Finite Group Databasebeta

← C127×#8499 #44572172

Subgroups — C127×#8499 #44572172

Order 32512.

676 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3552C211yesmaximal, characteristic
2C127×#1993C211yesmaximal, characteristic, complemented
3C127×#1556C211yesmaximal, characteristic, complemented
4C127×#1532C211yesmaximal, characteristic, complemented
5C127×#1532C211yesmaximal, characteristic, complemented
6C127×#1512C211yesmaximal, characteristic, complemented
7C127×#1512C211yesmaximal, characteristic, complemented
8#563×C127—22no—
9#557×C127C411yescharacteristic, complemented
10#556×C127C411yescharacteristic, complemented
11#554×C127—21no—
12#553×C127—21no—
13D4×Q8×C127—21no—
14D4×Q8×C127C411yescharacteristic, complemented
15#548×C127—21no—
16#547×C127C411yescharacteristic, complemented
17#544×C127—21no—
18#542×C127—21no—
19#541×C127—21no—
20#539×C127—22no—
21#536×C127—21no—
22C2×C4⋊Q8×C127C2211yescharacteristic
23#529×C127C2211yescharacteristic
24#529×C127C2211yescharacteristic
25#432×C127C2211yescharacteristic
26#432×C127C2211yescharacteristic
27C2×#97×C127C2211yescharacteristic
28#382×C127C2211yescharacteristic
29#340×C127—22no—
30#332×C127—22no—
31#330×C127—21no—
32#330×C127—21no—
33#329×C127—21no—
34#329×C127—21no—
35#328×C127—21no—
36#328×C127—21no—
37#327×C127—21no—
38#327×C127—21no—
39C2×#41×C127—21no—
40C22×Q8×C127—21no—
41C22×Q8×C127—21no—
42C22×C8×C127—21no—
43C4⋊Q8×C127—22no—
44C4⋊Q8×C127—21no—
45C4⋊Q8×C127—21no—
46C4⋊Q8×C127—21no—
47C4⋊Q8×C127—21no—
48C4⋊Q8×C127C2×C411yescharacteristic
49C4⋊Q8×C127C2×C411yescharacteristic
50C4⋊Q8×C127D412yes—
51#126×C127—22no—
52#126×C127—22no—
53#126×C127—22no—
54#126×C127—21no—
55#126×C127—21no—
56#125×C127—22no—
57#125×C127—22no—
58#125×C127—22no—
59#125×C127—21no—
60#125×C127D411yescharacteristic
61#125×C127D411yescharacteristic
62#124×C127—22no—
63#124×C127—21no—
64#124×C127D411yescharacteristic
65#124×C127D411yescharacteristic
66#123×C127—22no—
67#123×C127—22no—
68#123×C127—21no—
69#123×C127—21no—
70#123×C127—22no—
71C22⋊Q8×C127—22no—
72C22⋊Q8×C127—22no—
73C22⋊Q8×C127—22no—
74C22⋊Q8×C127—22no—
75C22⋊Q8×C127—22no—
76C22⋊Q8×C127—21no—
77C22⋊Q8×C127—22no—
78C22⋊Q8×C127—21no—
79C22⋊Q8×C127—21no—
80C22⋊Q8×C127D411yescharacteristic
81C22⋊Q8×C127D411yescharacteristic
82#121×C127—22no—
83#121×C127—21no—
84#121×C127D411yescharacteristic
85#121×C127D411yescharacteristic
86C4×Q8×C127—21no—
87C4×Q8×C127—21no—
88C4×Q8×C127—21no—
89C4×Q8×C127C2×C411yescharacteristic
90C4×Q8×C127C2×C411yescharacteristic
91C4×D4×C127—22no—
92C4×D4×C127—22no—
93C4×D4×C127—21no—
94C4×D4×C127—21no—
95C4×D4×C127—21no—
96C4×D4×C127C2×C411yescharacteristic
97C4×D4×C127C2×C411yescharacteristic
98#117×C127—21no—
99#117×C127—21no—
100#117×C127—21no—
101C2×C4⋊C4×C127—21no—
102C2×C4⋊C4×C127—21no—
103C2×C4⋊C4×C127—21no—
104C2×C4⋊C4×C127D412yes—
105C2×C42×C127C2311yescharacteristic
106C4⋊C8×C127—21no—
107C4⋊C8×C127—21no—
108C22⋊C8×C127—21no—
109C22⋊C8×C127—21no—
110#97×C127—21no—
111#97×C127—21no—
112#97×C127—21no—
113#97×C127—21no—
114#95×C127—21no—
115#95×C127—21no—
116#41×C127—82no—
117C2×Q8×C127—22no—
118C2×Q8×C127—21no—
119C2×Q8×C127—21no—
120C2×Q8×C127—22no—
121C2×Q8×C127—82no—
122C2×Q8×C127—82no—
123C2×Q8×C127C22⋊C411yescharacteristic
124C2×Q8×C127C22⋊C411yescharacteristic
125C2×D4×C127—21no—
126C2×D4×C127—21no—
127C2×D4×C127—22no—
128C2×D4×C127C22⋊C411yescharacteristic
129C2×D4×C127C22⋊C411yescharacteristic
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—21no—
134C22×C4×C127—21no—
135C22×C4×C127—41no—
136C22×C4×C127C2×D411yescharacteristic
137C22×C4×C127C2×D411yescharacteristic
138C22×C4×C127C2×D411yescharacteristic
139C2×C8×C127—22no—
140C2×C8×C127—41no—
141C2×C8×C127—41no—
142C2×C8×C127—41no—
143C2×C8×C127—41no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—22no—
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—21no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—21no—
157C4⋊C4×C127—21no—
158C4⋊C4×C127—21no—
159C4⋊C4×C127—21no—
160C4⋊C4×C127—21no—
161C4⋊C4×C127—21no—
162C4⋊C4×C127—42no—
163C4⋊C4×C127C22⋊C411yescharacteristic
164C4⋊C4×C127C22⋊C412yes—
165C4⋊C4×C127C22⋊C412yes—
166C4⋊C4×C127C22⋊C411yescharacteristic
167C4⋊C4×C127C22⋊C411yescharacteristic
168C4⋊C4×C127C22⋊C411yescharacteristic
169C22⋊C4×C127—22no—
170C22⋊C4×C127—22no—
171C22⋊C4×C127—22no—
172C22⋊C4×C127—22no—
173C22⋊C4×C127—21no—
174C22⋊C4×C127—21no—
175C22⋊C4×C127—21no—
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—21no—
183C42×C127—22no—
184C42×C127—22no—
185C42×C127—21no—
186C42×C127—21no—
187C42×C127C22×C411yescharacteristic
188C42×C127C2×D411yescharacteristic
189C42×C127C2×D411yescharacteristic
190C42×C127C2×D411yescharacteristic
191C23×C127—21no—
192C23×C127—21no—
193C23×C127#12011yescharacteristic
194Q8×C127—41no—
195Q8×C127—41no—
196Q8×C127—42no—
197Q8×C127—42no—
198Q8×C127—82no—
199Q8×C127—82no—
200D4×C127—41no—
201D4×C127—41no—
202D4×C127—41no—
203D4×C127—41no—
204D4×C127—41no—
205D4×C127—41no—
206D4×C127—82no—
207C2×C4×C127—21no—
208C2×C4×C127—21no—
209C2×C4×C127—21no—
210C2×C4×C127—21no—
211C2×C4×C127—21no—
212C2×C4×C127—21no—
213C2×C4×C127—21no—
214C2×C4×C127—22no—
215C2×C4×C127—22no—
216C2×C4×C127—21no—
217C2×C4×C127—41no—
218C2×C4×C127—41no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—82no—
222C2×C4×C127—82no—
223C2×C4×C127—82no—
224C2×C4×C127—81no—
225C2×C4×C127—81no—
226C2×C4×C127—81no—
227C2×C4×C127C2×C22⋊C411yescharacteristic
228C2×C4×C127C2×C22⋊C411yescharacteristic
229C2×C4×C127C2×C22⋊C411yescharacteristic
230C2×C4×C127#12011yescharacteristic
231C2×C4×C127#12011yescharacteristic
232C2×C4×C127#12011yescharacteristic
233C8×C127—42no—
234C8×C127—81no—
235C8×C127—81no—
236C22×C127—21no—
237C22×C127—21no—
238C22×C127—41no—
239C22×C127—41no—
240C22×C127—41no—
241C22×C127—41no—
242C22×C127—41no—
243C22×C127—41no—
244C22×C127#37911yescharacteristic
245C22×C127#45411yescharacteristic
246C22×C127#45611yescharacteristic
247C4×C127—21no—
248C4×C127—21no—
249C4×C127—21no—
250C4×C127—21no—
251C4×C127—21no—
252C4×C127—21no—
253C4×C127—41no—
254C4×C127—41no—
255C4×C127—41no—
256C4×C127—42no—
257C4×C127—42no—
258C4×C127—41no—
259C4×C127—41no—
260C4×C127—41no—
261C4×C127—161no—
262#8499C12711yesmaximal, characteristic, direct product factor, Sylow
263C2×C127—21no—
264C2×C127—21no—
265C2×C127—81no—
266C2×C127—81no—
267C2×C127#179311yescharacteristic
268C2×C127#179511yescharacteristic
269C2×C127#179611yescharacteristic
270#3552C2×C12711yescharacteristic
271#1993C2×C12711yescharacteristic, complemented
272#1556C2×C12711yescharacteristic, complemented
273#1532C2×C12711yescharacteristic, complemented
274#1532C2×C12711yescharacteristic, complemented
275#1512C2×C12711yescharacteristic, complemented
276#1512C2×C12711yescharacteristic, complemented
277C127#849911yescharacteristic, direct product factor, Sylow
278#563—22no—
279#557C4×C12711yescharacteristic, complemented
280#556C4×C12711yescharacteristic, complemented
281#554—21no—
282#553—21no—
283D4×Q8—21no—
284D4×Q8C4×C12711yescharacteristic, complemented
285#548—21no—
286#547C4×C12711yescharacteristic, complemented
287#544—21no—
288#542—21no—
289#541—21no—
290#539—22no—
291#536—21no—
292C2×C4⋊Q8C22×C12711yescharacteristic
293#529C22×C12711yescharacteristic
294#529C22×C12711yescharacteristic
295#432C22×C12711yescharacteristic
296#432C22×C12711yescharacteristic
297C2×#97C22×C12711yescharacteristic
298#382C22×C12711yescharacteristic
299#340—22no—
300#332—22no—
301#330—21no—
302#330—21no—
303#329—21no—
304#329—21no—
305#328—21no—
306#328—21no—
307#327—21no—
308#327—21no—
309C2×#41—21no—
310C22×Q8—21no—
311C22×Q8—21no—
312C22×C8—21no—
313C4⋊Q8—22no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8C2×C4×C12711yescharacteristic
319C4⋊Q8C2×C4×C12711yescharacteristic
320C4⋊Q8D4×C12712yes—
321#126—22no—
322#126—22no—
323#126—22no—
324#126—21no—
325#126—21no—
326#125—22no—
327#125—22no—
328#125—22no—
329#125—21no—
330#125D4×C12711yescharacteristic
331#125D4×C12711yescharacteristic
332#124—22no—
333#124—21no—
334#124D4×C12711yescharacteristic
335#124D4×C12711yescharacteristic
336#123—22no—
337#123—22no—
338#123—21no—
339#123—21no—
340#123—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—21no—
347C22⋊Q8—22no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8D4×C12711yescharacteristic
351C22⋊Q8D4×C12711yescharacteristic
352#121—22no—
353#121—21no—
354#121D4×C12711yescharacteristic
355#121D4×C12711yescharacteristic
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8C2×C4×C12711yescharacteristic
360C4×Q8C2×C4×C12711yescharacteristic
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4—21no—
366C4×D4C2×C4×C12711yescharacteristic
367C4×D4C2×C4×C12711yescharacteristic
368#117—21no—
369#117—21no—
370#117—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4D4×C12712yes—
375C2×C42C23×C12711yescharacteristic
376C4⋊C8—21no—
377C4⋊C8—21no—
378C22⋊C8—21no—
379C22⋊C8—21no—
380#97—21no—
381#97—21no—
382#97—21no—
383#97—21no—
384#95—21no—
385#95—21no—
386#41—82no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—82no—
392C2×Q8—82no—
393C2×Q8C22⋊C4×C12711yescharacteristic
394C2×Q8C22⋊C4×C12711yescharacteristic
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—22no—
398C2×D4C22⋊C4×C12711yescharacteristic
399C2×D4C22⋊C4×C12711yescharacteristic
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—41no—
406C22×C4C2×D4×C12711yescharacteristic
407C22×C4C2×D4×C12711yescharacteristic
408C22×C4C2×D4×C12711yescharacteristic
409C2×C8—22no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—41no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—42no—
433C4⋊C4C22⋊C4×C12711yescharacteristic
434C4⋊C4C22⋊C4×C12712yes—
435C4⋊C4C22⋊C4×C12712yes—
436C4⋊C4C22⋊C4×C12711yescharacteristic
437C4⋊C4C22⋊C4×C12711yescharacteristic
438C4⋊C4C22⋊C4×C12711yescharacteristic
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—21no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C42—22no—
454C42—22no—
455C42—21no—
456C42—21no—
457C42C22×C4×C12711yescharacteristic
458C42C2×D4×C12711yescharacteristic
459C42C2×D4×C12711yescharacteristic
460C42C2×D4×C12711yescharacteristic
461C23—21no—
462C23—21no—
463C23#120×C12711yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—42no—
467Q8—42no—
468Q8—82no—
469Q8—82no—
470D4—41no—
471D4—41no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—82no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—82no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4C2×C22⋊C4×C12711yescharacteristic
498C2×C4C2×C22⋊C4×C12711yescharacteristic
499C2×C4C2×C22⋊C4×C12711yescharacteristic
500C2×C4#120×C12711yescharacteristic
501C2×C4#120×C12711yescharacteristic
502C2×C4#120×C12711yescharacteristic
503C8—42no—
504C8—81no—
505C8—81no—
506C22—21no—
507C22—21no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22#379×C12711yescharacteristic
515C22#454×C12711yescharacteristic
516C22#456×C12711yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—42no—
527C4—42no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—161no—
532C2—21no—
533C2—21no—
534C2—81no—
535C2—81no—
536C2C127×#179311yescharacteristic
537C2C127×#179511yescharacteristic
538C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3552C2
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×#1993C2semidirect
3. C127×#1556C2semidirect
4. C127×#1532C2semidirect
5. C127×#1532C2semidirect
6. C127×#1512C2semidirect
7. C127×#1512C2semidirect
9. #557×C127C4semidirect
10. #556×C127C4semidirect
14. D4×Q8×C127C4semidirect
16. #547×C127C4semidirect
262. #8499C127direct (N × H)
271. #1993C2×C127semidirect
272. #1556C2×C127semidirect
273. #1532C2×C127semidirect
274. #1532C2×C127semidirect
275. #1512C2×C127semidirect
276. #1512C2×C127semidirect
277. C127#8499direct (N × H)
279. #557C4×C127semidirect
280. #556C4×C127semidirect
284. D4×Q8C4×C127semidirect
286. #547C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35522
C127×#19932
C127×#15562
C127×#15322
C127×#15122
#8499127