Finite Group Databasebeta

← C127×#8418 #44572091

Subgroups — C127×#8418 #44572091

Order 32512.

772 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3520C211yesmaximal, characteristic
2C127×#1986C211yesmaximal, characteristic, complemented
3C127×#1762C211yesmaximal, characteristic, complemented
4C127×#1531C211yesmaximal, characteristic, complemented
5C127×#1524C211yesmaximal, characteristic, complemented
6C127×#1509C211yesmaximal, characteristic, complemented
7C127×#1490C211yesmaximal, characteristic, complemented
8#556×C127C411yescharacteristic, complemented
9#554×C127—21no—
10#552×C127—21no—
11#551×C127—22no—
12D4×Q8×C127C411yescharacteristic, complemented
13#548×C127—21no—
14#547×C127C411yescharacteristic, complemented
15#547×C127C411yescharacteristic, complemented
16#546×C127—21no—
17#542×C127—21no—
18#539×C127—22no—
19#533×C127C2211yescharacteristic
20#529×C127C2211yescharacteristic
21#525×C127—21no—
22C2×C22⋊Q8×C127—21no—
23#520×C127—21no—
24C2×C4×D4×C127C2211yescharacteristic
25#432×C127C2211yescharacteristic
26C2×#102×C127—21no—
27C4×M16×C127C2211yescharacteristic
28C2×#97×C127C2211yescharacteristic
29C4×C4⋊C4×C127C2211yescharacteristic
30#340×C127—21no—
31#339×C127—22no—
32#330×C127—21no—
33#330×C127—22no—
34#329×C127—21no—
35#328×C127—21no—
36#327×C127—21no—
37D4⋊C8×C127—21no—
38D4⋊C8×C127—21no—
39C2×#41×C127—21no—
40C2×#41×C127—21no—
41C22×Q8×C127—21no—
42C22×D4×C127D411yescharacteristic
43C23×C4×C127—21no—
44C2×M16×C127—21no—
45C22×C8×C127—21no—
46C4⋊Q8×C127—21no—
47C4⋊Q8×C127C2×C411yescharacteristic
48C4⋊Q8×C127C2×C411yescharacteristic
49#126×C127—22no—
50#126×C127—22no—
51#126×C127—21no—
52#125×C127—22no—
53#125×C127D411yescharacteristic
54#125×C127D412yes—
55#124×C127—22no—
56#124×C127—21no—
57#124×C127D411yescharacteristic
58#123×C127—22no—
59#123×C127—22no—
60#123×C127—21no—
61#123×C127—22no—
62#123×C127—22no—
63C22⋊Q8×C127—22no—
64C22⋊Q8×C127—22no—
65C22⋊Q8×C127—22no—
66C22⋊Q8×C127—21no—
67C22⋊Q8×C127—21no—
68C22⋊Q8×C127—21no—
69C22⋊Q8×C127—21no—
70C22⋊Q8×C127—21no—
71C22⋊Q8×C127—22no—
72C22⋊Q8×C127—21no—
73C22⋊Q8×C127D411yescharacteristic
74#121×C127—22no—
75#121×C127—21no—
76#121×C127—21no—
77#121×C127D411yescharacteristic
78#120×C127—22no—
79C4×Q8×C127—21no—
80C4×Q8×C127—21no—
81C4×Q8×C127—21no—
82C4×Q8×C127C2×C411yescharacteristic
83C4×D4×C127—22no—
84C4×D4×C127—22no—
85C4×D4×C127—22no—
86C4×D4×C127—21no—
87C4×D4×C127—21no—
88C4×D4×C127—21no—
89C4×D4×C127—21no—
90C4×D4×C127C2×C411yescharacteristic
91C4×D4×C127C2×C411yescharacteristic
92C4×D4×C127C2×C411yescharacteristic
93C4×D4×C127D411yescharacteristic
94C4×D4×C127D411yescharacteristic
95#117×C127—22no—
96#117×C127—21no—
97#117×C127—21no—
98#117×C127D412yes—
99C2×C4⋊C4×C127—22no—
100C2×C4⋊C4×C127—21no—
101C2×C4⋊C4×C127—21no—
102C2×C4⋊C4×C127—21no—
103C2×C4⋊C4×C127D411yescharacteristic
104C2×C22⋊C4×C127—22no—
105C2×C22⋊C4×C127—21no—
106C2×C42×C127—21no—
107C2×C42×C127C2311yescharacteristic
108C4⋊C8×C127—21no—
109#102×C127—24no—
110C22⋊C8×C127—21no—
111#97×C127—21no—
112#97×C127—21no—
113#97×C127—21no—
114#97×C127—21no—
115C4×C8×C127—21no—
116#95×C127—21no—
117C24×C127—21no—
118#41×C127—42no—
119#41×C127—42no—
120#41×C127—82no—
121C2×Q8×C127—22no—
122C2×Q8×C127—21no—
123C2×Q8×C127—21no—
124C2×Q8×C127—82no—
125C2×Q8×C127C22⋊C411yescharacteristic
126C2×D4×C127—22no—
127C2×D4×C127—22no—
128C2×D4×C127—21no—
129C2×D4×C127—22no—
130C2×D4×C127—21no—
131C2×D4×C127—41no—
132C2×D4×C127C22⋊C411yescharacteristic
133C2×D4×C127C22⋊C411yescharacteristic
134C2×D4×C127C22⋊C411yescharacteristic
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—21no—
141C22×C4×C127—21no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—41no—
145C22×C4×C127—82no—
146C22×C4×C127C2×D411yescharacteristic
147C22×C4×C127C2×D411yescharacteristic
148C22×C4×C127C2×D411yescharacteristic
149M16×C127—22no—
150M16×C127—41no—
151C2×C8×C127—22no—
152C2×C8×C127—41no—
153C2×C8×C127—41no—
154C2×C8×C127—41no—
155C2×C8×C127—41no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127—22no—
159C4⋊C4×C127—22no—
160C4⋊C4×C127—21no—
161C4⋊C4×C127—21no—
162C4⋊C4×C127—21no—
163C4⋊C4×C127—21no—
164C4⋊C4×C127—22no—
165C4⋊C4×C127—21no—
166C4⋊C4×C127—21no—
167C4⋊C4×C127—21no—
168C4⋊C4×C127—22no—
169C4⋊C4×C127—22no—
170C4⋊C4×C127—41no—
171C4⋊C4×C127C22⋊C411yescharacteristic
172C4⋊C4×C127C22⋊C411yescharacteristic
173C4⋊C4×C127C22⋊C411yescharacteristic
174C4⋊C4×C127C22⋊C411yescharacteristic
175C4⋊C4×C127C22⋊C412yes—
176C4⋊C4×C127C22⋊C412yes—
177C22⋊C4×C127—22no—
178C22⋊C4×C127—22no—
179C22⋊C4×C127—22no—
180C22⋊C4×C127—22no—
181C22⋊C4×C127—22no—
182C22⋊C4×C127—21no—
183C22⋊C4×C127—22no—
184C22⋊C4×C127—21no—
185C22⋊C4×C127—21no—
186C22⋊C4×C127—21no—
187C22⋊C4×C127—21no—
188C22⋊C4×C127—21no—
189C22⋊C4×C127—21no—
190C22⋊C4×C127—21no—
191C22⋊C4×C127—21no—
192C42×C127—22no—
193C42×C127—21no—
194C42×C127—22no—
195C42×C127—42no—
196C42×C127C22×C411yescharacteristic
197C42×C127C2×D411yescharacteristic
198C42×C127C2×D411yescharacteristic
199C42×C127C2×D411yescharacteristic
200C23×C127—21no—
201C23×C127—21no—
202C23×C127—21no—
203C23×C127—42no—
204C23×C127—41no—
205C23×C127—41no—
206C23×C127—81no—
207C23×C127#12011yescharacteristic
208Q8×C127—41no—
209Q8×C127—42no—
210Q8×C127—41no—
211Q8×C127—41no—
212Q8×C127—82no—
213D4×C127—21no—
214D4×C127—21no—
215D4×C127—21no—
216D4×C127—42no—
217D4×C127—41no—
218D4×C127—44no—
219D4×C127—41no—
220D4×C127—41no—
221D4×C127—82no—
222D4×C127#10412yes—
223C2×C4×C127—21no—
224C2×C4×C127—21no—
225C2×C4×C127—21no—
226C2×C4×C127—21no—
227C2×C4×C127—21no—
228C2×C4×C127—22no—
229C2×C4×C127—21no—
230C2×C4×C127—21no—
231C2×C4×C127—22no—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—41no—
235C2×C4×C127—42no—
236C2×C4×C127—42no—
237C2×C4×C127—44no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—42no—
241C2×C4×C127—81no—
242C2×C4×C127—81no—
243C2×C4×C127—81no—
244C2×C4×C127—82no—
245C2×C4×C127—82no—
246C2×C4×C127—81no—
247C2×C4×C127—81no—
248C2×C4×C127C2×C22⋊C411yescharacteristic
249C2×C4×C127C2×C22⋊C411yescharacteristic
250C2×C4×C127C2×C22⋊C411yescharacteristic
251C2×C4×C127#12011yescharacteristic
252C2×C4×C127#12011yescharacteristic
253C2×C4×C127#12011yescharacteristic
254C8×C127—42no—
255C8×C127—42no—
256C8×C127—81no—
257C22×C127—21no—
258C22×C127—21no—
259C22×C127—22no—
260C22×C127—41no—
261C22×C127—41no—
262C22×C127—41no—
263C22×C127—41no—
264C22×C127—41no—
265C22×C127—41no—
266C22×C127—41no—
267C22×C127—41no—
268C22×C127—82no—
269C22×C127—82no—
270C22×C127#37911yescharacteristic
271C22×C127#45411yescharacteristic
272C22×C127#45611yescharacteristic
273C4×C127—21no—
274C4×C127—21no—
275C4×C127—21no—
276C4×C127—21no—
277C4×C127—21no—
278C4×C127—41no—
279C4×C127—41no—
280C4×C127—41no—
281C4×C127—42no—
282C4×C127—41no—
283C4×C127—41no—
284C4×C127—42no—
285C4×C127—82no—
286C4×C127C2×#10411yescharacteristic
287C4×C127#42111yescharacteristic
288#8418C12711yesmaximal, characteristic, direct product factor, Sylow
289C2×C127—21no—
290C2×C127—21no—
291C2×C127—42no—
292C2×C127—81no—
293C2×C127—81no—
294C2×C127#178911yescharacteristic
295C2×C127#179311yescharacteristic
296C2×C127#179511yescharacteristic
297#3520C2×C12711yescharacteristic
298#1986C2×C12711yescharacteristic, complemented
299#1762C2×C12711yescharacteristic, complemented
300#1531C2×C12711yescharacteristic, complemented
301#1524C2×C12711yescharacteristic, complemented
302#1509C2×C12711yescharacteristic, complemented
303#1490C2×C12711yescharacteristic, complemented
304C127#841811yescharacteristic, direct product factor, Sylow
305#556C4×C12711yescharacteristic, complemented
306#554—21no—
307#552—21no—
308#551—22no—
309D4×Q8C4×C12711yescharacteristic, complemented
310#548—21no—
311#547C4×C12711yescharacteristic, complemented
312#547C4×C12711yescharacteristic, complemented
313#546—21no—
314#542—21no—
315#539—22no—
316#533C22×C12711yescharacteristic
317#529C22×C12711yescharacteristic
318#525—21no—
319C2×C22⋊Q8—21no—
320#520—21no—
321C2×C4×D4C22×C12711yescharacteristic
322#432C22×C12711yescharacteristic
323C2×#102—21no—
324C4×M16C22×C12711yescharacteristic
325C2×#97C22×C12711yescharacteristic
326C4×C4⋊C4C22×C12711yescharacteristic
327#340—21no—
328#339—22no—
329#330—21no—
330#330—22no—
331#329—21no—
332#328—21no—
333#327—21no—
334D4⋊C8—21no—
335D4⋊C8—21no—
336C2×#41—21no—
337C2×#41—21no—
338C22×Q8—21no—
339C22×D4D4×C12711yescharacteristic
340C23×C4—21no—
341C2×M16—21no—
342C22×C8—21no—
343C4⋊Q8—21no—
344C4⋊Q8C2×C4×C12711yescharacteristic
345C4⋊Q8C2×C4×C12711yescharacteristic
346#126—22no—
347#126—22no—
348#126—21no—
349#125—22no—
350#125D4×C12711yescharacteristic
351#125D4×C12712yes—
352#124—22no—
353#124—21no—
354#124D4×C12711yescharacteristic
355#123—22no—
356#123—22no—
357#123—21no—
358#123—22no—
359#123—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370C22⋊Q8D4×C12711yescharacteristic
371#121—22no—
372#121—21no—
373#121—21no—
374#121D4×C12711yescharacteristic
375#120—22no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C2×C4×C12711yescharacteristic
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C2×C4×C12711yescharacteristic
388C4×D4C2×C4×C12711yescharacteristic
389C4×D4C2×C4×C12711yescharacteristic
390C4×D4D4×C12711yescharacteristic
391C4×D4D4×C12711yescharacteristic
392#117—22no—
393#117—21no—
394#117—21no—
395#117D4×C12712yes—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4D4×C12711yescharacteristic
401C2×C22⋊C4—22no—
402C2×C22⋊C4—21no—
403C2×C42—21no—
404C2×C42C23×C12711yescharacteristic
405C4⋊C8—21no—
406#102—24no—
407C22⋊C8—21no—
408#97—21no—
409#97—21no—
410#97—21no—
411#97—21no—
412C4×C8—21no—
413#95—21no—
414C24—21no—
415#41—42no—
416#41—42no—
417#41—82no—
418C2×Q8—22no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—82no—
422C2×Q8C22⋊C4×C12711yescharacteristic
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—41no—
429C2×D4C22⋊C4×C12711yescharacteristic
430C2×D4C22⋊C4×C12711yescharacteristic
431C2×D4C22⋊C4×C12711yescharacteristic
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—41no—
442C22×C4—82no—
443C22×C4C2×D4×C12711yescharacteristic
444C22×C4C2×D4×C12711yescharacteristic
445C22×C4C2×D4×C12711yescharacteristic
446M16—22no—
447M16—41no—
448C2×C8—22no—
449C2×C8—41no—
450C2×C8—41no—
451C2×C8—41no—
452C2×C8—41no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—41no—
468C4⋊C4C22⋊C4×C12711yescharacteristic
469C4⋊C4C22⋊C4×C12711yescharacteristic
470C4⋊C4C22⋊C4×C12711yescharacteristic
471C4⋊C4C22⋊C4×C12711yescharacteristic
472C4⋊C4C22⋊C4×C12712yes—
473C4⋊C4C22⋊C4×C12712yes—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C42—22no—
490C42—21no—
491C42—22no—
492C42—42no—
493C42C22×C4×C12711yescharacteristic
494C42C2×D4×C12711yescharacteristic
495C42C2×D4×C12711yescharacteristic
496C42C2×D4×C12711yescharacteristic
497C23—21no—
498C23—21no—
499C23—21no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—81no—
504C23#120×C12711yescharacteristic
505Q8—41no—
506Q8—42no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—42no—
514D4—41no—
515D4—44no—
516D4—41no—
517D4—41no—
518D4—82no—
519D4#104×C12712yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4C2×C22⋊C4×C12711yescharacteristic
546C2×C4C2×C22⋊C4×C12711yescharacteristic
547C2×C4C2×C22⋊C4×C12711yescharacteristic
548C2×C4#120×C12711yescharacteristic
549C2×C4#120×C12711yescharacteristic
550C2×C4#120×C12711yescharacteristic
551C8—42no—
552C8—42no—
553C8—81no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—82no—
566C22—82no—
567C22#379×C12711yescharacteristic
568C22#454×C12711yescharacteristic
569C22#456×C12711yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—41no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—42no—
581C4—41no—
582C4—82no—
583C4C2×#104×C12711yescharacteristic
584C4#421×C12711yescharacteristic
585C2—21no—
586C2—21no—
587C2—42no—
588C2—81no—
589C2—81no—
590C2C127×#178911yescharacteristic
591C2C127×#179311yescharacteristic
592C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3520C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1986C2semidirect
3. C127×#1762C2semidirect
4. C127×#1531C2semidirect
5. C127×#1524C2semidirect
6. C127×#1509C2semidirect
7. C127×#1490C2semidirect
8. #556×C127C4semidirect
12. D4×Q8×C127C4semidirect
14. #547×C127C4semidirect
15. #547×C127C4semidirect
288. #8418C127direct (N × H)
298. #1986C2×C127semidirect
299. #1762C2×C127semidirect
300. #1531C2×C127semidirect
301. #1524C2×C127semidirect
302. #1509C2×C127semidirect
303. #1490C2×C127semidirect
304. C127#8418direct (N × H)
305. #556C4×C127semidirect
309. D4×Q8C4×C127semidirect
311. #547C4×C127semidirect
312. #547C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35202
C127×#19862
C127×#17622
C127×#15312
C127×#15242
C127×#15092
C127×#14902
#8418127