Finite Group Databasebeta

← C127×#8414 #44572087

Subgroups — C127×#8414 #44572087

Order 32512.

758 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3517C211yesmaximal, characteristic
2C127×#1759C211yesmaximal, characteristic, complemented
3C127×#1529C211yesmaximal, characteristic, complemented
4C127×#1505C211yesmaximal, characteristic, complemented
5C127×#1500C211yesmaximal, characteristic, complemented
6C127×#1488C211yesmaximal, characteristic, complemented
7C127×#1484C211yesmaximal, characteristic, complemented
8#557×C127C411yescharacteristic, complemented
9#553×C127—22no—
10#553×C127—21no—
11#550×C127—21no—
12#550×C127—21no—
13#550×C127C411yescharacteristic, complemented
14#550×C127C411yescharacteristic, complemented
15#547×C127—21no—
16#547×C127C411yescharacteristic, complemented
17#540×C127—22no—
18#540×C127—21no—
19#532×C127—21no—
20#532×C127C2211yescharacteristic
21#529×C127—21no—
22#529×C127C2211yescharacteristic
23#520×C127—21no—
24C4×#41×C127C2211yescharacteristic
25#432×C127C2211yescharacteristic
26#431×C127C2211yescharacteristic
27C2×#104×C127—21no—
28C4×M16×C127C2211yescharacteristic
29#376×C127C2211yescharacteristic
30#339×C127—21no—
31#330×C127—21no—
32#329×C127—21no—
33#328×C127—21no—
34#327×C127—21no—
35#327×C127—22no—
36Q8⋊C8×C127—21no—
37D4⋊C8×C127—22no—
38D4⋊C8×C127—21no—
39C2×#41×C127—21no—
40C2×#41×C127—21no—
41C2×#41×C127—21no—
42C2×#41×C127—21no—
43C2×#41×C127D411yescharacteristic
44C2×M16×C127—21no—
45C4⋊Q8×C127—21no—
46C4⋊Q8×C127C2×C411yescharacteristic
47#127×C127—22no—
48#127×C127—21no—
49#127×C127—21no—
50#127×C127C2×C411yescharacteristic
51#126×C127—22no—
52#126×C127—21no—
53#125×C127—22no—
54#125×C127—21no—
55#125×C127D411yescharacteristic
56#124×C127—21no—
57#124×C127D411yescharacteristic
58#123×C127—22no—
59#123×C127—22no—
60#123×C127—22no—
61#123×C127—21no—
62#123×C127—22no—
63C22⋊Q8×C127—21no—
64C22⋊Q8×C127D411yescharacteristic
65#121×C127—22no—
66#121×C127—22no—
67#121×C127—22no—
68#121×C127—22no—
69#121×C127—22no—
70#121×C127—21no—
71#121×C127—22no—
72#121×C127—22no—
73#121×C127—21no—
74#121×C127—21no—
75#121×C127—21no—
76#121×C127D411yescharacteristic
77#121×C127D412yes—
78C4×Q8×C127—21no—
79C4×Q8×C127—21no—
80C4×Q8×C127C2×C411yescharacteristic
81C4×Q8×C127C2×C411yescharacteristic
82C4×Q8×C127D411yescharacteristic
83C4×D4×C127—22no—
84C4×D4×C127—22no—
85C4×D4×C127—22no—
86C4×D4×C127—22no—
87C4×D4×C127—21no—
88C4×D4×C127—21no—
89C4×D4×C127—21no—
90C4×D4×C127—21no—
91C4×D4×C127—21no—
92C4×D4×C127—21no—
93C4×D4×C127C2×C411yescharacteristic
94C4×D4×C127C2×C411yescharacteristic
95C4×D4×C127D411yescharacteristic
96C4×D4×C127D412yes—
97#117×C127—22no—
98#117×C127—21no—
99#117×C127—21no—
100#117×C127D411yescharacteristic
101C2×C4⋊C4×C127—22no—
102C2×C4⋊C4×C127—21no—
103C2×C42×C127—21no—
104C2×C42×C127—21no—
105C2×C42×C127C2311yescharacteristic
106C4⋊C8×C127—21no—
107C4⋊C8×C127—21no—
108#104×C127—24no—
109C22⋊C8×C127—21no—
110C22⋊C8×C127—21no—
111#97×C127—21no—
112#97×C127—21no—
113C4×C8×C127—21no—
114C4×C8×C127—21no—
115#95×C127—21no—
116#95×C127—21no—
117#41×C127—22no—
118#41×C127—41no—
119#41×C127—42no—
120#41×C127—42no—
121#41×C127—82no—
122#41×C127—82no—
123#41×C127—82no—
124C2×Q8×C127—21no—
125C2×Q8×C127C22⋊C411yescharacteristic
126C2×Q8×C127C22⋊C411yescharacteristic
127C2×D4×C127—22no—
128C2×D4×C127—21no—
129C2×D4×C127—22no—
130C2×D4×C127—22no—
131C2×D4×C127—22no—
132C2×D4×C127—22no—
133C2×D4×C127—21no—
134C2×D4×C127—22no—
135C2×D4×C127—21no—
136C2×D4×C127—21no—
137C2×D4×C127C22⋊C411yescharacteristic
138C2×D4×C127C22⋊C411yescharacteristic
139C2×D4×C127C22⋊C412yes—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—22no—
148C22×C4×C127—41no—
149C22×C4×C127C2×D411yescharacteristic
150C22×C4×C127C2×D411yescharacteristic
151C22×C4×C127C2×D411yescharacteristic
152M16×C127—22no—
153M16×C127—41no—
154C2×C8×C127—41no—
155C2×C8×C127—41no—
156C2×C8×C127—41no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127—22no—
159C4⋊C4×C127—22no—
160C4⋊C4×C127—22no—
161C4⋊C4×C127—21no—
162C4⋊C4×C127—21no—
163C4⋊C4×C127—21no—
164C4⋊C4×C127—21no—
165C4⋊C4×C127—21no—
166C4⋊C4×C127—21no—
167C4⋊C4×C127—21no—
168C4⋊C4×C127C22⋊C411yescharacteristic
169C4⋊C4×C127C22⋊C411yescharacteristic
170C4⋊C4×C127C22⋊C411yescharacteristic
171C4⋊C4×C127C22⋊C412yes—
172C4⋊C4×C127C22⋊C411yescharacteristic
173C22⋊C4×C127—22no—
174C22⋊C4×C127—22no—
175C22⋊C4×C127—22no—
176C22⋊C4×C127—21no—
177C22⋊C4×C127—21no—
178C22⋊C4×C127—21no—
179C22⋊C4×C127—21no—
180C22⋊C4×C127—21no—
181C22⋊C4×C127—21no—
182C22⋊C4×C127—22no—
183C22⋊C4×C127—21no—
184C22⋊C4×C127—21no—
185C22⋊C4×C127—22no—
186C42×C127—22no—
187C42×C127—21no—
188C42×C127—21no—
189C42×C127—21no—
190C42×C127—21no—
191C42×C127—22no—
192C42×C127—41no—
193C42×C127C22×C411yescharacteristic
194C42×C127C2×D411yescharacteristic
195C42×C127C2×D411yescharacteristic
196C42×C127C2×D411yescharacteristic
197C23×C127—21no—
198C23×C127—22no—
199C23×C127—21no—
200C23×C127#12011yescharacteristic
201Q8×C127—21no—
202Q8×C127—41no—
203Q8×C127—42no—
204Q8×C127#10412yes—
205D4×C127—21no—
206D4×C127—21no—
207D4×C127—42no—
208D4×C127—42no—
209D4×C127—41no—
210D4×C127—44no—
211D4×C127—42no—
212D4×C127—41no—
213D4×C127—41no—
214D4×C127—81no—
215D4×C127—82no—
216D4×C127—82no—
217D4×C127—82no—
218D4×C127—82no—
219D4×C127—82no—
220C2×C4×C127—21no—
221C2×C4×C127—21no—
222C2×C4×C127—21no—
223C2×C4×C127—21no—
224C2×C4×C127—21no—
225C2×C4×C127—21no—
226C2×C4×C127—21no—
227C2×C4×C127—22no—
228C2×C4×C127—21no—
229C2×C4×C127—41no—
230C2×C4×C127—41no—
231C2×C4×C127—42no—
232C2×C4×C127—44no—
233C2×C4×C127—42no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—42no—
237C2×C4×C127—81no—
238C2×C4×C127—82no—
239C2×C4×C127—82no—
240C2×C4×C127—82no—
241C2×C4×C127—81no—
242C2×C4×C127—81no—
243C2×C4×C127C2×C22⋊C411yescharacteristic
244C2×C4×C127C2×C22⋊C411yescharacteristic
245C2×C4×C127C2×C22⋊C411yescharacteristic
246C2×C4×C127#12011yescharacteristic
247C2×C4×C127#12011yescharacteristic
248C2×C4×C127#12011yescharacteristic
249C8×C127—42no—
250C8×C127—81no—
251C8×C127—81no—
252C22×C127—21no—
253C22×C127—21no—
254C22×C127—21no—
255C22×C127—41no—
256C22×C127—42no—
257C22×C127—41no—
258C22×C127—41no—
259C22×C127—42no—
260C22×C127—41no—
261C22×C127—41no—
262C22×C127—42no—
263C22×C127—41no—
264C22×C127#37911yescharacteristic
265C4×C127—21no—
266C4×C127—21no—
267C4×C127—21no—
268C4×C127—21no—
269C4×C127—21no—
270C4×C127—22no—
271C4×C127—41no—
272C4×C127—41no—
273C4×C127—41no—
274C4×C127—41no—
275C4×C127—42no—
276C4×C127—41no—
277C4×C127—82no—
278C4×C127C2×#10411yescharacteristic
279C4×C127#42111yescharacteristic
280#8414C12711yesmaximal, characteristic, direct product factor, Sylow
281C2×C127—41no—
282C2×C127—81no—
283C2×C127—82no—
284C2×C127—81no—
285C2×C127#178911yescharacteristic
286C2×C127#179411yescharacteristic
287C2×C127#179511yescharacteristic
288#3517C2×C12711yescharacteristic
289#1759C2×C12711yescharacteristic, complemented
290#1529C2×C12711yescharacteristic, complemented
291#1505C2×C12711yescharacteristic, complemented
292#1500C2×C12711yescharacteristic, complemented
293#1488C2×C12711yescharacteristic, complemented
294#1484C2×C12711yescharacteristic, complemented
295C127#841411yescharacteristic, direct product factor, Sylow
296#557C4×C12711yescharacteristic, complemented
297#553—22no—
298#553—21no—
299#550—21no—
300#550—21no—
301#550C4×C12711yescharacteristic, complemented
302#550C4×C12711yescharacteristic, complemented
303#547—21no—
304#547C4×C12711yescharacteristic, complemented
305#540—22no—
306#540—21no—
307#532—21no—
308#532C22×C12711yescharacteristic
309#529—21no—
310#529C22×C12711yescharacteristic
311#520—21no—
312C4×#41C22×C12711yescharacteristic
313#432C22×C12711yescharacteristic
314#431C22×C12711yescharacteristic
315C2×#104—21no—
316C4×M16C22×C12711yescharacteristic
317#376C22×C12711yescharacteristic
318#339—21no—
319#330—21no—
320#329—21no—
321#328—21no—
322#327—21no—
323#327—22no—
324Q8⋊C8—21no—
325D4⋊C8—22no—
326D4⋊C8—21no—
327C2×#41—21no—
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41D4×C12711yescharacteristic
332C2×M16—21no—
333C4⋊Q8—21no—
334C4⋊Q8C2×C4×C12711yescharacteristic
335#127—22no—
336#127—21no—
337#127—21no—
338#127C2×C4×C12711yescharacteristic
339#126—22no—
340#126—21no—
341#125—22no—
342#125—21no—
343#125D4×C12711yescharacteristic
344#124—21no—
345#124D4×C12711yescharacteristic
346#123—22no—
347#123—22no—
348#123—22no—
349#123—21no—
350#123—22no—
351C22⋊Q8—21no—
352C22⋊Q8D4×C12711yescharacteristic
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—22no—
358#121—21no—
359#121—22no—
360#121—22no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121D4×C12711yescharacteristic
365#121D4×C12712yes—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C2×C4×C12711yescharacteristic
369C4×Q8C2×C4×C12711yescharacteristic
370C4×Q8D4×C12711yescharacteristic
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4C2×C4×C12711yescharacteristic
382C4×D4C2×C4×C12711yescharacteristic
383C4×D4D4×C12711yescharacteristic
384C4×D4D4×C12712yes—
385#117—22no—
386#117—21no—
387#117—21no—
388#117D4×C12711yescharacteristic
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C12711yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396#104—24no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399#97—21no—
400#97—21no—
401C4×C8—21no—
402C4×C8—21no—
403#95—21no—
404#95—21no—
405#41—22no—
406#41—41no—
407#41—42no—
408#41—42no—
409#41—82no—
410#41—82no—
411#41—82no—
412C2×Q8—21no—
413C2×Q8C22⋊C4×C12711yescharacteristic
414C2×Q8C22⋊C4×C12711yescharacteristic
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4C22⋊C4×C12711yescharacteristic
426C2×D4C22⋊C4×C12711yescharacteristic
427C2×D4C22⋊C4×C12712yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—41no—
437C22×C4C2×D4×C12711yescharacteristic
438C22×C4C2×D4×C12711yescharacteristic
439C22×C4C2×D4×C12711yescharacteristic
440M16—22no—
441M16—41no—
442C2×C8—41no—
443C2×C8—41no—
444C2×C8—41no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4C22⋊C4×C12711yescharacteristic
457C4⋊C4C22⋊C4×C12711yescharacteristic
458C4⋊C4C22⋊C4×C12711yescharacteristic
459C4⋊C4C22⋊C4×C12712yes—
460C4⋊C4C22⋊C4×C12711yescharacteristic
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—22no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C42—22no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—22no—
480C42—41no—
481C42C22×C4×C12711yescharacteristic
482C42C2×D4×C12711yescharacteristic
483C42C2×D4×C12711yescharacteristic
484C42C2×D4×C12711yescharacteristic
485C23—21no—
486C23—22no—
487C23—21no—
488C23#120×C12711yescharacteristic
489Q8—21no—
490Q8—41no—
491Q8—42no—
492Q8#104×C12712yes—
493D4—21no—
494D4—21no—
495D4—42no—
496D4—41no—
497D4—42no—
498D4—44no—
499D4—42no—
500D4—41no—
501D4—41no—
502D4—82no—
503D4—81no—
504D4—82no—
505D4—82no—
506D4—82no—
507D4—82no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—81no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4C2×C22⋊C4×C12711yescharacteristic
532C2×C4C2×C22⋊C4×C12711yescharacteristic
533C2×C4C2×C22⋊C4×C12711yescharacteristic
534C2×C4#120×C12711yescharacteristic
535C2×C4#120×C12711yescharacteristic
536C2×C4#120×C12711yescharacteristic
537C8—42no—
538C8—81no—
539C8—81no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—42no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—41no—
552C22#379×C12711yescharacteristic
553C4—21no—
554C4—22no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—41no—
565C4—82no—
566C4C2×#104×C12711yescharacteristic
567C4#421×C12711yescharacteristic
568C2—41no—
569C2—81no—
570C2—82no—
571C2—81no—
572C2C127×#178911yescharacteristic
573C2C127×#179411yescharacteristic
574C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3517C2
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×#1759C2semidirect
3. C127×#1529C2semidirect
4. C127×#1505C2semidirect
5. C127×#1500C2semidirect
6. C127×#1488C2semidirect
7. C127×#1484C2semidirect
8. #557×C127C4semidirect
13. #550×C127C4semidirect
14. #550×C127C4semidirect
16. #547×C127C4semidirect
280. #8414C127direct (N × H)
289. #1759C2×C127semidirect
290. #1529C2×C127semidirect
291. #1505C2×C127semidirect
292. #1500C2×C127semidirect
293. #1488C2×C127semidirect
294. #1484C2×C127semidirect
295. C127#8414direct (N × H)
296. #557C4×C127semidirect
301. #550C4×C127semidirect
302. #550C4×C127semidirect
304. #547C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35172
C127×#17592
C127×#15292
C127×#15052
C127×#15002
C127×#14882
C127×#14842
#8414127