Finite Group Databasebeta

← C127×#20623 #44584296

Subgroups — C127×#20623 #44584296

Order 32512.

3644 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#585×C127C211yesmaximal, characteristic
2C2×#421×C127C212yesmaximal, complemented
3C127×#2896C212yesmaximal, complemented
4C2×#413×C127C211yesmaximal, characteristic, complemented
5C2×#410×C127C211yesmaximal, characteristic, complemented
6C127×#1796C214yesmaximal, complemented
7C127×#1795C214yesmaximal, complemented
8#585×C127—24no—
9#585×C127—24no—
10#585×C127—24no—
11#585×C127—24no—
12C2×2−1+4×C127—21no—
13C2×2−1+4×C127C412yescomplemented
14C2×2−1+4×C127C2212yes—
15C2×H(5,𝔽2)×C127—21no—
16C2×H(5,𝔽2)×C127—22no—
17C2×H(5,𝔽2)×C127C412yescomplemented
18C2×H(5,𝔽2)×C127C2212yes—
19C22×#41×C127—22no—
20C22×#41×C127—22no—
21C22×#41×C127C414yescomplemented
22C22×#41×C127C2211yescharacteristic
23C22×#41×C127C2211yescharacteristic
24C22×#41×C127C2211yescharacteristic
25C22×M16×C127C2212yescomplemented
26C2×#117×C127C2212yescomplemented
27#421×C127—24no—
28#421×C127C2218yescomplemented
29C2×#104×C127—24no—
30#419×C127C2214yescomplemented
31#418×C127C2214yescomplemented
32#417×C127—24no—
33#416×C127—24no—
34#413×C127—22no—
35#413×C127C2214yescomplemented
36C2×#101×C127—21no—
37C2×#100×C127—21no—
38#410×C127—22no—
39#410×C127C2214yescomplemented
40C2×#99×C127—22no—
412−1+4×C127—28no—
422−1+4×C127—28no—
432−1+4×C127—28no—
442−1+4×C127—28no—
452−1+4×C127—28no—
462−1+4×C127—28no—
47H(5,𝔽2)×C127—28no—
48H(5,𝔽2)×C127—28no—
49H(5,𝔽2)×C127—216no—
50H(5,𝔽2)×C127—216no—
51H(5,𝔽2)×C127—28no—
52H(5,𝔽2)×C127—28no—
53H(5,𝔽2)×C127—28no—
54H(5,𝔽2)×C127—28no—
55C2×#41×C127—216no—
56C2×#41×C127—216no—
57C2×#41×C127—216no—
58C2×#41×C127—216no—
59C2×#41×C127—28no—
60C2×#41×C127—28no—
61C2×#41×C127—28no—
62C2×#41×C127—28no—
63C2×#41×C127—22no—
64C2×#41×C127—22no—
65C2×#41×C127—24no—
66C2×#41×C127—22no—
67C2×#41×C127—22no—
68C2×#41×C127—24no—
69C2×#41×C127—24no—
70C2×#41×C127—24no—
71C2×#41×C127—21no—
72C2×#41×C127—21no—
73C2×#41×C127—21no—
74C2×#41×C127—21no—
75C2×#41×C127—22no—
76C2×#41×C127—22no—
77C2×#41×C127—22no—
78C2×#41×C127—22no—
79C2×#41×C127—22no—
80C2×#41×C127—22no—
81C2×#41×C127—22no—
82C2×#41×C127—22no—
83C2×#41×C127C2×C412yes—
84C2×#41×C127C2×C412yes—
85C2×#41×C127C2×C412yes—
86C2×#41×C127C2×C412yes—
87C2×#41×C127C2×C414yescomplemented
88C2×#41×C127C2×C414yescomplemented
89C2×#41×C127D414yes—
90C2×#41×C127D414yes—
91C2×#41×C127D414yes—
92C2×#41×C127D414yes—
93C2×#41×C127D412yes—
94C2×#41×C127D412yes—
95C2×#41×C127C2312yes—
96C2×#41×C127C2312yes—
97C22×Q8×C127—22no—
98C22×Q8×C127—22no—
99C22×Q8×C127C2×C411yescharacteristic
100C22×Q8×C127C2×C414yescomplemented
101C22×Q8×C127D411yescharacteristic
102C22×Q8×C127C2311yescharacteristic
103C22×D4×C127—24no—
104C22×D4×C127—21no—
105C22×D4×C127—21no—
106C22×D4×C127—22no—
107C22×D4×C127—24no—
108C22×D4×C127—24no—
109C22×D4×C127—22no—
110C22×D4×C127C2×C411yescharacteristic
111C22×D4×C127C2×C414yescomplemented
112C22×D4×C127D412yes—
113C22×D4×C127D411yescharacteristic
114C22×D4×C127C2311yescharacteristic
115C23×C4×C127—24no—
116C23×C4×C127—21no—
117C23×C4×C127—21no—
118C23×C4×C127C2×C412yes—
119C23×C4×C127C2311yescharacteristic
120C2×M16×C127—22no—
121C2×M16×C127—22no—
122C2×M16×C127—22no—
123C2×M16×C127—22no—
124C2×M16×C127—22no—
125C2×M16×C127C2314yes—
126C22×C8×C127—22no—
127#117×C127—22no—
128#117×C127—22no—
129#117×C127—22no—
130#117×C127C2314yes—
131C2×C4⋊C4×C127—22no—
132C2×C22⋊C4×C127—22no—
133C2×C42×C127—22no—
134#104×C127—216no—
135#103×C127—28no—
136#102×C127—28no—
137#101×C127—24no—
138#100×C127—24no—
139#99×C127—28no—
140C24×C127—21no—
141C24×C127—24no—
142C24×C127—21no—
143C24×C127C22⋊C412yes—
144C24×C127C2×D411yescharacteristic
145#41×C127—216no—
146#41×C127—216no—
147#41×C127—232no—
148#41×C127—232no—
149#41×C127—216no—
150#41×C127—216no—
151#41×C127—216no—
152#41×C127—216no—
153#41×C127—216no—
154#41×C127—216no—
155#41×C127—28no—
156#41×C127—28no—
157#41×C127—28no—
158#41×C127—28no—
159#41×C127—22no—
160#41×C127—22no—
161#41×C127—22no—
162#41×C127—22no—
163#41×C127—24no—
164#41×C127—24no—
165#41×C127—24no—
166#41×C127—24no—
167#41×C127—24no—
168#41×C127—24no—
169#41×C127—24no—
170#41×C127—24no—
171#41×C127—24no—
172#41×C127—24no—
173#41×C127—24no—
174#41×C127—24no—
175#41×C127—24no—
176#41×C127—24no—
177#41×C127—24no—
178#41×C127—24no—
179#41×C127—24no—
180#41×C127—24no—
181#41×C127C22⋊C414yes—
182#41×C127C22⋊C414yes—
183#41×C127C22⋊C414yes—
184#41×C127C22⋊C414yes—
185#41×C127C22⋊C418yes—
186#41×C127C2×D418yes—
187C2×Q8×C127—216no—
188C2×Q8×C127—216no—
189C2×Q8×C127—28no—
190C2×Q8×C127—28no—
191C2×Q8×C127—21no—
192C2×Q8×C127—24no—
193C2×Q8×C127—22no—
194C2×Q8×C127—22no—
195C2×Q8×C127—22no—
196C2×Q8×C127—21no—
197C2×Q8×C127—22no—
198C2×Q8×C127C22⋊C414yes—
199C2×Q8×C127C22⋊C412yes—
200C2×Q8×C127C22×C412yes—
201C2×Q8×C127C22×C412yes—
202C2×Q8×C127C2×D414yes—
203C2×Q8×C127C2×D412yes—
204C2×D4×C127—232no—
205C2×D4×C127—216no—
206C2×D4×C127—216no—
207C2×D4×C127—232no—
208C2×D4×C127—216no—
209C2×D4×C127—216no—
210C2×D4×C127—22no—
211C2×D4×C127—22no—
212C2×D4×C127—22no—
213C2×D4×C127—24no—
214C2×D4×C127—24no—
215C2×D4×C127—24no—
216C2×D4×C127—24no—
217C2×D4×C127—24no—
218C2×D4×C127—24no—
219C2×D4×C127—24no—
220C2×D4×C127—24no—
221C2×D4×C127—22no—
222C2×D4×C127—28no—
223C2×D4×C127—28no—
224C2×D4×C127—21no—
225C2×D4×C127—24no—
226C2×D4×C127—22no—
227C2×D4×C127—22no—
228C2×D4×C127—22no—
229C2×D4×C127—21no—
230C2×D4×C127—22no—
231C2×D4×C127C22⋊C414yes—
232C2×D4×C127C22⋊C412yes—
233C2×D4×C127C22⋊C414yes—
234C2×D4×C127C22×C412yes—
235C2×D4×C127C22×C412yes—
236C2×D4×C127C2×D414yes—
237C2×D4×C127C2×D412yes—
238C2×D4×C127C2×D414yes—
239C22×C4×C127—216no—
240C22×C4×C127—216no—
241C22×C4×C127—21no—
242C22×C4×C127—24no—
243C22×C4×C127—21no—
244C22×C4×C127—22no—
245C22×C4×C127—22no—
246C22×C4×C127—22no—
247C22×C4×C127—24no—
248C22×C4×C127—24no—
249C22×C4×C127—22no—
250C22×C4×C127—22no—
251C22×C4×C127—22no—
252C22×C4×C127—22no—
253C22×C4×C127—24no—
254C22×C4×C127—24no—
255C22×C4×C127—24no—
256C22×C4×C127—24no—
257C22×C4×C127—22no—
258C22×C4×C127—42no—
259C22×C4×C127C22⋊C414yes—
260C22×C4×C127C22⋊C412yes—
261C22×C4×C127C22×C414yes—
262C22×C4×C127C22×C411yescharacteristic
263C22×C4×C127C22×C411yescharacteristic
264C22×C4×C127C2×D411yescharacteristic
265C22×C4×C127C2×D412yes—
266C22×C4×C127C2×D412yes—
267C22×C4×C127C2×D412yes—
268C22×C4×C127C2×D412yes—
269C22×C4×C127C2×D411yescharacteristic
270C22×C4×C127C2×D411yescharacteristic
271C22×C4×C127C2411yescharacteristic
272M16×C127—24no—
273M16×C127—24no—
274M16×C127—42no—
275M16×C127—42no—
276C2×C8×C127—24no—
277C2×C8×C127—42no—
278C2×C8×C127—42no—
279C4⋊C4×C127—24no—
280C4⋊C4×C127—42no—
281C22⋊C4×C127—24no—
282C22⋊C4×C127—42no—
283C42×C127—24no—
284C42×C127—42no—
285C23×C127—216no—
286C23×C127—22no—
287C23×C127—22no—
288C23×C127—24no—
289C23×C127—22no—
290C23×C127—22no—
291C23×C127—24no—
292C23×C127—81no—
293C23×C127—82no—
294C23×C127—82no—
295C23×C127—82no—
296C23×C127—88no—
297C23×C127C2×C22⋊C414yes—
298C23×C127C2×C22⋊C411yescharacteristic
299C23×C127C2×C22⋊C411yescharacteristic
300C23×C127#12012yes—
301C23×C127#12012yes—
302C23×C127C22×D411yescharacteristic
303Q8×C127—216no—
304Q8×C127—22no—
305Q8×C127—22no—
306Q8×C127—24no—
307Q8×C127—24no—
308Q8×C127—24no—
309Q8×C127—24no—
310Q8×C127C2×C22⋊C414yes—
311Q8×C127C2×C22⋊C414yes—
312D4×C127—216no—
313D4×C127—216no—
314D4×C127—216no—
315D4×C127—28no—
316D4×C127—28no—
317D4×C127—24no—
318D4×C127—24no—
319D4×C127—24no—
320D4×C127—24no—
321D4×C127—28no—
322D4×C127—28no—
323D4×C127—22no—
324D4×C127—22no—
325D4×C127—24no—
326D4×C127—24no—
327D4×C127—24no—
328D4×C127—24no—
329D4×C127C2×C22⋊C414yes—
330D4×C127C2×C22⋊C414yes—
331C2×C4×C127—216no—
332C2×C4×C127—216no—
333C2×C4×C127—216no—
334C2×C4×C127—22no—
335C2×C4×C127—22no—
336C2×C4×C127—24no—
337C2×C4×C127—24no—
338C2×C4×C127—22no—
339C2×C4×C127—22no—
340C2×C4×C127—24no—
341C2×C4×C127—24no—
342C2×C4×C127—28no—
343C2×C4×C127—24no—
344C2×C4×C127—24no—
345C2×C4×C127—24no—
346C2×C4×C127—28no—
347C2×C4×C127—24no—
348C2×C4×C127—24no—
349C2×C4×C127—24no—
350C2×C4×C127—44no—
351C2×C4×C127—84no—
352C2×C4×C127C2×C22⋊C414yes—
353C2×C4×C127C2×C22⋊C411yescharacteristic
354C2×C4×C127C2×C22⋊C411yescharacteristic
355C2×C4×C127C2×C22⋊C412yes—
356C2×C4×C127C2×C22⋊C412yes—
357C2×C4×C127C2×C22⋊C411yescharacteristic
358C2×C4×C127C2×C22⋊C411yescharacteristic
359C2×C4×C127C2×C22⋊C411yescharacteristic
360C2×C4×C127C2×C22⋊C411yescharacteristic
361C2×C4×C127#12012yes—
362C2×C4×C127#12012yes—
363C2×C4×C127#12012yes—
364C2×C4×C127#12012yes—
365C2×C4×C127#12012yes—
366C2×C4×C127#12012yes—
367C2×C4×C127C23×C411yescharacteristic
368C2×C4×C127C22×D412yes—
369C2×C4×C127C22×D412yes—
370C2×C4×C127C22×D411yescharacteristic
371C8×C127—44no—
372C22×C127—24no—
373C22×C127—24no—
374C22×C127—24no—
375C22×C127—42no—
376C22×C127—41no—
377C22×C127—41no—
378C22×C127—41no—
379C22×C127—42no—
380C22×C127—44no—
381C22×C127—44no—
382C22×C127—44no—
383C22×C127—82no—
384C22×C127—82no—
385C22×C127—84no—
386C22×C127—84no—
387C22×C127—816no—
388C22×C127#37912yes—
389C22×C127#37911yescharacteristic
390C22×C127#37911yescharacteristic
391C22×C127C22×C22⋊C411yescharacteristic
392C22×C127C2×#12012yes—
393C4×C127—24no—
394C4×C127—24no—
395C4×C127—24no—
396C4×C127—84no—
397C4×C127#37911yescharacteristic
398C4×C127#37912yes—
399C4×C127#37911yescharacteristic
400C4×C127C22×C22⋊C411yescharacteristic
401C4×C127C22×C22⋊C411yescharacteristic
402C4×C127C2×#12012yes—
403#20623C12711yesmaximal, characteristic, direct product factor, Sylow
404C2×C127—22no—
405C2×C127—21no—
406C2×C127—21no—
407C2×C127—22no—
408C2×C127—21no—
409C2×C127—44no—
410C2×C127—44no—
411C2×C127—44no—
412C2×C127C2×#37911yescharacteristic
413C2×#585C2×C12711yescharacteristic
414C2×#421C2×C12712yescomplemented
415#2896C2×C12712yescomplemented
416C2×#413C2×C12711yescharacteristic, complemented
417C2×#410C2×C12711yescharacteristic, complemented
418#1796C2×C12714yescomplemented
419#1795C2×C12714yescomplemented
420C127#2062311yescharacteristic, direct product factor, Sylow
421#585—24no—
422#585—24no—
423#585—24no—
424#585—24no—
425C2×2−1+4—21no—
426C2×2−1+4C4×C12712yescomplemented
427C2×2−1+4C22×C12712yes—
428C2×H(5,𝔽2)—21no—
429C2×H(5,𝔽2)—22no—
430C2×H(5,𝔽2)C4×C12712yescomplemented
431C2×H(5,𝔽2)C22×C12712yes—
432C22×#41—22no—
433C22×#41—22no—
434C22×#41C4×C12714yescomplemented
435C22×#41C22×C12711yescharacteristic
436C22×#41C22×C12711yescharacteristic
437C22×#41C22×C12711yescharacteristic
438C22×M16C22×C12712yescomplemented
439C2×#117C22×C12712yescomplemented
440#421—24no—
441#421C22×C12718yescomplemented
442C2×#104—24no—
443#419C22×C12714yescomplemented
444#418C22×C12714yescomplemented
445#417—24no—
446#416—24no—
447#413—22no—
448#413C22×C12714yescomplemented
449C2×#101—21no—
450C2×#100—21no—
451#410—22no—
452#410C22×C12714yescomplemented
453C2×#99—22no—
4542−1+4—28no—
4552−1+4—28no—
4562−1+4—28no—
4572−1+4—28no—
4582−1+4—28no—
4592−1+4—28no—
460H(5,𝔽2)—28no—
461H(5,𝔽2)—28no—
462H(5,𝔽2)—216no—
463H(5,𝔽2)—216no—
464H(5,𝔽2)—28no—
465H(5,𝔽2)—28no—
466H(5,𝔽2)—28no—
467H(5,𝔽2)—28no—
468C2×#41—216no—
469C2×#41—216no—
470C2×#41—216no—
471C2×#41—216no—
472C2×#41—28no—
473C2×#41—28no—
474C2×#41—28no—
475C2×#41—28no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—24no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—24no—
482C2×#41—24no—
483C2×#41—24no—
484C2×#41—21no—
485C2×#41—21no—
486C2×#41—21no—
487C2×#41—21no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41C2×C4×C12712yes—
497C2×#41C2×C4×C12712yes—
498C2×#41C2×C4×C12712yes—
499C2×#41C2×C4×C12712yes—
500C2×#41C2×C4×C12714yescomplemented
501C2×#41C2×C4×C12714yescomplemented
502C2×#41D4×C12714yes—
503C2×#41D4×C12714yes—
504C2×#41D4×C12714yes—
505C2×#41D4×C12714yes—
506C2×#41D4×C12712yes—
507C2×#41D4×C12712yes—
508C2×#41C23×C12712yes—
509C2×#41C23×C12712yes—
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8C2×C4×C12711yescharacteristic
513C22×Q8C2×C4×C12714yescomplemented
514C22×Q8D4×C12711yescharacteristic
515C22×Q8C23×C12711yescharacteristic
516C22×D4—24no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—24no—
521C22×D4—24no—
522C22×D4—22no—
523C22×D4C2×C4×C12711yescharacteristic
524C22×D4C2×C4×C12714yescomplemented
525C22×D4D4×C12712yes—
526C22×D4D4×C12711yescharacteristic
527C22×D4C23×C12711yescharacteristic
528C23×C4—24no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2×C4×C12712yes—
532C23×C4C23×C12711yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16C23×C12714yes—
539C22×C8—22no—
540#117—22no—
541#117—22no—
542#117—22no—
543#117C23×C12714yes—
544C2×C4⋊C4—22no—
545C2×C22⋊C4—22no—
546C2×C42—22no—
547#104—216no—
548#103—28no—
549#102—28no—
550#101—24no—
551#100—24no—
552#99—28no—
553C24—21no—
554C24—24no—
555C24—21no—
556C24C22⋊C4×C12712yes—
557C24C2×D4×C12711yescharacteristic
558#41—216no—
559#41—216no—
560#41—232no—
561#41—232no—
562#41—216no—
563#41—216no—
564#41—216no—
565#41—216no—
566#41—216no—
567#41—216no—
568#41—28no—
569#41—28no—
570#41—28no—
571#41—28no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—24no—
577#41—24no—
578#41—24no—
579#41—24no—
580#41—24no—
581#41—24no—
582#41—24no—
583#41—24no—
584#41—24no—
585#41—24no—
586#41—24no—
587#41—24no—
588#41—24no—
589#41—24no—
590#41—24no—
591#41—24no—
592#41—24no—
593#41—24no—
594#41C22⋊C4×C12714yes—
595#41C22⋊C4×C12714yes—
596#41C22⋊C4×C12714yes—
597#41C22⋊C4×C12714yes—
598#41C22⋊C4×C12718yes—
599#41C2×D4×C12718yes—
600C2×Q8—216no—
601C2×Q8—216no—
602C2×Q8—28no—
603C2×Q8—28no—
604C2×Q8—21no—
605C2×Q8—24no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—21no—
610C2×Q8—22no—
611C2×Q8C22⋊C4×C12714yes—
612C2×Q8C22⋊C4×C12712yes—
613C2×Q8C22×C4×C12712yes—
614C2×Q8C22×C4×C12712yes—
615C2×Q8C2×D4×C12714yes—
616C2×Q8C2×D4×C12712yes—
617C2×D4—232no—
618C2×D4—216no—
619C2×D4—216no—
620C2×D4—232no—
621C2×D4—216no—
622C2×D4—216no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—24no—
633C2×D4—24no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—28no—
637C2×D4—21no—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4C22⋊C4×C12714yes—
645C2×D4C22⋊C4×C12712yes—
646C2×D4C22⋊C4×C12714yes—
647C2×D4C22×C4×C12712yes—
648C2×D4C22×C4×C12712yes—
649C2×D4C2×D4×C12714yes—
650C2×D4C2×D4×C12712yes—
651C2×D4C2×D4×C12714yes—
652C22×C4—216no—
653C22×C4—216no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—22no—
671C22×C4—42no—
672C22×C4C22⋊C4×C12714yes—
673C22×C4C22⋊C4×C12712yes—
674C22×C4C22×C4×C12714yes—
675C22×C4C22×C4×C12711yescharacteristic
676C22×C4C22×C4×C12711yescharacteristic
677C22×C4C2×D4×C12711yescharacteristic
678C22×C4C2×D4×C12712yes—
679C22×C4C2×D4×C12712yes—
680C22×C4C2×D4×C12712yes—
681C22×C4C2×D4×C12712yes—
682C22×C4C2×D4×C12711yescharacteristic
683C22×C4C2×D4×C12711yescharacteristic
684C22×C4C24×C12711yescharacteristic
685M16—24no—
686M16—24no—
687M16—42no—
688M16—42no—
689C2×C8—24no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—24no—
693C4⋊C4—42no—
694C22⋊C4—24no—
695C22⋊C4—42no—
696C42—24no—
697C42—42no—
698C23—216no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—81no—
706C23—82no—
707C23—82no—
708C23—82no—
709C23—88no—
710C23C2×C22⋊C4×C12714yes—
711C23C2×C22⋊C4×C12711yescharacteristic
712C23C2×C22⋊C4×C12711yescharacteristic
713C23#120×C12712yes—
714C23#120×C12712yes—
715C23C22×D4×C12711yescharacteristic
716Q8—216no—
717Q8—22no—
718Q8—22no—
719Q8—24no—
720Q8—24no—
721Q8—24no—
722Q8—24no—
723Q8C2×C22⋊C4×C12714yes—
724Q8C2×C22⋊C4×C12714yes—
725D4—216no—
726D4—216no—
727D4—216no—
728D4—28no—
729D4—28no—
730D4—24no—
731D4—24no—
732D4—24no—
733D4—24no—
734D4—28no—
735D4—28no—
736D4—22no—
737D4—22no—
738D4—24no—
739D4—24no—
740D4—24no—
741D4—24no—
742D4C2×C22⋊C4×C12714yes—
743D4C2×C22⋊C4×C12714yes—
744C2×C4—216no—
745C2×C4—216no—
746C2×C4—216no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—44no—
764C2×C4—84no—
765C2×C4C2×C22⋊C4×C12714yes—
766C2×C4C2×C22⋊C4×C12711yescharacteristic
767C2×C4C2×C22⋊C4×C12711yescharacteristic
768C2×C4C2×C22⋊C4×C12711yescharacteristic
769C2×C4C2×C22⋊C4×C12711yescharacteristic
770C2×C4C2×C22⋊C4×C12712yes—
771C2×C4C2×C22⋊C4×C12712yes—
772C2×C4C2×C22⋊C4×C12711yescharacteristic
773C2×C4C2×C22⋊C4×C12711yescharacteristic
774C2×C4#120×C12712yes—
775C2×C4#120×C12712yes—
776C2×C4#120×C12712yes—
777C2×C4#120×C12712yes—
778C2×C4#120×C12712yes—
779C2×C4#120×C12712yes—
780C2×C4C23×C4×C12711yescharacteristic
781C2×C4C22×D4×C12712yes—
782C2×C4C22×D4×C12712yes—
783C2×C4C22×D4×C12711yescharacteristic
784C8—44no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—84no—
797C22—84no—
798C22—82no—
799C22—82no—
800C22—816no—
801C22#379×C12712yes—
802C22#379×C12711yescharacteristic
803C22#379×C12711yescharacteristic
804C22C22×C22⋊C4×C12711yescharacteristic
805C22C2×#120×C12712yes—
806C4—24no—
807C4—24no—
808C4—24no—
809C4—84no—
810C4#379×C12711yescharacteristic
811C4#379×C12711yescharacteristic
812C4#379×C12712yes—
813C4C22×C22⋊C4×C12711yescharacteristic
814C4C22×C22⋊C4×C12711yescharacteristic
815C4C2×#120×C12712yes—
816C2—22no—
817C2—21no—
818C2—21no—
819C2—22no—
820C2—21no—
821C2—44no—
822C2—44no—
823C2—44no—
824C2C2×#379×C12711yescharacteristic
subgroupG/H
centerC4×C127#379
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC2×C127C2×#379
prime radicalC2×#585×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#421×C127C2semidirect
3. C127×#2896C2semidirect
4. C2×#413×C127C2semidirect
5. C2×#410×C127C2semidirect
6. C127×#1796C2semidirect
7. C127×#1795C2semidirect
13. C2×2−1+4×C127C4semidirect
17. C2×H(5,𝔽2)×C127C4semidirect
21. C22×#41×C127C4semidirect
25. C22×M16×C127C22semidirect
26. C2×#117×C127C22semidirect
28. #421×C127C22semidirect
30. #419×C127C22semidirect
31. #418×C127C22semidirect
35. #413×C127C22semidirect
39. #410×C127C22semidirect
87. C2×#41×C127C2×C4semidirect
88. C2×#41×C127C2×C4semidirect
100. C22×Q8×C127C2×C4semidirect
111. C22×D4×C127C2×C4semidirect
403. #20623C127direct (N × H)
414. C2×#421C2×C127semidirect
415. #2896C2×C127semidirect
416. C2×#413C2×C127semidirect
417. C2×#410C2×C127semidirect
418. #1796C2×C127semidirect
419. #1795C2×C127semidirect
420. C127#20623direct (N × H)
426. C2×2−1+4C4×C127semidirect
430. C2×H(5,𝔽2)C4×C127semidirect
434. C22×#41C4×C127semidirect
438. C22×M16C22×C127semidirect
439. C2×#117C22×C127semidirect
441. #421C22×C127semidirect
443. #419C22×C127semidirect
444. #418C22×C127semidirect
448. #413C22×C127semidirect
452. #410C22×C127semidirect
500. C2×#41C2×C4×C127semidirect
501. C2×#41C2×C4×C127semidirect
513. C22×Q8C2×C4×C127semidirect
524. C22×D4C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#585×C1272
C2×#421×C1272
C127×#28962
C2×#413×C1272
C2×#410×C1272
C127×#17962
C127×#17952
#20623127