Finite Group Databasebeta

← C127×#18440 #44582113

Subgroups — C127×#18440 #44582113

Order 32512.

904 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3559C211yesmaximal, characteristic
2C127×#3238C211yesmaximal, characteristic, complemented
3C127×#3226C211yesmaximal, characteristic, complemented
4C127×#2660C211yesmaximal, characteristic, complemented
5C127×#1610C214yesmaximal, complemented
6C127×#1609C214yesmaximal, complemented
7C127×#1505C211yesmaximal, characteristic, complemented
8C127×#1500C211yesmaximal, characteristic, complemented
9C127×#1470C211yesmaximal, characteristic, complemented
10#563×C127—21no—
11#562×C127—21no—
12#554×C127—21no—
13#553×C127—21no—
14#553×C127—21no—
15#547×C127—22no—
16#547×C127—21no—
17#544×C127—21no—
18#540×C127—21no—
19#539×C127—22no—
20#539×C127C2212yes—
21#537×C127C2212yes—
22#532×C127C2211yescharacteristic
23C2×C4⋊Q8×C127C2211yescharacteristic
24#529×C127C2211yescharacteristic
25C2×#125×C127C2211yescharacteristic
26#501×C127—21no—
27#500×C127—21no—
28#489×C127—21no—
29#486×C127—21no—
30#483×C127C2212yes—
31#480×C127C2214yes—
32#480×C127C2212yes—
33#477×C127—21no—
34#476×C127—21no—
35#474×C127—22no—
36#432×C127C2211yescharacteristic
37#431×C127C2211yescharacteristic
38#398×C127C2214yes—
39#395×C127—22no—
40#384×C127—21no—
41#382×C127—21no—
42#376×C127C2211yescharacteristic
43#328×C127C2212yes—
44#327×C127C2214yes—
45#327×C127C2212yes—
46#324×C127C2214yes—
47C2×#41×C127—21no—
48C2×#41×C127—22no—
49C22×Q8×C127—21no—
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127—22no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127—21no—
55C4⋊Q8×C127—21no—
56C4⋊Q8×C127D411yescharacteristic
57#127×C127D411yescharacteristic
58#126×C127—22no—
59#126×C127—22no—
60#126×C127—21no—
61#125×C127—21no—
62#125×C127—22no—
63#125×C127—21no—
64#125×C127—21no—
65#125×C127—21no—
66#125×C127—21no—
67#125×C127D411yescharacteristic
68#124×C127—21no—
69#124×C127D411yescharacteristic
70#123×C127—22no—
71#123×C127—22no—
72#123×C127—22no—
73#123×C127—22no—
74#123×C127—22no—
75#123×C127—21no—
76#123×C127—22no—
77C22⋊Q8×C127—22no—
78C22⋊Q8×C127—22no—
79C22⋊Q8×C127—22no—
80C22⋊Q8×C127—22no—
81C22⋊Q8×C127—22no—
82C22⋊Q8×C127—22no—
83C22⋊Q8×C127C2311yescharacteristic
84#121×C127—21no—
85#121×C127—22no—
86#121×C127—21no—
87#121×C127—22no—
88#121×C127—22no—
89#121×C127—21no—
90#121×C127—22no—
91#121×C127C2311yescharacteristic
92#121×C127C2312yes—
93C4×Q8×C127D411yescharacteristic
94C4×D4×C127—22no—
95C4×D4×C127—21no—
96C4×D4×C127—21no—
97C4×D4×C127—21no—
98C4×D4×C127—22no—
99C4×D4×C127—21no—
100C4×D4×C127D411yescharacteristic
101C4×D4×C127D412yes—
102#117×C127—21no—
103#117×C127—21no—
104C2×C4⋊C4×C127—22no—
105C2×C4⋊C4×C127—21no—
106C2×C4⋊C4×C127—21no—
107C2×C4⋊C4×C127—24no—
108C2×C4⋊C4×C127D411yescharacteristic
109C2×C4⋊C4×C127D412yes—
110C2×C4⋊C4×C127D411yescharacteristic
111C2×C4⋊C4×C127C2312yes—
112C2×C4⋊C4×C127C2312yes—
113C2×C42×C127—21no—
114C2×C42×C127C2311yescharacteristic
115#107×C127—24no—
116#107×C127—22no—
117#106×C127—22no—
118C4⋊C8×C127—21no—
119C4⋊C8×C127—21no—
120#103×C127—22no—
121#102×C127—24no—
122#102×C127—22no—
123C22⋊C8×C127C2312yes—
124C22⋊C8×C127C2312yes—
125#97×C127—21no—
126C4×C8×C127—21no—
127#95×C127—21no—
128#95×C127—24no—
129#95×C127C2312yes—
130#41×C127—82no—
131#41×C127—84no—
132C2×Q8×C127—22no—
133C2×Q8×C127—21no—
134C2×Q8×C127—41no—
135C2×Q8×C127—41no—
136C2×Q8×C127—82no—
137C2×Q8×C127C2×D411yescharacteristic
138C2×D4×C127—21no—
139C2×D4×C127—22no—
140C2×D4×C127—22no—
141C2×D4×C127—22no—
142C2×D4×C127—21no—
143C2×D4×C127—21no—
144C2×D4×C127C2×D411yescharacteristic
145C2×D4×C127C2×D412yes—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—21no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127C2×D412yes—
154C22×C4×C127C2×D411yescharacteristic
155C22×C4×C127C2×D411yescharacteristic
156C22×C4×C127C2×D412yes—
157C22×C4×C127C2411yescharacteristic
158C2×C8×C127—22no—
159C2×C8×C127—22no—
160C4⋊C4×C127—22no—
161C4⋊C4×C127—22no—
162C4⋊C4×C127—22no—
163C4⋊C4×C127—22no—
164C4⋊C4×C127—21no—
165C4⋊C4×C127—21no—
166C4⋊C4×C127—22no—
167C4⋊C4×C127—21no—
168C4⋊C4×C127—21no—
169C4⋊C4×C127—22no—
170C4⋊C4×C127—21no—
171C4⋊C4×C127—21no—
172C4⋊C4×C127—21no—
173C4⋊C4×C127—21no—
174C4⋊C4×C127—22no—
175C4⋊C4×C127—22no—
176C4⋊C4×C127—21no—
177C4⋊C4×C127—22no—
178C4⋊C4×C127—22no—
179C4⋊C4×C127—41no—
180C4⋊C4×C127—41no—
181C4⋊C4×C127—84no—
182C4⋊C4×C127C2×D411yescharacteristic
183C4⋊C4×C127C2×D412yes—
184C4⋊C4×C127C2×D411yescharacteristic
185C22⋊C4×C127—22no—
186C22⋊C4×C127—22no—
187C22⋊C4×C127—22no—
188C22⋊C4×C127—22no—
189C22⋊C4×C127—22no—
190C22⋊C4×C127—21no—
191C22⋊C4×C127—21no—
192C22⋊C4×C127—21no—
193C22⋊C4×C127—21no—
194C22⋊C4×C127—22no—
195C22⋊C4×C127—21no—
196C22⋊C4×C127—22no—
197C42×C127—24no—
198C42×C127—22no—
199C42×C127—21no—
200C42×C127C2×D411yescharacteristic
201C42×C127C2×D411yescharacteristic
202C42×C127C2×D411yescharacteristic
203C42×C127C2×D411yescharacteristic
204C23×C127—21no—
205C23×C127—22no—
206C23×C127C22×D411yescharacteristic
207Q8×C127—41no—
208Q8×C127—81no—
209Q8×C127—82no—
210Q8×C127—82no—
211Q8×C127—82no—
212D4×C127—42no—
213D4×C127—41no—
214D4×C127—44no—
215D4×C127—42no—
216D4×C127—42no—
217D4×C127—81no—
218D4×C127—82no—
219D4×C127—82no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—24no—
223C2×C4×C127—21no—
224C2×C4×C127—21no—
225C2×C4×C127—22no—
226C2×C4×C127—22no—
227C2×C4×C127—21no—
228C2×C4×C127—22no—
229C2×C4×C127—24no—
230C2×C4×C127—41no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—42no—
235C2×C4×C127—42no—
236C2×C4×C127—44no—
237C2×C4×C127—82no—
238C2×C4×C127—82no—
239C2×C4×C127—82no—
240C2×C4×C127—82no—
241C2×C4×C127#12011yescharacteristic
242C2×C4×C127#12011yescharacteristic
243C2×C4×C127#12011yescharacteristic
244C2×C4×C127#12011yescharacteristic
245C2×C4×C127C22×D411yescharacteristic
246C2×C4×C127C22×D411yescharacteristic
247C8×C127—42no—
248C8×C127—42no—
249C22×C127—21no—
250C22×C127—21no—
251C22×C127—42no—
252C22×C127—41no—
253C22×C127—41no—
254C22×C127—42no—
255C22×C127—42no—
256C22×C127—41no—
257C22×C127C2×#12011yescharacteristic
258C22×C127#57612yes—
259C4×C127—21no—
260C4×C127—21no—
261C4×C127—21no—
262C4×C127—21no—
263C4×C127—21no—
264C4×C127—44no—
265C4×C127—42no—
266C4×C127—42no—
267C4×C127—41no—
268C4×C127—41no—
269C4×C127—42no—
270C4×C127—41no—
271C4×C127—82no—
272C4×C127#45612yes—
273#18440C12711yesmaximal, characteristic, direct product factor, Sylow
274C2×C127—22no—
275C2×C127—81no—
276C2×C127—82no—
277C2×C127#300811yescharacteristic
278C2×C127C2×#45611yescharacteristic
279C2×C127#302811yescharacteristic
280#3559C2×C12711yescharacteristic
281#3238C2×C12711yescharacteristic, complemented
282#3226C2×C12711yescharacteristic, complemented
283#2660C2×C12711yescharacteristic, complemented
284#1610C2×C12714yescomplemented
285#1609C2×C12714yescomplemented
286#1505C2×C12711yescharacteristic, complemented
287#1500C2×C12711yescharacteristic, complemented
288#1470C2×C12711yescharacteristic, complemented
289C127#1844011yescharacteristic, direct product factor, Sylow
290#563—21no—
291#562—21no—
292#554—21no—
293#553—21no—
294#553—21no—
295#547—22no—
296#547—21no—
297#544—21no—
298#540—21no—
299#539—22no—
300#539C22×C12712yes—
301#537C22×C12712yes—
302#532C22×C12711yescharacteristic
303C2×C4⋊Q8C22×C12711yescharacteristic
304#529C22×C12711yescharacteristic
305C2×#125C22×C12711yescharacteristic
306#501—21no—
307#500—21no—
308#489—21no—
309#486—21no—
310#483C22×C12712yes—
311#480C22×C12714yes—
312#480C22×C12712yes—
313#477—21no—
314#476—21no—
315#474—22no—
316#432C22×C12711yescharacteristic
317#431C22×C12711yescharacteristic
318#398C22×C12714yes—
319#395—22no—
320#384—21no—
321#382—21no—
322#376C22×C12711yescharacteristic
323#328C22×C12712yes—
324#327C22×C12714yes—
325#327C22×C12712yes—
326#324C22×C12714yes—
327C2×#41—21no—
328C2×#41—22no—
329C22×Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8—22no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8D4×C12711yescharacteristic
337#127D4×C12711yescharacteristic
338#126—22no—
339#126—22no—
340#126—21no—
341#125—21no—
342#125—22no—
343#125—21no—
344#125—21no—
345#125—21no—
346#125—21no—
347#125D4×C12711yescharacteristic
348#124—21no—
349#124D4×C12711yescharacteristic
350#123—22no—
351#123—22no—
352#123—22no—
353#123—22no—
354#123—22no—
355#123—21no—
356#123—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8C23×C12711yescharacteristic
364#121—21no—
365#121—22no—
366#121—21no—
367#121—22no—
368#121—22no—
369#121—21no—
370#121—22no—
371#121C23×C12711yescharacteristic
372#121C23×C12712yes—
373C4×Q8D4×C12711yescharacteristic
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4D4×C12711yescharacteristic
381C4×D4D4×C12712yes—
382#117—21no—
383#117—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4D4×C12711yescharacteristic
389C2×C4⋊C4D4×C12712yes—
390C2×C4⋊C4D4×C12711yescharacteristic
391C2×C4⋊C4C23×C12712yes—
392C2×C4⋊C4C23×C12712yes—
393C2×C42—21no—
394C2×C42C23×C12711yescharacteristic
395#107—24no—
396#107—22no—
397#106—22no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400#103—22no—
401#102—24no—
402#102—22no—
403C22⋊C8C23×C12712yes—
404C22⋊C8C23×C12712yes—
405#97—21no—
406C4×C8—21no—
407#95—21no—
408#95—24no—
409#95C23×C12712yes—
410#41—82no—
411#41—84no—
412C2×Q8—22no—
413C2×Q8—21no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—82no—
417C2×Q8C2×D4×C12711yescharacteristic
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C2×D4×C12711yescharacteristic
425C2×D4C2×D4×C12712yes—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4C2×D4×C12712yes—
434C22×C4C2×D4×C12711yescharacteristic
435C22×C4C2×D4×C12711yescharacteristic
436C22×C4C2×D4×C12712yes—
437C22×C4C24×C12711yescharacteristic
438C2×C8—22no—
439C2×C8—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—84no—
462C4⋊C4C2×D4×C12711yescharacteristic
463C4⋊C4C2×D4×C12712yes—
464C4⋊C4C2×D4×C12711yescharacteristic
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—22no—
475C22⋊C4—21no—
476C22⋊C4—22no—
477C42—24no—
478C42—22no—
479C42—21no—
480C42C2×D4×C12711yescharacteristic
481C42C2×D4×C12711yescharacteristic
482C42C2×D4×C12711yescharacteristic
483C42C2×D4×C12711yescharacteristic
484C23—21no—
485C23—22no—
486C23C22×D4×C12711yescharacteristic
487Q8—41no—
488Q8—81no—
489Q8—82no—
490Q8—82no—
491Q8—82no—
492D4—42no—
493D4—41no—
494D4—44no—
495D4—42no—
496D4—42no—
497D4—81no—
498D4—82no—
499D4—82no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4#120×C12711yescharacteristic
522C2×C4#120×C12711yescharacteristic
523C2×C4#120×C12711yescharacteristic
524C2×C4#120×C12711yescharacteristic
525C2×C4C22×D4×C12711yescharacteristic
526C2×C4C22×D4×C12711yescharacteristic
527C8—42no—
528C8—42no—
529C22—21no—
530C22—21no—
531C22—42no—
532C22—41no—
533C22—41no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22C2×#120×C12711yescharacteristic
538C22#576×C12712yes—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—44no—
545C4—42no—
546C4—42no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—41no—
551C4—82no—
552C4#456×C12712yes—
553C2—22no—
554C2—81no—
555C2—82no—
556C2C127×#300811yescharacteristic
557C2C2×#456×C12711yescharacteristic
558C2C127×#302811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#3559C2
LCSG ▷ C22×C4 ▷ 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×#3238C2semidirect
3. C127×#3226C2semidirect
4. C127×#2660C2semidirect
5. C127×#1610C2semidirect
6. C127×#1609C2semidirect
7. C127×#1505C2semidirect
8. C127×#1500C2semidirect
9. C127×#1470C2semidirect
273. #18440C127direct (N × H)
281. #3238C2×C127semidirect
282. #3226C2×C127semidirect
283. #2660C2×C127semidirect
284. #1610C2×C127semidirect
285. #1609C2×C127semidirect
286. #1505C2×C127semidirect
287. #1500C2×C127semidirect
288. #1470C2×C127semidirect
289. C127#18440direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35592
C127×#32382
C127×#32262
C127×#26602
C127×#16102
C127×#16092
C127×#15052
C127×#15002
C127×#14702
#18440127