Finite Group Databasebeta

← C127×#21516 #44585189

Subgroups — C127×#21516 #44585189

Order 32512.

932 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#462×C127C211yesmaximal, characteristic
2C2×#441×C127C211yesmaximal, characteristic
3C2×C4×Q16×C127C211yesmaximal, characteristic
4C127×#2327C211yesmaximal, characteristic
5C127×#2276C211yesmaximal, characteristic
6C127×#1981C211yesmaximal, characteristic
7C127×#1949C211yesmaximal, characteristic
8C127×#1928C211yesmaximal, characteristic
9C127×#1927C211yesmaximal, characteristic
10C127×#1878C211yesmaximal, characteristic
11C127×#1878C211yesmaximal, characteristic
12C127×#1805C211yesmaximal, characteristic
13C127×#1768C211yesmaximal, characteristic
14C127×#1763C211yesmaximal, characteristic
15C4×#103×C127C211yesmaximal, characteristic
16C22×Q16×C127C2211yescharacteristic
17C22×Q16×C127C2211yescharacteristic
18C2×C4⋊Q8×C127C2211yescharacteristic
19C2×C4×Q8×C127C2211yescharacteristic
20C2×C4×Q8×C127C2211yescharacteristic
21C2×C4×Q8×C127C2211yescharacteristic
22C2×C4×Q8×C127C2211yescharacteristic
23C2×C4×Q8×C127C2211yescharacteristic
24#462×C127C418yescomplemented
25#441×C127—24no—
26C4×Q16×C127—24no—
27C2×#107×C127C2211yescharacteristic
28C2×#106×C127C2211yescharacteristic
29C2×C4⋊C8×C127C2211yescharacteristic
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×#103×C127C2211yescharacteristic
32C2×#103×C127C2211yescharacteristic
33C2×#103×C127C2211yescharacteristic
34C2×#103×C127C2211yescharacteristic
35C2×#103×C127C2211yescharacteristic
36C2×#103×C127C2211yescharacteristic
37C2×#103×C127C2211yescharacteristic
38C2×#103×C127C2211yescharacteristic
39C2×#97×C127C2211yescharacteristic
40C2×C4×C8×C127C2211yescharacteristic
41#391×C127C2211yescharacteristic
42#391×C127C2211yescharacteristic
43#387×C127—21no—
44#387×C127—21no—
45#387×C127—21no—
46#387×C127—21no—
47#382×C127C2211yescharacteristic
48C4×C4⋊C4×C127—21no—
49C4×C4⋊C4×C127—21no—
50C4×C4⋊C4×C127—21no—
51C4×C4⋊C4×C127C2211yescharacteristic
52C4×C4⋊C4×C127C2211yescharacteristic
53C4×C4⋊C4×C127C2211yescharacteristic
54#376×C127—21no—
55#376×C127C2211yescharacteristic
56#340×C127C2211yescharacteristic
57#340×C127C2211yescharacteristic
58#340×C127C2211yescharacteristic
59#340×C127C2211yescharacteristic
60#336×C127C2211yescharacteristic
61#336×C127C2211yescharacteristic
62C22×Q8×C127C2311yescharacteristic
63C22×Q8×C127C2311yescharacteristic
64C22×Q8×C127C2311yescharacteristic
65C2×Q16×C127—22no—
66C2×Q16×C127—22no—
67C2×Q16×C127—22no—
68C2×Q16×C127—22no—
69C2×Q16×C127C2×C414yes—
70C2×Q16×C127C2×C414yes—
71C22×C8×C127C2311yescharacteristic
72C22×C8×C127C2311yescharacteristic
73C22×C8×C127C2311yescharacteristic
74C22×C8×C127C2311yescharacteristic
75C4⋊Q8×C127—22no—
76C4⋊Q8×C127C2×C414yes—
77C4×Q8×C127—22no—
78C4×Q8×C127—22no—
79C4×Q8×C127—22no—
80C4×Q8×C127—22no—
81C4×Q8×C127—22no—
82C4×Q8×C127—22no—
83C4×Q8×C127—22no—
84C4×Q8×C127—22no—
85C4×Q8×C127C2×C414yes—
86C4×Q8×C127D414yes—
87C2×C4⋊C4×C127—21no—
88C2×C4⋊C4×C127—21no—
89C2×C4⋊C4×C127—21no—
90C2×C4⋊C4×C127—21no—
91C2×C4⋊C4×C127—21no—
92C2×C4⋊C4×C127—21no—
93C2×C4⋊C4×C127—21no—
94C2×C4⋊C4×C127C2311yescharacteristic
95C2×C4⋊C4×C127C2311yescharacteristic
96C2×C4⋊C4×C127C2311yescharacteristic
97C2×C4⋊C4×C127C2311yescharacteristic
98C2×C4⋊C4×C127C2311yescharacteristic
99C2×C42×C127—21no—
100C2×C42×C127—21no—
101C2×C42×C127—21no—
102C2×C42×C127—21no—
103C2×C42×C127—21no—
104C2×C42×C127—21no—
105C2×C42×C127—21no—
106C2×C42×C127—21no—
107C2×C42×C127C2311yescharacteristic
108C2×C42×C127C2311yescharacteristic
109C2×C42×C127C2311yescharacteristic
110#107×C127—22no—
111#106×C127—22no—
112C4⋊C8×C127—22no—
113C4⋊C8×C127C2×C414yes—
114#103×C127—22no—
115#103×C127—22no—
116#103×C127—22no—
117#103×C127—22no—
118#103×C127—22no—
119#103×C127—22no—
120#103×C127C2×C414yes—
121#103×C127C2×C414yes—
122#97×C127—22no—
123C4×C8×C127—22no—
124#95×C127—21no—
125#95×C127—21no—
126#95×C127—21no—
127#95×C127—21no—
128#95×C127—21no—
129#95×C127—21no—
130#95×C127—21no—
131#95×C127—21no—
132#95×C127—21no—
133#95×C127D411yescharacteristic
134#95×C127D411yescharacteristic
135#95×C127D411yescharacteristic
136#95×C127D411yescharacteristic
137C2×Q8×C127—21no—
138C2×Q8×C127—21no—
139C2×Q8×C127—21no—
140C2×Q8×C127—21no—
141C2×Q8×C127—21no—
142C2×Q8×C127—21no—
143C2×Q8×C127—21no—
144C2×Q8×C127—21no—
145C2×Q8×C127—21no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127—21no—
149C2×Q8×C127—21no—
150C2×Q8×C127C22×C412yes—
151C2×Q8×C127C22×C412yes—
152C2×Q8×C127C22×C412yes—
153C2×Q8×C127C2×D412yes—
154C2×Q8×C127#4112yes—
155C22×C4×C127—21no—
156C22×C4×C127—21no—
157C22×C4×C127—21no—
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—21no—
163C22×C4×C127C2×D411yescharacteristic
164C22×C4×C127C2×D411yescharacteristic
165C22×C4×C127C2×D411yescharacteristic
166C22×C4×C127C2×D411yescharacteristic
167C22×C4×C127C2×D411yescharacteristic
168C22×C4×C127C2×D411yescharacteristic
169C22×C4×C127C2411yescharacteristic
170Q16×C127—28no—
171Q16×C127—28no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—21no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—21no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—21no—
182C2×C8×C127C22×C412yes—
183C2×C8×C127C22×C412yes—
184C4⋊C4×C127—24no—
185C4⋊C4×C127—24no—
186C4⋊C4×C127—24no—
187C4⋊C4×C127—24no—
188C4⋊C4×C127—24no—
189C4⋊C4×C127—21no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—21no—
192C4⋊C4×C127—21no—
193C4⋊C4×C127—21no—
194C4⋊C4×C127—21no—
195C4⋊C4×C127—21no—
196C4⋊C4×C127—42no—
197C4⋊C4×C127—42no—
198C4⋊C4×C127C22×C412yes—
199C4⋊C4×C127C2×D412yes—
200C4⋊C4×C127#4112yes—
201C42×C127—24no—
202C42×C127—24no—
203C42×C127—24no—
204C42×C127—21no—
205C42×C127—21no—
206C42×C127—42no—
207C42×C127—42no—
208C42×C127—81no—
209C42×C127—81no—
210C42×C127—81no—
211C42×C127C22×C412yes—
212C42×C127C2×D412yes—
213C42×C127#4112yes—
214C42×C127#4112yes—
215C23×C127C22×D411yescharacteristic
216Q8×C127—22no—
217Q8×C127—22no—
218Q8×C127—22no—
219Q8×C127—22no—
220Q8×C127—22no—
221Q8×C127—22no—
222Q8×C127—22no—
223Q8×C127—41no—
224Q8×C127—41no—
225Q8×C127—41no—
226Q8×C127—41no—
227Q8×C127C4×D414yes—
228C2×C4×C127—22no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—21no—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—21no—
235C2×C4×C127—21no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—21no—
239C2×C4×C127—22no—
240C2×C4×C127—22no—
241C2×C4×C127—22no—
242C2×C4×C127—22no—
243C2×C4×C127—21no—
244C2×C4×C127—21no—
245C2×C4×C127—22no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—21no—
250C2×C4×C127—41no—
251C2×C4×C127—41no—
252C2×C4×C127—41no—
253C2×C4×C127—41no—
254C2×C4×C127—41no—
255C2×C4×C127—41no—
256C2×C4×C127—41no—
257C2×C4×C127—41no—
258C2×C4×C127—41no—
259C2×C4×C127—41no—
260C2×C4×C127—41no—
261C2×C4×C127—41no—
262C2×C4×C127—41no—
263C2×C4×C127—41no—
264C2×C4×C127—41no—
265C2×C4×C127—41no—
266C2×C4×C127C4×D412yes—
267C2×C4×C127C4×D412yes—
268C2×C4×C127#12112yes—
269C2×C4×C127#12112yes—
270C2×C4×C127C23×C411yescharacteristic
271C2×C4×C127C22×D411yescharacteristic
272C2×C4×C127C2×#4111yescharacteristic
273C2×C4×C127C2×#4111yescharacteristic
274C2×C4×C127C2×#4111yescharacteristic
275C2×C4×C127C2×#4111yescharacteristic
276C8×C127—22no—
277C8×C127—22no—
278C8×C127—41no—
279C8×C127—41no—
280C22×C127C2×C4×D411yescharacteristic
281C22×C127C2×#12111yescharacteristic
282C22×C127#52511yescharacteristic
283C22×C127#57711yescharacteristic
284C22×C127#57811yescharacteristic
285C22×C127#57811yescharacteristic
286C22×C127#57811yescharacteristic
287C4×C127—22no—
288C4×C127—22no—
289C4×C127—22no—
290C4×C127—22no—
291C4×C127—24no—
292C4×C127—41no—
293C4×C127—42no—
294C4×C127—41no—
295C4×C127—42no—
296C4×C127—42no—
297C4×C127—42no—
298C4×C127—42no—
299C4×C127—81no—
300C4×C127—81no—
301C4×C127C2×C4×D411yescharacteristic
302C4×C127C4×#4111yescharacteristic
303C4×C127#52911yescharacteristic
304C4×C127#53211yescharacteristic
305#21516C12711yesmaximal, characteristic, direct product factor, Sylow
306C2×C127C4×#12111yescharacteristic
307C2×C127#294711yescharacteristic
308C2×C127#295011yescharacteristic
309C2×C127#304411yescharacteristic
310C2×C127#304611yescharacteristic
311C2×C127#312011yescharacteristic
312C2×C127#312711yescharacteristic
313C2×#462C2×C12711yescharacteristic
314C2×#441C2×C12711yescharacteristic
315C2×C4×Q16C2×C12711yescharacteristic
316#2327C2×C12711yescharacteristic
317#2276C2×C12711yescharacteristic
318#1981C2×C12711yescharacteristic
319#1949C2×C12711yescharacteristic
320#1928C2×C12711yescharacteristic
321#1927C2×C12711yescharacteristic
322#1878C2×C12711yescharacteristic
323#1878C2×C12711yescharacteristic
324#1805C2×C12711yescharacteristic
325#1768C2×C12711yescharacteristic
326#1763C2×C12711yescharacteristic
327C4×#103C2×C12711yescharacteristic
328C127#2151611yescharacteristic, direct product factor, Sylow
329C22×Q16C22×C12711yescharacteristic
330C22×Q16C22×C12711yescharacteristic
331C2×C4⋊Q8C22×C12711yescharacteristic
332C2×C4×Q8C22×C12711yescharacteristic
333C2×C4×Q8C22×C12711yescharacteristic
334C2×C4×Q8C22×C12711yescharacteristic
335C2×C4×Q8C22×C12711yescharacteristic
336C2×C4×Q8C22×C12711yescharacteristic
337#462C4×C12718yescomplemented
338#441—24no—
339C4×Q16—24no—
340C2×#107C22×C12711yescharacteristic
341C2×#106C22×C12711yescharacteristic
342C2×C4⋊C8C22×C12711yescharacteristic
343C2×C4⋊C8C22×C12711yescharacteristic
344C2×#103C22×C12711yescharacteristic
345C2×#103C22×C12711yescharacteristic
346C2×#103C22×C12711yescharacteristic
347C2×#103C22×C12711yescharacteristic
348C2×#103C22×C12711yescharacteristic
349C2×#103C22×C12711yescharacteristic
350C2×#103C22×C12711yescharacteristic
351C2×#103C22×C12711yescharacteristic
352C2×#97C22×C12711yescharacteristic
353C2×C4×C8C22×C12711yescharacteristic
354#391C22×C12711yescharacteristic
355#391C22×C12711yescharacteristic
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#382C22×C12711yescharacteristic
361C4×C4⋊C4—21no—
362C4×C4⋊C4—21no—
363C4×C4⋊C4—21no—
364C4×C4⋊C4C22×C12711yescharacteristic
365C4×C4⋊C4C22×C12711yescharacteristic
366C4×C4⋊C4C22×C12711yescharacteristic
367#376—21no—
368#376C22×C12711yescharacteristic
369#340C22×C12711yescharacteristic
370#340C22×C12711yescharacteristic
371#340C22×C12711yescharacteristic
372#340C22×C12711yescharacteristic
373#336C22×C12711yescharacteristic
374#336C22×C12711yescharacteristic
375C22×Q8C23×C12711yescharacteristic
376C22×Q8C23×C12711yescharacteristic
377C22×Q8C23×C12711yescharacteristic
378C2×Q16—22no—
379C2×Q16—22no—
380C2×Q16—22no—
381C2×Q16—22no—
382C2×Q16C2×C4×C12714yes—
383C2×Q16C2×C4×C12714yes—
384C22×C8C23×C12711yescharacteristic
385C22×C8C23×C12711yescharacteristic
386C22×C8C23×C12711yescharacteristic
387C22×C8C23×C12711yescharacteristic
388C4⋊Q8—22no—
389C4⋊Q8C2×C4×C12714yes—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8C2×C4×C12714yes—
399C4×Q8D4×C12714yes—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4C23×C12711yescharacteristic
408C2×C4⋊C4C23×C12711yescharacteristic
409C2×C4⋊C4C23×C12711yescharacteristic
410C2×C4⋊C4C23×C12711yescharacteristic
411C2×C4⋊C4C23×C12711yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42C23×C12711yescharacteristic
421C2×C42C23×C12711yescharacteristic
422C2×C42C23×C12711yescharacteristic
423#107—22no—
424#106—22no—
425C4⋊C8—22no—
426C4⋊C8C2×C4×C12714yes—
427#103—22no—
428#103—22no—
429#103—22no—
430#103—22no—
431#103—22no—
432#103—22no—
433#103C2×C4×C12714yes—
434#103C2×C4×C12714yes—
435#97—22no—
436C4×C8—22no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95D4×C12711yescharacteristic
447#95D4×C12711yescharacteristic
448#95D4×C12711yescharacteristic
449#95D4×C12711yescharacteristic
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8C22×C4×C12712yes—
464C2×Q8C22×C4×C12712yes—
465C2×Q8C22×C4×C12712yes—
466C2×Q8C2×D4×C12712yes—
467C2×Q8#41×C12712yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4C2×D4×C12711yescharacteristic
477C22×C4C2×D4×C12711yescharacteristic
478C22×C4C2×D4×C12711yescharacteristic
479C22×C4C2×D4×C12711yescharacteristic
480C22×C4C2×D4×C12711yescharacteristic
481C22×C4C2×D4×C12711yescharacteristic
482C22×C4C24×C12711yescharacteristic
483Q16—28no—
484Q16—28no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8C22×C4×C12712yes—
496C2×C8C22×C4×C12712yes—
497C4⋊C4—24no—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—24no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4C22×C4×C12712yes—
512C4⋊C4C2×D4×C12712yes—
513C4⋊C4#41×C12712yes—
514C42—24no—
515C42—24no—
516C42—24no—
517C42—21no—
518C42—21no—
519C42—42no—
520C42—42no—
521C42—81no—
522C42—81no—
523C42—81no—
524C42C22×C4×C12712yes—
525C42C2×D4×C12712yes—
526C42#41×C12712yes—
527C42#41×C12712yes—
528C23C22×D4×C12711yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540Q8C4×D4×C12714yes—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4C4×D4×C12712yes—
580C2×C4C4×D4×C12712yes—
581C2×C4#121×C12712yes—
582C2×C4#121×C12712yes—
583C2×C4C23×C4×C12711yescharacteristic
584C2×C4C22×D4×C12711yescharacteristic
585C2×C4C2×#41×C12711yescharacteristic
586C2×C4C2×#41×C12711yescharacteristic
587C2×C4C2×#41×C12711yescharacteristic
588C2×C4C2×#41×C12711yescharacteristic
589C8—22no—
590C8—22no—
591C8—41no—
592C8—41no—
593C22C2×C4×D4×C12711yescharacteristic
594C22C2×#121×C12711yescharacteristic
595C22#525×C12711yescharacteristic
596C22#577×C12711yescharacteristic
597C22#578×C12711yescharacteristic
598C22#578×C12711yescharacteristic
599C22#578×C12711yescharacteristic
600C4—22no—
601C4—22no—
602C4—22no—
603C4—22no—
604C4—24no—
605C4—41no—
606C4—42no—
607C4—41no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—42no—
612C4—81no—
613C4—81no—
614C4C2×C4×D4×C12711yescharacteristic
615C4C4×#41×C12711yescharacteristic
616C4#529×C12711yescharacteristic
617C4#532×C12711yescharacteristic
618C2C4×#121×C12711yescharacteristic
619C2C127×#294711yescharacteristic
620C2C127×#295011yescharacteristic
621C2C127×#304411yescharacteristic
622C2C127×#304611yescharacteristic
623C2C127×#312011yescharacteristic
624C2C127×#312711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ #376×C127 ◁ G

Complements

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

NH ≅ G/Ntype
24. #462×C127C4semidirect
305. #21516C127direct (N × H)
328. C127#21516direct (N × H)
337. #462C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#462×C1272
C2×#441×C1272
C2×C4×Q16×C1272
C127×#23272
C127×#22762
C127×#19812
C127×#19492
C127×#19282
C127×#19272
C127×#18782
C127×#18052
C127×#17682
C127×#17632
C4×#103×C1272
#21516127