Finite Group Databasebeta

← C127×#21528 #44585201

Subgroups — C127×#21528 #44585201

Order 32512.

1098 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C127C211yesmaximal, characteristic
2C2×#440×C127C211yesmaximal, characteristic, complemented
3C22×#97×C127C211yesmaximal, characteristic, complemented
4C4×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
5C4×#121×C127C211yesmaximal, characteristic
6C127×#1973C211yesmaximal, characteristic, complemented
7C127×#1944C211yesmaximal, characteristic, complemented
8C127×#1936C211yesmaximal, characteristic, complemented
9C127×#1935C211yesmaximal, characteristic, complemented
10C127×#1893C211yesmaximal, characteristic
11C127×#1892C211yesmaximal, characteristic, complemented
12C127×#1808C211yesmaximal, characteristic, complemented
13C127×#1776C211yesmaximal, characteristic, complemented
14C127×#1763C211yesmaximal, characteristic, complemented
15C127×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C127C2211yescharacteristic
17C23×C8×C127C2211yescharacteristic
18C23×C8×C127C2211yescharacteristic
19C2×C22⋊Q8×C127C2211yescharacteristic
20C2×#121×C127C2211yescharacteristic
21C2×C4×Q8×C127C2211yescharacteristic
22C2×C4×D4×C127—21no—
23C2×C4×D4×C127C2211yescharacteristic
24C22×C42×C127C2211yescharacteristic
25#465×C127C418yescomplemented
26#440×C127—24no—
27C2×#107×C127C2211yescharacteristic
28C2×#107×C127C2211yescharacteristic
29C2×#106×C127C2211yescharacteristic
30C2×#103×C127C2211yescharacteristic
31C2×#103×C127C2211yescharacteristic
32C2×#103×C127C2211yescharacteristic
33C2×#102×C127C2211yescharacteristic
34C2×#102×C127C2211yescharacteristic
35C2×#102×C127C2211yescharacteristic
36C2×#97×C127—24no—
37C2×#97×C127C2211yescharacteristic
38C2×#97×C127C2211yescharacteristic
39C2×#97×C127C2211yescharacteristic
40C2×#97×C127C2211yescharacteristic
41#391×C127C2211yescharacteristic
42#390×C127C2211yescharacteristic
43#389×C127C2211yescharacteristic
44#389×C127C2211yescharacteristic
45#388×C127—21no—
46#387×C127—21no—
47#386×C127—21no—
48#385×C127—21no—
49#380×C127C2211yescharacteristic
50#380×C127C2211yescharacteristic
51C4×C4⋊C4×C127—21no—
52C4×C4⋊C4×C127C2211yescharacteristic
53C4×C4⋊C4×C127C2211yescharacteristic
54C4×C22⋊C4×C127—21no—
55C4×C22⋊C4×C127—21no—
56#340×C127C2211yescharacteristic
57#340×C127C2211yescharacteristic
58#340×C127C2211yescharacteristic
59#340×C127C2211yescharacteristic
60#340×C127C2211yescharacteristic
61#340×C127C2211yescharacteristic
62C22×Q8×C127C2311yescharacteristic
63C22×D4×C127—21no—
64C22×D4×C127C2311yescharacteristic
65C23×C4×C127—21no—
66C23×C4×C127D411yescharacteristic
67C23×C4×C127D411yescharacteristic
68C23×C4×C127C2311yescharacteristic
69C2×SD16×C127—22no—
70C2×SD16×C127—22no—
71C2×SD16×C127C2×C414yescomplemented
72C22×C8×C127—22no—
73C22×C8×C127—22no—
74C22×C8×C127—22no—
75C22×C8×C127—22no—
76C22×C8×C127—22no—
77C22×C8×C127C2×C414yescomplemented
78C22×C8×C127C2311yescharacteristic
79C22×C8×C127C2311yescharacteristic
80C22×C8×C127C2311yescharacteristic
81C22×C8×C127C2311yescharacteristic
82C22⋊Q8×C127—22no—
83C22⋊Q8×C127C2×C414yescomplemented
84#121×C127—22no—
85#121×C127C2×C414yes—
86C4×Q8×C127—22no—
87C4×Q8×C127—22no—
88C4×D4×C127—22no—
89C4×D4×C127—22no—
90C4×D4×C127—44no—
91C2×C4⋊C4×C127—21no—
92C2×C4⋊C4×C127—21no—
93C2×C4⋊C4×C127—21no—
94C2×C4⋊C4×C127—21no—
95C2×C4⋊C4×C127C2311yescharacteristic
96C2×C4⋊C4×C127C2311yescharacteristic
97C2×C4⋊C4×C127C2311yescharacteristic
98C2×C4⋊C4×C127C2311yescharacteristic
99C2×C4⋊C4×C127C2311yescharacteristic
100C2×C4⋊C4×C127C2311yescharacteristic
101C2×C22⋊C4×C127—21no—
102C2×C22⋊C4×C127—21no—
103C2×C22⋊C4×C127—21no—
104C2×C22⋊C4×C127—21no—
105C2×C22⋊C4×C127—21no—
106C2×C22⋊C4×C127—21no—
107C2×C22⋊C4×C127—21no—
108C2×C42×C127—22no—
109C2×C42×C127—22no—
110C2×C42×C127—21no—
111C2×C42×C127—21no—
112C2×C42×C127—21no—
113C2×C42×C127D411yescharacteristic
114C2×C42×C127D411yescharacteristic
115C2×C42×C127C2311yescharacteristic
116C2×C42×C127C2311yescharacteristic
117#107×C127—22no—
118#107×C127—22no—
119#106×C127C2×C414yescomplemented
120#103×C127—22no—
121#103×C127—22no—
122#103×C127C2×C414yescomplemented
123#102×C127—22no—
124#102×C127—22no—
125#102×C127C2×C414yescomplemented
126#97×C127—22no—
127#97×C127—22no—
128#97×C127—22no—
129#97×C127D414yescomplemented
130#95×C127—21no—
131#95×C127—21no—
132#95×C127—21no—
133#95×C127—21no—
134#95×C127—21no—
135#95×C127—21no—
136#95×C127—21no—
137#95×C127—21no—
138C24×C127—21no—
139C24×C127C2×D411yescharacteristic
140C2×Q8×C127—21no—
141C2×Q8×C127—21no—
142C2×Q8×C127—21no—
143C2×Q8×C127—21no—
144C2×Q8×C127—21no—
145C2×Q8×C127C22×C412yes—
146C2×D4×C127—24no—
147C2×D4×C127—21no—
148C2×D4×C127—21no—
149C2×D4×C127—21no—
150C2×D4×C127—21no—
151C2×D4×C127—21no—
152C2×D4×C127—42no—
153C2×D4×C127—42no—
154C2×D4×C127C22×C412yes—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—22no—
160C22×C4×C127—22no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127—21no—
164C22×C4×C127—22no—
165C22×C4×C127—22no—
166C22×C4×C127—21no—
167C22×C4×C127—21no—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—41no—
171C22×C4×C127—41no—
172C22×C4×C127—42no—
173C22×C4×C127—42no—
174C22×C4×C127—42no—
175C22×C4×C127C22×C412yes—
176C22×C4×C127C2×D411yescharacteristic
177C22×C4×C127C2×D411yescharacteristic
178C22×C4×C127C2×D411yescharacteristic
179C22×C4×C127C2×D411yescharacteristic
180C22×C4×C127C2×D411yescharacteristic
181C22×C4×C127#4112yes—
182C22×C4×C127C2411yescharacteristic
183SD16×C127—28no—
184C2×C8×C127—28no—
185C2×C8×C127—21no—
186C2×C8×C127—21no—
187C2×C8×C127—21no—
188C2×C8×C127—21no—
189C2×C8×C127—21no—
190C2×C8×C127—21no—
191C2×C8×C127—28no—
192C2×C8×C127C22×C412yes—
193C2×C8×C127C22×C412yes—
194C2×C8×C127C2×D412yes—
195C2×C8×C127C2×D412yes—
196C2×C8×C127#4112yes—
197C2×C8×C127#4112yes—
198C4⋊C4×C127—24no—
199C4⋊C4×C127—21no—
200C4⋊C4×C127—21no—
201C4⋊C4×C127—21no—
202C4⋊C4×C127—21no—
203C4⋊C4×C127—21no—
204C4⋊C4×C127—21no—
205C4⋊C4×C127—21no—
206C4⋊C4×C127—21no—
207C4⋊C4×C127—21no—
208C4⋊C4×C127—21no—
209C4⋊C4×C127—42no—
210C4⋊C4×C127—42no—
211C4⋊C4×C127—42no—
212C4⋊C4×C127C22×C412yes—
213C4⋊C4×C127C22×C412yes—
214C22⋊C4×C127—24no—
215C22⋊C4×C127—24no—
216C22⋊C4×C127—42no—
217C22⋊C4×C127—42no—
218C22⋊C4×C127—42no—
219C22⋊C4×C127—42no—
220C22⋊C4×C127—42no—
221C42×C127—22no—
222C42×C127—22no—
223C42×C127—21no—
224C42×C127—21no—
225C42×C127—42no—
226C42×C127—42no—
227C42×C127—42no—
228C42×C127C2×D412yes—
229C42×C127#4112yes—
230C23×C127—21no—
231C23×C127—21no—
232C23×C127—21no—
233C23×C127—21no—
234C23×C127—22no—
235C23×C127—41no—
236C23×C127—41no—
237C23×C127—41no—
238C23×C127—41no—
239C23×C127—41no—
240C23×C127—41no—
241C23×C127C4×D412yes—
242C23×C127AGL(1,ℤ/8)12yes—
243C23×C127#13712yes—
244C23×C127C22×D411yescharacteristic
245Q8×C127—22no—
246Q8×C127—22no—
247Q8×C127—41no—
248Q8×C127—41no—
249D4×C127—22no—
250D4×C127—22no—
251D4×C127—48no—
252D4×C127—41no—
253D4×C127—41no—
254C2×C4×C127—21no—
255C2×C4×C127—21no—
256C2×C4×C127—21no—
257C2×C4×C127—21no—
258C2×C4×C127—21no—
259C2×C4×C127—21no—
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—21no—
268C2×C4×C127—21no—
269C2×C4×C127—21no—
270C2×C4×C127—21no—
271C2×C4×C127—21no—
272C2×C4×C127—21no—
273C2×C4×C127—44no—
274C2×C4×C127—44no—
275C2×C4×C127—41no—
276C2×C4×C127—41no—
277C2×C4×C127—41no—
278C2×C4×C127—41no—
279C2×C4×C127—41no—
280C2×C4×C127—41no—
281C2×C4×C127—41no—
282C2×C4×C127—41no—
283C2×C4×C127—41no—
284C2×C4×C127—41no—
285C2×C4×C127—41no—
286C2×C4×C127—41no—
287C2×C4×C127—41no—
288C2×C4×C127—41no—
289C2×C4×C127—41no—
290C2×C4×C127—41no—
291C2×C4×C127—41no—
292C2×C4×C127—41no—
293C2×C4×C127—84no—
294C2×C4×C127C4×D412yes—
295C2×C4×C127#12112yes—
296C2×C4×C127#12112yes—
297C2×C4×C127C23×C411yescharacteristic
298C2×C4×C127C22×D411yescharacteristic
299C2×C4×C127C2×#4111yescharacteristic
300C2×C4×C127C2×#4111yescharacteristic
301C2×C4×C127C2×#4111yescharacteristic
302C2×C4×C127C2×#4111yescharacteristic
303C8×C127—22no—
304C8×C127—22no—
305C8×C127—22no—
306C8×C127C4×D414yescomplemented
307C22×C127—22no—
308C22×C127—22no—
309C22×C127—22no—
310C22×C127—22no—
311C22×C127—22no—
312C22×C127—22no—
313C22×C127—42no—
314C22×C127—42no—
315C22×C127—42no—
316C22×C127—81no—
317C22×C127—81no—
318C22×C127—81no—
319C22×C127—81no—
320C22×C127#44014yescomplemented
321C22×C127C2×C4×D411yescharacteristic
322C22×C127C2×#12111yescharacteristic
323C22×C127#53211yescharacteristic
324C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C127C2×#13711yescharacteristic
326C22×C127#57511yescharacteristic
327C22×C127#57511yescharacteristic
328C4×C127—22no—
329C4×C127—22no—
330C4×C127—22no—
331C4×C127—42no—
332C4×C127—42no—
333C4×C127—41no—
334C4×C127—41no—
335C4×C127—42no—
336C4×C127—81no—
337C4×C127—81no—
338C4×C127—81no—
339C4×C127—81no—
340C4×C127C2×C4×D411yescharacteristic
341C4×C127C4×#4111yescharacteristic
342C4×C127#52511yescharacteristic
343C4×C127#52911yescharacteristic
344#21528C12711yesmaximal, characteristic, direct product factor, Sylow
345C2×C127—24no—
346C2×C127—82no—
347C2×C127C4×#12111yescharacteristic
348C2×C127C2×#44011yescharacteristic
349C2×C127#294311yescharacteristic
350C2×C127#305511yescharacteristic
351C2×C127#305611yescharacteristic
352C2×C127#318011yescharacteristic
353C2×C127#318111yescharacteristic
354C2×#465C2×C12711yescharacteristic
355C2×#440C2×C12711yescharacteristic, complemented
356C22×#97C2×C12711yescharacteristic, complemented
357C4×C22⋊Q8C2×C12711yescharacteristic, complemented
358C4×#121C2×C12711yescharacteristic
359#1973C2×C12711yescharacteristic, complemented
360#1944C2×C12711yescharacteristic, complemented
361#1936C2×C12711yescharacteristic, complemented
362#1935C2×C12711yescharacteristic, complemented
363#1893C2×C12711yescharacteristic
364#1892C2×C12711yescharacteristic, complemented
365#1808C2×C12711yescharacteristic, complemented
366#1776C2×C12711yescharacteristic, complemented
367#1763C2×C12711yescharacteristic, complemented
368#1762C2×C12711yescharacteristic, complemented
369C127#2152811yescharacteristic, direct product factor, Sylow
370C22×SD16C22×C12711yescharacteristic
371C23×C8C22×C12711yescharacteristic
372C23×C8C22×C12711yescharacteristic
373C2×C22⋊Q8C22×C12711yescharacteristic
374C2×#121C22×C12711yescharacteristic
375C2×C4×Q8C22×C12711yescharacteristic
376C2×C4×D4—21no—
377C2×C4×D4C22×C12711yescharacteristic
378C22×C42C22×C12711yescharacteristic
379#465C4×C12718yescomplemented
380#440—24no—
381C2×#107C22×C12711yescharacteristic
382C2×#107C22×C12711yescharacteristic
383C2×#106C22×C12711yescharacteristic
384C2×#103C22×C12711yescharacteristic
385C2×#103C22×C12711yescharacteristic
386C2×#103C22×C12711yescharacteristic
387C2×#102C22×C12711yescharacteristic
388C2×#102C22×C12711yescharacteristic
389C2×#102C22×C12711yescharacteristic
390C2×#97—24no—
391C2×#97C22×C12711yescharacteristic
392C2×#97C22×C12711yescharacteristic
393C2×#97C22×C12711yescharacteristic
394C2×#97C22×C12711yescharacteristic
395#391C22×C12711yescharacteristic
396#390C22×C12711yescharacteristic
397#389C22×C12711yescharacteristic
398#389C22×C12711yescharacteristic
399#388—21no—
400#387—21no—
401#386—21no—
402#385—21no—
403#380C22×C12711yescharacteristic
404#380C22×C12711yescharacteristic
405C4×C4⋊C4—21no—
406C4×C4⋊C4C22×C12711yescharacteristic
407C4×C4⋊C4C22×C12711yescharacteristic
408C4×C22⋊C4—21no—
409C4×C22⋊C4—21no—
410#340C22×C12711yescharacteristic
411#340C22×C12711yescharacteristic
412#340C22×C12711yescharacteristic
413#340C22×C12711yescharacteristic
414#340C22×C12711yescharacteristic
415#340C22×C12711yescharacteristic
416C22×Q8C23×C12711yescharacteristic
417C22×D4—21no—
418C22×D4C23×C12711yescharacteristic
419C23×C4—21no—
420C23×C4D4×C12711yescharacteristic
421C23×C4D4×C12711yescharacteristic
422C23×C4C23×C12711yescharacteristic
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16C2×C4×C12714yescomplemented
426C22×C8—22no—
427C22×C8—22no—
428C22×C8—22no—
429C22×C8—22no—
430C22×C8—22no—
431C22×C8C2×C4×C12714yescomplemented
432C22×C8C23×C12711yescharacteristic
433C22×C8C23×C12711yescharacteristic
434C22×C8C23×C12711yescharacteristic
435C22×C8C23×C12711yescharacteristic
436C22⋊Q8—22no—
437C22⋊Q8C2×C4×C12714yescomplemented
438#121—22no—
439#121C2×C4×C12714yes—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—44no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C23×C12711yescharacteristic
450C2×C4⋊C4C23×C12711yescharacteristic
451C2×C4⋊C4C23×C12711yescharacteristic
452C2×C4⋊C4C23×C12711yescharacteristic
453C2×C4⋊C4C23×C12711yescharacteristic
454C2×C4⋊C4C23×C12711yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42D4×C12711yescharacteristic
468C2×C42D4×C12711yescharacteristic
469C2×C42C23×C12711yescharacteristic
470C2×C42C23×C12711yescharacteristic
471#107—22no—
472#107—22no—
473#106C2×C4×C12714yescomplemented
474#103—22no—
475#103—22no—
476#103C2×C4×C12714yescomplemented
477#102—22no—
478#102—22no—
479#102C2×C4×C12714yescomplemented
480#97—22no—
481#97—22no—
482#97—22no—
483#97D4×C12714yescomplemented
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492C24—21no—
493C24C2×D4×C12711yescharacteristic
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C22×C4×C12712yes—
500C2×D4—24no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—42no—
507C2×D4—42no—
508C2×D4C22×C4×C12712yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4C22×C4×C12712yes—
530C22×C4C2×D4×C12711yescharacteristic
531C22×C4C2×D4×C12711yescharacteristic
532C22×C4C2×D4×C12711yescharacteristic
533C22×C4C2×D4×C12711yescharacteristic
534C22×C4C2×D4×C12711yescharacteristic
535C22×C4#41×C12712yes—
536C22×C4C24×C12711yescharacteristic
537SD16—28no—
538C2×C8—28no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—28no—
546C2×C8C22×C4×C12712yes—
547C2×C8C22×C4×C12712yes—
548C2×C8C2×D4×C12712yes—
549C2×C8C2×D4×C12712yes—
550C2×C8#41×C12712yes—
551C2×C8#41×C12712yes—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—42no—
566C4⋊C4C22×C4×C12712yes—
567C4⋊C4C22×C4×C12712yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C42—22no—
576C42—22no—
577C42—21no—
578C42—21no—
579C42—42no—
580C42—42no—
581C42—42no—
582C42C2×D4×C12712yes—
583C42#41×C12712yes—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—22no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C4×D4×C12712yes—
596C23AGL(1,ℤ/8)×C12712yes—
597C23#137×C12712yes—
598C23C22×D4×C12711yescharacteristic
599Q8—22no—
600Q8—22no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—48no—
606D4—41no—
607D4—41no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4C4×D4×C12712yes—
649C2×C4#121×C12712yes—
650C2×C4#121×C12712yes—
651C2×C4C23×C4×C12711yescharacteristic
652C2×C4C22×D4×C12711yescharacteristic
653C2×C4C2×#41×C12711yescharacteristic
654C2×C4C2×#41×C12711yescharacteristic
655C2×C4C2×#41×C12711yescharacteristic
656C2×C4C2×#41×C12711yescharacteristic
657C8—22no—
658C8—22no—
659C8—22no—
660C8C4×D4×C12714yescomplemented
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22#440×C12714yescomplemented
675C22C2×C4×D4×C12711yescharacteristic
676C22C2×#121×C12711yescharacteristic
677C22#532×C12711yescharacteristic
678C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
679C22C2×#137×C12711yescharacteristic
680C22#575×C12711yescharacteristic
681C22#575×C12711yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—41no—
688C4—41no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4C2×C4×D4×C12711yescharacteristic
695C4C4×#41×C12711yescharacteristic
696C4#525×C12711yescharacteristic
697C4#529×C12711yescharacteristic
698C2—24no—
699C2—82no—
700C2C4×#121×C12711yescharacteristic
701C2C2×#440×C12711yescharacteristic
702C2C127×#294311yescharacteristic
703C2C127×#305511yescharacteristic
704C2C127×#305611yescharacteristic
705C2C127×#318011yescharacteristic
706C2C127×#318111yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC2×#121×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#440×C127C2semidirect
3. C22×#97×C127C2semidirect
4. C4×C22⋊Q8×C127C2semidirect
6. C127×#1973C2semidirect
7. C127×#1944C2semidirect
8. C127×#1936C2semidirect
9. C127×#1935C2semidirect
11. C127×#1892C2semidirect
12. C127×#1808C2semidirect
13. C127×#1776C2semidirect
14. C127×#1763C2semidirect
15. C127×#1762C2semidirect
25. #465×C127C4semidirect
71. C2×SD16×C127C2×C4semidirect
77. C22×C8×C127C2×C4semidirect
83. C22⋊Q8×C127C2×C4semidirect
119. #106×C127C2×C4semidirect
122. #103×C127C2×C4semidirect
125. #102×C127C2×C4semidirect
129. #97×C127D4semidirect
306. C8×C127C4×D4semidirect
320. C22×C127#440semidirect
344. #21528C127direct (N × H)
355. C2×#440C2×C127semidirect
356. C22×#97C2×C127semidirect
357. C4×C22⋊Q8C2×C127semidirect
359. #1973C2×C127semidirect
360. #1944C2×C127semidirect
361. #1936C2×C127semidirect
362. #1935C2×C127semidirect
364. #1892C2×C127semidirect
365. #1808C2×C127semidirect
366. #1776C2×C127semidirect
367. #1763C2×C127semidirect
368. #1762C2×C127semidirect
369. C127#21528direct (N × H)
379. #465C4×C127semidirect
425. C2×SD16C2×C4×C127semidirect
431. C22×C8C2×C4×C127semidirect
437. C22⋊Q8C2×C4×C127semidirect
473. #106C2×C4×C127semidirect
476. #103C2×C4×C127semidirect
479. #102C2×C4×C127semidirect
483. #97D4×C127semidirect
660. C8C4×D4×C127semidirect
674. C22#440×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C1272
C2×#440×C1272
C22×#97×C1272
C4×C22⋊Q8×C1272
C4×#121×C1272
C127×#19732
C127×#19442
C127×#19362
C127×#19352
C127×#18932
C127×#18922
C127×#18082
C127×#17762
C127×#17632
C127×#17622
#21528127