Finite Group Databasebeta

← C2×C127×#1932 #44584752

Subgroups — C2×C127×#1932 #44584752

Order 32512.

1046 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#430×C127C211yesmaximal, characteristic, complemented
2C2×#421×C127C211yesmaximal, characteristic
3C22×#104×C127C211yesmaximal, characteristic
4C2×#413×C127C211yesmaximal, characteristic
5C2×C4×M16×C127C211yesmaximal, characteristic, complemented
6C127×#1932C218yesmaximal, direct product factor
7C2×#344×C127C211yesmaximal, characteristic, complemented
8C2×#339×C127C211yesmaximal, characteristic, complemented
9C22×#41×C127C2211yescharacteristic
10C22×M16×C127C2211yescharacteristic
11C22×M16×C127C2211yescharacteristic
12C22×M16×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C2×#117×C127C2211yescharacteristic
15C22×C42×C127C2211yescharacteristic
16#430×C127—22no—
17#430×C127C2214yescomplemented
18C2×#108×C127—22no—
19#421×C127—22no—
20#421×C127C2214yes—
21C2×#104×C127—22no—
22C2×#104×C127—21no—
23C2×#104×C127—21no—
24C2×#104×C127—22no—
25C2×#104×C127C2214yes—
26#413×C127C414yescomplemented
27#413×C127C2214yes—
28C2×#101×C127C412yescomplemented
29C2×#100×C127C412yescomplemented
30C4×M16×C127—22no—
31C4×M16×C127C2214yescomplemented
32C2×#97×C127—21no—
33C2×C4×C8×C127—21no—
34#344×C127C2214yescomplemented
35#339×C127C2214yescomplemented
36C2×#41×C127—21no—
37C2×#41×C127—21no—
38C2×#41×C127—21no—
39C2×#41×C127—21no—
40C2×#41×C127—21no—
41C2×#41×C127—21no—
42C2×#41×C127—21no—
43C2×#41×C127—21no—
44C2×#41×C127—21no—
45C2×#41×C127—21no—
46C2×#41×C127C2×C412yes—
47C2×#41×C127C2312yes—
48C22×Q8×C127C2×C411yescharacteristic
49C22×D4×C127—21no—
50C22×D4×C127C2×C411yescharacteristic
51C23×C4×C127—21no—
52C23×C4×C127—21no—
53C23×C4×C127C2311yescharacteristic
54C2×M16×C127—21no—
55C2×M16×C127—21no—
56C2×M16×C127—21no—
57C2×M16×C127—21no—
58C2×M16×C127—21no—
59C2×M16×C127—21no—
60C2×M16×C127—21no—
61C2×M16×C127—21no—
62C2×M16×C127—21no—
63C2×M16×C127—21no—
64C2×M16×C127—21no—
65C2×M16×C127—21no—
66C2×M16×C127—21no—
67C2×M16×C127—21no—
68C2×M16×C127C2×C412yes—
69C2×M16×C127C2×C412yes—
70C2×M16×C127C2×C412yes—
71C2×M16×C127C2×C412yes—
72C2×M16×C127D412yes—
73C2×M16×C127D412yes—
74C2×M16×C127C2312yes—
75C2×M16×C127C2312yes—
76C2×M16×C127C2312yes—
77C2×M16×C127C2312yes—
78C22×C8×C127—21no—
79C22×C8×C127—21no—
80C22×C8×C127—21no—
81C22×C8×C127—21no—
82#117×C127—21no—
83#117×C127—21no—
84#117×C127—21no—
85#117×C127C2312yes—
86C2×C4⋊C4×C127—21no—
87C2×C22⋊C4×C127—21no—
88C2×C42×C127—21no—
89C2×C42×C127—21no—
90C2×C42×C127—21no—
91C2×C42×C127—21no—
92C2×C42×C127D411yescharacteristic
93C2×C42×C127D411yescharacteristic
94C2×C42×C127D412yes—
95C2×C42×C127C2312yes—
96#108×C127—28no—
97#104×C127—28no—
98#104×C127—24no—
99#104×C127—24no—
100#101×C127C2×C418yescomplemented
101#100×C127C2×C418yescomplemented
102#97×C127—24no—
103C4×C8×C127—24no—
104C24×C127—21no—
105C24×C127#4111yescharacteristic
106#41×C127—22no—
107#41×C127—22no—
108#41×C127—22no—
109#41×C127—22no—
110#41×C127—22no—
111#41×C127—22no—
112#41×C127—22no—
113#41×C127—22no—
114#41×C127—41no—
115#41×C127—41no—
116#41×C127—41no—
117#41×C127—41no—
118#41×C127—41no—
119#41×C127—41no—
120#41×C127—41no—
121#41×C127—41no—
122C2×Q8×C127—21no—
123C2×Q8×C127—21no—
124C2×Q8×C127—21no—
125C2×Q8×C127—21no—
126C2×Q8×C127—21no—
127C2×Q8×C127C22×C412yes—
128C2×D4×C127—22no—
129C2×D4×C127—22no—
130C2×D4×C127—21no—
131C2×D4×C127—21no—
132C2×D4×C127—21no—
133C2×D4×C127—21no—
134C2×D4×C127—21no—
135C2×D4×C127—41no—
136C2×D4×C127—41no—
137C2×D4×C127—41no—
138C2×D4×C127—41no—
139C2×D4×C127C22×C412yes—
140C22×C4×C127—21no—
141C22×C4×C127—21no—
142C22×C4×C127—22no—
143C22×C4×C127—21no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—44no—
148C22×C4×C127—41no—
149C22×C4×C127—41no—
150C22×C4×C127—41no—
151C22×C4×C127—41no—
152C22×C4×C127—41no—
153C22×C4×C127C22×C411yescharacteristic
154C22×C4×C127C22×C411yescharacteristic
155C22×C4×C127C2×D411yescharacteristic
156C22×C4×C127C2×D411yescharacteristic
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127#4111yescharacteristic
160C22×C4×C127#4111yescharacteristic
161C22×C4×C127#4111yescharacteristic
162C22×C4×C127#4111yescharacteristic
163C22×C4×C127#4111yescharacteristic
164C22×C4×C127#4111yescharacteristic
165C22×C4×C127#4111yescharacteristic
166C22×C4×C127C2411yescharacteristic
167M16×C127—22no—
168M16×C127—22no—
169M16×C127—22no—
170M16×C127—22no—
171M16×C127—22no—
172M16×C127—22no—
173M16×C127—22no—
174M16×C127—22no—
175M16×C127—22no—
176M16×C127—22no—
177M16×C127—22no—
178M16×C127—41no—
179M16×C127—41no—
180M16×C127C22×C414yes—
181M16×C127C22×C414yes—
182M16×C127C2×D414yes—
183C2×C8×C127—22no—
184C2×C8×C127—22no—
185C2×C8×C127—22no—
186C2×C8×C127—22no—
187C2×C8×C127—22no—
188C2×C8×C127—22no—
189C2×C8×C127—22no—
190C2×C8×C127—22no—
191C2×C8×C127—22no—
192C2×C8×C127—22no—
193C2×C8×C127—41no—
194C2×C8×C127—41no—
195C4⋊C4×C127—22no—
196C4⋊C4×C127—41no—
197C22⋊C4×C127—22no—
198C22⋊C4×C127—41no—
199C42×C127—21no—
200C42×C127—22no—
201C42×C127—21no—
202C42×C127—22no—
203C42×C127—22no—
204C42×C127—41no—
205C42×C127C2×D412yes—
206C42×C127C2×D412yes—
207C23×C127—22no—
208C23×C127—42no—
209C23×C127—41no—
210C23×C127—41no—
211C23×C127—82no—
212C23×C127#11711yescharacteristic
213C23×C127#11711yescharacteristic
214C23×C127#12311yescharacteristic
215C23×C127#12311yescharacteristic
216C23×C127#12411yescharacteristic
217C23×C127#12411yescharacteristic
218C23×C127C2×#4111yescharacteristic
219Q8×C127—22no—
220Q8×C127—22no—
221Q8×C127—41no—
222Q8×C127—41no—
223D4×C127—22no—
224D4×C127—22no—
225D4×C127—42no—
226D4×C127—42no—
227D4×C127—42no—
228D4×C127—42no—
229D4×C127—41no—
230D4×C127—41no—
231C2×C4×C127—24no—
232C2×C4×C127—22no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—44no—
236C2×C4×C127—44no—
237C2×C4×C127—42no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127—42no—
243C2×C4×C127—42no—
244C2×C4×C127—42no—
245C2×C4×C127—82no—
246C2×C4×C127#11711yescharacteristic
247C2×C4×C127#11711yescharacteristic
248C2×C4×C127C4×D411yescharacteristic
249C2×C4×C127C4×D411yescharacteristic
250C2×C4×C127C4×D411yescharacteristic
251C2×C4×C127C4×D411yescharacteristic
252C2×C4×C127C4×D411yescharacteristic
253C2×C4×C127C4×D411yescharacteristic
254C2×C4×C127C4×D411yescharacteristic
255C2×C4×C127C4×D411yescharacteristic
256C2×C4×C127#12111yescharacteristic
257C2×C4×C127#12111yescharacteristic
258C2×C4×C127#12111yescharacteristic
259C2×C4×C127#12111yescharacteristic
260C2×C4×C127#12311yescharacteristic
261C2×C4×C127#12311yescharacteristic
262C2×C4×C127#12411yescharacteristic
263C2×C4×C127#12411yescharacteristic
264C2×C4×C127#12611yescharacteristic
265C2×C4×C127#12611yescharacteristic
266C2×C4×C127#12611yescharacteristic
267C2×C4×C127#12611yescharacteristic
268C2×C4×C127C23×C411yescharacteristic
269C2×C4×C127C22×D411yescharacteristic
270C2×C4×C127C22×D411yescharacteristic
271C2×C4×C127C2×#4111yescharacteristic
272C2×C4×C127C2×#4111yescharacteristic
273C2×C4×C127C2×#4111yescharacteristic
274C8×C127—24no—
275C8×C127—24no—
276C8×C127—24no—
277C8×C127—42no—
278C22×C127—22no—
279C22×C127—22no—
280C22×C127—22no—
281C22×C127—41no—
282C22×C127—41no—
283C22×C127—41no—
284C22×C127—41no—
285C22×C127—42no—
286C22×C127—82no—
287C22×C127—82no—
288C22×C127—82no—
289C22×C127#38811yescharacteristic
290C22×C127#38811yescharacteristic
291C22×C127#38811yescharacteristic
292C22×C127#38811yescharacteristic
293C22×C127C2×#11711yescharacteristic
294C22×C127C2×#12311yescharacteristic
295C22×C127C2×#12411yescharacteristic
296C4×C127—24no—
297C4×C127—42no—
298C4×C127—42no—
299C4×C127—82no—
300C4×C127#38811yescharacteristic
301C4×C127#38811yescharacteristic
302C4×C127#38811yescharacteristic
303C4×C127#38811yescharacteristic
304C4×C127C2×C4×D411yescharacteristic
305C4×C127C2×C4×D411yescharacteristic
306C4×C127C2×#12111yescharacteristic
307C4×C127C2×#12611yescharacteristic
308C2×#1932C12711yesmaximal, characteristic, direct product factor, Sylow
309C2×C127—21no—
310C2×C127—21no—
311C2×C127—21no—
312C2×C127—21no—
313C2×C127—21no—
314C2×C127—21no—
315C2×C127—82no—
316C2×C127#193212yesdirect product factor
317C2×C127C2×#38811yescharacteristic
318C2×#430C2×C12711yescharacteristic, complemented
319C2×#421C2×C12711yescharacteristic
320C22×#104C2×C12711yescharacteristic
321C2×#413C2×C12711yescharacteristic
322C2×C4×M16C2×C12711yescharacteristic, complemented
323#1932C2×C12718yesdirect product factor
324C2×#344C2×C12711yescharacteristic, complemented
325C2×#339C2×C12711yescharacteristic, complemented
326C127C2×#193211yescharacteristic, direct product factor, Sylow
327C22×#41C22×C12711yescharacteristic
328C22×M16C22×C12711yescharacteristic
329C22×M16C22×C12711yescharacteristic
330C22×M16C22×C12711yescharacteristic
331C22×M16C22×C12711yescharacteristic
332C2×#117C22×C12711yescharacteristic
333C22×C42C22×C12711yescharacteristic
334#430—22no—
335#430C22×C12714yescomplemented
336C2×#108—22no—
337#421—22no—
338#421C22×C12714yes—
339C2×#104—22no—
340C2×#104—21no—
341C2×#104—21no—
342C2×#104—22no—
343C2×#104C22×C12714yes—
344#413C4×C12714yescomplemented
345#413C22×C12714yes—
346C2×#101C4×C12712yescomplemented
347C2×#100C4×C12712yescomplemented
348C4×M16—22no—
349C4×M16C22×C12714yescomplemented
350C2×#97—21no—
351C2×C4×C8—21no—
352#344C22×C12714yescomplemented
353#339C22×C12714yescomplemented
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41C2×C4×C12712yes—
365C2×#41C23×C12712yes—
366C22×Q8C2×C4×C12711yescharacteristic
367C22×D4—21no—
368C22×D4C2×C4×C12711yescharacteristic
369C23×C4—21no—
370C23×C4—21no—
371C23×C4C23×C12711yescharacteristic
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16C2×C4×C12712yes—
387C2×M16C2×C4×C12712yes—
388C2×M16C2×C4×C12712yes—
389C2×M16C2×C4×C12712yes—
390C2×M16D4×C12712yes—
391C2×M16D4×C12712yes—
392C2×M16C23×C12712yes—
393C2×M16C23×C12712yes—
394C2×M16C23×C12712yes—
395C2×M16C23×C12712yes—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—21no—
399C22×C8—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117C23×C12712yes—
404C2×C4⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42D4×C12711yescharacteristic
411C2×C42D4×C12711yescharacteristic
412C2×C42D4×C12712yes—
413C2×C42C23×C12712yes—
414#108—28no—
415#104—28no—
416#104—24no—
417#104—24no—
418#101C2×C4×C12718yescomplemented
419#100C2×C4×C12718yescomplemented
420#97—24no—
421C4×C8—24no—
422C24—21no—
423C24#41×C12711yescharacteristic
424#41—22no—
425#41—22no—
426#41—22no—
427#41—22no—
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—41no—
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C22×C4×C12712yes—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4C22×C4×C12712yes—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—44no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4C22×C4×C12711yescharacteristic
472C22×C4C22×C4×C12711yescharacteristic
473C22×C4C2×D4×C12711yescharacteristic
474C22×C4C2×D4×C12711yescharacteristic
475C22×C4C2×D4×C12711yescharacteristic
476C22×C4C2×D4×C12711yescharacteristic
477C22×C4#41×C12711yescharacteristic
478C22×C4#41×C12711yescharacteristic
479C22×C4#41×C12711yescharacteristic
480C22×C4#41×C12711yescharacteristic
481C22×C4#41×C12711yescharacteristic
482C22×C4#41×C12711yescharacteristic
483C22×C4#41×C12711yescharacteristic
484C22×C4C24×C12711yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—22no—
492M16—22no—
493M16—22no—
494M16—22no—
495M16—22no—
496M16—41no—
497M16—41no—
498M16C22×C4×C12714yes—
499M16C22×C4×C12714yes—
500M16C2×D4×C12714yes—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—41no—
512C2×C8—41no—
513C4⋊C4—22no—
514C4⋊C4—41no—
515C22⋊C4—22no—
516C22⋊C4—41no—
517C42—21no—
518C42—22no—
519C42—21no—
520C42—22no—
521C42—22no—
522C42—41no—
523C42C2×D4×C12712yes—
524C42C2×D4×C12712yes—
525C23—22no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—82no—
530C23#117×C12711yescharacteristic
531C23#117×C12711yescharacteristic
532C23#123×C12711yescharacteristic
533C23#123×C12711yescharacteristic
534C23#124×C12711yescharacteristic
535C23#124×C12711yescharacteristic
536C23C2×#41×C12711yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541D4—22no—
542D4—22no—
543D4—42no—
544D4—42no—
545D4—42no—
546D4—42no—
547D4—41no—
548D4—41no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—82no—
564C2×C4#117×C12711yescharacteristic
565C2×C4#117×C12711yescharacteristic
566C2×C4C4×D4×C12711yescharacteristic
567C2×C4C4×D4×C12711yescharacteristic
568C2×C4C4×D4×C12711yescharacteristic
569C2×C4C4×D4×C12711yescharacteristic
570C2×C4C4×D4×C12711yescharacteristic
571C2×C4C4×D4×C12711yescharacteristic
572C2×C4C4×D4×C12711yescharacteristic
573C2×C4C4×D4×C12711yescharacteristic
574C2×C4#121×C12711yescharacteristic
575C2×C4#121×C12711yescharacteristic
576C2×C4#121×C12711yescharacteristic
577C2×C4#121×C12711yescharacteristic
578C2×C4#123×C12711yescharacteristic
579C2×C4#123×C12711yescharacteristic
580C2×C4#124×C12711yescharacteristic
581C2×C4#124×C12711yescharacteristic
582C2×C4#126×C12711yescharacteristic
583C2×C4#126×C12711yescharacteristic
584C2×C4#126×C12711yescharacteristic
585C2×C4#126×C12711yescharacteristic
586C2×C4C23×C4×C12711yescharacteristic
587C2×C4C22×D4×C12711yescharacteristic
588C2×C4C22×D4×C12711yescharacteristic
589C2×C4C2×#41×C12711yescharacteristic
590C2×C4C2×#41×C12711yescharacteristic
591C2×C4C2×#41×C12711yescharacteristic
592C8—24no—
593C8—24no—
594C8—24no—
595C8—42no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—42no—
604C22—82no—
605C22—82no—
606C22—82no—
607C22#388×C12711yescharacteristic
608C22#388×C12711yescharacteristic
609C22#388×C12711yescharacteristic
610C22#388×C12711yescharacteristic
611C22C2×#117×C12711yescharacteristic
612C22C2×#123×C12711yescharacteristic
613C22C2×#124×C12711yescharacteristic
614C4—24no—
615C4—42no—
616C4—42no—
617C4—82no—
618C4#388×C12711yescharacteristic
619C4#388×C12711yescharacteristic
620C4#388×C12711yescharacteristic
621C4#388×C12711yescharacteristic
622C4C2×C4×D4×C12711yescharacteristic
623C4C2×C4×D4×C12711yescharacteristic
624C4C2×#121×C12711yescharacteristic
625C4C2×#126×C12711yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2C127×#193212yesdirect product factor
634C2C2×#388×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127#121
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127#388
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#430×C127C2semidirect
5. C2×C4×M16×C127C2semidirect
6. C127×#1932C2direct (N × H)
7. C2×#344×C127C2semidirect
8. C2×#339×C127C2semidirect
17. #430×C127C22semidirect
26. #413×C127C4semidirect
28. C2×#101×C127C4semidirect
29. C2×#100×C127C4semidirect
31. C4×M16×C127C22semidirect
34. #344×C127C22semidirect
35. #339×C127C22semidirect
100. #101×C127C2×C4semidirect
101. #100×C127C2×C4semidirect
308. C2×#1932C127direct (N × H)
316. C2×C127#1932direct (N × H)
318. C2×#430C2×C127semidirect
322. C2×C4×M16C2×C127semidirect
323. #1932C2×C127direct (N × H)
324. C2×#344C2×C127semidirect
325. C2×#339C2×C127semidirect
326. C127C2×#1932direct (N × H)
335. #430C22×C127semidirect
344. #413C4×C127semidirect
346. C2×#101C4×C127semidirect
347. C2×#100C4×C127semidirect
349. C4×M16C22×C127semidirect
352. #344C22×C127semidirect
353. #339C22×C127semidirect
418. #101C2×C4×C127semidirect
419. #100C2×C4×C127semidirect
633. C2C127×#1932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#430×C1272
C2×#421×C1272
C22×#104×C1272
C2×#413×C1272
C2×C4×M16×C1272
C127×#19322
C2×#344×C1272
C2×#339×C1272
C2×#1932127