Finite Group Databasebeta

← C127×#8412 #44572085

Subgroups — C127×#8412 #44572085

Order 32512.

768 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3514C211yesmaximal, 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#559×C127C411yescharacteristic, complemented
9#556×C127C411yescharacteristic, complemented
10#555×C127—21no—
11#551×C127—22no—
12D4×Q8×C127C411yescharacteristic, complemented
13#548×C127—21no—
14#546×C127—21no—
15#546×C127—21no—
16D42×C127C411yescharacteristic, complemented
17#542×C127—21no—
18#538×C127—22no—
19#532×C127C2211yescharacteristic
20#529×C127—21no—
21#529×C127C2211yescharacteristic
22C2×#124×C127—21no—
23#518×C127—21no—
24C4×#41×C127C2211yescharacteristic
25#432×C127C2211yescharacteristic, complemented
26#431×C127C2211yescharacteristic, complemented
27C2×#104×C127—21no—
28C4×M16×C127C2211yescharacteristic, complemented
29#376×C127C2211yescharacteristic, complemented
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×C127D411yescharacteristic
41C22×Q8×C127—21no—
42C22×D4×C127—21no—
43C22×D4×C127—21no—
44C2×M16×C127—21no—
45C4⋊Q8×C127—21no—
46C4⋊Q8×C127C2×C411yescharacteristic
47#127×C127C2×C411yescharacteristic
48#126×C127—22no—
49#126×C127—22no—
50#126×C127—21no—
51#125×C127D411yescharacteristic
52#124×C127—22no—
53#124×C127—22no—
54#124×C127—22no—
55#124×C127—21no—
56#124×C127—21no—
57#124×C127—21no—
58#124×C127—21no—
59#124×C127D411yescharacteristic
60#123×C127—22no—
61#123×C127—22no—
62#123×C127—22no—
63#123×C127—21no—
64C22⋊Q8×C127—22no—
65C22⋊Q8×C127—21no—
66C22⋊Q8×C127—21no—
67C22⋊Q8×C127—22no—
68C22⋊Q8×C127D411yescharacteristic
69#121×C127—22no—
70#121×C127—22no—
71#121×C127—21no—
72#121×C127—21no—
73#121×C127—21no—
74#121×C127D411yescharacteristic
75#121×C127D412yes—
76#120×C127—22no—
77#120×C127—22no—
78C4×Q8×C127—21no—
79C4×Q8×C127C2×C411yescharacteristic
80C4×Q8×C127C2×C411yescharacteristic
81C4×Q8×C127D411yescharacteristic
82C4×D4×C127—22no—
83C4×D4×C127—22no—
84C4×D4×C127—21no—
85C4×D4×C127—21no—
86C4×D4×C127—21no—
87C4×D4×C127—21no—
88C4×D4×C127—21no—
89C4×D4×C127—21no—
90C4×D4×C127—21no—
91C4×D4×C127C2×C411yescharacteristic
92C4×D4×C127C2×C411yescharacteristic
93C4×D4×C127D411yescharacteristic
94C4×D4×C127D412yes—
95#117×C127—22no—
96#117×C127—21no—
97#117×C127—21no—
98#117×C127—21no—
99#117×C127D411yescharacteristic
100C2×C22⋊C4×C127—22no—
101C2×C22⋊C4×C127—22no—
102C2×C22⋊C4×C127—22no—
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—
117C24×C127—22no—
118#41×C127—22no—
119#41×C127—41no—
120#41×C127—82no—
121C2×Q8×C127—22no—
122C2×Q8×C127—21no—
123C2×Q8×C127—82no—
124C2×Q8×C127C22⋊C411yescharacteristic
125C2×Q8×C127C22⋊C411yescharacteristic
126C2×D4×C127—22no—
127C2×D4×C127—21no—
128C2×D4×C127—22no—
129C2×D4×C127—21no—
130C2×D4×C127—22no—
131C2×D4×C127—21no—
132C2×D4×C127—21no—
133C2×D4×C127—42no—
134C2×D4×C127—42no—
135C2×D4×C127—82no—
136C2×D4×C127C22⋊C411yescharacteristic
137C2×D4×C127C22⋊C411yescharacteristic
138C2×D4×C127C22⋊C412yes—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—21no—
142C22×C4×C127—21no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—22no—
146C22×C4×C127—41no—
147C22×C4×C127C2×D411yescharacteristic
148C22×C4×C127C2×D411yescharacteristic
149C22×C4×C127C2×D411yescharacteristic
150M16×C127—22no—
151M16×C127—41no—
152C2×C8×C127—41no—
153C2×C8×C127—41no—
154C2×C8×C127—41no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—21no—
158C4⋊C4×C127—21no—
159C4⋊C4×C127—21no—
160C4⋊C4×C127—21no—
161C4⋊C4×C127—21no—
162C4⋊C4×C127—21no—
163C4⋊C4×C127—21no—
164C4⋊C4×C127C22⋊C411yescharacteristic
165C4⋊C4×C127C22⋊C411yescharacteristic
166C4⋊C4×C127C22⋊C411yescharacteristic
167C4⋊C4×C127C22⋊C411yescharacteristic
168C4⋊C4×C127C22⋊C412yes—
169C22⋊C4×C127—22no—
170C22⋊C4×C127—22no—
171C22⋊C4×C127—22no—
172C22⋊C4×C127—22no—
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—21no—
183C22⋊C4×C127—21no—
184C22⋊C4×C127—22no—
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—21no—
199C23×C127—22no—
200C23×C127—44no—
201C23×C127—82no—
202C23×C127—82no—
203C23×C127#12011yescharacteristic
204Q8×C127—21no—
205Q8×C127—21no—
206Q8×C127—41no—
207Q8×C127—42no—
208Q8×C127—82no—
209D4×C127—21no—
210D4×C127—41no—
211D4×C127—42no—
212D4×C127—42no—
213D4×C127—42no—
214D4×C127—44no—
215D4×C127—41no—
216D4×C127—41no—
217D4×C127—81no—
218D4×C127—82no—
219D4×C127—82no—
220D4×C127#10412yes—
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—21no—
228C2×C4×C127—21no—
229C2×C4×C127—22no—
230C2×C4×C127—41no—
231C2×C4×C127—41no—
232C2×C4×C127—42no—
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—22no—
256C22×C127—41no—
257C22×C127—41no—
258C22×C127—42no—
259C22×C127—41no—
260C22×C127—42no—
261C22×C127—41no—
262C22×C127—41no—
263C22×C127—42no—
264C22×C127—164no—
265C22×C127#37911yescharacteristic
266C4×C127—21no—
267C4×C127—21no—
268C4×C127—21no—
269C4×C127—21no—
270C4×C127—21no—
271C4×C127—41no—
272C4×C127—41no—
273C4×C127—41no—
274C4×C127—42no—
275C4×C127—41no—
276C4×C127—41no—
277C4×C127—41no—
278C4×C127—82no—
279C4×C127C2×#10411yescharacteristic
280C4×C127#42111yescharacteristic
281#8412C12711yesmaximal, characteristic, direct product factor, Sylow
282C2×C127—41no—
283C2×C127—42no—
284C2×C127—82no—
285C2×C127—81no—
286C2×C127#178911yescharacteristic
287C2×C127#179411yescharacteristic
288C2×C127#179511yescharacteristic
289#3514C2×C12711yescharacteristic
290#1759C2×C12711yescharacteristic, complemented
291#1529C2×C12711yescharacteristic, complemented
292#1505C2×C12711yescharacteristic, complemented
293#1500C2×C12711yescharacteristic, complemented
294#1488C2×C12711yescharacteristic, complemented
295#1484C2×C12711yescharacteristic, complemented
296C127#841211yescharacteristic, direct product factor, Sylow
297#559C4×C12711yescharacteristic, complemented
298#556C4×C12711yescharacteristic, complemented
299#555—21no—
300#551—22no—
301D4×Q8C4×C12711yescharacteristic, complemented
302#548—21no—
303#546—21no—
304#546—21no—
305D42C4×C12711yescharacteristic, complemented
306#542—21no—
307#538—22no—
308#532C22×C12711yescharacteristic
309#529—21no—
310#529C22×C12711yescharacteristic
311C2×#124—21no—
312#518—21no—
313C4×#41C22×C12711yescharacteristic
314#432C22×C12711yescharacteristic, complemented
315#431C22×C12711yescharacteristic, complemented
316C2×#104—21no—
317C4×M16C22×C12711yescharacteristic, complemented
318#376C22×C12711yescharacteristic, complemented
319#339—21no—
320#330—21no—
321#329—21no—
322#328—21no—
323#327—21no—
324#327—22no—
325Q8⋊C8—21no—
326D4⋊C8—22no—
327D4⋊C8—21no—
328C2×#41—21no—
329C2×#41D4×C12711yescharacteristic
330C22×Q8—21no—
331C22×D4—21no—
332C22×D4—21no—
333C2×M16—21no—
334C4⋊Q8—21no—
335C4⋊Q8C2×C4×C12711yescharacteristic
336#127C2×C4×C12711yescharacteristic
337#126—22no—
338#126—22no—
339#126—21no—
340#125D4×C12711yescharacteristic
341#124—22no—
342#124—22no—
343#124—22no—
344#124—21no—
345#124—21no—
346#124—21no—
347#124—21no—
348#124D4×C12711yescharacteristic
349#123—22no—
350#123—22no—
351#123—22no—
352#123—21no—
353C22⋊Q8—22no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8—22no—
357C22⋊Q8D4×C12711yescharacteristic
358#121—22no—
359#121—22no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121D4×C12711yescharacteristic
364#121D4×C12712yes—
365#120—22no—
366#120—22no—
367C4×Q8—21no—
368C4×Q8C2×C4×C12711yescharacteristic
369C4×Q8C2×C4×C12711yescharacteristic
370C4×Q8D4×C12711yescharacteristic
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C2×C4×C12711yescharacteristic
381C4×D4C2×C4×C12711yescharacteristic
382C4×D4D4×C12711yescharacteristic
383C4×D4D4×C12712yes—
384#117—22no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117D4×C12711yescharacteristic
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42C23×C12711yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—21no—
397#104—24no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400#97—21no—
401#97—21no—
402C4×C8—21no—
403C4×C8—21no—
404#95—21no—
405#95—21no—
406C24—22no—
407#41—22no—
408#41—41no—
409#41—82no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—82no—
413C2×Q8C22⋊C4×C12711yescharacteristic
414C2×Q8C22⋊C4×C12711yescharacteristic
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—82no—
425C2×D4C22⋊C4×C12711yescharacteristic
426C2×D4C22⋊C4×C12711yescharacteristic
427C2×D4C22⋊C4×C12712yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—41no—
436C22×C4C2×D4×C12711yescharacteristic
437C22×C4C2×D4×C12711yescharacteristic
438C22×C4C2×D4×C12711yescharacteristic
439M16—22no—
440M16—41no—
441C2×C8—41no—
442C2×C8—41no—
443C2×C8—41no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4C22⋊C4×C12711yescharacteristic
454C4⋊C4C22⋊C4×C12711yescharacteristic
455C4⋊C4C22⋊C4×C12711yescharacteristic
456C4⋊C4C22⋊C4×C12711yescharacteristic
457C4⋊C4C22⋊C4×C12712yes—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C42—22no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—22no—
481C42—41no—
482C42C22×C4×C12711yescharacteristic
483C42C2×D4×C12711yescharacteristic
484C42C2×D4×C12711yescharacteristic
485C42C2×D4×C12711yescharacteristic
486C23—21no—
487C23—21no—
488C23—22no—
489C23—44no—
490C23—82no—
491C23—82no—
492C23#120×C12711yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—41no—
496Q8—42no—
497Q8—82no—
498D4—21no—
499D4—41no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—44no—
504D4—41no—
505D4—41no—
506D4—82no—
507D4—81no—
508D4—82no—
509D4#104×C12712yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—82no—
527C2×C4—81no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4C2×C22⋊C4×C12711yescharacteristic
533C2×C4C2×C22⋊C4×C12711yescharacteristic
534C2×C4C2×C22⋊C4×C12711yescharacteristic
535C2×C4#120×C12711yescharacteristic
536C2×C4#120×C12711yescharacteristic
537C2×C4#120×C12711yescharacteristic
538C8—42no—
539C8—81no—
540C8—81no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—21no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—164no—
554C22#379×C12711yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—42no—
566C4—41no—
567C4—82no—
568C4C2×#104×C12711yescharacteristic
569C4#421×C12711yescharacteristic
570C2—41no—
571C2—42no—
572C2—81no—
573C2—82no—
574C2C127×#178911yescharacteristic
575C2C127×#179411yescharacteristic
576C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3514C2
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. #559×C127C4semidirect
9. #556×C127C4semidirect
12. D4×Q8×C127C4semidirect
16. D42×C127C4semidirect
25. #432×C127C22semidirect
26. #431×C127C22semidirect
28. C4×M16×C127C22semidirect
29. #376×C127C22semidirect
281. #8412C127direct (N × H)
290. #1759C2×C127semidirect
291. #1529C2×C127semidirect
292. #1505C2×C127semidirect
293. #1500C2×C127semidirect
294. #1488C2×C127semidirect
295. #1484C2×C127semidirect
296. C127#8412direct (N × H)
297. #559C4×C127semidirect
298. #556C4×C127semidirect
301. D4×Q8C4×C127semidirect
305. D42C4×C127semidirect
314. #432C22×C127semidirect
315. #431C22×C127semidirect
317. C4×M16C22×C127semidirect
318. #376C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35142
C127×#17592
C127×#15292
C127×#15052
C127×#15002
C127×#14882
C127×#14842
#8412127