
648C23C2×#41×C12711yescharacteristic
649C23C2×#41×C12711yescharacteristic
650C23C2×#41×C12711yescharacteristic
651C23C2×#41×C12711yescharacteristic
652C23C2×#41×C12711yescharacteristic
653C23C2×#41×C12711yescharacteristic
654C23C2×#41×C12711yescharacteristic
655C23H(5,𝔽2)×C12711yescharacteristic
656C23H(5,𝔽2)×C12711yescharacteristic
657C232−1+4×C12711yescharacteristic
658C232−1+4×C12711yescharacteristic
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4#126×C12714yes—
763C2×C4#126×C12714yes—
764C22C4×#41×C12711yescharacteristic
765C22C4×#41×C12711yescharacteristic
766C22C4×#41×C12711yescharacteristic
767C22C4×#41×C12711yescharacteristic
768C22C4×#41×C12711yescharacteristic
769C22#520×C12711yescharacteristic
770C22#520×C12711yescharacteristic
771C22C2×#126×C12711yescharacteristic
772C22C2×#126×C12711yescharacteristic
773C22#529×C12711yescharacteristic
774C22#529×C12711yescharacteristic
775C22#529×C12711yescharacteristic
776C22#529×C12711yescharacteristic
777C22#529×C12711yescharacteristic
778C22#529×C12711yescharacteristic
779C22#538×C12711yescharacteristic
780C22#539×C12711yescharacteristic
781C22#541×C12711yescharacteristic
782C22#542×C12711yescharacteristic
783C22#551×C12711yescharacteristic
784C22#551×C12711yescharacteristic
785C22#551×C12711yescharacteristic
786C22#551×C12711yescharacteristic
787C22#552×C12711yescharacteristic
788C22#552×C12711yescharacteristic
789C22#552×C12711yescharacteristic
790C22#552×C12711yescharacteristic
791C22#553×C12711yescharacteristic
792C22#553×C12711yescharacteristic
793C22#553×C12711yescharacteristic
794C22#553×C12711yescharacteristic
795C22#556×C12711yescharacteristic
796C22#556×C12711yescharacteristic
797C22#556×C12711yescharacteristic
798C22#556×C12711yescharacteristic
799C4—24no—
800C4—24no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—81no—
813C4—81no—
814C2C4×#126×C12711yescharacteristic
815C2C4×#126×C12711yescharacteristic
816C2C127×#233411yescharacteristic
817C2C127×#237311yescharacteristic
818C2C127×#237311yescharacteristic
819C2C127×#237311yescharacteristic
820C2C127×#237311yescharacteristic
821C2C127×#249311yescharacteristic
822C2C127×#249411yescharacteristic
823C2C127×#251011yescharacteristic
824C2C127×#251411yescharacteristic
825C2C127×#252711yescharacteristic
826C2C127×#252811yescharacteristic
827C2C127×#257611yescharacteristic
828C2C127×#259411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
23. #401×C127C4semidirect
399. #14251C127direct (N × H)
430. C127#14251direct (N × H)
438. #401C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#401×C1272
C127×#14432
C127×#14422
C127×#14362
C127×#14342
C4×#95×C1272
#14251127