Finite Group Databasebeta

← C127×#19782 #44583455

Subgroups — C127×#19782 #44583455

Order 32512.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D8×C127C211yesmaximal, characteristic
2C127×#3360C211yesmaximal, characteristic
3C127×#3328C211yesmaximal, characteristic, complemented
4C127×#3299C211yesmaximal, characteristic, complemented
5C127×#1718C211yesmaximal, characteristic, complemented
6C127×#1703C211yesmaximal, characteristic, complemented
7C127×#1684C211yesmaximal, characteristic, complemented
8C127×#1679C211yesmaximal, characteristic, complemented
9C127×#1674C211yesmaximal, characteristic, complemented
10C127×#1652C211yesmaximal, characteristic, complemented
11C127×#1651C211yesmaximal, characteristic, complemented
12C127×#1644C211yesmaximal, characteristic, complemented
13C127×#1637C211yesmaximal, characteristic, complemented
14C127×#1581C211yesmaximal, characteristic
15C127×#1579C211yesmaximal, characteristic, complemented
16#556×C127C2211yescharacteristic
17#554×C127C2211yescharacteristic
18D4×Q8×C127C2211yescharacteristic
19D4×Q8×C127C2211yescharacteristic
20#500×C127—21no—
21#500×C127C2211yescharacteristic
22#498×C127C2211yescharacteristic
23#488×C127—21no—
24#487×C127C2211yescharacteristic
25#487×C127C2211yescharacteristic
26#487×C127C2211yescharacteristic
27#487×C127C2211yescharacteristic
28#485×C127—21no—
29#484×C127—21no—
30#479×C127—21no—
31#477×C127C2211yescharacteristic
32#476×C127C2211yescharacteristic
33#475×C127C2211yescharacteristic
34#474×C127—21no—
35#474×C127—21no—
36#474×C127C2211yescharacteristic
37#474×C127C2211yescharacteristic
38#470×C127—21no—
39#467×C127—21no—
40#463×C127—21no—
41#462×C127C2211yescharacteristic
42#462×C127C2211yescharacteristic
43#461×C127C2211yescharacteristic
44#451×C127—21no—
45#451×C127—21no—
46C8×Q8×C127C2211yescharacteristic
47C8×Q8×C127C2211yescharacteristic
48C4×Q16×C127C2211yescharacteristic
49C4×SD16×C127—21no—
50C4×D8×C127—21no—
51C4×D8×C127C2211yescharacteristic
52#436×C127C2211yescharacteristic
53C8×D4×C127C2211yescharacteristic
54#419×C127—21no—
55C2×#103×C127—21no—
56#335×C127C2211yescharacteristic
57#334×C127C2211yescharacteristic
58#333×C127C2211yescharacteristic
59#332×C127C2211yescharacteristic
60#332×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62Q8⋊C8×C127C2211yescharacteristic
63Q8⋊C8×C127C2211yescharacteristic
64D4⋊C8×C127C2211yescharacteristic
65D4⋊C8×C127C2211yescharacteristic
66#322×C127C2211yescharacteristic
67C22×Q8×C127—21no—
68C22×Q8×C127—21no—
69C2×Q16×C127—21no—
70C2×Q16×C127—21no—
71C2×Q16×C127D411yescharacteristic
72C2×SD16×C127—21no—
73C2×D8×C127D411yescharacteristic
74C2×M16×C127—21no—
75C22×C8×C127—21no—
76C4⋊Q8×C127—21no—
77C4⋊Q8×C127—21no—
78C4⋊Q8×C127C2311yescharacteristic
79C4⋊Q8×C127C2311yescharacteristic
80C4⋊Q8×C127C2311yescharacteristic
81C4⋊Q8×C127C2311yescharacteristic
82#126×C127—41no—
83#125×C127—21no—
84#124×C127—21no—
85C22⋊Q8×C127—21no—
86C22⋊Q8×C127—21no—
87C22⋊Q8×C127—21no—
88C22⋊Q8×C127—21no—
89C22⋊Q8×C127—41no—
90C22⋊Q8×C127—41no—
91C22⋊Q8×C127—41no—
92C4×Q8×C127—21no—
93C4×Q8×C127C2311yescharacteristic
94C4×Q8×C127C2311yescharacteristic
95C4×D4×C127—21no—
96C4×D4×C127—21no—
97C4×D4×C127—21no—
98C4×D4×C127C2311yescharacteristic
99C4×D4×C127C2311yescharacteristic
100#117×C127—21no—
101C2×C4⋊C4×C127—21no—
102#107×C127—21no—
103#107×C127—21no—
104#107×C127—21no—
105#107×C127—21no—
106#107×C127—21no—
107#107×C127D411yescharacteristic
108#107×C127D411yescharacteristic
109#106×C127—21no—
110#106×C127—21no—
111#106×C127—41no—
112C4⋊C8×C127—21no—
113C4⋊C8×C127—21no—
114C4⋊C8×C127C2311yescharacteristic
115C4⋊C8×C127C2311yescharacteristic
116C4⋊C8×C127C2311yescharacteristic
117C4⋊C8×C127C2311yescharacteristic
118#103×C127—21no—
119#103×C127—21no—
120#103×C127—21no—
121#103×C127—21no—
122#103×C127—21no—
123#103×C127—21no—
124#103×C127—21no—
125#103×C127—21no—
126#103×C127—21no—
127#103×C127—21no—
128#103×C127—21no—
129#103×C127—41no—
130#103×C127D411yescharacteristic
131#103×C127D411yescharacteristic
132#102×C127—21no—
133#102×C127—21no—
134#102×C127—21no—
135#102×C127D411yescharacteristic
136#102×C127D411yescharacteristic
137C22⋊C8×C127—21no—
138C22⋊C8×C127—21no—
139C4×C8×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127C2311yescharacteristic
142C4×C8×C127C2311yescharacteristic
143C4×C8×C127C2311yescharacteristic
144C2×Q8×C127—21no—
145C2×Q8×C127—21no—
146C2×Q8×C127—21no—
147C2×Q8×C127—21no—
148C2×Q8×C127—41no—
149C2×Q8×C127—41no—
150C2×Q8×C127—42no—
151C2×Q8×C127—42no—
152C2×Q8×C127—81no—
153C2×Q8×C127—81no—
154C2×Q8×C127C2×D411yescharacteristic
155C2×Q8×C127C2×D411yescharacteristic
156C2×D4×C127C2×D411yescharacteristic
157C2×D4×C127C2×D411yescharacteristic
158C22×C4×C127—21no—
159C22×C4×C127—21no—
160C22×C4×C127—41no—
161C22×C4×C127—41no—
162C22×C4×C127—41no—
163Q16×C127—22no—
164Q16×C127—81no—
165Q16×C127—81no—
166SD16×C127—42no—
167D8×C127—22no—
168M16×C127—81no—
169C2×C8×C127—21no—
170C2×C8×C127—21no—
171C2×C8×C127—21no—
172C2×C8×C127—21no—
173C2×C8×C127—21no—
174C2×C8×C127—81no—
175C2×C8×C127C2×D411yescharacteristic
176C2×C8×C127C2×D411yescharacteristic
177C2×C8×C127C2×D411yescharacteristic
178C2×C8×C127C2×D411yescharacteristic
179C4⋊C4×C127—21no—
180C4⋊C4×C127—21no—
181C4⋊C4×C127—21no—
182C4⋊C4×C127—21no—
183C4⋊C4×C127—21no—
184C4⋊C4×C127—21no—
185C4⋊C4×C127—21no—
186C4⋊C4×C127—21no—
187C4⋊C4×C127—21no—
188C4⋊C4×C127—21no—
189C4⋊C4×C127—41no—
190C4⋊C4×C127—41no—
191C4⋊C4×C127—41no—
192C4⋊C4×C127—41no—
193C4⋊C4×C127—41no—
194C4⋊C4×C127C2×D411yescharacteristic
195C4⋊C4×C127C2×D411yescharacteristic
196C4⋊C4×C127C2×D411yescharacteristic
197C4⋊C4×C127C2×D411yescharacteristic
198C22⋊C4×C127—21no—
199C22⋊C4×C127—21no—
200C22⋊C4×C127—41no—
201C22⋊C4×C127—41no—
202C22⋊C4×C127—41no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C42×C127—21no—
206C42×C127—21no—
207C42×C127—41no—
208C42×C127C2411yescharacteristic
209C23×C127—21no—
210C23×C127—21no—
211Q8×C127—21no—
212Q8×C127—21no—
213Q8×C127—21no—
214Q8×C127—41no—
215Q8×C127—41no—
216Q8×C127—41no—
217Q8×C127—41no—
218Q8×C127—41no—
219Q8×C127—41no—
220Q8×C127—82no—
221Q8×C127—82no—
222Q8×C127—81no—
223Q8×C127#13512yes—
224D4×C127—21no—
225D4×C127—21no—
226D4×C127—21no—
227D4×C127#13712yes—
228C2×C4×C127—21no—
229C2×C4×C127—21no—
230C2×C4×C127—21no—
231C2×C4×C127—21no—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—41no—
237C2×C4×C127—41no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—82no—
243C2×C4×C127—82no—
244C2×C4×C127—161no—
245C2×C4×C127C22×D411yescharacteristic
246C2×C4×C127C22×D411yescharacteristic
247C2×C4×C127H(5,𝔽2)11yescharacteristic
248C8×C127—21no—
249C8×C127—21no—
250C8×C127—21no—
251C8×C127—21no—
252C8×C127—41no—
253C8×C127—41no—
254C8×C127—41no—
255C8×C127—41no—
256C8×C127—41no—
257C22×C127—22no—
258C22×C127—41no—
259C22×C127—41no—
260C22×C127—41no—
261C22×C127—41no—
262C22×C127—41no—
263C22×C127D4211yescharacteristic
264C4×C127—22no—
265C4×C127—21no—
266C4×C127—41no—
267C4×C127—41no—
268C4×C127—41no—
269C4×C127—41no—
270C4×C127—41no—
271C4×C127—81no—
272C4×C127—81no—
273C4×C127—81no—
274C4×C127—81no—
275C4×C127C2×#13511yescharacteristic
276C4×C127C2×#13711yescharacteristic
277C4×C127#57611yescharacteristic
278C4×C127#57811yescharacteristic
279#19782C12711yesmaximal, characteristic, direct product factor, Sylow
280C2×C127—42no—
281C2×C127—81no—
282C2×C127#327011yescharacteristic
283C2×C127#328011yescharacteristic
284C2×C127#328911yescharacteristic
285Q8×D8C2×C12711yescharacteristic
286#3360C2×C12711yescharacteristic
287#3328C2×C12711yescharacteristic, complemented
288#3299C2×C12711yescharacteristic, complemented
289#1718C2×C12711yescharacteristic, complemented
290#1703C2×C12711yescharacteristic, complemented
291#1684C2×C12711yescharacteristic, complemented
292#1679C2×C12711yescharacteristic, complemented
293#1674C2×C12711yescharacteristic, complemented
294#1652C2×C12711yescharacteristic, complemented
295#1651C2×C12711yescharacteristic, complemented
296#1644C2×C12711yescharacteristic, complemented
297#1637C2×C12711yescharacteristic, complemented
298#1581C2×C12711yescharacteristic
299#1579C2×C12711yescharacteristic, complemented
300C127#1978211yescharacteristic, direct product factor, Sylow
301#556C22×C12711yescharacteristic
302#554C22×C12711yescharacteristic
303D4×Q8C22×C12711yescharacteristic
304D4×Q8C22×C12711yescharacteristic
305#500—21no—
306#500C22×C12711yescharacteristic
307#498C22×C12711yescharacteristic
308#488—21no—
309#487C22×C12711yescharacteristic
310#487C22×C12711yescharacteristic
311#487C22×C12711yescharacteristic
312#487C22×C12711yescharacteristic
313#485—21no—
314#484—21no—
315#479—21no—
316#477C22×C12711yescharacteristic
317#476C22×C12711yescharacteristic
318#475C22×C12711yescharacteristic
319#474—21no—
320#474—21no—
321#474C22×C12711yescharacteristic
322#474C22×C12711yescharacteristic
323#470—21no—
324#467—21no—
325#463—21no—
326#462C22×C12711yescharacteristic
327#462C22×C12711yescharacteristic
328#461C22×C12711yescharacteristic
329#451—21no—
330#451—21no—
331C8×Q8C22×C12711yescharacteristic
332C8×Q8C22×C12711yescharacteristic
333C4×Q16C22×C12711yescharacteristic
334C4×SD16—21no—
335C4×D8—21no—
336C4×D8C22×C12711yescharacteristic
337#436C22×C12711yescharacteristic
338C8×D4C22×C12711yescharacteristic
339#419—21no—
340C2×#103—21no—
341#335C22×C12711yescharacteristic
342#334C22×C12711yescharacteristic
343#333C22×C12711yescharacteristic
344#332C22×C12711yescharacteristic
345#332C22×C12711yescharacteristic
346#332C22×C12711yescharacteristic
347Q8⋊C8C22×C12711yescharacteristic
348Q8⋊C8C22×C12711yescharacteristic
349D4⋊C8C22×C12711yescharacteristic
350D4⋊C8C22×C12711yescharacteristic
351#322C22×C12711yescharacteristic
352C22×Q8—21no—
353C22×Q8—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×Q16D4×C12711yescharacteristic
357C2×SD16—21no—
358C2×D8D4×C12711yescharacteristic
359C2×M16—21no—
360C22×C8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8C23×C12711yescharacteristic
364C4⋊Q8C23×C12711yescharacteristic
365C4⋊Q8C23×C12711yescharacteristic
366C4⋊Q8C23×C12711yescharacteristic
367#126—41no—
368#125—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—41no—
376C22⋊Q8—41no—
377C4×Q8—21no—
378C4×Q8C23×C12711yescharacteristic
379C4×Q8C23×C12711yescharacteristic
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C12711yescharacteristic
384C4×D4C23×C12711yescharacteristic
385#117—21no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107D4×C12711yescharacteristic
393#107D4×C12711yescharacteristic
394#106—21no—
395#106—21no—
396#106—41no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C12711yescharacteristic
400C4⋊C8C23×C12711yescharacteristic
401C4⋊C8C23×C12711yescharacteristic
402C4⋊C8C23×C12711yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—41no—
415#103D4×C12711yescharacteristic
416#103D4×C12711yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102D4×C12711yescharacteristic
421#102D4×C12711yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—21no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8C23×C12711yescharacteristic
427C4×C8C23×C12711yescharacteristic
428C4×C8C23×C12711yescharacteristic
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—81no—
438C2×Q8—81no—
439C2×Q8C2×D4×C12711yescharacteristic
440C2×Q8C2×D4×C12711yescharacteristic
441C2×D4C2×D4×C12711yescharacteristic
442C2×D4C2×D4×C12711yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448Q16—22no—
449Q16—81no—
450Q16—81no—
451SD16—42no—
452D8—22no—
453M16—81no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8C2×D4×C12711yescharacteristic
461C2×C8C2×D4×C12711yescharacteristic
462C2×C8C2×D4×C12711yescharacteristic
463C2×C8C2×D4×C12711yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C12711yescharacteristic
480C4⋊C4C2×D4×C12711yescharacteristic
481C4⋊C4C2×D4×C12711yescharacteristic
482C4⋊C4C2×D4×C12711yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42C24×C12711yescharacteristic
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—82no—
506Q8—82no—
507Q8—81no—
508Q8#135×C12712yes—
509D4—21no—
510D4—21no—
511D4—21no—
512D4#137×C12712yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—161no—
530C2×C4C22×D4×C12711yescharacteristic
531C2×C4C22×D4×C12711yescharacteristic
532C2×C4H(5,𝔽2)×C12711yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22D42×C12711yescharacteristic
549C4—22no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4C2×#135×C12711yescharacteristic
561C4C2×#137×C12711yescharacteristic
562C4#576×C12711yescharacteristic
563C4#578×C12711yescharacteristic
564C2—42no—
565C2—81no—
566C2C127×#327011yescharacteristic
567C2C127×#328011yescharacteristic
568C2C127×#328911yescharacteristic
subgroupG/H
center, socleC22×C127D42
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×D8×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#3328C2semidirect
4. C127×#3299C2semidirect
5. C127×#1718C2semidirect
6. C127×#1703C2semidirect
7. C127×#1684C2semidirect
8. C127×#1679C2semidirect
9. C127×#1674C2semidirect
10. C127×#1652C2semidirect
11. C127×#1651C2semidirect
12. C127×#1644C2semidirect
13. C127×#1637C2semidirect
15. C127×#1579C2semidirect
279. #19782C127direct (N × H)
287. #3328C2×C127semidirect
288. #3299C2×C127semidirect
289. #1718C2×C127semidirect
290. #1703C2×C127semidirect
291. #1684C2×C127semidirect
292. #1679C2×C127semidirect
293. #1674C2×C127semidirect
294. #1652C2×C127semidirect
295. #1651C2×C127semidirect
296. #1644C2×C127semidirect
297. #1637C2×C127semidirect
299. #1579C2×C127semidirect
300. C127#19782direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×D8×C1272
C127×#33602
C127×#33282
C127×#32992
C127×#17182
C127×#17032
C127×#16842
C127×#16792
C127×#16742
C127×#16522
C127×#16512
C127×#16442
C127×#16372
C127×#15812
C127×#15792
#19782127