Finite Group Databasebeta

← C127×#8411 #44572084

Subgroups — C127×#8411 #44572084

Order 32512.

714 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3455C211yesmaximal, characteristic
2C127×#1798C211yesmaximal, characteristic, complemented
3C127×#1542C211yesmaximal, characteristic, complemented
4C127×#1540C211yesmaximal, characteristic, complemented
5C127×#1481C211yesmaximal, characteristic, complemented
6C127×#1480C211yesmaximal, characteristic, complemented
7C127×#1458C211yesmaximal, characteristic, complemented
8#542×C127—21no—
9#542×C127—21no—
10#541×C127—21no—
11#540×C127—21no—
12#539×C127—21no—
13#539×C127C412yes—
14#538×C127—21no—
15#538×C127C412yes—
16#533×C127C2211yescharacteristic
17#532×C127C2211yescharacteristic
18#529×C127—22no—
19#529×C127—22no—
20#525×C127—21no—
21C4×#41×C127—21no—
22C2×#117×C127C2211yescharacteristic
23#431×C127C2211yescharacteristic
24#431×C127C2211yescharacteristic
25C2×C4⋊C8×C127C2211yescharacteristic
26C2×C4⋊C8×C127C2211yescharacteristic
27C2×C22⋊C8×C127—21no—
28#336×C127—21no—
29#333×C127—21no—
30#332×C127—21no—
31#332×C127—21no—
32#331×C127—21no—
33Q8⋊C8×C127—22no—
34D4⋊C8×C127—22no—
35#324×C127—21no—
36#323×C127—21no—
37C2×#41×C127—21no—
38C23×C4×C127D411yescharacteristic
39C22×C8×C127—21no—
40C22×C8×C127—21no—
41C4⋊Q8×C127D411yescharacteristic
42C4⋊Q8×C127D411yescharacteristic
43C4⋊Q8×C127D411yescharacteristic
44#127×C127D411yescharacteristic
45#126×C127—22no—
46#126×C127—22no—
47#126×C127—22no—
48#126×C127—22no—
49#125×C127—22no—
50#125×C127—22no—
51#125×C127—21no—
52#124×C127—22no—
53#124×C127—22no—
54#124×C127—21no—
55#123×C127—22no—
56#123×C127—22no—
57#123×C127—22no—
58#123×C127—22no—
59#123×C127—22no—
60C22⋊Q8×C127—21no—
61C22⋊Q8×C127—21no—
62C22⋊Q8×C127—22no—
63C22⋊Q8×C127—22no—
64C22⋊Q8×C127—21no—
65C22⋊Q8×C127C2×C412yes—
66#121×C127—21no—
67#121×C127—21no—
68#121×C127—22no—
69#121×C127—22no—
70#121×C127—21no—
71#121×C127C2×C412yes—
72#120×C127—22no—
73C4×Q8×C127—21no—
74C4×Q8×C127—21no—
75C4×Q8×C127—21no—
76C4×Q8×C127D412yes—
77C4×D4×C127—21no—
78C4×D4×C127—21no—
79C4×D4×C127—22no—
80C4×D4×C127—22no—
81C4×D4×C127—22no—
82C4×D4×C127—22no—
83C4×D4×C127—21no—
84C4×D4×C127D412yes—
85#117×C127—22no—
86#117×C127—21no—
87#117×C127—21no—
88#117×C127—21no—
89#117×C127—21no—
90#117×C127—21no—
91C2×C4⋊C4×C127C2×C411yescharacteristic
92C2×C4⋊C4×C127D411yescharacteristic
93C2×C22⋊C4×C127C2×C411yescharacteristic
94C2×C22⋊C4×C127D411yescharacteristic
95C2×C42×C127—22no—
96C2×C42×C127D411yescharacteristic
97C2×C42×C127C2311yescharacteristic
98C4⋊C8×C127—21no—
99C4⋊C8×C127—21no—
100C4⋊C8×C127—21no—
101C4⋊C8×C127—21no—
102C4⋊C8×C127—21no—
103C4⋊C8×C127—21no—
104C22⋊C8×C127—21no—
105C22⋊C8×C127—21no—
106C22⋊C8×C127—42no—
107C4×C8×C127—21no—
108C4×C8×C127—21no—
109C24×C127C22⋊C411yescharacteristic
110#41×C127—41no—
111#41×C127—41no—
112#41×C127—41no—
113#41×C127—41no—
114C2×Q8×C127—21no—
115C2×Q8×C127—21no—
116C2×Q8×C127C22⋊C412yes—
117C2×D4×C127—22no—
118C2×D4×C127—22no—
119C2×D4×C127—22no—
120C2×D4×C127—21no—
121C2×D4×C127—21no—
122C2×D4×C127C22⋊C412yes—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—21no—
130C22×C4×C127—21no—
131C22×C4×C127—21no—
132C22×C4×C127C22⋊C411yescharacteristic
133C22×C4×C127C22⋊C411yescharacteristic
134C22×C4×C127C22⋊C411yescharacteristic
135C22×C4×C127C22×C411yescharacteristic
136C22×C4×C127C2×D411yescharacteristic
137C22×C4×C127C2×D411yescharacteristic
138C2×C8×C127—41no—
139C2×C8×C127—41no—
140C2×C8×C127—41no—
141C2×C8×C127—41no—
142C2×C8×C127—41no—
143C2×C8×C127—41no—
144C2×C8×C127—41no—
145C2×C8×C127—41no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—21no—
155C4⋊C4×C127—21no—
156C4⋊C4×C127—21no—
157C4⋊C4×C127—21no—
158C4⋊C4×C127—21no—
159C4⋊C4×C127—22no—
160C4⋊C4×C127C22⋊C412yes—
161C4⋊C4×C127C22⋊C412yes—
162C22⋊C4×C127—22no—
163C22⋊C4×C127—22no—
164C22⋊C4×C127—22no—
165C22⋊C4×C127—22no—
166C22⋊C4×C127—22no—
167C22⋊C4×C127—22no—
168C22⋊C4×C127—22no—
169C22⋊C4×C127—21no—
170C22⋊C4×C127—21no—
171C22⋊C4×C127—22no—
172C22⋊C4×C127—21no—
173C22⋊C4×C127—21no—
174C22⋊C4×C127—22no—
175C42×C127—22no—
176C42×C127—22no—
177C42×C127—21no—
178C42×C127—21no—
179C42×C127—22no—
180C42×C127C2×D411yescharacteristic
181C42×C127C2×D411yescharacteristic
182C42×C127C2×D411yescharacteristic
183C42×C127C2×D411yescharacteristic
184C23×C127—21no—
185C23×C127—22no—
186C23×C127—21no—
187C23×C127—21no—
188C23×C127—41no—
189C23×C127—41no—
190C23×C127C2×C22⋊C411yescharacteristic
191Q8×C127—42no—
192Q8×C127—41no—
193Q8×C127—41no—
194Q8×C127—81no—
195D4×C127—42no—
196D4×C127—42no—
197D4×C127—42no—
198D4×C127—41no—
199D4×C127—41no—
200D4×C127—81no—
201D4×C127—82no—
202D4×C127—82no—
203C2×C4×C127—21no—
204C2×C4×C127—21no—
205C2×C4×C127—22no—
206C2×C4×C127—22no—
207C2×C4×C127—22no—
208C2×C4×C127—21no—
209C2×C4×C127—21no—
210C2×C4×C127—21no—
211C2×C4×C127—41no—
212C2×C4×C127—41no—
213C2×C4×C127—41no—
214C2×C4×C127—41no—
215C2×C4×C127—42no—
216C2×C4×C127—41no—
217C2×C4×C127—41no—
218C2×C4×C127—42no—
219C2×C4×C127—41no—
220C2×C4×C127—41no—
221C2×C4×C127—82no—
222C2×C4×C127—82no—
223C2×C4×C127C2×C22⋊C411yescharacteristic
224C2×C4×C127C2×C22⋊C411yescharacteristic
225C2×C4×C127#12011yescharacteristic
226C2×C4×C127#12011yescharacteristic
227C2×C4×C127#12011yescharacteristic
228C2×C4×C127#12011yescharacteristic
229C2×C4×C127#13511yescharacteristic
230C2×C4×C127#13511yescharacteristic
231C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
232C2×C4×C127#13711yescharacteristic
233C8×C127—81no—
234C8×C127—81no—
235C8×C127—81no—
236C8×C127—81no—
237C22×C127—21no—
238C22×C127—21no—
239C22×C127—42no—
240C22×C127—42no—
241C22×C127—41no—
242C22×C127—41no—
243C22×C127—42no—
244C22×C127—42no—
245C22×C127—41no—
246C22×C127—81no—
247C22×C127#37911yescharacteristic
248C22×C127#41611yescharacteristic
249C22×C127#41711yescharacteristic
250C4×C127—21no—
251C4×C127—21no—
252C4×C127—21no—
253C4×C127—21no—
254C4×C127—41no—
255C4×C127—42no—
256C4×C127—41no—
257C4×C127—42no—
258C4×C127—41no—
259C4×C127—42no—
260C4×C127#44911yescharacteristic
261C4×C127#44911yescharacteristic
262C4×C127#45211yescharacteristic
263C4×C127#45211yescharacteristic
264#8411C12711yesmaximal, characteristic, direct product factor, Sylow
265C2×C127—21no—
266C2×C127—21no—
267C2×C127—82no—
268C2×C127—81no—
269C2×C127#178811yescharacteristic
270C2×C127#179111yescharacteristic
271C2×C127#179411yescharacteristic
272#3455C2×C12711yescharacteristic
273#1798C2×C12711yescharacteristic, complemented
274#1542C2×C12711yescharacteristic, complemented
275#1540C2×C12711yescharacteristic, complemented
276#1481C2×C12711yescharacteristic, complemented
277#1480C2×C12711yescharacteristic, complemented
278#1458C2×C12711yescharacteristic, complemented
279C127#841111yescharacteristic, direct product factor, Sylow
280#542—21no—
281#542—21no—
282#541—21no—
283#540—21no—
284#539—21no—
285#539C4×C12712yes—
286#538—21no—
287#538C4×C12712yes—
288#533C22×C12711yescharacteristic
289#532C22×C12711yescharacteristic
290#529—22no—
291#529—22no—
292#525—21no—
293C4×#41—21no—
294C2×#117C22×C12711yescharacteristic
295#431C22×C12711yescharacteristic
296#431C22×C12711yescharacteristic
297C2×C4⋊C8C22×C12711yescharacteristic
298C2×C4⋊C8C22×C12711yescharacteristic
299C2×C22⋊C8—21no—
300#336—21no—
301#333—21no—
302#332—21no—
303#332—21no—
304#331—21no—
305Q8⋊C8—22no—
306D4⋊C8—22no—
307#324—21no—
308#323—21no—
309C2×#41—21no—
310C23×C4D4×C12711yescharacteristic
311C22×C8—21no—
312C22×C8—21no—
313C4⋊Q8D4×C12711yescharacteristic
314C4⋊Q8D4×C12711yescharacteristic
315C4⋊Q8D4×C12711yescharacteristic
316#127D4×C12711yescharacteristic
317#126—22no—
318#126—22no—
319#126—22no—
320#126—22no—
321#125—22no—
322#125—22no—
323#125—21no—
324#124—22no—
325#124—22no—
326#124—21no—
327#123—22no—
328#123—22no—
329#123—22no—
330#123—22no—
331#123—22no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—21no—
337C22⋊Q8C2×C4×C12712yes—
338#121—21no—
339#121—21no—
340#121—22no—
341#121—22no—
342#121—21no—
343#121C2×C4×C12712yes—
344#120—22no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8D4×C12712yes—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—21no—
356C4×D4D4×C12712yes—
357#117—22no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363C2×C4⋊C4C2×C4×C12711yescharacteristic
364C2×C4⋊C4D4×C12711yescharacteristic
365C2×C22⋊C4C2×C4×C12711yescharacteristic
366C2×C22⋊C4D4×C12711yescharacteristic
367C2×C42—22no—
368C2×C42D4×C12711yescharacteristic
369C2×C42C23×C12711yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—21no—
375C4⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8—21no—
378C22⋊C8—42no—
379C4×C8—21no—
380C4×C8—21no—
381C24C22⋊C4×C12711yescharacteristic
382#41—41no—
383#41—41no—
384#41—41no—
385#41—41no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8C22⋊C4×C12712yes—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C22⋊C4×C12712yes—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4C22⋊C4×C12711yescharacteristic
405C22×C4C22⋊C4×C12711yescharacteristic
406C22×C4C22⋊C4×C12711yescharacteristic
407C22×C4C22×C4×C12711yescharacteristic
408C22×C4C2×D4×C12711yescharacteristic
409C22×C4C2×D4×C12711yescharacteristic
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—41no—
414C2×C8—41no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—41no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4C22⋊C4×C12712yes—
433C4⋊C4C22⋊C4×C12712yes—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—22no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C42—22no—
448C42—22no—
449C42—21no—
450C42—22no—
451C42—21no—
452C42C2×D4×C12711yescharacteristic
453C42C2×D4×C12711yescharacteristic
454C42C2×D4×C12711yescharacteristic
455C42C2×D4×C12711yescharacteristic
456C23—21no—
457C23—22no—
458C23—21no—
459C23—21no—
460C23—41no—
461C23—41no—
462C23C2×C22⋊C4×C12711yescharacteristic
463Q8—42no—
464Q8—41no—
465Q8—41no—
466Q8—81no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—41no—
471D4—41no—
472D4—81no—
473D4—82no—
474D4—82no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4C2×C22⋊C4×C12711yescharacteristic
496C2×C4C2×C22⋊C4×C12711yescharacteristic
497C2×C4#120×C12711yescharacteristic
498C2×C4#120×C12711yescharacteristic
499C2×C4#120×C12711yescharacteristic
500C2×C4#120×C12711yescharacteristic
501C2×C4#135×C12711yescharacteristic
502C2×C4#135×C12711yescharacteristic
503C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
504C2×C4#137×C12711yescharacteristic
505C8—81no—
506C8—81no—
507C8—81no—
508C8—81no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—41no—
513C22—42no—
514C22—42no—
515C22—41no—
516C22—42no—
517C22—41no—
518C22—81no—
519C22#379×C12711yescharacteristic
520C22#416×C12711yescharacteristic
521C22#417×C12711yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—41no—
527C4—42no—
528C4—41no—
529C4—42no—
530C4—41no—
531C4—42no—
532C4#449×C12711yescharacteristic
533C4#449×C12711yescharacteristic
534C4#452×C12711yescharacteristic
535C4#452×C12711yescharacteristic
536C2—21no—
537C2—21no—
538C2—81no—
539C2—82no—
540C2C127×#178811yescharacteristic
541C2C127×#179111yescharacteristic
542C2C127×#179411yescharacteristic
subgroupG/H
centerC2×C4×C127#120
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
socleC22×C127#379
prime radicalC127×#3455C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1798C2semidirect
3. C127×#1542C2semidirect
4. C127×#1540C2semidirect
5. C127×#1481C2semidirect
6. C127×#1480C2semidirect
7. C127×#1458C2semidirect
264. #8411C127direct (N × H)
273. #1798C2×C127semidirect
274. #1542C2×C127semidirect
275. #1540C2×C127semidirect
276. #1481C2×C127semidirect
277. #1480C2×C127semidirect
278. #1458C2×C127semidirect
279. C127#8411direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34552
C127×#17982
C127×#15422
C127×#15402
C127×#14812
C127×#14802
C127×#14582
#8411127