Finite Group Databasebeta

← C2×C127×#1913 #44584686

Subgroups — C2×C127×#1913 #44584686

Order 32512.

2078 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C127C211yesmaximal, characteristic
2C2×#518×C127C211yesmaximal, characteristic, complemented
3C22×#99×C127C211yesmaximal, characteristic, complemented
4C22×#99×C127C212yesmaximal, complemented
5C127×#1913C218yesmaximal, direct product factor
6C2×#342×C127C212yesmaximal, complemented
7C23×D4×C127C2211yescharacteristic
8C23×D4×C127C2211yescharacteristic
9#534×C127—22no—
10#534×C127—22no—
11#534×C127C414yescomplemented
12#534×C127C2214yes—
13C2×#123×C127—21no—
14C2×#123×C127C412yescomplemented
15C2×#121×C127—22no—
16C2×#120×C127—21no—
17C2×#120×C127C412yescomplemented
18#518×C127—22no—
19#518×C127—24no—
20#518×C127C2214yescomplemented
21C2×C4×D4×C127—24no—
22C2×#117×C127—21no—
23C22×C22⋊C4×C127—21no—
24C22×C22⋊C4×C127C2212yes—
25C22×C22⋊C4×C127C2211yescharacteristic
26C22×C22⋊C4×C127C2212yes—
27C2×#99×C127—22no—
28C2×#99×C127—22no—
29C2×#99×C127—24no—
30C2×#99×C127—24no—
31C2×#99×C127C2214yescomplemented
32C2×#99×C127C2218yescomplemented
33#342×C127C2218yescomplemented
34C25×C127C2×C411yescharacteristic, complemented
35C25×C127D411yescharacteristic
36C25×C127C2311yescharacteristic
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127—22no—
40C22×D4×C127—22no—
41C22×D4×C127—21no—
42C22×D4×C127—21no—
43C22×D4×C127—21no—
44C22×D4×C127—21no—
45C22×D4×C127—22no—
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127—22no—
49C22×D4×C127—22no—
50C22×D4×C127C2×C412yes—
51C22×D4×C127C2×C412yes—
52C22×D4×C127C2×C412yescomplemented
53C22×D4×C127D412yes—
54C22×D4×C127D412yes—
55C22×D4×C127D412yes—
56C22×D4×C127C2312yes—
57C22×D4×C127C2312yes—
58C23×C4×C127—22no—
59C23×C4×C127—22no—
60C23×C4×C127—21no—
61C23×C4×C127—22no—
62C23×C4×C127C2×C411yescharacteristic, complemented
63C23×C4×C127D411yescharacteristic
64#123×C127—24no—
65#123×C127—24no—
66#123×C127—24no—
67#123×C127C2×C418yescomplemented
68#121×C127—28no—
69#121×C127—28no—
70#120×C127—24no—
71#120×C127—24no—
72#120×C127—24no—
73#120×C127C2×C418yescomplemented
74C4×D4×C127—216no—
75C4×D4×C127—216no—
76#117×C127—24no—
77#117×C127—24no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—22no—
80C2×C22⋊C4×C127—22no—
81C2×C22⋊C4×C127—24no—
82C2×C22⋊C4×C127—22no—
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—24no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—21no—
88C2×C22⋊C4×C127—21no—
89C2×C22⋊C4×C127—21no—
90C2×C22⋊C4×C127—22no—
91C2×C22⋊C4×C127—22no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—22no—
94C2×C22⋊C4×C127—22no—
95C2×C22⋊C4×C127—22no—
96C2×C22⋊C4×C127C2×C412yescomplemented
97C2×C22⋊C4×C127C2×C412yescomplemented
98C2×C22⋊C4×C127D414yescomplemented
99C2×C22⋊C4×C127D414yescomplemented
100C2×C22⋊C4×C127C2314yes—
101C2×C22⋊C4×C127C2312yes—
102C2×C22⋊C4×C127C2314yes—
103C2×C42×C127—22no—
104#99×C127—28no—
105#99×C127—216no—
106C24×C127—21no—
107C24×C127—21no—
108C24×C127—21no—
109C24×C127—21no—
110C24×C127—21no—
111C24×C127—21no—
112C24×C127—22no—
113C24×C127—22no—
114C24×C127—82no—
115C24×C127—82no—
116C24×C127—82no—
117C24×C127C22⋊C412yes—
118C24×C127C22⋊C412yes—
119C24×C127C22×C411yescharacteristic
120C24×C127C22×C411yescharacteristic
121C24×C127C22×C412yescomplemented
122C24×C127C2×D412yes—
123C24×C127C2×D411yescharacteristic
124C24×C127C2×D411yescharacteristic
125C24×C127C2×D412yes—
126C24×C127C2×D411yescharacteristic
127C24×C127C2×D411yescharacteristic
128C24×C127C2×D412yes—
129C24×C127#4112yes—
130C24×C127#4112yes—
131C24×C127C2411yescharacteristic
132C2×D4×C127—24no—
133C2×D4×C127—24no—
134C2×D4×C127—24no—
135C2×D4×C127—24no—
136C2×D4×C127—24no—
137C2×D4×C127—24no—
138C2×D4×C127—24no—
139C2×D4×C127—24no—
140C2×D4×C127—24no—
141C2×D4×C127—24no—
142C2×D4×C127—24no—
143C2×D4×C127—24no—
144C2×D4×C127—22no—
145C2×D4×C127—22no—
146C2×D4×C127—24no—
147C2×D4×C127—24no—
148C2×D4×C127—24no—
149C2×D4×C127—22no—
150C2×D4×C127—22no—
151C2×D4×C127—24no—
152C2×D4×C127—28no—
153C2×D4×C127—41no—
154C2×D4×C127—42no—
155C2×D4×C127—41no—
156C2×D4×C127—42no—
157C2×D4×C127—42no—
158C2×D4×C127—42no—
159C2×D4×C127—42no—
160C2×D4×C127—41no—
161C2×D4×C127—42no—
162C2×D4×C127—41no—
163C2×D4×C127—84no—
164C2×D4×C127C22⋊C414yes—
165C2×D4×C127C22⋊C414yes—
166C2×D4×C127C22×C414yes—
167C2×D4×C127C2×D414yes—
168C22×C4×C127—21no—
169C22×C4×C127—21no—
170C22×C4×C127—21no—
171C22×C4×C127—21no—
172C22×C4×C127—22no—
173C22×C4×C127—21no—
174C22×C4×C127—21no—
175C22×C4×C127—22no—
176C22×C4×C127—22no—
177C22×C4×C127—24no—
178C22×C4×C127—28no—
179C22×C4×C127—22no—
180C22×C4×C127—24no—
181C22×C4×C127—24no—
182C22×C4×C127—22no—
183C22×C4×C127—24no—
184C22×C4×C127—42no—
185C22×C4×C127—42no—
186C22×C4×C127—84no—
187C22×C4×C127—84no—
188C22×C4×C127—82no—
189C22×C4×C127—84no—
190C22×C4×C127C22⋊C412yes—
191C22×C4×C127C22⋊C412yes—
192C22×C4×C127C22×C412yescomplemented
193C22×C4×C127C2×D412yes—
194C4⋊C4×C127—28no—
195C4⋊C4×C127—28no—
196C22⋊C4×C127—28no—
197C22⋊C4×C127—22no—
198C22⋊C4×C127—22no—
199C22⋊C4×C127—28no—
200C22⋊C4×C127—24no—
201C22⋊C4×C127—24no—
202C22⋊C4×C127—24no—
203C22⋊C4×C127—22no—
204C22⋊C4×C127—28no—
205C22⋊C4×C127—24no—
206C22⋊C4×C127—24no—
207C22⋊C4×C127—42no—
208C22⋊C4×C127—42no—
209C22⋊C4×C127C22×C414yescomplemented
210C22⋊C4×C127C2×D418yescomplemented
211C42×C127—28no—
212C23×C127—22no—
213C23×C127—22no—
214C23×C127—22no—
215C23×C127—22no—
216C23×C127—22no—
217C23×C127—22no—
218C23×C127—22no—
219C23×C127—24no—
220C23×C127—44no—
221C23×C127—42no—
222C23×C127—44no—
223C23×C127—42no—
224C23×C127—42no—
225C23×C127—44no—
226C23×C127—44no—
227C23×C127—44no—
228C23×C127—41no—
229C23×C127—42no—
230C23×C127—41no—
231C23×C127—82no—
232C23×C127—84no—
233C23×C127—81no—
234C23×C127—81no—
235C23×C127—82no—
236C23×C127—81no—
237C23×C127—82no—
238C23×C127—81no—
239C23×C127—82no—
240C23×C127—82no—
241C23×C127—82no—
242C23×C127—82no—
243C23×C127—82no—
244C23×C127—82no—
245C23×C127—84no—
246C23×C127C2×C22⋊C411yescharacteristic
247C23×C127C2×C22⋊C414yes—
248C23×C127C2×C22⋊C411yescharacteristic
249C23×C127C2×C22⋊C411yescharacteristic
250C23×C127C2×C22⋊C411yescharacteristic
251C23×C127C4×D412yes—
252C23×C127C4×D412yes—
253C23×C127C4×D412yes—
254C23×C127C4×D412yes—
255C23×C127#12011yescharacteristic
256C23×C127#12011yescharacteristic
257C23×C127#12012yes—
258C23×C127#12112yes—
259C23×C127#12112yes—
260C23×C127#12112yes—
261C23×C127#12112yes—
262C23×C127#12311yescharacteristic
263C23×C127#12311yescharacteristic
264C23×C127#12312yes—
265C23×C127C23×C411yescharacteristic
266C23×C127C22×D411yescharacteristic
267C23×C127C22×D411yescharacteristic
268C23×C127C22×D412yes—
269C23×C127C2×#4112yes—
270D4×C127—28no—
271D4×C127—28no—
272D4×C127—28no—
273D4×C127—28no—
274D4×C127—42no—
275D4×C127—44no—
276D4×C127—42no—
277D4×C127—42no—
278D4×C127—42no—
279D4×C127—44no—
280D4×C127—88no—
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—24no—
288C2×C4×C127—22no—
289C2×C4×C127—24no—
290C2×C4×C127—28no—
291C2×C4×C127—48no—
292C2×C4×C127—44no—
293C2×C4×C127—41no—
294C2×C4×C127—42no—
295C2×C4×C127—41no—
296C2×C4×C127—44no—
297C2×C4×C127—84no—
298C2×C4×C127—84no—
299C2×C4×C127—88no—
300C2×C4×C127—82no—
301C2×C4×C127—82no—
302C2×C4×C127—84no—
303C2×C4×C127—84no—
304C2×C4×C127—84no—
305C2×C4×C127C2×C22⋊C414yes—
306C22×C127—22no—
307C22×C127—22no—
308C22×C127—24no—
309C22×C127—24no—
310C22×C127—22no—
311C22×C127—24no—
312C22×C127—41no—
313C22×C127—42no—
314C22×C127—42no—
315C22×C127—42no—
316C22×C127—41no—
317C22×C127—42no—
318C22×C127—41no—
319C22×C127—41no—
320C22×C127—42no—
321C22×C127—41no—
322C22×C127—41no—
323C22×C127—41no—
324C22×C127—41no—
325C22×C127—42no—
326C22×C127—42no—
327C22×C127—42no—
328C22×C127—42no—
329C22×C127—42no—
330C22×C127—44no—
331C22×C127—44no—
332C22×C127—44no—
333C22×C127—44no—
334C22×C127—44no—
335C22×C127—42no—
336C22×C127—82no—
337C22×C127—82no—
338C22×C127—82no—
339C22×C127—84no—
340C22×C127—82no—
341C22×C127—84no—
342C22×C127—82no—
343C22×C127#38611yescharacteristic
344C22×C127#38611yescharacteristic
345C22×C127#38611yescharacteristic
346C22×C127#38612yes—
347C22×C127#38612yes—
348C22×C127#38611yescharacteristic
349C22×C127C22×C22⋊C411yescharacteristic
350C22×C127C2×C4×D412yes—
351C22×C127C2×#12011yescharacteristic
352C22×C127C2×#12112yes—
353C22×C127C2×#12311yescharacteristic
354C4×C127—24no—
355C4×C127—48no—
356C4×C127—44no—
357C4×C127—42no—
358C4×C127—84no—
359C2×#1913C12711yesmaximal, characteristic, direct product factor, Sylow
360C2×C127—21no—
361C2×C127—21no—
362C2×C127—22no—
363C2×C127—21no—
364C2×C127—21no—
365C2×C127—22no—
366C2×C127—21no—
367C2×C127—22no—
368C2×C127—21no—
369C2×C127—22no—
370C2×C127—44no—
371C2×C127—82no—
372C2×C127#191312yesdirect product factor
373C2×C127C2×#38611yescharacteristic
374C2×#534C2×C12711yescharacteristic
375C2×#518C2×C12711yescharacteristic, complemented
376C22×#99C2×C12711yescharacteristic, complemented
377C22×#99C2×C12712yescomplemented
378#1913C2×C12718yesdirect product factor
379C2×#342C2×C12712yescomplemented
380C127C2×#191311yescharacteristic, direct product factor, Sylow
381C23×D4C22×C12711yescharacteristic
382C23×D4C22×C12711yescharacteristic
383#534—22no—
384#534—22no—
385#534C4×C12714yescomplemented
386#534C22×C12714yes—
387C2×#123—21no—
388C2×#123C4×C12712yescomplemented
389C2×#121—22no—
390C2×#120—21no—
391C2×#120C4×C12712yescomplemented
392#518—22no—
393#518—24no—
394#518C22×C12714yescomplemented
395C2×C4×D4—24no—
396C2×#117—21no—
397C22×C22⋊C4—21no—
398C22×C22⋊C4C22×C12712yes—
399C22×C22⋊C4C22×C12711yescharacteristic
400C22×C22⋊C4C22×C12712yes—
401C2×#99—22no—
402C2×#99—22no—
403C2×#99—24no—
404C2×#99—24no—
405C2×#99C22×C12714yescomplemented
406C2×#99C22×C12718yescomplemented
407#342C22×C12718yescomplemented
408C25C2×C4×C12711yescharacteristic, complemented
409C25D4×C12711yescharacteristic
410C25C23×C12711yescharacteristic
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—22no—
414C22×D4—22no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4—22no—
420C22×D4—22no—
421C22×D4—22no—
422C22×D4—22no—
423C22×D4—22no—
424C22×D4C2×C4×C12712yes—
425C22×D4C2×C4×C12712yes—
426C22×D4C2×C4×C12712yescomplemented
427C22×D4D4×C12712yes—
428C22×D4D4×C12712yes—
429C22×D4D4×C12712yes—
430C22×D4C23×C12712yes—
431C22×D4C23×C12712yes—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—21no—
435C23×C4—22no—
436C23×C4C2×C4×C12711yescharacteristic, complemented
437C23×C4D4×C12711yescharacteristic
438#123—24no—
439#123—24no—
440#123—24no—
441#123C2×C4×C12718yescomplemented
442#121—28no—
443#121—28no—
444#120—24no—
445#120—24no—
446#120—24no—
447#120C2×C4×C12718yescomplemented
448C4×D4—216no—
449C4×D4—216no—
450#117—24no—
451#117—24no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4C2×C4×C12712yescomplemented
471C2×C22⋊C4C2×C4×C12712yescomplemented
472C2×C22⋊C4D4×C12714yescomplemented
473C2×C22⋊C4D4×C12714yescomplemented
474C2×C22⋊C4C23×C12714yes—
475C2×C22⋊C4C23×C12712yes—
476C2×C22⋊C4C23×C12714yes—
477C2×C42—22no—
478#99—28no—
479#99—216no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—82no—
489C24—82no—
490C24—82no—
491C24C22⋊C4×C12712yes—
492C24C22⋊C4×C12712yes—
493C24C22×C4×C12711yescharacteristic
494C24C22×C4×C12711yescharacteristic
495C24C22×C4×C12712yescomplemented
496C24C2×D4×C12712yes—
497C24C2×D4×C12711yescharacteristic
498C24C2×D4×C12711yescharacteristic
499C24C2×D4×C12712yes—
500C24C2×D4×C12711yescharacteristic
501C24C2×D4×C12711yescharacteristic
502C24C2×D4×C12712yes—
503C24#41×C12712yes—
504C24#41×C12712yes—
505C24C24×C12711yescharacteristic
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—28no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—42no—
537C2×D4—84no—
538C2×D4C22⋊C4×C12714yes—
539C2×D4C22⋊C4×C12714yes—
540C2×D4C22×C4×C12714yes—
541C2×D4C2×D4×C12714yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—82no—
563C22×C4—84no—
564C22×C4C22⋊C4×C12712yes—
565C22×C4C22⋊C4×C12712yes—
566C22×C4C22×C4×C12712yescomplemented
567C22×C4C2×D4×C12712yes—
568C4⋊C4—28no—
569C4⋊C4—28no—
570C22⋊C4—28no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—28no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—28no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4C22×C4×C12714yescomplemented
584C22⋊C4C2×D4×C12718yescomplemented
585C42—28no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—24no—
594C23—44no—
595C23—42no—
596C23—44no—
597C23—42no—
598C23—42no—
599C23—44no—
600C23—44no—
601C23—44no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—82no—
606C23—84no—
607C23—81no—
608C23—81no—
609C23—82no—
610C23—81no—
611C23—82no—
612C23—81no—
613C23—82no—
614C23—82no—
615C23—82no—
616C23—82no—
617C23—82no—
618C23—82no—
619C23—84no—
620C23C2×C22⋊C4×C12711yescharacteristic
621C23C2×C22⋊C4×C12714yes—
622C23C2×C22⋊C4×C12711yescharacteristic
623C23C2×C22⋊C4×C12711yescharacteristic
624C23C2×C22⋊C4×C12711yescharacteristic
625C23C4×D4×C12712yes—
626C23C4×D4×C12712yes—
627C23C4×D4×C12712yes—
628C23C4×D4×C12712yes—
629C23#120×C12711yescharacteristic
630C23#120×C12711yescharacteristic
631C23#120×C12712yes—
632C23#121×C12712yes—
633C23#121×C12712yes—
634C23#121×C12712yes—
635C23#121×C12712yes—
636C23#123×C12711yescharacteristic
637C23#123×C12711yescharacteristic
638C23#123×C12712yes—
639C23C23×C4×C12711yescharacteristic
640C23C22×D4×C12711yescharacteristic
641C23C22×D4×C12711yescharacteristic
642C23C22×D4×C12712yes—
643C23C2×#41×C12712yes—
644D4—28no—
645D4—28no—
646D4—28no—
647D4—28no—
648D4—42no—
649D4—44no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—44no—
654D4—88no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—28no—
665C2×C4—48no—
666C2×C4—44no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—44no—
671C2×C4—84no—
672C2×C4—84no—
673C2×C4—88no—
674C2×C4—82no—
675C2×C4—82no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—84no—
679C2×C4C2×C22⋊C4×C12714yes—
680C22—22no—
681C22—22no—
682C22—24no—
683C22—24no—
684C22—22no—
685C22—24no—
686C22—41no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22—41no—
691C22—42no—
692C22—41no—
693C22—41no—
694C22—42no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—44no—
705C22—44no—
706C22—44no—
707C22—44no—
708C22—44no—
709C22—42no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—84no—
714C22—82no—
715C22—84no—
716C22—82no—
717C22#386×C12711yescharacteristic
718C22#386×C12711yescharacteristic
719C22#386×C12711yescharacteristic
720C22#386×C12712yes—
721C22#386×C12712yes—
722C22#386×C12711yescharacteristic
723C22C22×C22⋊C4×C12711yescharacteristic
724C22C2×C4×D4×C12712yes—
725C22C2×#120×C12711yescharacteristic
726C22C2×#121×C12712yes—
727C22C2×#123×C12711yescharacteristic
728C4—24no—
729C4—48no—
730C4—44no—
731C4—42no—
732C4—84no—
733C2—21no—
734C2—21no—
735C2—22no—
736C2—21no—
737C2—21no—
738C2—22no—
739C2—21no—
740C2—22no—
741C2—21no—
742C2—22no—
743C2—44no—
744C2—82no—
745C2C127×#191312yesdirect product factor
746C2C2×#386×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×#534×C127C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#518×C127C2semidirect
3. C22×#99×C127C2semidirect
4. C22×#99×C127C2semidirect
5. C127×#1913C2direct (N × H)
6. C2×#342×C127C2semidirect
11. #534×C127C4semidirect
14. C2×#123×C127C4semidirect
17. C2×#120×C127C4semidirect
20. #518×C127C22semidirect
31. C2×#99×C127C22semidirect
32. C2×#99×C127C22semidirect
33. #342×C127C22semidirect
34. C25×C127C2×C4semidirect
52. C22×D4×C127C2×C4semidirect
62. C23×C4×C127C2×C4semidirect
67. #123×C127C2×C4semidirect
73. #120×C127C2×C4semidirect
96. C2×C22⋊C4×C127C2×C4semidirect
97. C2×C22⋊C4×C127C2×C4semidirect
98. C2×C22⋊C4×C127D4semidirect
99. C2×C22⋊C4×C127D4semidirect
121. C24×C127C22×C4semidirect
192. C22×C4×C127C22×C4semidirect
209. C22⋊C4×C127C22×C4semidirect
210. C22⋊C4×C127C2×D4semidirect
359. C2×#1913C127direct (N × H)
372. C2×C127#1913direct (N × H)
375. C2×#518C2×C127semidirect
376. C22×#99C2×C127semidirect
377. C22×#99C2×C127semidirect
378. #1913C2×C127direct (N × H)
379. C2×#342C2×C127semidirect
380. C127C2×#1913direct (N × H)
385. #534C4×C127semidirect
388. C2×#123C4×C127semidirect
391. C2×#120C4×C127semidirect
394. #518C22×C127semidirect
405. C2×#99C22×C127semidirect
406. C2×#99C22×C127semidirect
407. #342C22×C127semidirect
408. C25C2×C4×C127semidirect
426. C22×D4C2×C4×C127semidirect
436. C23×C4C2×C4×C127semidirect
441. #123C2×C4×C127semidirect
447. #120C2×C4×C127semidirect
470. C2×C22⋊C4C2×C4×C127semidirect
471. C2×C22⋊C4C2×C4×C127semidirect
472. C2×C22⋊C4D4×C127semidirect
473. C2×C22⋊C4D4×C127semidirect
495. C24C22×C4×C127semidirect
566. C22×C4C22×C4×C127semidirect
583. C22⋊C4C22×C4×C127semidirect
584. C22⋊C4C2×D4×C127semidirect
745. C2C127×#1913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#534×C1272
C2×#518×C1272
C22×#99×C1272
C127×#19132
C2×#342×C1272
C2×#1913127