Finite Group Databasebeta

← C127×#20703 #44584376

Subgroups — C127×#20703 #44584376

Order 32512.

1374 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C127C211yesmaximal, characteristic
2C2×#408×C127C211yesmaximal, characteristic
3C127×#2311C211yesmaximal, characteristic
4C127×#1825C212yesmaximal, complemented
5C127×#1825C212yesmaximal, complemented
6C127×#1824C212yesmaximal, complemented
7C127×#1823C212yesmaximal, complemented
8C127×#1736C211yesmaximal, characteristic, complemented
9C127×#1736C211yesmaximal, characteristic, complemented
10C127×#1735C211yesmaximal, characteristic, complemented
11C2×#340×C127C211yesmaximal, characteristic, complemented
12C22×#41×C127C2211yescharacteristic
13C22×M16×C127C2211yescharacteristic
14C23×C8×C127C2211yescharacteristic
15#520×C127—24no—
16#520×C127C418yescomplemented
17C2×C4×Q8×C127—21no—
18C2×C4×D4×C127—22no—
19C2×C4×D4×C127—21no—
20C2×#117×C127C2211yescharacteristic
21C2×#117×C127C2211yescharacteristic
22C2×#117×C127C2212yes—
23C22×C4⋊C4×C127C2211yescharacteristic
24C22×C4⋊C4×C127C2211yescharacteristic
25C22×C4⋊C4×C127C2212yes—
26#408×C127—24no—
27C2×C22⋊C8×C127C2212yes—
28C2×C22⋊C8×C127C2212yes—
29#391×C127—21no—
30#390×C127—21no—
31#386×C127—22no—
32#380×C127C2212yes—
33#380×C127C2212yes—
34#340×C127C2211yescharacteristic
35#340×C127C2212yes—
36#340×C127C2212yes—
37#340×C127C2212yes—
38#340×C127C2211yescharacteristic
39#340×C127C2212yes—
40#340×C127C2212yes—
41#340×C127C2211yescharacteristic
42#340×C127C2211yescharacteristic
43#340×C127C2212yes—
44C2×#41×C127—22no—
45C2×#41×C127—22no—
46C2×#41×C127—22no—
47C2×#41×C127—22no—
48C2×#41×C127C2×C414yes—
49C2×#41×C127D414yes—
50C22×Q8×C127D411yescharacteristic
51C22×D4×C127D412yes—
52C22×D4×C127D411yescharacteristic
53C23×C4×C127—21no—
54C23×C4×C127—22no—
55C23×C4×C127—21no—
56C23×C4×C127C2312yes—
57C23×C4×C127C2311yescharacteristic
58C2×M16×C127—22no—
59C2×M16×C127—22no—
60C2×M16×C127—22no—
61C22×C8×C127—22no—
62C22×C8×C127—22no—
63C22×C8×C127—22no—
64C22×C8×C127C2311yescharacteristic
65C22×C8×C127C2311yescharacteristic
66C22×C8×C127C2312yes—
67C4×Q8×C127—28no—
68C4×D4×C127—28no—
69C4×D4×C127—216no—
70#117×C127—22no—
71#117×C127—24no—
72#117×C127—22no—
73#117×C127—22no—
74#117×C127C2×C414yes—
75#117×C127C2×C418yescomplemented
76C2×C4⋊C4×C127—21no—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—22no—
79C2×C4⋊C4×C127—24no—
80C2×C4⋊C4×C127—22no—
81C2×C4⋊C4×C127—22no—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127C2×C414yes—
84C2×C4⋊C4×C127C2×C418yescomplemented
85C2×C4⋊C4×C127C2312yes—
86C2×C4⋊C4×C127C2311yescharacteristic
87C2×C4⋊C4×C127C2311yescharacteristic
88C2×C4⋊C4×C127C2312yes—
89C2×C4⋊C4×C127C2311yescharacteristic
90C2×C4⋊C4×C127C2311yescharacteristic
91C2×C22⋊C4×C127—21no—
92C2×C22⋊C4×C127—22no—
93C2×C22⋊C4×C127—21no—
94C2×C22⋊C4×C127—22no—
95C2×C22⋊C4×C127—22no—
96C2×C42×C127—21no—
97C2×C42×C127—22no—
98C2×C42×C127—21no—
99C22⋊C8×C127—24no—
100C22⋊C8×C127—24no—
101#95×C127—22no—
102#95×C127—22no—
103C24×C127C2×D412yes—
104C24×C127C2×D411yescharacteristic
105#41×C127—28no—
106#41×C127—28no—
107#41×C127—28no—
108#41×C127—28no—
109C2×Q8×C127—22no—
110C2×Q8×C127—22no—
111C2×Q8×C127C22⋊C414yes—
112C2×D4×C127—24no—
113C2×D4×C127—24no—
114C2×D4×C127—22no—
115C2×D4×C127—22no—
116C2×D4×C127C22⋊C418yes—
117C2×D4×C127C22⋊C414yes—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—22no—
125C22×C4×C127—24no—
126C22×C4×C127—28no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—22no—
130C22×C4×C127—42no—
131C22×C4×C127—81no—
132C22×C4×C127—82no—
133C22×C4×C127—81no—
134C22×C4×C127—82no—
135C22×C4×C127—81no—
136C22×C4×C127—81no—
137C22×C4×C127C22×C414yes—
138C22×C4×C127C22×C412yes—
139C22×C4×C127C2×D412yes—
140C22×C4×C127C2×D414yes—
141C22×C4×C127C2×D411yescharacteristic
142C22×C4×C127C2×D412yes—
143C22×C4×C127#4112yes—
144C22×C4×C127#4112yes—
145C22×C4×C127#4112yes—
146C22×C4×C127#4112yes—
147C22×C4×C127C2411yescharacteristic
148M16×C127—44no—
149C2×C8×C127—21no—
150C2×C8×C127—21no—
151C2×C8×C127—22no—
152C2×C8×C127—21no—
153C2×C8×C127—21no—
154C2×C8×C127—21no—
155C2×C8×C127—21no—
156C2×C8×C127—22no—
157C2×C8×C127—22no—
158C2×C8×C127—44no—
159C4⋊C4×C127—24no—
160C4⋊C4×C127—28no—
161C4⋊C4×C127—21no—
162C4⋊C4×C127—22no—
163C4⋊C4×C127—21no—
164C4⋊C4×C127—22no—
165C4⋊C4×C127—22no—
166C4⋊C4×C127—21no—
167C4⋊C4×C127—21no—
168C4⋊C4×C127—21no—
169C4⋊C4×C127—21no—
170C4⋊C4×C127—42no—
171C4⋊C4×C127C22×C414yes—
172C4⋊C4×C127C22×C412yes—
173C4⋊C4×C127C22×C412yes—
174C22⋊C4×C127—24no—
175C22⋊C4×C127—28no—
176C22⋊C4×C127—42no—
177C22⋊C4×C127—82no—
178C22⋊C4×C127—82no—
179C42×C127—24no—
180C42×C127—28no—
181C42×C127—42no—
182C23×C127—21no—
183C23×C127—21no—
184C23×C127—21no—
185C23×C127—21no—
186C23×C127—22no—
187C23×C127—22no—
188C23×C127—22no—
189C23×C127—22no—
190C23×C127—22no—
191C23×C127—22no—
192C23×C127C2×C22⋊C414yes—
193C23×C127C2×C22⋊C412yes—
194C23×C127#12312yes—
195C23×C127#12312yes—
196C23×C127C22×D411yescharacteristic
197Q8×C127—28no—
198D4×C127—216no—
199D4×C127—28no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—22no—
207C2×C4×C127—22no—
208C2×C4×C127—24no—
209C2×C4×C127—42no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—42no—
213C2×C4×C127—41no—
214C2×C4×C127—41no—
215C2×C4×C127—41no—
216C2×C4×C127—41no—
217C2×C4×C127—42no—
218C2×C4×C127—41no—
219C2×C4×C127—42no—
220C2×C4×C127—41no—
221C2×C4×C127—42no—
222C2×C4×C127—41no—
223C2×C4×C127—41no—
224C2×C4×C127—84no—
225C2×C4×C127—88no—
226C2×C4×C127—84no—
227C2×C4×C127C2×C22⋊C414yes—
228C2×C4×C127C2×C22⋊C412yes—
229C2×C4×C127#11714yes—
230C2×C4×C127#11714yes—
231C2×C4×C127#12314yes—
232C2×C4×C127#12314yes—
233C2×C4×C127#12312yes—
234C2×C4×C127#12312yes—
235C2×C4×C127C23×C411yescharacteristic
236C2×C4×C127C22×D411yescharacteristic
237C2×C4×C127C2×#4111yescharacteristic
238C2×C4×C127C2×#4111yescharacteristic
239C2×C4×C127C2×#4111yescharacteristic
240C2×C4×C127C2×#4111yescharacteristic
241C8×C127—41no—
242C8×C127—41no—
243C8×C127—42no—
244C22×C127—22no—
245C22×C127—22no—
246C22×C127—22no—
247C22×C127—22no—
248C22×C127—22no—
249C22×C127—22no—
250C22×C127—24no—
251C22×C127—24no—
252C22×C127—24no—
253C22×C127—42no—
254C22×C127—42no—
255C22×C127—42no—
256C22×C127—42no—
257C22×C127#38114yes—
258C22×C127C22×C22⋊C411yescharacteristic
259C22×C127C2×#12311yescharacteristic
260C22×C127C2×#12311yescharacteristic
261C22×C127#57611yescharacteristic
262C22×C127#57711yescharacteristic
263C22×C127#57711yescharacteristic
264C22×C127#57811yescharacteristic
265C4×C127—24no—
266C4×C127—42no—
267C4×C127—44no—
268C4×C127—42no—
269C4×C127—82no—
270C4×C127—81no—
271C4×C127—81no—
272C4×C127#38114yes—
273C4×C127C2×#11711yescharacteristic
274C4×C127C2×#11711yescharacteristic
275C4×C127C2×#12311yescharacteristic
276C4×C127C2×#12311yescharacteristic
277#20703C12711yesmaximal, characteristic, direct product factor, Sylow
278C2×C127—24no—
279C2×C127—44no—
280C2×C127C2×#38111yescharacteristic
281C2×C127#289711yescharacteristic
282C2×C127#289811yescharacteristic
283C2×C127#309611yescharacteristic
284C2×C127#309711yescharacteristic
285C2×C127#309811yescharacteristic
286C2×C127#309911yescharacteristic
287C2×#520C2×C12711yescharacteristic
288C2×#408C2×C12711yescharacteristic
289#2311C2×C12711yescharacteristic
290#1825C2×C12712yescomplemented
291#1825C2×C12712yescomplemented
292#1824C2×C12712yescomplemented
293#1823C2×C12712yescomplemented
294#1736C2×C12711yescharacteristic, complemented
295#1736C2×C12711yescharacteristic, complemented
296#1735C2×C12711yescharacteristic, complemented
297C2×#340C2×C12711yescharacteristic, complemented
298C127#2070311yescharacteristic, direct product factor, Sylow
299C22×#41C22×C12711yescharacteristic
300C22×M16C22×C12711yescharacteristic
301C23×C8C22×C12711yescharacteristic
302#520—24no—
303#520C4×C12718yescomplemented
304C2×C4×Q8—21no—
305C2×C4×D4—22no—
306C2×C4×D4—21no—
307C2×#117C22×C12711yescharacteristic
308C2×#117C22×C12711yescharacteristic
309C2×#117C22×C12712yes—
310C22×C4⋊C4C22×C12711yescharacteristic
311C22×C4⋊C4C22×C12711yescharacteristic
312C22×C4⋊C4C22×C12712yes—
313#408—24no—
314C2×C22⋊C8C22×C12712yes—
315C2×C22⋊C8C22×C12712yes—
316#391—21no—
317#390—21no—
318#386—22no—
319#380C22×C12712yes—
320#380C22×C12712yes—
321#340C22×C12711yescharacteristic
322#340C22×C12712yes—
323#340C22×C12712yes—
324#340C22×C12712yes—
325#340C22×C12711yescharacteristic
326#340C22×C12712yes—
327#340C22×C12712yes—
328#340C22×C12711yescharacteristic
329#340C22×C12711yescharacteristic
330#340C22×C12712yes—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41C2×C4×C12714yes—
336C2×#41D4×C12714yes—
337C22×Q8D4×C12711yescharacteristic
338C22×D4D4×C12712yes—
339C22×D4D4×C12711yescharacteristic
340C23×C4—21no—
341C23×C4—22no—
342C23×C4—21no—
343C23×C4C23×C12712yes—
344C23×C4C23×C12711yescharacteristic
345C2×M16—22no—
346C2×M16—22no—
347C2×M16—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—22no—
351C22×C8C23×C12711yescharacteristic
352C22×C8C23×C12711yescharacteristic
353C22×C8C23×C12712yes—
354C4×Q8—28no—
355C4×D4—28no—
356C4×D4—216no—
357#117—22no—
358#117—24no—
359#117—22no—
360#117—22no—
361#117C2×C4×C12714yes—
362#117C2×C4×C12718yescomplemented
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C2×C4×C12714yes—
371C2×C4⋊C4C2×C4×C12718yescomplemented
372C2×C4⋊C4C23×C12712yes—
373C2×C4⋊C4C23×C12711yescharacteristic
374C2×C4⋊C4C23×C12711yescharacteristic
375C2×C4⋊C4C23×C12712yes—
376C2×C4⋊C4C23×C12711yescharacteristic
377C2×C4⋊C4C23×C12711yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C42—21no—
384C2×C42—22no—
385C2×C42—21no—
386C22⋊C8—24no—
387C22⋊C8—24no—
388#95—22no—
389#95—22no—
390C24C2×D4×C12712yes—
391C24C2×D4×C12711yescharacteristic
392#41—28no—
393#41—28no—
394#41—28no—
395#41—28no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8C22⋊C4×C12714yes—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4C22⋊C4×C12718yes—
404C2×D4C22⋊C4×C12714yes—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—28no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—42no—
418C22×C4—81no—
419C22×C4—82no—
420C22×C4—81no—
421C22×C4—82no—
422C22×C4—81no—
423C22×C4—81no—
424C22×C4C22×C4×C12714yes—
425C22×C4C22×C4×C12712yes—
426C22×C4C2×D4×C12712yes—
427C22×C4C2×D4×C12714yes—
428C22×C4C2×D4×C12711yescharacteristic
429C22×C4C2×D4×C12712yes—
430C22×C4#41×C12712yes—
431C22×C4#41×C12712yes—
432C22×C4#41×C12712yes—
433C22×C4#41×C12712yes—
434C22×C4C24×C12711yescharacteristic
435M16—44no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—22no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—44no—
446C4⋊C4—24no—
447C4⋊C4—28no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4C22×C4×C12714yes—
459C4⋊C4C22×C4×C12712yes—
460C4⋊C4C22×C4×C12712yes—
461C22⋊C4—24no—
462C22⋊C4—28no—
463C22⋊C4—42no—
464C22⋊C4—82no—
465C22⋊C4—82no—
466C42—24no—
467C42—28no—
468C42—42no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23C2×C22⋊C4×C12714yes—
480C23C2×C22⋊C4×C12712yes—
481C23#123×C12712yes—
482C23#123×C12712yes—
483C23C22×D4×C12711yescharacteristic
484Q8—28no—
485D4—216no—
486D4—28no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—84no—
512C2×C4—88no—
513C2×C4—84no—
514C2×C4C2×C22⋊C4×C12714yes—
515C2×C4C2×C22⋊C4×C12712yes—
516C2×C4#117×C12714yes—
517C2×C4#117×C12714yes—
518C2×C4#123×C12714yes—
519C2×C4#123×C12714yes—
520C2×C4#123×C12712yes—
521C2×C4#123×C12712yes—
522C2×C4C23×C4×C12711yescharacteristic
523C2×C4C22×D4×C12711yescharacteristic
524C2×C4C2×#41×C12711yescharacteristic
525C2×C4C2×#41×C12711yescharacteristic
526C2×C4C2×#41×C12711yescharacteristic
527C2×C4C2×#41×C12711yescharacteristic
528C8—41no—
529C8—41no—
530C8—42no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—24no—
538C22—24no—
539C22—24no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22#381×C12714yes—
545C22C22×C22⋊C4×C12711yescharacteristic
546C22C2×#123×C12711yescharacteristic
547C22C2×#123×C12711yescharacteristic
548C22#576×C12711yescharacteristic
549C22#577×C12711yescharacteristic
550C22#577×C12711yescharacteristic
551C22#578×C12711yescharacteristic
552C4—24no—
553C4—42no—
554C4—44no—
555C4—42no—
556C4—82no—
557C4—81no—
558C4—81no—
559C4#381×C12714yes—
560C4C2×#117×C12711yescharacteristic
561C4C2×#117×C12711yescharacteristic
562C4C2×#123×C12711yescharacteristic
563C4C2×#123×C12711yescharacteristic
564C2—24no—
565C2—44no—
566C2C2×#381×C12711yescharacteristic
567C2C127×#289711yescharacteristic
568C2C127×#289811yescharacteristic
569C2C127×#309611yescharacteristic
570C2C127×#309711yescharacteristic
571C2C127×#309811yescharacteristic
572C2C127×#309911yescharacteristic
subgroupG/H
center, socleC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1825C2semidirect
5. C127×#1825C2semidirect
6. C127×#1824C2semidirect
7. C127×#1823C2semidirect
8. C127×#1736C2semidirect
9. C127×#1736C2semidirect
10. C127×#1735C2semidirect
11. C2×#340×C127C2semidirect
16. #520×C127C4semidirect
75. #117×C127C2×C4semidirect
84. C2×C4⋊C4×C127C2×C4semidirect
277. #20703C127direct (N × H)
290. #1825C2×C127semidirect
291. #1825C2×C127semidirect
292. #1824C2×C127semidirect
293. #1823C2×C127semidirect
294. #1736C2×C127semidirect
295. #1736C2×C127semidirect
296. #1735C2×C127semidirect
297. C2×#340C2×C127semidirect
298. C127#20703direct (N × H)
303. #520C4×C127semidirect
362. #117C2×C4×C127semidirect
371. C2×C4⋊C4C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#520×C1272
C2×#408×C1272
C127×#23112
C127×#18252
C127×#18242
C127×#18232
C127×#17362
C127×#17352
C2×#340×C1272
#20703127