Finite Group Databasebeta

← C127×#18313 #44581986

Subgroups — C127×#18313 #44581986

Order 32512.

910 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3455C211yesmaximal, characteristic
2C127×#3230C211yesmaximal, characteristic, complemented
3C127×#3227C211yesmaximal, characteristic, complemented
4C127×#2628C211yesmaximal, characteristic, complemented
5C127×#1618C214yesmaximal, complemented
6C127×#1615C214yesmaximal, complemented
7C127×#1518C211yesmaximal, characteristic, complemented
8C127×#1517C211yesmaximal, characteristic, complemented
9C127×#1458C211yesmaximal, characteristic, complemented
10#542×C127—21no—
11#542×C127—21no—
12#541×C127—21no—
13#540×C127—21no—
14#539×C127—21no—
15#539×C127C2212yes—
16#538×C127—21no—
17#538×C127C2212yes—
18#533×C127C2211yescharacteristic
19#532×C127C2211yescharacteristic
20C2×C4⋊Q8×C127C2211yescharacteristic
21#529×C127—22no—
22#529×C127—22no—
23#525×C127—21no—
24C4×#41×C127—21no—
25C2×#117×C127C2211yescharacteristic
26#500×C127—21no—
27#498×C127—21no—
28#487×C127—21no—
29#486×C127—21no—
30#484×C127C2214yes—
31#481×C127C2214yes—
32#477×C127—22no—
33#476×C127—22no—
34#431×C127C2211yescharacteristic
35#431×C127C2211yescharacteristic
36#400×C127C2212yes—
37#399×C127C2212yes—
38#395×C127—21no—
39#393×C127—21no—
40#389×C127—21no—
41#382×C127C2211yescharacteristic
42#380×C127—21no—
43#328×C127C2214yes—
44#327×C127C2214yes—
45#324×C127C2212yes—
46#323×C127C2212yes—
47C2×#41×C127—21no—
48C22×Q8×C127—21no—
49C23×C4×C127D411yescharacteristic
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127D411yescharacteristic
55C4⋊Q8×C127D411yescharacteristic
56C4⋊Q8×C127D411yescharacteristic
57#127×C127D411yescharacteristic
58#126×C127—22no—
59#126×C127—22no—
60#126×C127—22no—
61#126×C127—22no—
62#125×C127—22no—
63#125×C127—22no—
64#125×C127—21no—
65#124×C127—22no—
66#124×C127—22no—
67#124×C127—21no—
68#123×C127—22no—
69#123×C127—22no—
70#123×C127—22no—
71#123×C127—22no—
72#123×C127—22no—
73C22⋊Q8×C127—21no—
74C22⋊Q8×C127—21no—
75C22⋊Q8×C127—22no—
76C22⋊Q8×C127—22no—
77C22⋊Q8×C127—21no—
78C22⋊Q8×C127C2312yes—
79#121×C127—21no—
80#121×C127—21no—
81#121×C127—22no—
82#121×C127—22no—
83#121×C127—21no—
84#121×C127C2312yes—
85#120×C127—22no—
86C4×Q8×C127—21no—
87C4×Q8×C127—21no—
88C4×Q8×C127—21no—
89C4×Q8×C127D412yes—
90C4×D4×C127—21no—
91C4×D4×C127—21no—
92C4×D4×C127—22no—
93C4×D4×C127—22no—
94C4×D4×C127—22no—
95C4×D4×C127—22no—
96C4×D4×C127—21no—
97C4×D4×C127D412yes—
98#117×C127—22no—
99#117×C127—21no—
100#117×C127—21no—
101#117×C127—21no—
102#117×C127—21no—
103#117×C127—21no—
104C2×C4⋊C4×C127—21no—
105C2×C4⋊C4×C127—21no—
106C2×C4⋊C4×C127—22no—
107C2×C4⋊C4×C127D411yescharacteristic
108C2×C4⋊C4×C127C2312yes—
109C2×C4⋊C4×C127C2311yescharacteristic
110C2×C22⋊C4×C127—22no—
111C2×C22⋊C4×C127D411yescharacteristic
112C2×C22⋊C4×C127C2311yescharacteristic
113C2×C42×C127—22no—
114C2×C42×C127D411yescharacteristic
115C2×C42×C127C2311yescharacteristic
116#107×C127—24no—
117#106×C127—24no—
118C4⋊C8×C127—21no—
119C4⋊C8×C127—21no—
120#103×C127—24no—
121#102×C127—24no—
122C22⋊C8×C127C2312yes—
123C22⋊C8×C127C2312yes—
124C4×C8×C127—21no—
125C4×C8×C127—21no—
126#95×C127—22no—
127#95×C127—21no—
128#95×C127—22no—
129#95×C127C2312yes—
130C24×C127C2×D411yescharacteristic
131#41×C127—42no—
132#41×C127—42no—
133C2×Q8×C127—21no—
134C2×Q8×C127—21no—
135C2×Q8×C127—41no—
136C2×Q8×C127—41no—
137C2×Q8×C127—82no—
138C2×Q8×C127C2×D412yes—
139C2×D4×C127—22no—
140C2×D4×C127—22no—
141C2×D4×C127—22no—
142C2×D4×C127—21no—
143C2×D4×C127—21no—
144C2×D4×C127C2×D412yes—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—21no—
149C22×C4×C127—21no—
150C22×C4×C127—22no—
151C22×C4×C127—22no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127C2×D411yescharacteristic
155C22×C4×C127C2×D411yescharacteristic
156C22×C4×C127C2×D411yescharacteristic
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127C2411yescharacteristic
160C2×C8×C127—22no—
161C2×C8×C127—22no—
162C4⋊C4×C127—22no—
163C4⋊C4×C127—22no—
164C4⋊C4×C127—22no—
165C4⋊C4×C127—22no—
166C4⋊C4×C127—21no—
167C4⋊C4×C127—21no—
168C4⋊C4×C127—21no—
169C4⋊C4×C127—21no—
170C4⋊C4×C127—21no—
171C4⋊C4×C127—21no—
172C4⋊C4×C127—22no—
173C4⋊C4×C127—21no—
174C4⋊C4×C127—21no—
175C4⋊C4×C127—22no—
176C4⋊C4×C127—22no—
177C4⋊C4×C127—22no—
178C4⋊C4×C127—41no—
179C4⋊C4×C127—41no—
180C4⋊C4×C127—42no—
181C4⋊C4×C127—82no—
182C4⋊C4×C127C2×D412yes—
183C4⋊C4×C127C2×D412yes—
184C22⋊C4×C127—22no—
185C22⋊C4×C127—22no—
186C22⋊C4×C127—22no—
187C22⋊C4×C127—22no—
188C22⋊C4×C127—22no—
189C22⋊C4×C127—22no—
190C22⋊C4×C127—22no—
191C22⋊C4×C127—21no—
192C22⋊C4×C127—21no—
193C22⋊C4×C127—22no—
194C22⋊C4×C127—21no—
195C22⋊C4×C127—21no—
196C22⋊C4×C127—22no—
197C22⋊C4×C127—82no—
198C42×C127—22no—
199C42×C127—22no—
200C42×C127—21no—
201C42×C127—22no—
202C42×C127—21no—
203C42×C127C2×D411yescharacteristic
204C42×C127C2×D411yescharacteristic
205C42×C127C2×D411yescharacteristic
206C42×C127C2×D411yescharacteristic
207C23×C127—21no—
208C23×C127—22no—
209C23×C127—21no—
210C23×C127—21no—
211C23×C127—41no—
212C23×C127—41no—
213C23×C127C22×D411yescharacteristic
214Q8×C127—42no—
215Q8×C127—42no—
216Q8×C127—81no—
217Q8×C127—82no—
218Q8×C127—82no—
219D4×C127—42no—
220D4×C127—42no—
221D4×C127—42no—
222D4×C127—42no—
223D4×C127—81no—
224D4×C127—82no—
225D4×C127—82no—
226C2×C4×C127—21no—
227C2×C4×C127—21no—
228C2×C4×C127—22no—
229C2×C4×C127—22no—
230C2×C4×C127—22no—
231C2×C4×C127—21no—
232C2×C4×C127—21no—
233C2×C4×C127—21no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—42no—
237C2×C4×C127—42no—
238C2×C4×C127—44no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—42no—
242C2×C4×C127—42no—
243C2×C4×C127—42no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127—42no—
247C2×C4×C127—82no—
248C2×C4×C127—82no—
249C2×C4×C127#12011yescharacteristic
250C2×C4×C127#12011yescharacteristic
251C2×C4×C127#12011yescharacteristic
252C2×C4×C127#12011yescharacteristic
253C2×C4×C127#13512yes—
254C2×C4×C127#13712yes—
255C2×C4×C127C22×D411yescharacteristic
256C2×C4×C127C22×D411yescharacteristic
257C8×C127—42no—
258C8×C127—42no—
259C22×C127—21no—
260C22×C127—21no—
261C22×C127—42no—
262C22×C127—41no—
263C22×C127—42no—
264C22×C127—42no—
265C22×C127—41no—
266C22×C127—42no—
267C22×C127—41no—
268C22×C127—81no—
269C22×C127C2×#12011yescharacteristic
270C22×C127C2×#13511yescharacteristic
271C22×C127C2×#13711yescharacteristic
272C4×C127—21no—
273C4×C127—21no—
274C4×C127—21no—
275C4×C127—21no—
276C4×C127—41no—
277C4×C127—42no—
278C4×C127—41no—
279C4×C127—42no—
280C4×C127—41no—
281C4×C127—42no—
282C4×C127—82no—
283C4×C127—82no—
284C4×C127#45212yes—
285C4×C127#45212yes—
286#18313C12711yesmaximal, characteristic, direct product factor, Sylow
287C2×C127—21no—
288C2×C127—21no—
289C2×C127—82no—
290C2×C127—81no—
291C2×C127C2×#45211yescharacteristic
292C2×C127#302111yescharacteristic
293C2×C127#302811yescharacteristic
294#3455C2×C12711yescharacteristic
295#3230C2×C12711yescharacteristic, complemented
296#3227C2×C12711yescharacteristic, complemented
297#2628C2×C12711yescharacteristic, complemented
298#1618C2×C12714yescomplemented
299#1615C2×C12714yescomplemented
300#1518C2×C12711yescharacteristic, complemented
301#1517C2×C12711yescharacteristic, complemented
302#1458C2×C12711yescharacteristic, complemented
303C127#1831311yescharacteristic, direct product factor, Sylow
304#542—21no—
305#542—21no—
306#541—21no—
307#540—21no—
308#539—21no—
309#539C22×C12712yes—
310#538—21no—
311#538C22×C12712yes—
312#533C22×C12711yescharacteristic
313#532C22×C12711yescharacteristic
314C2×C4⋊Q8C22×C12711yescharacteristic
315#529—22no—
316#529—22no—
317#525—21no—
318C4×#41—21no—
319C2×#117C22×C12711yescharacteristic
320#500—21no—
321#498—21no—
322#487—21no—
323#486—21no—
324#484C22×C12714yes—
325#481C22×C12714yes—
326#477—22no—
327#476—22no—
328#431C22×C12711yescharacteristic
329#431C22×C12711yescharacteristic
330#400C22×C12712yes—
331#399C22×C12712yes—
332#395—21no—
333#393—21no—
334#389—21no—
335#382C22×C12711yescharacteristic
336#380—21no—
337#328C22×C12714yes—
338#327C22×C12714yes—
339#324C22×C12712yes—
340#323C22×C12712yes—
341C2×#41—21no—
342C22×Q8—21no—
343C23×C4D4×C12711yescharacteristic
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8D4×C12711yescharacteristic
349C4⋊Q8D4×C12711yescharacteristic
350C4⋊Q8D4×C12711yescharacteristic
351#127D4×C12711yescharacteristic
352#126—22no—
353#126—22no—
354#126—22no—
355#126—22no—
356#125—22no—
357#125—22no—
358#125—21no—
359#124—22no—
360#124—22no—
361#124—21no—
362#123—22no—
363#123—22no—
364#123—22no—
365#123—22no—
366#123—22no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8C23×C12712yes—
373#121—21no—
374#121—21no—
375#121—22no—
376#121—22no—
377#121—21no—
378#121C23×C12712yes—
379#120—22no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8D4×C12712yes—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—21no—
391C4×D4D4×C12712yes—
392#117—22no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4D4×C12711yescharacteristic
402C2×C4⋊C4C23×C12712yes—
403C2×C4⋊C4C23×C12711yescharacteristic
404C2×C22⋊C4—22no—
405C2×C22⋊C4D4×C12711yescharacteristic
406C2×C22⋊C4C23×C12711yescharacteristic
407C2×C42—22no—
408C2×C42D4×C12711yescharacteristic
409C2×C42C23×C12711yescharacteristic
410#107—24no—
411#106—24no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414#103—24no—
415#102—24no—
416C22⋊C8C23×C12712yes—
417C22⋊C8C23×C12712yes—
418C4×C8—21no—
419C4×C8—21no—
420#95—22no—
421#95—21no—
422#95—22no—
423#95C23×C12712yes—
424C24C2×D4×C12711yescharacteristic
425#41—42no—
426#41—42no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—82no—
432C2×Q8C2×D4×C12712yes—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4C2×D4×C12712yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4C2×D4×C12711yescharacteristic
449C22×C4C2×D4×C12711yescharacteristic
450C22×C4C2×D4×C12711yescharacteristic
451C22×C4C2×D4×C12711yescharacteristic
452C22×C4C2×D4×C12711yescharacteristic
453C22×C4C24×C12711yescharacteristic
454C2×C8—22no—
455C2×C8—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—42no—
475C4⋊C4—82no—
476C4⋊C4C2×D4×C12712yes—
477C4⋊C4C2×D4×C12712yes—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—22no—
491C22⋊C4—82no—
492C42—22no—
493C42—22no—
494C42—21no—
495C42—22no—
496C42—21no—
497C42C2×D4×C12711yescharacteristic
498C42C2×D4×C12711yescharacteristic
499C42C2×D4×C12711yescharacteristic
500C42C2×D4×C12711yescharacteristic
501C23—21no—
502C23—22no—
503C23—21no—
504C23—21no—
505C23—41no—
506C23—41no—
507C23C22×D4×C12711yescharacteristic
508Q8—42no—
509Q8—42no—
510Q8—81no—
511Q8—82no—
512Q8—82no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—81no—
518D4—82no—
519D4—82no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#120×C12711yescharacteristic
544C2×C4#120×C12711yescharacteristic
545C2×C4#120×C12711yescharacteristic
546C2×C4#120×C12711yescharacteristic
547C2×C4#135×C12712yes—
548C2×C4#137×C12712yes—
549C2×C4C22×D4×C12711yescharacteristic
550C2×C4C22×D4×C12711yescharacteristic
551C8—42no—
552C8—42no—
553C22—21no—
554C22—21no—
555C22—42no—
556C22—41no—
557C22—42no—
558C22—42no—
559C22—41no—
560C22—42no—
561C22—41no—
562C22—81no—
563C22C2×#120×C12711yescharacteristic
564C22C2×#135×C12711yescharacteristic
565C22C2×#137×C12711yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—82no—
577C4—82no—
578C4#452×C12712yes—
579C4#452×C12712yes—
580C2—21no—
581C2—21no—
582C2—81no—
583C2—82no—
584C2C2×#452×C12711yescharacteristic
585C2C127×#302111yescharacteristic
586C2C127×#302811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC127×#3455C2
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×#3230C2semidirect
3. C127×#3227C2semidirect
4. C127×#2628C2semidirect
5. C127×#1618C2semidirect
6. C127×#1615C2semidirect
7. C127×#1518C2semidirect
8. C127×#1517C2semidirect
9. C127×#1458C2semidirect
286. #18313C127direct (N × H)
295. #3230C2×C127semidirect
296. #3227C2×C127semidirect
297. #2628C2×C127semidirect
298. #1618C2×C127semidirect
299. #1615C2×C127semidirect
300. #1518C2×C127semidirect
301. #1517C2×C127semidirect
302. #1458C2×C127semidirect
303. C127#18313direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34552
C127×#32302
C127×#32272
C127×#26282
C127×#16182
C127×#16152
C127×#15182
C127×#15172
C127×#14582
#18313127