Finite Group Databasebeta

← C127×#17376 #44581049

Subgroups — C127×#17376 #44581049

Order 32512.

1020 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C127C211yesmaximal, characteristic
2C127×#2920C211yesmaximal, characteristic, complemented
3C2×#431×C127C211yesmaximal, characteristic, complemented
4C127×#1470C212yesmaximal, complemented
5C127×#1469C212yesmaximal, complemented
6C127×#1468C214yesmaximal, complemented
7C127×#1458C214yesmaximal, complemented
8#529×C127—21no—
9#529×C127—21no—
10#529×C127—21no—
11#529×C127—21no—
12#529×C127—21no—
13#529×C127—21no—
14#529×C127—21no—
15#529×C127—21no—
16C2×#126×C127C412yes—
17C2×#125×C127C2211yescharacteristic
18C2×#124×C127C2211yescharacteristic
19C2×#123×C127C2212yes—
20C2×C22⋊Q8×C127C411yescharacteristic
21C2×#121×C127C411yescharacteristic
22C2×C4×Q8×C127C411yescharacteristic
23C2×C4×D4×C127C412yes—
24C2×C4×D4×C127C411yescharacteristic
25C2×#117×C127C2212yes—
26C22×C42×C127C2211yescharacteristic
27#432×C127—21no—
28#432×C127C2212yes—
29#431×C127—21no—
30#431×C127—21no—
31#431×C127—21no—
32#431×C127C2212yes—
33#431×C127C2212yes—
34#431×C127C2212yes—
35#423×C127—21no—
36C2×C4⋊C8×C127—21no—
37#407×C127C2212yes—
38C2×C22⋊C8×C127C2212yes—
39C4×M16×C127—21no—
40C2×C4×C8×C127—21no—
41#324×C127C2218yes—
42#323×C127C2218yes—
43C22×Q8×C127C2×C411yescharacteristic
44C22×D4×C127C2×C412yes—
45C22×D4×C127C2×C411yescharacteristic
46C23×C4×C127C2×C412yes—
47C23×C4×C127C2×C411yescharacteristic
48C23×C4×C127C2×C411yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C2×M16×C127—22no—
51C22×C8×C127—22no—
52#126×C127—22no—
53#126×C127—22no—
54#126×C127—22no—
55#126×C127—22no—
56#125×C127—21no—
57#125×C127—21no—
58#125×C127—21no—
59#125×C127—21no—
60#124×C127—21no—
61#124×C127—21no—
62#124×C127—21no—
63#124×C127—21no—
64#123×C127—22no—
65#123×C127—22no—
66#123×C127—22no—
67#123×C127—22no—
68C22⋊Q8×C127—21no—
69C22⋊Q8×C127—21no—
70C22⋊Q8×C127—21no—
71C22⋊Q8×C127—21no—
72#121×C127—21no—
73#121×C127—21no—
74#121×C127—21no—
75#121×C127—21no—
76C4×Q8×C127—21no—
77C4×Q8×C127—21no—
78C4×Q8×C127—21no—
79C4×Q8×C127—21no—
80C4×D4×C127—22no—
81C4×D4×C127—22no—
82C4×D4×C127—22no—
83C4×D4×C127—22no—
84C4×D4×C127—21no—
85C4×D4×C127—21no—
86C4×D4×C127—21no—
87C4×D4×C127—21no—
88#117×C127—22no—
89#117×C127—22no—
90#117×C127—22no—
91#117×C127—22no—
92C2×C4⋊C4×C127C2×C412yes—
93C2×C4⋊C4×C127C2×C411yescharacteristic
94C2×C4⋊C4×C127C2×C412yes—
95C2×C4⋊C4×C127C2×C411yescharacteristic
96C2×C4⋊C4×C127C2×C412yes—
97C2×C4⋊C4×C127C2312yes—
98C2×C22⋊C4×C127C2×C412yes—
99C2×C22⋊C4×C127C2×C412yes—
100C2×C22⋊C4×C127C2×C412yes—
101C2×C22⋊C4×C127C2×C412yes—
102C2×C22⋊C4×C127C2312yes—
103C2×C42×C127C2×C412yes—
104C2×C42×C127C2×C411yescharacteristic
105C2×C42×C127C2×C411yescharacteristic
106C2×C42×C127D411yescharacteristic
107C2×C42×C127D411yescharacteristic
108C2×C42×C127D411yescharacteristic
109C2×C42×C127D411yescharacteristic
110C2×C42×C127D411yescharacteristic
111C2×C42×C127D411yescharacteristic
112C2×C42×C127D411yescharacteristic
113C2×C42×C127D411yescharacteristic
114C2×C42×C127C2311yescharacteristic
115C2×C42×C127C2311yescharacteristic
116C4⋊C8×C127—22no—
117C4⋊C8×C127—22no—
118C4⋊C8×C127—22no—
119C4⋊C8×C127—22no—
120C22⋊C8×C127—22no—
121C22⋊C8×C127—22no—
122C22⋊C8×C127C2314yes—
123C22⋊C8×C127C2314yes—
124#97×C127—22no—
125C4×C8×C127—22no—
126C4×C8×C127—22no—
127C4×C8×C127—22no—
128C24×C127C22×C411yescharacteristic
129C24×C127C22×C412yes—
130C2×Q8×C127—21no—
131C2×Q8×C127—21no—
132C2×Q8×C127—42no—
133C2×D4×C127—22no—
134C2×D4×C127—22no—
135C2×D4×C127—21no—
136C2×D4×C127—21no—
137C2×D4×C127—42no—
138C2×D4×C127—44no—
139C22×C4×C127—24no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—28no—
143C22×C4×C127—42no—
144C22×C4×C127—42no—
145C22×C4×C127C22⋊C411yescharacteristic
146C22×C4×C127C22⋊C411yescharacteristic
147C22×C4×C127C22⋊C411yescharacteristic
148C22×C4×C127C22⋊C411yescharacteristic
149C22×C4×C127C22⋊C411yescharacteristic
150C22×C4×C127C22⋊C411yescharacteristic
151C22×C4×C127C22⋊C411yescharacteristic
152C22×C4×C127C22⋊C411yescharacteristic
153C22×C4×C127C22×C412yes—
154C22×C4×C127C22×C411yescharacteristic
155C22×C4×C127C22×C411yescharacteristic
156C22×C4×C127C22×C412yes—
157C22×C4×C127C22×C412yes—
158C22×C4×C127C22×C411yescharacteristic
159C22×C4×C127C22×C411yescharacteristic
160C22×C4×C127C22×C411yescharacteristic
161C22×C4×C127C2×D411yescharacteristic
162C22×C4×C127C2×D411yescharacteristic
163C22×C4×C127C2×D411yescharacteristic
164C22×C4×C127C2×D411yescharacteristic
165C22×C4×C127C2411yescharacteristic
166M16×C127—44no—
167C2×C8×C127—24no—
168C2×C8×C127—24no—
169C2×C8×C127—44no—
170C4⋊C4×C127—22no—
171C4⋊C4×C127—22no—
172C4⋊C4×C127—21no—
173C4⋊C4×C127—21no—
174C4⋊C4×C127—22no—
175C4⋊C4×C127—22no—
176C4⋊C4×C127—21no—
177C4⋊C4×C127—21no—
178C4⋊C4×C127—22no—
179C4⋊C4×C127—22no—
180C4⋊C4×C127—22no—
181C4⋊C4×C127—22no—
182C22⋊C4×C127—22no—
183C22⋊C4×C127—22no—
184C22⋊C4×C127—22no—
185C22⋊C4×C127—22no—
186C22⋊C4×C127—22no—
187C22⋊C4×C127—22no—
188C22⋊C4×C127—22no—
189C22⋊C4×C127—22no—
190C22⋊C4×C127—22no—
191C22⋊C4×C127—22no—
192C42×C127—22no—
193C42×C127—22no—
194C42×C127C22⋊C411yescharacteristic
195C42×C127C22⋊C411yescharacteristic
196C42×C127C22⋊C411yescharacteristic
197C42×C127C22⋊C411yescharacteristic
198C42×C127C22⋊C411yescharacteristic
199C42×C127C22⋊C411yescharacteristic
200C42×C127C22⋊C411yescharacteristic
201C42×C127C22⋊C411yescharacteristic
202C42×C127C2×D411yescharacteristic
203C42×C127C2×D411yescharacteristic
204C42×C127C2×D411yescharacteristic
205C42×C127C2×D411yescharacteristic
206C42×C127C2×D411yescharacteristic
207C42×C127C2×D411yescharacteristic
208C42×C127C2×D411yescharacteristic
209C42×C127C2×D411yescharacteristic
210C23×C127—22no—
211C23×C127—22no—
212C23×C127—22no—
213C23×C127—24no—
214C23×C127—41no—
215C23×C127—42no—
216C23×C127—42no—
217C23×C127C2×C22⋊C411yescharacteristic
218C23×C127C2×C22⋊C411yescharacteristic
219C23×C127C23×C411yescharacteristic
220Q8×C127—42no—
221Q8×C127—42no—
222D4×C127—42no—
223D4×C127—44no—
224D4×C127—44no—
225D4×C127—42no—
226C2×C4×C127—22no—
227C2×C4×C127—22no—
228C2×C4×C127—22no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—22no—
232C2×C4×C127—22no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—22no—
236C2×C4×C127—22no—
237C2×C4×C127—22no—
238C2×C4×C127—22no—
239C2×C4×C127—24no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—41no—
243C2×C4×C127—41no—
244C2×C4×C127—41no—
245C2×C4×C127—41no—
246C2×C4×C127—41no—
247C2×C4×C127—44no—
248C2×C4×C127—44no—
249C2×C4×C127—42no—
250C2×C4×C127—42no—
251C2×C4×C127C2×C22⋊C411yescharacteristic
252C2×C4×C127C2×C22⋊C411yescharacteristic
253C2×C4×C127C2×C22⋊C411yescharacteristic
254C2×C4×C127C2×C22⋊C411yescharacteristic
255C2×C4×C127C2×C22⋊C411yescharacteristic
256C2×C4×C127C2×C22⋊C411yescharacteristic
257C2×C4×C127C2×C22⋊C411yescharacteristic
258C2×C4×C127C2×C22⋊C411yescharacteristic
259C2×C4×C127C2×C22⋊C411yescharacteristic
260C2×C4×C127C2×C22⋊C411yescharacteristic
261C2×C4×C127#13114yes—
262C2×C4×C127C22×D411yescharacteristic
263C2×C4×C127C22×D411yescharacteristic
264C8×C127—44no—
265C8×C127—44no—
266C22×C127—21no—
267C22×C127—21no—
268C22×C127—21no—
269C22×C127—21no—
270C22×C127—21no—
271C22×C127—21no—
272C22×C127—21no—
273C22×C127—44no—
274C22×C127—42no—
275C22×C127—42no—
276C22×C127—42no—
277C22×C127—84no—
278C22×C127#41012yes—
279C22×C127C22×C22⋊C411yescharacteristic
280C22×C127C2×#13112yes—
281C4×C127—21no—
282C4×C127—21no—
283C4×C127—21no—
284C4×C127—21no—
285C4×C127—21no—
286C4×C127—21no—
287C4×C127—21no—
288C4×C127—21no—
289C4×C127—21no—
290C4×C127—42no—
291C4×C127—42no—
292C4×C127—42no—
293C4×C127#40812yes—
294C4×C127#40812yes—
295C4×C127#41312yes—
296#17376C12711yesmaximal, characteristic, direct product factor, Sylow
297C2×C127—22no—
298C2×C127—22no—
299C2×C127—41no—
300C2×C127—82no—
301C2×C127C2×#40811yescharacteristic
302C2×C127C2×#41011yescharacteristic
303C2×C127C2×#41311yescharacteristic
304C2×#529C2×C12711yescharacteristic
305#2920C2×C12711yescharacteristic, complemented
306C2×#431C2×C12711yescharacteristic, complemented
307#1470C2×C12712yescomplemented
308#1469C2×C12712yescomplemented
309#1468C2×C12714yescomplemented
310#1458C2×C12714yescomplemented
311C127#1737611yescharacteristic, direct product factor, Sylow
312#529—21no—
313#529—21no—
314#529—21no—
315#529—21no—
316#529—21no—
317#529—21no—
318#529—21no—
319#529—21no—
320C2×#126C4×C12712yes—
321C2×#125C22×C12711yescharacteristic
322C2×#124C22×C12711yescharacteristic
323C2×#123C22×C12712yes—
324C2×C22⋊Q8C4×C12711yescharacteristic
325C2×#121C4×C12711yescharacteristic
326C2×C4×Q8C4×C12711yescharacteristic
327C2×C4×D4C4×C12712yes—
328C2×C4×D4C4×C12711yescharacteristic
329C2×#117C22×C12712yes—
330C22×C42C22×C12711yescharacteristic
331#432—21no—
332#432C22×C12712yes—
333#431—21no—
334#431—21no—
335#431—21no—
336#431C22×C12712yes—
337#431C22×C12712yes—
338#431C22×C12712yes—
339#423—21no—
340C2×C4⋊C8—21no—
341#407C22×C12712yes—
342C2×C22⋊C8C22×C12712yes—
343C4×M16—21no—
344C2×C4×C8—21no—
345#324C22×C12718yes—
346#323C22×C12718yes—
347C22×Q8C2×C4×C12711yescharacteristic
348C22×D4C2×C4×C12712yes—
349C22×D4C2×C4×C12711yescharacteristic
350C23×C4C2×C4×C12712yes—
351C23×C4C2×C4×C12711yescharacteristic
352C23×C4C2×C4×C12711yescharacteristic
353C23×C4C23×C12711yescharacteristic
354C2×M16—22no—
355C22×C8—22no—
356#126—22no—
357#126—22no—
358#126—22no—
359#126—22no—
360#125—21no—
361#125—21no—
362#125—21no—
363#125—21no—
364#124—21no—
365#124—21no—
366#124—21no—
367#124—21no—
368#123—22no—
369#123—22no—
370#123—22no—
371#123—22no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—21no—
377#121—21no—
378#121—21no—
379#121—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392#117—22no—
393#117—22no—
394#117—22no—
395#117—22no—
396C2×C4⋊C4C2×C4×C12712yes—
397C2×C4⋊C4C2×C4×C12711yescharacteristic
398C2×C4⋊C4C2×C4×C12712yes—
399C2×C4⋊C4C2×C4×C12711yescharacteristic
400C2×C4⋊C4C2×C4×C12712yes—
401C2×C4⋊C4C23×C12712yes—
402C2×C22⋊C4C2×C4×C12712yes—
403C2×C22⋊C4C2×C4×C12712yes—
404C2×C22⋊C4C2×C4×C12712yes—
405C2×C22⋊C4C2×C4×C12712yes—
406C2×C22⋊C4C23×C12712yes—
407C2×C42C2×C4×C12712yes—
408C2×C42C2×C4×C12711yescharacteristic
409C2×C42C2×C4×C12711yescharacteristic
410C2×C42D4×C12711yescharacteristic
411C2×C42D4×C12711yescharacteristic
412C2×C42D4×C12711yescharacteristic
413C2×C42D4×C12711yescharacteristic
414C2×C42D4×C12711yescharacteristic
415C2×C42D4×C12711yescharacteristic
416C2×C42D4×C12711yescharacteristic
417C2×C42D4×C12711yescharacteristic
418C2×C42C23×C12711yescharacteristic
419C2×C42C23×C12711yescharacteristic
420C4⋊C8—22no—
421C4⋊C8—22no—
422C4⋊C8—22no—
423C4⋊C8—22no—
424C22⋊C8—22no—
425C22⋊C8—22no—
426C22⋊C8C23×C12714yes—
427C22⋊C8C23×C12714yes—
428#97—22no—
429C4×C8—22no—
430C4×C8—22no—
431C4×C8—22no—
432C24C22×C4×C12711yescharacteristic
433C24C22×C4×C12712yes—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—42no—
442C2×D4—44no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—28no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4C22⋊C4×C12711yescharacteristic
450C22×C4C22⋊C4×C12711yescharacteristic
451C22×C4C22⋊C4×C12711yescharacteristic
452C22×C4C22⋊C4×C12711yescharacteristic
453C22×C4C22⋊C4×C12711yescharacteristic
454C22×C4C22⋊C4×C12711yescharacteristic
455C22×C4C22⋊C4×C12711yescharacteristic
456C22×C4C22⋊C4×C12711yescharacteristic
457C22×C4C22×C4×C12712yes—
458C22×C4C22×C4×C12711yescharacteristic
459C22×C4C22×C4×C12711yescharacteristic
460C22×C4C22×C4×C12712yes—
461C22×C4C22×C4×C12712yes—
462C22×C4C22×C4×C12711yescharacteristic
463C22×C4C22×C4×C12711yescharacteristic
464C22×C4C22×C4×C12711yescharacteristic
465C22×C4C2×D4×C12711yescharacteristic
466C22×C4C2×D4×C12711yescharacteristic
467C22×C4C2×D4×C12711yescharacteristic
468C22×C4C2×D4×C12711yescharacteristic
469C22×C4C24×C12711yescharacteristic
470M16—44no—
471C2×C8—24no—
472C2×C8—24no—
473C2×C8—44no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C42—22no—
497C42—22no—
498C42C22⋊C4×C12711yescharacteristic
499C42C22⋊C4×C12711yescharacteristic
500C42C22⋊C4×C12711yescharacteristic
501C42C22⋊C4×C12711yescharacteristic
502C42C22⋊C4×C12711yescharacteristic
503C42C22⋊C4×C12711yescharacteristic
504C42C22⋊C4×C12711yescharacteristic
505C42C22⋊C4×C12711yescharacteristic
506C42C2×D4×C12711yescharacteristic
507C42C2×D4×C12711yescharacteristic
508C42C2×D4×C12711yescharacteristic
509C42C2×D4×C12711yescharacteristic
510C42C2×D4×C12711yescharacteristic
511C42C2×D4×C12711yescharacteristic
512C42C2×D4×C12711yescharacteristic
513C42C2×D4×C12711yescharacteristic
514C23—22no—
515C23—22no—
516C23—22no—
517C23—24no—
518C23—41no—
519C23—42no—
520C23—42no—
521C23C2×C22⋊C4×C12711yescharacteristic
522C23C2×C22⋊C4×C12711yescharacteristic
523C23C23×C4×C12711yescharacteristic
524Q8—42no—
525Q8—42no—
526D4—42no—
527D4—44no—
528D4—44no—
529D4—42no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—44no—
552C2×C4—44no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4C2×C22⋊C4×C12711yescharacteristic
556C2×C4C2×C22⋊C4×C12711yescharacteristic
557C2×C4C2×C22⋊C4×C12711yescharacteristic
558C2×C4C2×C22⋊C4×C12711yescharacteristic
559C2×C4C2×C22⋊C4×C12711yescharacteristic
560C2×C4C2×C22⋊C4×C12711yescharacteristic
561C2×C4C2×C22⋊C4×C12711yescharacteristic
562C2×C4C2×C22⋊C4×C12711yescharacteristic
563C2×C4C2×C22⋊C4×C12711yescharacteristic
564C2×C4C2×C22⋊C4×C12711yescharacteristic
565C2×C4#131×C12714yes—
566C2×C4C22×D4×C12711yescharacteristic
567C2×C4C22×D4×C12711yescharacteristic
568C8—44no—
569C8—44no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—44no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—84no—
582C22#410×C12712yes—
583C22C22×C22⋊C4×C12711yescharacteristic
584C22C2×#131×C12712yes—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—42no—
595C4—42no—
596C4—42no—
597C4#408×C12712yes—
598C4#408×C12712yes—
599C4#413×C12712yes—
600C2—22no—
601C2—22no—
602C2—41no—
603C2—82no—
604C2C2×#408×C12711yescharacteristic
605C2C2×#410×C12711yescharacteristic
606C2C2×#413×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC2×#121×C127C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2920C2semidirect
3. C2×#431×C127C2semidirect
4. C127×#1470C2semidirect
5. C127×#1469C2semidirect
6. C127×#1468C2semidirect
7. C127×#1458C2semidirect
296. #17376C127direct (N × H)
305. #2920C2×C127semidirect
306. C2×#431C2×C127semidirect
307. #1470C2×C127semidirect
308. #1469C2×C127semidirect
309. #1468C2×C127semidirect
310. #1458C2×C127semidirect
311. C127#17376direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#529×C1272
C127×#29202
C2×#431×C1272
C127×#14702
C127×#14692
C127×#14682
C127×#14582
#17376127