Finite Group Databasebeta

← C127×#15509 #44579182

Subgroups — C127×#15509 #44579182

Order 32512.

1282 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C127C211yesmaximal, characteristic
2C2×#398×C127C211yesmaximal, characteristic
3C2×#391×C127C211yesmaximal, characteristic
4C2×#391×C127C211yesmaximal, characteristic
5C127×#1446C211yesmaximal, characteristic
6C127×#1445C211yesmaximal, characteristic
7C127×#1443C211yesmaximal, characteristic
8C127×#1442C211yesmaximal, characteristic
9C127×#1442C211yesmaximal, characteristic
10C127×#1442C211yesmaximal, characteristic
11C127×#1441C211yesmaximal, characteristic
12C127×#1436C211yesmaximal, characteristic
13C127×#1436C211yesmaximal, characteristic
14C127×C4⋊#95C211yesmaximal, characteristic
15C127×#1434C211yesmaximal, characteristic
16C23×Q8×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C42×C127C2211yescharacteristic
24C22×C42×C127C2211yescharacteristic
25#400×C127—24no—
26#398×C127—24no—
27#391×C127—24no—
28#391×C127—24no—
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
52C2×#95×C127C2211yescharacteristic
53C2×#95×C127C2211yescharacteristic
54C2×#95×C127C2211yescharacteristic
55C22×Q8×C127—22no—
56C22×Q8×C127—22no—
57C22×Q8×C127—22no—
58C22×Q8×C127—22no—
59C22×Q8×C127—41no—
60C22×Q8×C127—41no—
61C22×Q8×C127Q814yes—
62C23×C4×C127C2311yescharacteristic
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
76C23×C4×C127C2311yescharacteristic
77C2×C4⋊C4×C127—22no—
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—22no—
86C2×C4⋊C4×C127—22no—
87C2×C4⋊C4×C127—22no—
88C2×C4⋊C4×C127—22no—
89C2×C4⋊C4×C127—22no—
90C2×C4⋊C4×C127—22no—
91C2×C4⋊C4×C127—41no—
92C2×C4⋊C4×C127—41no—
93C2×C4⋊C4×C127—41no—
94C2×C4⋊C4×C127—41no—
95C2×C42×C127—22no—
96C2×C42×C127—22no—
97C2×C42×C127—22no—
98C2×C42×C127—22no—
99C2×C42×C127—41no—
100C2×C42×C127—41no—
101#95×C127—22no—
102#95×C127—22no—
103#95×C127—22no—
104#95×C127—22no—
105#95×C127—22no—
106#95×C127—22no—
107#95×C127—22no—
108#95×C127—22no—
109#95×C127—22no—
110#95×C127—22no—
111#95×C127—22no—
112#95×C127—22no—
113#95×C127—22no—
114#95×C127—22no—
115#95×C127—22no—
116#95×C127—22no—
117#95×C127—22no—
118#95×C127—22no—
119#95×C127—22no—
120#95×C127—22no—
121#95×C127—41no—
122#95×C127—41no—
123#95×C127—41no—
124#95×C127—41no—
125#95×C127D414yes—
126#95×C127D414yes—
127C24×C127C2411yescharacteristic
128C2×Q8×C127—28no—
129C2×Q8×C127—28no—
130C2×Q8×C127—44no—
131C2×Q8×C127—44no—
132C2×Q8×C127—44no—
133C2×Q8×C127—44no—
134C2×Q8×C127—44no—
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×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×C127C2×D412yes—
226C22×C4×C127C2×D412yes—
227C22×C4×C127C2×D412yes—
228C22×C4×C127C2×D412yes—
229C22×C4×C127C2×D412yes—
230C22×C4×C127C2×D412yes—
231C22×C4×C127C2×Q812yes—
232C22×C4×C127C2×Q812yes—
233C22×C4×C127C2×Q812yes—
234C22×C4×C127#4112yes—
235C22×C4×C127#4112yes—
236C22×C4×C127#4112yes—
237C22×C4×C127#4112yes—
238C22×C4×C127#4112yes—
239C22×C4×C127#4112yes—
240C4⋊C4×C127—44no—
241C4⋊C4×C127—44no—
242C4⋊C4×C127—44no—
243C4⋊C4×C127—44no—
244C4⋊C4×C127—44no—
245C4⋊C4×C127—44no—
246C42×C127—44no—
247C42×C127—44no—
248C23×C127C22×D411yescharacteristic
249C23×C127C22×D411yescharacteristic
250C23×C127C22×Q811yescharacteristic
251C23×C127C2×#4111yescharacteristic
252C23×C127C2×#4111yescharacteristic
253C23×C127C2×#4111yescharacteristic
254C23×C127C2×#4111yescharacteristic
255C23×C127C2×#4111yescharacteristic
256C23×C127C2×#4111yescharacteristic
257C23×C127H(5,𝔽2)11yescharacteristic
258C23×C127H(5,𝔽2)11yescharacteristic
259C23×C1272−1+411yescharacteristic
260C23×C1272−1+411yescharacteristic
261C23×C1272−1+411yescharacteristic
262C23×C1272−1+411yescharacteristic
263Q8×C127—416no—
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—22no—
290C2×C4×C127—22no—
291C2×C4×C127—22no—
292C2×C4×C127—22no—
293C2×C4×C127—22no—
294C2×C4×C127—22no—
295C2×C4×C127—22no—
296C2×C4×C127—22no—
297C2×C4×C127—22no—
298C2×C4×C127—22no—
299C2×C4×C127—22no—
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—41no—
348C2×C4×C127—41no—
349C2×C4×C127—41no—
350C2×C4×C127—41no—
351C2×C4×C127—41no—
352C2×C4×C127—41no—
353C2×C4×C127—41no—
354C2×C4×C127—41no—
355C2×C4×C127—41no—
356C2×C4×C127—41no—
357C2×C4×C127—41no—
358C2×C4×C127—41no—
359C2×C4×C127—41no—
360C2×C4×C127—41no—
361C2×C4×C127—41no—
362C2×C4×C127—41no—
363C2×C4×C127—41no—
364C2×C4×C127—41no—
365C2×C4×C127—41no—
366C2×C4×C127C22⋊Q814yes—
367C2×C4×C127C22⋊Q814yes—
368C2×C4×C127#12414yes—
369C22×C127C2×C22⋊Q811yescharacteristic
370C22×C127C2×C22⋊Q811yescharacteristic
371C22×C127C2×#12411yescharacteristic
372C22×C127#52911yescharacteristic
373C22×C127#52911yescharacteristic
374C22×C127#53211yescharacteristic
375C22×C127#53611yescharacteristic
376C22×C127#53611yescharacteristic
377C22×C127#53911yescharacteristic
378C22×C127#53911yescharacteristic
379C22×C127#54111yescharacteristic
380C22×C127#54111yescharacteristic
381C22×C127#54211yescharacteristic
382C22×C127#54211yescharacteristic
383C22×C127#54311yescharacteristic
384C22×C127D4211yescharacteristic
385C22×C127#54611yescharacteristic
386C22×C127#54611yescharacteristic
387C22×C127#54711yescharacteristic
388C22×C127#54711yescharacteristic
389C22×C127#54811yescharacteristic
390C22×C127#54811yescharacteristic
391C22×C127#55111yescharacteristic
392C22×C127#55111yescharacteristic
393C22×C127#55211yescharacteristic
394C22×C127#55211yescharacteristic
395C22×C127#55511yescharacteristic
396C22×C127#55611yescharacteristic
397C22×C127#55611yescharacteristic
398C22×C127#55711yescharacteristic
399C22×C127#55711yescharacteristic
400C22×C127#55711yescharacteristic
401C22×C127#55711yescharacteristic
402C22×C127#56311yescharacteristic
403C22×C127#56311yescharacteristic
404C4×C127—24no—
405C4×C127—24no—
406C4×C127—24no—
407C4×C127—42no—
408C4×C127—42no—
409C4×C127—42no—
410C4×C127—42no—
411C4×C127—42no—
412C4×C127—42no—
413C4×C127—81no—
414C4×C127—81no—
415C4×C127—81no—
416C4×C127—81no—
417C4×C127—81no—
418C4×C127—81no—
419#15509C12711yesmaximal, characteristic, direct product factor, Sylow
420C2×C127#243711yescharacteristic
421C2×C127#245311yescharacteristic
422C2×C127#245311yescharacteristic
423C2×C127#248811yescharacteristic
424C2×C127#249111yescharacteristic
425C2×C127#253211yescharacteristic
426C2×C127#256011yescharacteristic
427C2×C127#256511yescharacteristic
428C2×C127#256811yescharacteristic
429C2×C127#267411yescharacteristic
430C2×C127#268911yescharacteristic
431C2×C127#269011yescharacteristic
432C2×C127#276211yescharacteristic
433C2×C127#279911yescharacteristic
434C2×C127#280911yescharacteristic
435C2×#400C2×C12711yescharacteristic
436C2×#398C2×C12711yescharacteristic
437C2×#391C2×C12711yescharacteristic
438C2×#391C2×C12711yescharacteristic
439#1446C2×C12711yescharacteristic
440#1445C2×C12711yescharacteristic
441#1443C2×C12711yescharacteristic
442#1442C2×C12711yescharacteristic
443#1442C2×C12711yescharacteristic
444#1442C2×C12711yescharacteristic
445#1441C2×C12711yescharacteristic
446#1436C2×C12711yescharacteristic
447#1436C2×C12711yescharacteristic
448C4⋊#95C2×C12711yescharacteristic
449#1434C2×C12711yescharacteristic
450C127#1550911yescharacteristic, direct product factor, Sylow
451C23×Q8C22×C12711yescharacteristic
452C22×C4⋊C4C22×C12711yescharacteristic
453C22×C4⋊C4C22×C12711yescharacteristic
454C22×C4⋊C4C22×C12711yescharacteristic
455C22×C4⋊C4C22×C12711yescharacteristic
456C22×C4⋊C4C22×C12711yescharacteristic
457C22×C4⋊C4C22×C12711yescharacteristic
458C22×C42C22×C12711yescharacteristic
459C22×C42C22×C12711yescharacteristic
460#400—24no—
461#398—24no—
462#391—24no—
463#391—24no—
464C2×#95C22×C12711yescharacteristic
465C2×#95C22×C12711yescharacteristic
466C2×#95C22×C12711yescharacteristic
467C2×#95C22×C12711yescharacteristic
468C2×#95C22×C12711yescharacteristic
469C2×#95C22×C12711yescharacteristic
470C2×#95C22×C12711yescharacteristic
471C2×#95C22×C12711yescharacteristic
472C2×#95C22×C12711yescharacteristic
473C2×#95C22×C12711yescharacteristic
474C2×#95C22×C12711yescharacteristic
475C2×#95C22×C12711yescharacteristic
476C2×#95C22×C12711yescharacteristic
477C2×#95C22×C12711yescharacteristic
478C2×#95C22×C12711yescharacteristic
479C2×#95C22×C12711yescharacteristic
480C2×#95C22×C12711yescharacteristic
481C2×#95C22×C12711yescharacteristic
482C2×#95C22×C12711yescharacteristic
483C2×#95C22×C12711yescharacteristic
484C2×#95C22×C12711yescharacteristic
485C2×#95C22×C12711yescharacteristic
486C2×#95C22×C12711yescharacteristic
487C2×#95C22×C12711yescharacteristic
488C2×#95C22×C12711yescharacteristic
489C2×#95C22×C12711yescharacteristic
490C22×Q8—22no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8Q8×C12714yes—
497C23×C4C23×C12711yescharacteristic
498C23×C4C23×C12711yescharacteristic
499C23×C4C23×C12711yescharacteristic
500C23×C4C23×C12711yescharacteristic
501C23×C4C23×C12711yescharacteristic
502C23×C4C23×C12711yescharacteristic
503C23×C4C23×C12711yescharacteristic
504C23×C4C23×C12711yescharacteristic
505C23×C4C23×C12711yescharacteristic
506C23×C4C23×C12711yescharacteristic
507C23×C4C23×C12711yescharacteristic
508C23×C4C23×C12711yescharacteristic
509C23×C4C23×C12711yescharacteristic
510C23×C4C23×C12711yescharacteristic
511C23×C4C23×C12711yescharacteristic
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—41no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—41no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—41no—
535C2×C42—41no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—41no—
557#95—41no—
558#95—41no—
559#95—41no—
560#95D4×C12714yes—
561#95D4×C12714yes—
562C24C24×C12711yescharacteristic
563C2×Q8—28no—
564C2×Q8—28no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8—44no—
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×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4C2×D4×C12712yes—
661C22×C4C2×D4×C12712yes—
662C22×C4C2×D4×C12712yes—
663C22×C4C2×D4×C12712yes—
664C22×C4C2×D4×C12712yes—
665C22×C4C2×D4×C12712yes—
666C22×C4C2×Q8×C12712yes—
667C22×C4C2×Q8×C12712yes—
668C22×C4C2×Q8×C12712yes—
669C22×C4#41×C12712yes—
670C22×C4#41×C12712yes—
671C22×C4#41×C12712yes—
672C22×C4#41×C12712yes—
673C22×C4#41×C12712yes—
674C22×C4#41×C12712yes—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C42—44no—
682C42—44no—
683C23C22×D4×C12711yescharacteristic
684C23C22×D4×C12711yescharacteristic
685C23C22×Q8×C12711yescharacteristic
686C23C2×#41×C12711yescharacteristic
687C23C2×#41×C12711yescharacteristic
688C23C2×#41×C12711yescharacteristic
689C23C2×#41×C12711yescharacteristic
690C23C2×#41×C12711yescharacteristic
691C23C2×#41×C12711yescharacteristic
692C23H(5,𝔽2)×C12711yescharacteristic
693C23H(5,𝔽2)×C12711yescharacteristic
694C232−1+4×C12711yescharacteristic
695C232−1+4×C12711yescharacteristic
696C232−1+4×C12711yescharacteristic
697C232−1+4×C12711yescharacteristic
698Q8—416no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
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—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4C22⋊Q8×C12714yes—
802C2×C4C22⋊Q8×C12714yes—
803C2×C4#124×C12714yes—
804C22C2×C22⋊Q8×C12711yescharacteristic
805C22C2×C22⋊Q8×C12711yescharacteristic
806C22C2×#124×C12711yescharacteristic
807C22#529×C12711yescharacteristic
808C22#529×C12711yescharacteristic
809C22#532×C12711yescharacteristic
810C22#536×C12711yescharacteristic
811C22#536×C12711yescharacteristic
812C22#539×C12711yescharacteristic
813C22#539×C12711yescharacteristic
814C22#541×C12711yescharacteristic
815C22#541×C12711yescharacteristic
816C22#542×C12711yescharacteristic
817C22#542×C12711yescharacteristic
818C22#543×C12711yescharacteristic
819C22D42×C12711yescharacteristic
820C22#546×C12711yescharacteristic
821C22#546×C12711yescharacteristic
822C22#547×C12711yescharacteristic
823C22#547×C12711yescharacteristic
824C22#548×C12711yescharacteristic
825C22#548×C12711yescharacteristic
826C22#551×C12711yescharacteristic
827C22#551×C12711yescharacteristic
828C22#552×C12711yescharacteristic
829C22#552×C12711yescharacteristic
830C22#555×C12711yescharacteristic
831C22#556×C12711yescharacteristic
832C22#556×C12711yescharacteristic
833C22#557×C12711yescharacteristic
834C22#557×C12711yescharacteristic
835C22#557×C12711yescharacteristic
836C22#557×C12711yescharacteristic
837C22#563×C12711yescharacteristic
838C22#563×C12711yescharacteristic
839C4—24no—
840C4—24no—
841C4—24no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—81no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C2C127×#243711yescharacteristic
855C2C127×#245311yescharacteristic
856C2C127×#245311yescharacteristic
857C2C127×#248811yescharacteristic
858C2C127×#249111yescharacteristic
859C2C127×#253211yescharacteristic
860C2C127×#256011yescharacteristic
861C2C127×#256511yescharacteristic
862C2C127×#256811yescharacteristic
863C2C127×#267411yescharacteristic
864C2C127×#268911yescharacteristic
865C2C127×#269011yescharacteristic
866C2C127×#276211yescharacteristic
867C2C127×#279911yescharacteristic
868C2C127×#280911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
419. #15509C127direct (N × H)
450. C127#15509direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#400×C1272
C2×#398×C1272
C2×#391×C1272
C127×#14462
C127×#14452
C127×#14432
C127×#14422
C127×#14412
C127×#14362
C127×C4⋊#952
C127×#14342
#15509127