Finite Group Databasebeta

← C127×#8501 #44572174

Subgroups — C127×#8501 #44572174

Order 32512.

616 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3555C211yesmaximal, characteristic
2C127×#1554C211yesmaximal, characteristic, complemented
3C127×#1535C211yesmaximal, characteristic
4C127×#1521C211yesmaximal, characteristic
5C127×#1515C211yesmaximal, characteristic, complemented
6C127×#1515C211yesmaximal, characteristic, complemented
7C127×#1497C211yesmaximal, characteristic, complemented
8#563×C127—22no—
9Q82×C127C411yescharacteristic, complemented
10#557×C127—21no—
11#557×C127C411yescharacteristic, complemented
12#556×C127—21no—
13#556×C127—21no—
14#556×C127C411yescharacteristic, complemented
15#554×C127C411yescharacteristic, complemented
16#552×C127—21no—
17#544×C127—21no—
18#542×C127—21no—
19#541×C127—21no—
20#541×C127—21no—
21#541×C127—22no—
22#533×C127C2211yescharacteristic
23#533×C127C2211yescharacteristic
24#529×C127C2211yescharacteristic
25#432×C127C2211yescharacteristic
26#432×C127C2211yescharacteristic
27#431×C127C2211yescharacteristic
28#383×C127C2211yescharacteristic
29#333×C127—21no—
30#332×C127—21no—
31#330×C127—21no—
32#329×C127—21no—
33#328×C127—21no—
34#328×C127—21no—
35#328×C127—22no—
36#328×C127—21no—
37#327×C127—21no—
38Q8⋊C8×C127—22no—
39C4⋊Q8×C127—22no—
40C4⋊Q8×C127—21no—
41C4⋊Q8×C127—22no—
42C4⋊Q8×C127—21no—
43C4⋊Q8×C127—21no—
44C4⋊Q8×C127C2×C411yescharacteristic
45C4⋊Q8×C127C2×C411yescharacteristic
46C4⋊Q8×C127D411yescharacteristic
47C4⋊Q8×C127D411yescharacteristic
48#126×C127—22no—
49#126×C127—22no—
50#126×C127—22no—
51#126×C127—22no—
52#126×C127—22no—
53#126×C127—22no—
54#126×C127—21no—
55#125×C127—22no—
56#125×C127—22no—
57#125×C127—22no—
58#125×C127—22no—
59#125×C127—21no—
60#125×C127—22no—
61#125×C127—21no—
62#125×C127—21no—
63#125×C127—21no—
64#125×C127D411yescharacteristic
65#124×C127—22no—
66#124×C127—21no—
67#124×C127D411yescharacteristic
68#123×C127—22no—
69#123×C127—21no—
70C22⋊Q8×C127—22no—
71C22⋊Q8×C127—22no—
72C22⋊Q8×C127—21no—
73C22⋊Q8×C127—21no—
74C22⋊Q8×C127—22no—
75C22⋊Q8×C127—21no—
76C22⋊Q8×C127—21no—
77C22⋊Q8×C127D411yescharacteristic
78C22⋊Q8×C127D411yescharacteristic
79C22⋊Q8×C127D411yescharacteristic
80C22⋊Q8×C127D412yes—
81#121×C127D411yescharacteristic
82C4×Q8×C127—22no—
83C4×Q8×C127—21no—
84C4×Q8×C127—21no—
85C4×Q8×C127—21no—
86C4×Q8×C127—21no—
87C4×Q8×C127—21no—
88C4×Q8×C127—21no—
89C4×Q8×C127—21no—
90C4×Q8×C127C2×C411yescharacteristic
91C4×Q8×C127C2×C411yescharacteristic
92C4×Q8×C127C2×C411yescharacteristic
93C4×Q8×C127D412yes—
94C4×D4×C127—21no—
95C4×D4×C127—21no—
96C4×D4×C127C2×C411yescharacteristic
97#117×C127—22no—
98#117×C127—21no—
99#117×C127—21no—
100#117×C127—21no—
101#117×C127—21no—
102C2×C4⋊C4×C127—21no—
103C2×C42×C127C2311yescharacteristic
104C4⋊C8×C127—21no—
105C4⋊C8×C127—21no—
106C4⋊C8×C127—21no—
107C22⋊C8×C127—21no—
108C22⋊C8×C127—21no—
109C22⋊C8×C127—21no—
110#97×C127—21no—
111#97×C127—21no—
112C4×C8×C127—21no—
113#95×C127—21no—
114#95×C127—21no—
115#95×C127—21no—
116C2×Q8×C127—22no—
117C2×Q8×C127—21no—
118C2×Q8×C127—21no—
119C2×Q8×C127C22⋊C411yescharacteristic
120C2×Q8×C127C22⋊C411yescharacteristic
121C2×Q8×C127C22⋊C411yescharacteristic
122C2×Q8×C127C22⋊C412yes—
123C2×D4×C127—21no—
124C2×D4×C127C22⋊C411yescharacteristic
125C22×C4×C127—22no—
126C22×C4×C127—21no—
127C22×C4×C127—41no—
128C22×C4×C127C2×D411yescharacteristic
129C22×C4×C127C2×D411yescharacteristic
130C22×C4×C127C2×D411yescharacteristic
131C2×C8×C127—41no—
132C2×C8×C127—41no—
133C2×C8×C127—41no—
134C4⋊C4×C127—22no—
135C4⋊C4×C127—22no—
136C4⋊C4×C127—22no—
137C4⋊C4×C127—22no—
138C4⋊C4×C127—22no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—21no—
146C4⋊C4×C127—21no—
147C4⋊C4×C127—21no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—21no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—21no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—21no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127C22⋊C411yescharacteristic
159C4⋊C4×C127C22⋊C411yescharacteristic
160C4⋊C4×C127C22⋊C411yescharacteristic
161C4⋊C4×C127C22⋊C411yescharacteristic
162C4⋊C4×C127C22⋊C412yes—
163C22⋊C4×C127—22no—
164C22⋊C4×C127—22no—
165C22⋊C4×C127—22no—
166C22⋊C4×C127—21no—
167C22⋊C4×C127—22no—
168C22⋊C4×C127—21no—
169C22⋊C4×C127—21no—
170C22⋊C4×C127—21no—
171C22⋊C4×C127—21no—
172C22⋊C4×C127—21no—
173C22⋊C4×C127—21no—
174C42×C127—22no—
175C42×C127—22no—
176C42×C127—22no—
177C42×C127—21no—
178C42×C127—21no—
179C42×C127—21no—
180C42×C127—22no—
181C42×C127C22×C411yescharacteristic
182C42×C127C2×D411yescharacteristic
183C42×C127C2×D411yescharacteristic
184C42×C127C2×D411yescharacteristic
185C23×C127—21no—
186C23×C127#12011yescharacteristic
187Q8×C127—42no—
188Q8×C127—41no—
189Q8×C127—41no—
190Q8×C127—41no—
191Q8×C127—42no—
192Q8×C127—81no—
193Q8×C127—82no—
194D4×C127—41no—
195D4×C127—81no—
196C2×C4×C127—21no—
197C2×C4×C127—21no—
198C2×C4×C127—21no—
199C2×C4×C127—22no—
200C2×C4×C127—21no—
201C2×C4×C127—21no—
202C2×C4×C127—21no—
203C2×C4×C127—22no—
204C2×C4×C127—21no—
205C2×C4×C127—41no—
206C2×C4×C127—41no—
207C2×C4×C127—41no—
208C2×C4×C127—42no—
209C2×C4×C127—82no—
210C2×C4×C127—81no—
211C2×C4×C127—81no—
212C2×C4×C127—81no—
213C2×C4×C127C2×C22⋊C411yescharacteristic
214C2×C4×C127C2×C22⋊C411yescharacteristic
215C2×C4×C127C2×C22⋊C411yescharacteristic
216C2×C4×C127#12011yescharacteristic
217C2×C4×C127#12011yescharacteristic
218C2×C4×C127#12011yescharacteristic
219C8×C127—81no—
220C8×C127—81no—
221C8×C127—81no—
222C22×C127—21no—
223C22×C127—21no—
224C22×C127—21no—
225C22×C127—41no—
226C22×C127—41no—
227C22×C127—41no—
228C22×C127#37911yescharacteristic
229C4×C127—21no—
230C4×C127—21no—
231C4×C127—21no—
232C4×C127—21no—
233C4×C127—21no—
234C4×C127—21no—
235C4×C127—41no—
236C4×C127—42no—
237C4×C127—41no—
238C4×C127—41no—
239C4×C127—41no—
240C4×C127—41no—
241C4×C127—41no—
242C4×C127—41no—
243C4×C127—42no—
244C4×C127—161no—
245#8501C12711yesmaximal, characteristic, direct product factor, Sylow
246C2×C127—41no—
247C2×C127—81no—
248C2×C127#179411yescharacteristic
249C2×C127#179611yescharacteristic
250C2×C127#179611yescharacteristic
251#3555C2×C12711yescharacteristic
252#1554C2×C12711yescharacteristic, complemented
253#1535C2×C12711yescharacteristic
254#1521C2×C12711yescharacteristic
255#1515C2×C12711yescharacteristic, complemented
256#1515C2×C12711yescharacteristic, complemented
257#1497C2×C12711yescharacteristic, complemented
258C127#850111yescharacteristic, direct product factor, Sylow
259#563—22no—
260Q82C4×C12711yescharacteristic, complemented
261#557—21no—
262#557C4×C12711yescharacteristic, complemented
263#556—21no—
264#556—21no—
265#556C4×C12711yescharacteristic, complemented
266#554C4×C12711yescharacteristic, complemented
267#552—21no—
268#544—21no—
269#542—21no—
270#541—21no—
271#541—21no—
272#541—22no—
273#533C22×C12711yescharacteristic
274#533C22×C12711yescharacteristic
275#529C22×C12711yescharacteristic
276#432C22×C12711yescharacteristic
277#432C22×C12711yescharacteristic
278#431C22×C12711yescharacteristic
279#383C22×C12711yescharacteristic
280#333—21no—
281#332—21no—
282#330—21no—
283#329—21no—
284#328—21no—
285#328—21no—
286#328—22no—
287#328—21no—
288#327—21no—
289Q8⋊C8—22no—
290C4⋊Q8—22no—
291C4⋊Q8—21no—
292C4⋊Q8—22no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8C2×C4×C12711yescharacteristic
296C4⋊Q8C2×C4×C12711yescharacteristic
297C4⋊Q8D4×C12711yescharacteristic
298C4⋊Q8D4×C12711yescharacteristic
299#126—22no—
300#126—22no—
301#126—22no—
302#126—22no—
303#126—22no—
304#126—22no—
305#126—21no—
306#125—22no—
307#125—22no—
308#125—22no—
309#125—22no—
310#125—21no—
311#125—22no—
312#125—21no—
313#125—21no—
314#125—21no—
315#125D4×C12711yescharacteristic
316#124—22no—
317#124—21no—
318#124D4×C12711yescharacteristic
319#123—22no—
320#123—21no—
321C22⋊Q8—22no—
322C22⋊Q8—22no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—22no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8D4×C12711yescharacteristic
329C22⋊Q8D4×C12711yescharacteristic
330C22⋊Q8D4×C12711yescharacteristic
331C22⋊Q8D4×C12712yes—
332#121D4×C12711yescharacteristic
333C4×Q8—22no—
334C4×Q8—21no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8—21no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8C2×C4×C12711yescharacteristic
342C4×Q8C2×C4×C12711yescharacteristic
343C4×Q8C2×C4×C12711yescharacteristic
344C4×Q8D4×C12712yes—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4C2×C4×C12711yescharacteristic
348#117—22no—
349#117—21no—
350#117—21no—
351#117—21no—
352#117—21no—
353C2×C4⋊C4—21no—
354C2×C42C23×C12711yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361#97—21no—
362#97—21no—
363C4×C8—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8C22⋊C4×C12711yescharacteristic
371C2×Q8C22⋊C4×C12711yescharacteristic
372C2×Q8C22⋊C4×C12711yescharacteristic
373C2×Q8C22⋊C4×C12712yes—
374C2×D4—21no—
375C2×D4C22⋊C4×C12711yescharacteristic
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4C2×D4×C12711yescharacteristic
380C22×C4C2×D4×C12711yescharacteristic
381C22×C4C2×D4×C12711yescharacteristic
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—41no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4C22⋊C4×C12711yescharacteristic
410C4⋊C4C22⋊C4×C12711yescharacteristic
411C4⋊C4C22⋊C4×C12711yescharacteristic
412C4⋊C4C22⋊C4×C12711yescharacteristic
413C4⋊C4C22⋊C4×C12712yes—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—21no—
418C22⋊C4—22no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—21no—
425C42—22no—
426C42—22no—
427C42—22no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—22no—
432C42C22×C4×C12711yescharacteristic
433C42C2×D4×C12711yescharacteristic
434C42C2×D4×C12711yescharacteristic
435C42C2×D4×C12711yescharacteristic
436C23—21no—
437C23#120×C12711yescharacteristic
438Q8—42no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—42no—
443Q8—81no—
444Q8—82no—
445D4—41no—
446D4—81no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—21no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—82no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4C2×C22⋊C4×C12711yescharacteristic
465C2×C4C2×C22⋊C4×C12711yescharacteristic
466C2×C4C2×C22⋊C4×C12711yescharacteristic
467C2×C4#120×C12711yescharacteristic
468C2×C4#120×C12711yescharacteristic
469C2×C4#120×C12711yescharacteristic
470C8—81no—
471C8—81no—
472C8—81no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22#379×C12711yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—41no—
487C4—42no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—42no—
492C4—41no—
493C4—41no—
494C4—41no—
495C4—161no—
496C2—41no—
497C2—81no—
498C2C127×#179411yescharacteristic
499C2C127×#179611yescharacteristic
500C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#121×C127D4
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×#1554C2semidirect
5. C127×#1515C2semidirect
6. C127×#1515C2semidirect
7. C127×#1497C2semidirect
9. Q82×C127C4semidirect
11. #557×C127C4semidirect
14. #556×C127C4semidirect
15. #554×C127C4semidirect
245. #8501C127direct (N × H)
252. #1554C2×C127semidirect
255. #1515C2×C127semidirect
256. #1515C2×C127semidirect
257. #1497C2×C127semidirect
258. C127#8501direct (N × H)
260. Q82C4×C127semidirect
262. #557C4×C127semidirect
265. #556C4×C127semidirect
266. #554C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35552
C127×#15542
C127×#15352
C127×#15212
C127×#15152
C127×#14972
#8501127