Finite Group Databasebeta

← C2×C127×#1903 #44584667

Subgroups — C2×C127×#1903 #44584667

Order 32512.

1782 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C127C211yesmaximal, characteristic
2C2×#568×C127C211yesmaximal, characteristic, complemented
3C2×#421×C127C211yesmaximal, characteristic, complemented
4C2×#418×C127C211yesmaximal, characteristic, complemented
5C22×#100×C127C211yesmaximal, characteristic, complemented
6C127×#1903C218yesmaximal, direct product factor
7C2×#344×C127C211yesmaximal, characteristic, complemented
8C2×#338×C127C211yesmaximal, characteristic, complemented
9C22×#41×C127C2211yescharacteristic
10C23×D4×C127C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C127—22no—
12C2×AGL(1,ℤ/8)×C127—22no—
13C2×AGL(1,ℤ/8)×C127—22no—
14C2×AGL(1,ℤ/8)×C127—22no—
15C2×AGL(1,ℤ/8)×C127C414yescomplemented
16C2×AGL(1,ℤ/8)×C127C2214yes—
17C22×SD16×C127C412yescomplemented
18C22×D8×C127C412yescomplemented
19#568×C127—22no—
20#568×C127—22no—
21#568×C127—22no—
22#568×C127C2214yescomplemented
23C2×#131×C127—22no—
24C2×#131×C127—22no—
25C22×M16×C127—22no—
26C22×M16×C127C2211yescharacteristic
27C22×M16×C127C2211yescharacteristic
28C22×M16×C127C2211yescharacteristic
29C22×M16×C127C2211yescharacteristic
30C2×#117×C127C2211yescharacteristic
31#421×C127—22no—
32#421×C127C2214yescomplemented
33C2×#104×C127—22no—
34#418×C127—22no—
35#418×C127C2214yescomplemented
36C2×#102×C127—22no—
37C2×#100×C127—22no—
38C2×#100×C127—22no—
39C2×#100×C127C2214yescomplemented
40#344×C127C2214yescomplemented
41#338×C127C2214yescomplemented
42C25×C127—21no—
43C2×#41×C127—21no—
44C2×#41×C127—21no—
45C2×#41×C127—21no—
46C2×#41×C127—21no—
47C2×#41×C127—21no—
48C2×#41×C127—21no—
49C2×#41×C127C2×C412yes—
50C2×#41×C127D412yes—
51C2×#41×C127D412yes—
52C2×#41×C127D412yes—
53C2×#41×C127D412yes—
54C2×#41×C127C2312yes—
55C22×Q8×C127C2×C411yescharacteristic
56C22×D4×C127—21no—
57C22×D4×C127—21no—
58C22×D4×C127—21no—
59C22×D4×C127—21no—
60C22×D4×C127—21no—
61C22×D4×C127—21no—
62C22×D4×C127—21no—
63C22×D4×C127—21no—
64C22×D4×C127—21no—
65C22×D4×C127—21no—
66C22×D4×C127—21no—
67C22×D4×C127—21no—
68C22×D4×C127C2×C412yes—
69C22×D4×C127C2×C412yes—
70C22×D4×C127C2×C411yescharacteristic
71C22×D4×C127C2312yes—
72C23×C4×C127—21no—
73C23×C4×C127C2311yescharacteristic
74AGL(1,ℤ/8)×C127—28no—
75AGL(1,ℤ/8)×C127—28no—
76AGL(1,ℤ/8)×C127—28no—
77AGL(1,ℤ/8)×C127—28no—
78C2×SD16×C127—24no—
79C2×SD16×C127—24no—
80C2×SD16×C127C2×C418yescomplemented
81C2×D8×C127—24no—
82C2×D8×C127—24no—
83C2×D8×C127C2×C418yescomplemented
84#131×C127—28no—
85#131×C127—28no—
86#131×C127—28no—
87#131×C127—28no—
88C2×M16×C127—24no—
89C2×M16×C127—28no—
90C2×M16×C127—21no—
91C2×M16×C127—21no—
92C2×M16×C127—21no—
93C2×M16×C127—21no—
94C2×M16×C127—21no—
95C2×M16×C127—21no—
96C2×M16×C127—21no—
97C2×M16×C127—21no—
98C2×M16×C127—21no—
99C2×M16×C127—21no—
100C2×M16×C127—21no—
101C2×M16×C127—28no—
102C2×M16×C127—21no—
103C2×M16×C127—21no—
104C2×M16×C127—21no—
105C2×M16×C127—21no—
106C2×M16×C127—21no—
107C2×M16×C127C2×C412yes—
108C2×M16×C127D412yes—
109C2×M16×C127D412yes—
110C2×M16×C127D412yes—
111C2×M16×C127C2312yes—
112C2×M16×C127C2312yes—
113C2×M16×C127C2312yes—
114C2×M16×C127C2312yes—
115C22×C8×C127—24no—
116C22×C8×C127—21no—
117C22×C8×C127—21no—
118C22×C8×C127C2×C412yes—
119C22×C8×C127D412yes—
120#117×C127—21no—
121#117×C127—21no—
122#117×C127—21no—
123#117×C127C2312yes—
124C2×C4⋊C4×C127—21no—
125C2×C22⋊C4×C127—21no—
126C2×C42×C127—21no—
127#104×C127—28no—
128#102×C127—28no—
129#100×C127—28no—
130C24×C127—21no—
131C24×C127—22no—
132C24×C127—22no—
133C24×C127—22no—
134C24×C127—41no—
135C24×C127—41no—
136C24×C127—41no—
137C24×C127—41no—
138C24×C127—84no—
139C24×C127#4111yescharacteristic
140#41×C127—22no—
141#41×C127—22no—
142#41×C127—22no—
143#41×C127—22no—
144#41×C127—22no—
145#41×C127—22no—
146#41×C127—22no—
147#41×C127—22no—
148#41×C127—22no—
149#41×C127—22no—
150#41×C127—22no—
151#41×C127—22no—
152#41×C127C22⋊C414yes—
153#41×C127C22⋊C414yes—
154#41×C127C2×D414yes—
155#41×C127C2×D414yes—
156C2×Q8×C127—21no—
157C2×Q8×C127—21no—
158C2×Q8×C127—21no—
159C2×Q8×C127C22⋊C412yes—
160C2×Q8×C127C22⋊C412yes—
161C2×Q8×C127C22×C412yes—
162C2×D4×C127—22no—
163C2×D4×C127—22no—
164C2×D4×C127—22no—
165C2×D4×C127—22no—
166C2×D4×C127—22no—
167C2×D4×C127—22no—
168C2×D4×C127—22no—
169C2×D4×C127—22no—
170C2×D4×C127—22no—
171C2×D4×C127—22no—
172C2×D4×C127—21no—
173C2×D4×C127—21no—
174C2×D4×C127—21no—
175C2×D4×C127—22no—
176C2×D4×C127—22no—
177C2×D4×C127—22no—
178C2×D4×C127—22no—
179C2×D4×C127—22no—
180C2×D4×C127—22no—
181C2×D4×C127—22no—
182C2×D4×C127—22no—
183C2×D4×C127—22no—
184C2×D4×C127—22no—
185C2×D4×C127—22no—
186C2×D4×C127—41no—
187C2×D4×C127—41no—
188C2×D4×C127—41no—
189C2×D4×C127—41no—
190C2×D4×C127—41no—
191C2×D4×C127—41no—
192C2×D4×C127—41no—
193C2×D4×C127—41no—
194C2×D4×C127—41no—
195C2×D4×C127—41no—
196C2×D4×C127—41no—
197C2×D4×C127—41no—
198C2×D4×C127C22⋊C412yes—
199C2×D4×C127C22⋊C412yes—
200C2×D4×C127C22×C414yes—
201C2×D4×C127C22×C412yes—
202C22×C4×C127—21no—
203C22×C4×C127—22no—
204C22×C4×C127—22no—
205C22×C4×C127—22no—
206C22×C4×C127—22no—
207C22×C4×C127—22no—
208C22×C4×C127—22no—
209C22×C4×C127—41no—
210C22×C4×C127C22×C411yescharacteristic
211C22×C4×C127C22×C411yescharacteristic
212C22×C4×C127C2×D411yescharacteristic
213C22×C4×C127C2×D411yescharacteristic
214C22×C4×C127C2×D411yescharacteristic
215C22×C4×C127C2×D411yescharacteristic
216C22×C4×C127C2×D411yescharacteristic
217C22×C4×C127C2×D411yescharacteristic
218C22×C4×C127C2×D411yescharacteristic
219C22×C4×C127C2×D411yescharacteristic
220C22×C4×C127#4111yescharacteristic
221C22×C4×C127#4111yescharacteristic
222C22×C4×C127#4111yescharacteristic
223C22×C4×C127C2411yescharacteristic
224SD16×C127—216no—
225D8×C127—216no—
226M16×C127—216no—
227M16×C127—22no—
228M16×C127—22no—
229M16×C127—22no—
230M16×C127—22no—
231M16×C127—22no—
232M16×C127—22no—
233M16×C127—22no—
234M16×C127—22no—
235M16×C127—22no—
236M16×C127—22no—
237M16×C127—22no—
238M16×C127—22no—
239M16×C127—22no—
240M16×C127—41no—
241M16×C127—41no—
242M16×C127C2×D414yes—
243C2×C8×C127—216no—
244C2×C8×C127—22no—
245C2×C8×C127—22no—
246C2×C8×C127—22no—
247C2×C8×C127—22no—
248C2×C8×C127—22no—
249C2×C8×C127—22no—
250C2×C8×C127—22no—
251C2×C8×C127—22no—
252C2×C8×C127—41no—
253C2×C8×C127—41no—
254C2×C8×C127C22×C414yes—
255C2×C8×C127C2×D414yes—
256C4⋊C4×C127—22no—
257C4⋊C4×C127—41no—
258C22⋊C4×C127—22no—
259C22⋊C4×C127—41no—
260C42×C127—22no—
261C42×C127—41no—
262C23×C127—22no—
263C23×C127—22no—
264C23×C127—22no—
265C23×C127—24no—
266C23×C127—42no—
267C23×C127—42no—
268C23×C127—42no—
269C23×C127—42no—
270C23×C127—42no—
271C23×C127—42no—
272C23×C127—42no—
273C23×C127—82no—
274C23×C127—84no—
275C23×C127—84no—
276C23×C127—84no—
277C23×C127—84no—
278C23×C127—84no—
279C23×C127—84no—
280C23×C127—84no—
281C23×C127C4×D411yescharacteristic
282C23×C127C4×D411yescharacteristic
283C23×C127#12111yescharacteristic
284C23×C127#12111yescharacteristic
285C23×C127#12311yescharacteristic
286C23×C127#12311yescharacteristic
287C23×C127C2×#4111yescharacteristic
288Q8×C127—22no—
289Q8×C127—22no—
290Q8×C127—22no—
291Q8×C127C2×C22⋊C414yes—
292D4×C127—24no—
293D4×C127—24no—
294D4×C127—24no—
295D4×C127—24no—
296D4×C127—24no—
297D4×C127—22no—
298D4×C127—24no—
299D4×C127—22no—
300D4×C127—22no—
301D4×C127—42no—
302D4×C127—42no—
303D4×C127—42no—
304D4×C127—42no—
305D4×C127—42no—
306D4×C127—42no—
307D4×C127C2×C22⋊C414yes—
308C2×C4×C127—22no—
309C2×C4×C127—22no—
310C2×C4×C127—22no—
311C2×C4×C127—24no—
312C2×C4×C127—24no—
313C2×C4×C127—24no—
314C2×C4×C127—24no—
315C2×C4×C127—42no—
316C2×C4×C127—82no—
317C2×C4×C127C2×C22⋊C411yescharacteristic
318C2×C4×C127C2×C22⋊C411yescharacteristic
319C2×C4×C127C2×C22⋊C411yescharacteristic
320C2×C4×C127C2×C22⋊C411yescharacteristic
321C2×C4×C127C4×D411yescharacteristic
322C2×C4×C127C4×D411yescharacteristic
323C2×C4×C127C4×D411yescharacteristic
324C2×C4×C127C4×D411yescharacteristic
325C2×C4×C127C4×D411yescharacteristic
326C2×C4×C127C4×D411yescharacteristic
327C2×C4×C127#12011yescharacteristic
328C2×C4×C127#12011yescharacteristic
329C2×C4×C127#12011yescharacteristic
330C2×C4×C127#12011yescharacteristic
331C2×C4×C127#12111yescharacteristic
332C2×C4×C127#12111yescharacteristic
333C2×C4×C127#12111yescharacteristic
334C2×C4×C127#12111yescharacteristic
335C2×C4×C127#12111yescharacteristic
336C2×C4×C127#12111yescharacteristic
337C2×C4×C127#12311yescharacteristic
338C2×C4×C127#12311yescharacteristic
339C2×C4×C127C23×C411yescharacteristic
340C2×C4×C127C22×D411yescharacteristic
341C2×C4×C127C22×D411yescharacteristic
342C2×C4×C127C22×D411yescharacteristic
343C2×C4×C127C22×D411yescharacteristic
344C2×C4×C127C2×#4111yescharacteristic
345C8×C127—24no—
346C8×C127—24no—
347C8×C127—24no—
348C8×C127—42no—
349C22×C127—22no—
350C22×C127—22no—
351C22×C127—22no—
352C22×C127—24no—
353C22×C127—41no—
354C22×C127—41no—
355C22×C127—41no—
356C22×C127—41no—
357C22×C127—44no—
358C22×C127—44no—
359C22×C127—82no—
360C22×C127—82no—
361C22×C127—84no—
362C22×C127—84no—
363C22×C127—84no—
364C22×C127—84no—
365C22×C127—84no—
366C22×C127—84no—
367C22×C127—84no—
368C22×C127#38611yescharacteristic
369C22×C127#38611yescharacteristic
370C22×C127#38611yescharacteristic
371C22×C127#38611yescharacteristic
372C22×C127C2×C4×D411yescharacteristic
373C22×C127C2×#12111yescharacteristic
374C22×C127C2×#12311yescharacteristic
375C4×C127—24no—
376C4×C127—82no—
377C4×C127#38611yescharacteristic
378C4×C127#38611yescharacteristic
379C4×C127#38611yescharacteristic
380C4×C127#38611yescharacteristic
381C4×C127C22×C22⋊C411yescharacteristic
382C4×C127C2×C4×D411yescharacteristic
383C4×C127C2×#12011yescharacteristic
384C4×C127C2×#12111yescharacteristic
385C2×#1903C12711yesmaximal, characteristic, direct product factor, Sylow
386C2×C127—21no—
387C2×C127—21no—
388C2×C127—21no—
389C2×C127—21no—
390C2×C127—21no—
391C2×C127—21no—
392C2×C127—44no—
393C2×C127—84no—
394C2×C127#190312yesdirect product factor
395C2×C127C2×#38611yescharacteristic
396C22×AGL(1,ℤ/8)C2×C12711yescharacteristic
397C2×#568C2×C12711yescharacteristic, complemented
398C2×#421C2×C12711yescharacteristic, complemented
399C2×#418C2×C12711yescharacteristic, complemented
400C22×#100C2×C12711yescharacteristic, complemented
401#1903C2×C12718yesdirect product factor
402C2×#344C2×C12711yescharacteristic, complemented
403C2×#338C2×C12711yescharacteristic, complemented
404C127C2×#190311yescharacteristic, direct product factor, Sylow
405C22×#41C22×C12711yescharacteristic
406C23×D4C22×C12711yescharacteristic
407C2×AGL(1,ℤ/8)—22no—
408C2×AGL(1,ℤ/8)—22no—
409C2×AGL(1,ℤ/8)—22no—
410C2×AGL(1,ℤ/8)—22no—
411C2×AGL(1,ℤ/8)C4×C12714yescomplemented
412C2×AGL(1,ℤ/8)C22×C12714yes—
413C22×SD16C4×C12712yescomplemented
414C22×D8C4×C12712yescomplemented
415#568—22no—
416#568—22no—
417#568—22no—
418#568C22×C12714yescomplemented
419C2×#131—22no—
420C2×#131—22no—
421C22×M16—22no—
422C22×M16C22×C12711yescharacteristic
423C22×M16C22×C12711yescharacteristic
424C22×M16C22×C12711yescharacteristic
425C22×M16C22×C12711yescharacteristic
426C2×#117C22×C12711yescharacteristic
427#421—22no—
428#421C22×C12714yescomplemented
429C2×#104—22no—
430#418—22no—
431#418C22×C12714yescomplemented
432C2×#102—22no—
433C2×#100—22no—
434C2×#100—22no—
435C2×#100C22×C12714yescomplemented
436#344C22×C12714yescomplemented
437#338C22×C12714yescomplemented
438C25—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41C2×C4×C12712yes—
446C2×#41D4×C12712yes—
447C2×#41D4×C12712yes—
448C2×#41D4×C12712yes—
449C2×#41D4×C12712yes—
450C2×#41C23×C12712yes—
451C22×Q8C2×C4×C12711yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C2×C4×C12712yes—
465C22×D4C2×C4×C12712yes—
466C22×D4C2×C4×C12711yescharacteristic
467C22×D4C23×C12712yes—
468C23×C4—21no—
469C23×C4C23×C12711yescharacteristic
470AGL(1,ℤ/8)—28no—
471AGL(1,ℤ/8)—28no—
472AGL(1,ℤ/8)—28no—
473AGL(1,ℤ/8)—28no—
474C2×SD16—24no—
475C2×SD16—24no—
476C2×SD16C2×C4×C12718yescomplemented
477C2×D8—24no—
478C2×D8—24no—
479C2×D8C2×C4×C12718yescomplemented
480#131—28no—
481#131—28no—
482#131—28no—
483#131—28no—
484C2×M16—24no—
485C2×M16—28no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—28no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16C2×C4×C12712yes—
504C2×M16D4×C12712yes—
505C2×M16D4×C12712yes—
506C2×M16D4×C12712yes—
507C2×M16C23×C12712yes—
508C2×M16C23×C12712yes—
509C2×M16C23×C12712yes—
510C2×M16C23×C12712yes—
511C22×C8—24no—
512C22×C8—21no—
513C22×C8—21no—
514C22×C8C2×C4×C12712yes—
515C22×C8D4×C12712yes—
516#117—21no—
517#117—21no—
518#117—21no—
519#117C23×C12712yes—
520C2×C4⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C42—21no—
523#104—28no—
524#102—28no—
525#100—28no—
526C24—21no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24—41no—
534C24—84no—
535C24#41×C12711yescharacteristic
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41C22⋊C4×C12714yes—
549#41C22⋊C4×C12714yes—
550#41C2×D4×C12714yes—
551#41C2×D4×C12714yes—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8C22⋊C4×C12712yes—
556C2×Q8C22⋊C4×C12712yes—
557C2×Q8C22×C4×C12712yes—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4C22⋊C4×C12712yes—
595C2×D4C22⋊C4×C12712yes—
596C2×D4C22×C4×C12714yes—
597C2×D4C22×C4×C12712yes—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—41no—
606C22×C4C22×C4×C12711yescharacteristic
607C22×C4C22×C4×C12711yescharacteristic
608C22×C4C2×D4×C12711yescharacteristic
609C22×C4C2×D4×C12711yescharacteristic
610C22×C4C2×D4×C12711yescharacteristic
611C22×C4C2×D4×C12711yescharacteristic
612C22×C4C2×D4×C12711yescharacteristic
613C22×C4C2×D4×C12711yescharacteristic
614C22×C4C2×D4×C12711yescharacteristic
615C22×C4C2×D4×C12711yescharacteristic
616C22×C4#41×C12711yescharacteristic
617C22×C4#41×C12711yescharacteristic
618C22×C4#41×C12711yescharacteristic
619C22×C4C24×C12711yescharacteristic
620SD16—216no—
621D8—216no—
622M16—216no—
623M16—22no—
624M16—22no—
625M16—22no—
626M16—22no—
627M16—22no—
628M16—22no—
629M16—22no—
630M16—22no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—41no—
637M16—41no—
638M16C2×D4×C12714yes—
639C2×C8—216no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8C22×C4×C12714yes—
651C2×C8C2×D4×C12714yes—
652C4⋊C4—22no—
653C4⋊C4—41no—
654C22⋊C4—22no—
655C22⋊C4—41no—
656C42—22no—
657C42—41no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—82no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23C4×D4×C12711yescharacteristic
678C23C4×D4×C12711yescharacteristic
679C23#121×C12711yescharacteristic
680C23#121×C12711yescharacteristic
681C23#123×C12711yescharacteristic
682C23#123×C12711yescharacteristic
683C23C2×#41×C12711yescharacteristic
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8C2×C22⋊C4×C12714yes—
688D4—24no—
689D4—24no—
690D4—24no—
691D4—24no—
692D4—24no—
693D4—22no—
694D4—24no—
695D4—22no—
696D4—22no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—42no—
703D4C2×C22⋊C4×C12714yes—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—82no—
713C2×C4C2×C22⋊C4×C12711yescharacteristic
714C2×C4C2×C22⋊C4×C12711yescharacteristic
715C2×C4C2×C22⋊C4×C12711yescharacteristic
716C2×C4C2×C22⋊C4×C12711yescharacteristic
717C2×C4C4×D4×C12711yescharacteristic
718C2×C4C4×D4×C12711yescharacteristic
719C2×C4C4×D4×C12711yescharacteristic
720C2×C4C4×D4×C12711yescharacteristic
721C2×C4C4×D4×C12711yescharacteristic
722C2×C4C4×D4×C12711yescharacteristic
723C2×C4#120×C12711yescharacteristic
724C2×C4#120×C12711yescharacteristic
725C2×C4#120×C12711yescharacteristic
726C2×C4#120×C12711yescharacteristic
727C2×C4#121×C12711yescharacteristic
728C2×C4#121×C12711yescharacteristic
729C2×C4#121×C12711yescharacteristic
730C2×C4#121×C12711yescharacteristic
731C2×C4#121×C12711yescharacteristic
732C2×C4#121×C12711yescharacteristic
733C2×C4#123×C12711yescharacteristic
734C2×C4#123×C12711yescharacteristic
735C2×C4C23×C4×C12711yescharacteristic
736C2×C4C22×D4×C12711yescharacteristic
737C2×C4C22×D4×C12711yescharacteristic
738C2×C4C22×D4×C12711yescharacteristic
739C2×C4C22×D4×C12711yescharacteristic
740C2×C4C2×#41×C12711yescharacteristic
741C8—24no—
742C8—24no—
743C8—24no—
744C8—42no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—24no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—44no—
754C22—44no—
755C22—82no—
756C22—82no—
757C22—84no—
758C22—84no—
759C22—84no—
760C22—84no—
761C22—84no—
762C22—84no—
763C22—84no—
764C22#386×C12711yescharacteristic
765C22#386×C12711yescharacteristic
766C22#386×C12711yescharacteristic
767C22#386×C12711yescharacteristic
768C22C2×C4×D4×C12711yescharacteristic
769C22C2×#121×C12711yescharacteristic
770C22C2×#123×C12711yescharacteristic
771C4—24no—
772C4—82no—
773C4#386×C12711yescharacteristic
774C4#386×C12711yescharacteristic
775C4#386×C12711yescharacteristic
776C4#386×C12711yescharacteristic
777C4C22×C22⋊C4×C12711yescharacteristic
778C4C2×C4×D4×C12711yescharacteristic
779C4C2×#120×C12711yescharacteristic
780C4C2×#121×C12711yescharacteristic
781C2—21no—
782C2—21no—
783C2—21no—
784C2—21no—
785C2—21no—
786C2—21no—
787C2—44no—
788C2—84no—
789C2C127×#190312yesdirect product factor
790C2C2×#386×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×AGL(1,ℤ/8)×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#568×C127C2semidirect
3. C2×#421×C127C2semidirect
4. C2×#418×C127C2semidirect
5. C22×#100×C127C2semidirect
6. C127×#1903C2direct (N × H)
7. C2×#344×C127C2semidirect
8. C2×#338×C127C2semidirect
15. C2×AGL(1,ℤ/8)×C127C4semidirect
17. C22×SD16×C127C4semidirect
18. C22×D8×C127C4semidirect
22. #568×C127C22semidirect
32. #421×C127C22semidirect
35. #418×C127C22semidirect
39. C2×#100×C127C22semidirect
40. #344×C127C22semidirect
41. #338×C127C22semidirect
80. C2×SD16×C127C2×C4semidirect
83. C2×D8×C127C2×C4semidirect
385. C2×#1903C127direct (N × H)
394. C2×C127#1903direct (N × H)
397. C2×#568C2×C127semidirect
398. C2×#421C2×C127semidirect
399. C2×#418C2×C127semidirect
400. C22×#100C2×C127semidirect
401. #1903C2×C127direct (N × H)
402. C2×#344C2×C127semidirect
403. C2×#338C2×C127semidirect
404. C127C2×#1903direct (N × H)
411. C2×AGL(1,ℤ/8)C4×C127semidirect
413. C22×SD16C4×C127semidirect
414. C22×D8C4×C127semidirect
418. #568C22×C127semidirect
428. #421C22×C127semidirect
431. #418C22×C127semidirect
435. C2×#100C22×C127semidirect
436. #344C22×C127semidirect
437. #338C22×C127semidirect
476. C2×SD16C2×C4×C127semidirect
479. C2×D8C2×C4×C127semidirect
789. C2C127×#1903direct (N × H)

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1272
C2×#568×C1272
C2×#421×C1272
C2×#418×C1272
C22×#100×C1272
C127×#19032
C2×#344×C1272
C2×#338×C1272
C2×#1903127