Finite Group Databasebeta

← C127×#19156 #44582829

Subgroups — C127×#19156 #44582829

Order 32512.

650 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3167C211yesmaximal, characteristic, complemented
2C127×#3076C211yesmaximal, characteristic, complemented
3C127×#3035C211yesmaximal, characteristic
4C127×#2965C211yesmaximal, characteristic, complemented
5C127×#1700C211yesmaximal, characteristic, complemented
6C127×#1699C211yesmaximal, characteristic, complemented
7C127×#1698C211yesmaximal, characteristic, complemented
8C127×#1697C211yesmaximal, characteristic, complemented
9C127×#1692C211yesmaximal, characteristic, complemented
10C127×#1691C211yesmaximal, characteristic, complemented
11C127×#1686C211yesmaximal, characteristic, complemented
12C127×#1685C211yesmaximal, characteristic, complemented
13C2×#335×C127C211yesmaximal, characteristic, complemented
14C127×#1542C211yesmaximal, characteristic, complemented
15C127×#1540C211yesmaximal, characteristic, complemented
16C2×#135×C127—21no—
17#533×C127C2211yescharacteristic
18#532×C127C2211yescharacteristic
19C4×#41×C127C2211yescharacteristic
20#498×C127C2211yescharacteristic
21#492×C127C2211yescharacteristic
22#487×C127C2211yescharacteristic
23#486×C127C2211yescharacteristic
24#479×C127—21no—
25#478×C127—21no—
26#477×C127C2211yescharacteristic
27#476×C127C2211yescharacteristic
28#475×C127C2211yescharacteristic
29#474×C127C2211yescharacteristic
30#465×C127—21no—
31#465×C127—21no—
32#464×C127—21no—
33#463×C127—21no—
34#462×C127C2211yescharacteristic
35#461×C127C2211yescharacteristic
36#460×C127C2211yescharacteristic
37#459×C127C2211yescharacteristic
38#446×C127C2211yescharacteristic
39#446×C127C2211yescharacteristic
40C4×SD16×C127—21no—
41C4×SD16×C127—21no—
42#436×C127C2211yescharacteristic
43#436×C127C2211yescharacteristic
44#435×C127—21no—
45#435×C127—21no—
46#431×C127—21no—
47#431×C127C2211yescharacteristic
48#427×C127—21no—
49C2×C4⋊C8×C127C2211yescharacteristic
50C2×C4⋊C8×C127C2211yescharacteristic
51#416×C127—21no—
52#416×C127—21no—
53C4×M16×C127—21no—
54C2×C4×C8×C127C2211yescharacteristic
55#335×C127C2211yescharacteristic
56#335×C127C2211yescharacteristic
57#335×C127C2211yescharacteristic
58#335×C127C2211yescharacteristic
59#333×C127C2211yescharacteristic
60#333×C127C2211yescharacteristic
61#332×C127C2211yescharacteristic
62#332×C127C2211yescharacteristic
63#332×C127C2211yescharacteristic
64#332×C127C2211yescharacteristic
65#331×C127C2211yescharacteristic
66#331×C127C2211yescharacteristic
67C2×#41×C127—21no—
68C2×#41×C127D411yescharacteristic
69#135×C127—44no—
70C2×Q16×C127—21no—
71C2×SD16×C127—21no—
72C2×SD16×C127—21no—
73C2×SD16×C127—21no—
74C2×SD16×C127—21no—
75C2×D8×C127—21no—
76C2×M16×C127—21no—
77C2×M16×C127—21no—
78C22×C8×C127—21no—
79C22×C8×C127—21no—
80C22×C8×C127D411yescharacteristic
81C22×C8×C127D411yescharacteristic
82C4⋊Q8×C127C2311yescharacteristic
83C4⋊Q8×C127C2311yescharacteristic
84C4⋊Q8×C127C2311yescharacteristic
85#127×C127C2311yescharacteristic
86#125×C127—21no—
87#124×C127—21no—
88C22⋊Q8×C127—21no—
89C22⋊Q8×C127—21no—
90#121×C127—21no—
91#121×C127—21no—
92C4×Q8×C127—21no—
93C4×Q8×C127—21no—
94C4×Q8×C127D411yescharacteristic
95C4×Q8×C127C2311yescharacteristic
96C4×D4×C127—21no—
97C4×D4×C127—21no—
98C4×D4×C127—21no—
99C4×D4×C127—21no—
100C4×D4×C127D411yescharacteristic
101C4×D4×C127C2311yescharacteristic
102#117×C127—21no—
103#117×C127—21no—
104#117×C127D411yescharacteristic
105C2×C42×C127—21no—
106C2×C42×C127C2311yescharacteristic
107#107×C127—21no—
108#107×C127—21no—
109#106×C127—21no—
110#106×C127—21no—
111#106×C127—21no—
112#106×C127—21no—
113C4⋊C8×C127—21no—
114C4⋊C8×C127—21no—
115C4⋊C8×C127—21no—
116C4⋊C8×C127—21no—
117C4⋊C8×C127C2311yescharacteristic
118C4⋊C8×C127C2311yescharacteristic
119C4⋊C8×C127C2311yescharacteristic
120C4⋊C8×C127C2311yescharacteristic
121C4⋊C8×C127C2311yescharacteristic
122C4⋊C8×C127C2311yescharacteristic
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#102×C127—21no—
130#102×C127—21no—
131#102×C127—21no—
132#102×C127—21no—
133#102×C127—21no—
134#102×C127—21no—
135C22⋊C8×C127—21no—
136C22⋊C8×C127—21no—
137C22⋊C8×C127—21no—
138#97×C127—21no—
139#97×C127—21no—
140C4×C8×C127—21no—
141C4×C8×C127D411yescharacteristic
142C4×C8×C127D411yescharacteristic
143C4×C8×C127C2311yescharacteristic
144C4×C8×C127C2311yescharacteristic
145#41×C127—22no—
146#41×C127—22no—
147#41×C127—42no—
148#41×C127—42no—
149C2×Q8×C127—21no—
150C2×Q8×C127—21no—
151C2×Q8×C127—21no—
152C2×Q8×C127C2×D411yescharacteristic
153C2×D4×C127—21no—
154C2×D4×C127—21no—
155C2×D4×C127—21no—
156C2×D4×C127—21no—
157C2×D4×C127—41no—
158C2×D4×C127C2×D411yescharacteristic
159C22×C4×C127—21no—
160C22×C4×C127—21no—
161C22×C4×C127—21no—
162C22×C4×C127—41no—
163C22×C4×C127C2×D411yescharacteristic
164C22×C4×C127C2×D411yescharacteristic
165C22×C4×C127#4111yescharacteristic
166Q16×C127—42no—
167SD16×C127—42no—
168SD16×C127—42no—
169SD16×C127—42no—
170SD16×C127—42no—
171D8×C127—42no—
172M16×C127—42no—
173M16×C127—42no—
174C2×C8×C127—22no—
175C2×C8×C127—21no—
176C2×C8×C127—21no—
177C2×C8×C127—21no—
178C2×C8×C127—21no—
179C2×C8×C127—21no—
180C2×C8×C127—21no—
181C2×C8×C127—41no—
182C2×C8×C127—42no—
183C2×C8×C127—42no—
184C2×C8×C127C2×D411yescharacteristic
185C2×C8×C127C2×D411yescharacteristic
186C2×C8×C127C2×D411yescharacteristic
187C2×C8×C127C2×D411yescharacteristic
188C4⋊C4×C127—21no—
189C4⋊C4×C127—21no—
190C4⋊C4×C127—21no—
191C4⋊C4×C127—21no—
192C4⋊C4×C127—21no—
193C4⋊C4×C127—21no—
194C4⋊C4×C127—21no—
195C4⋊C4×C127—21no—
196C4⋊C4×C127—41no—
197C4⋊C4×C127—41no—
198C4⋊C4×C127C2×D411yescharacteristic
199C4⋊C4×C127C2×D411yescharacteristic
200C22⋊C4×C127—21no—
201C22⋊C4×C127—21no—
202C22⋊C4×C127—21no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C22⋊C4×C127—41no—
206C42×C127—21no—
207C42×C127—21no—
208C42×C127—21no—
209C42×C127—41no—
210C42×C127C2×D411yescharacteristic
211C42×C127C2×D411yescharacteristic
212C42×C127#4111yescharacteristic
213C42×C127C2411yescharacteristic
214C23×C127—21no—
215C23×C127—41no—
216C23×C127#12111yescharacteristic
217Q8×C127—21no—
218Q8×C127—21no—
219Q8×C127—41no—
220Q8×C127—41no—
221Q8×C127—41no—
222Q8×C127—41no—
223Q8×C127—81no—
224D4×C127—21no—
225D4×C127—21no—
226D4×C127—42no—
227D4×C127—41no—
228D4×C127—41no—
229D4×C127—41no—
230D4×C127—41no—
231D4×C127—81no—
232D4×C127—82no—
233C2×C4×C127—21no—
234C2×C4×C127—21no—
235C2×C4×C127—21no—
236C2×C4×C127—21no—
237C2×C4×C127—21no—
238C2×C4×C127—41no—
239C2×C4×C127—42no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—42no—
243C2×C4×C127—41no—
244C2×C4×C127—41no—
245C2×C4×C127—41no—
246C2×C4×C127—82no—
247C2×C4×C127#12111yescharacteristic
248C2×C4×C127#12111yescharacteristic
249C2×C4×C127#12111yescharacteristic
250C2×C4×C127AGL(1,ℤ/8)12yes—
251C2×C4×C127#13712yes—
252C2×C4×C127C22×D411yescharacteristic
253C2×C4×C127C22×D411yescharacteristic
254C2×C4×C127C2×#4111yescharacteristic
255C8×C127—21no—
256C8×C127—21no—
257C8×C127—21no—
258C8×C127—41no—
259C8×C127—41no—
260C8×C127—41no—
261C8×C127—41no—
262C8×C127—41no—
263C8×C127—41no—
264C8×C127#13512yescomplemented
265C22×C127—21no—
266C22×C127—21no—
267C22×C127—41no—
268C22×C127—41no—
269C22×C127—41no—
270C22×C127—81no—
271C22×C127—81no—
272C22×C127—81no—
273C22×C127#46812yes—
274C22×C127C2×#12111yescharacteristic
275C4×C127—21no—
276C4×C127—21no—
277C4×C127—21no—
278C4×C127—41no—
279C4×C127—41no—
280C4×C127—41no—
281C4×C127—81no—
282C4×C127—81no—
283C4×C127—81no—
284C4×C127#46812yes—
285C4×C127C2×#13511yescharacteristic
286C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C127C2×#13711yescharacteristic
288C4×C127#57511yescharacteristic
289#19156C12711yesmaximal, characteristic, direct product factor, Sylow
290C2×C127—22no—
291C2×C127—81no—
292C2×C127—161no—
293C2×C127#303511yescharacteristic
294C2×C127C2×#46811yescharacteristic
295C2×C127#306711yescharacteristic
296#3167C2×C12711yescharacteristic, complemented
297#3076C2×C12711yescharacteristic, complemented
298#3035C2×C12711yescharacteristic
299#2965C2×C12711yescharacteristic, complemented
300#1700C2×C12711yescharacteristic, complemented
301#1699C2×C12711yescharacteristic, complemented
302#1698C2×C12711yescharacteristic, complemented
303#1697C2×C12711yescharacteristic, complemented
304#1692C2×C12711yescharacteristic, complemented
305#1691C2×C12711yescharacteristic, complemented
306#1686C2×C12711yescharacteristic, complemented
307#1685C2×C12711yescharacteristic, complemented
308C2×#335C2×C12711yescharacteristic, complemented
309#1542C2×C12711yescharacteristic, complemented
310#1540C2×C12711yescharacteristic, complemented
311C127#1915611yescharacteristic, direct product factor, Sylow
312C2×#135—21no—
313#533C22×C12711yescharacteristic
314#532C22×C12711yescharacteristic
315C4×#41C22×C12711yescharacteristic
316#498C22×C12711yescharacteristic
317#492C22×C12711yescharacteristic
318#487C22×C12711yescharacteristic
319#486C22×C12711yescharacteristic
320#479—21no—
321#478—21no—
322#477C22×C12711yescharacteristic
323#476C22×C12711yescharacteristic
324#475C22×C12711yescharacteristic
325#474C22×C12711yescharacteristic
326#465—21no—
327#465—21no—
328#464—21no—
329#463—21no—
330#462C22×C12711yescharacteristic
331#461C22×C12711yescharacteristic
332#460C22×C12711yescharacteristic
333#459C22×C12711yescharacteristic
334#446C22×C12711yescharacteristic
335#446C22×C12711yescharacteristic
336C4×SD16—21no—
337C4×SD16—21no—
338#436C22×C12711yescharacteristic
339#436C22×C12711yescharacteristic
340#435—21no—
341#435—21no—
342#431—21no—
343#431C22×C12711yescharacteristic
344#427—21no—
345C2×C4⋊C8C22×C12711yescharacteristic
346C2×C4⋊C8C22×C12711yescharacteristic
347#416—21no—
348#416—21no—
349C4×M16—21no—
350C2×C4×C8C22×C12711yescharacteristic
351#335C22×C12711yescharacteristic
352#335C22×C12711yescharacteristic
353#335C22×C12711yescharacteristic
354#335C22×C12711yescharacteristic
355#333C22×C12711yescharacteristic
356#333C22×C12711yescharacteristic
357#332C22×C12711yescharacteristic
358#332C22×C12711yescharacteristic
359#332C22×C12711yescharacteristic
360#332C22×C12711yescharacteristic
361#331C22×C12711yescharacteristic
362#331C22×C12711yescharacteristic
363C2×#41—21no—
364C2×#41D4×C12711yescharacteristic
365#135—44no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×D8—21no—
372C2×M16—21no—
373C2×M16—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8D4×C12711yescharacteristic
377C22×C8D4×C12711yescharacteristic
378C4⋊Q8C23×C12711yescharacteristic
379C4⋊Q8C23×C12711yescharacteristic
380C4⋊Q8C23×C12711yescharacteristic
381#127C23×C12711yescharacteristic
382#125—21no—
383#124—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386#121—21no—
387#121—21no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8D4×C12711yescharacteristic
391C4×Q8C23×C12711yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4D4×C12711yescharacteristic
397C4×D4C23×C12711yescharacteristic
398#117—21no—
399#117—21no—
400#117D4×C12711yescharacteristic
401C2×C42—21no—
402C2×C42C23×C12711yescharacteristic
403#107—21no—
404#107—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408#106—21no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8C23×C12711yescharacteristic
414C4⋊C8C23×C12711yescharacteristic
415C4⋊C8C23×C12711yescharacteristic
416C4⋊C8C23×C12711yescharacteristic
417C4⋊C8C23×C12711yescharacteristic
418C4⋊C8C23×C12711yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434#97—21no—
435#97—21no—
436C4×C8—21no—
437C4×C8D4×C12711yescharacteristic
438C4×C8D4×C12711yescharacteristic
439C4×C8C23×C12711yescharacteristic
440C4×C8C23×C12711yescharacteristic
441#41—22no—
442#41—22no—
443#41—42no—
444#41—42no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×D4×C12711yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4C2×D4×C12711yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4C2×D4×C12711yescharacteristic
460C22×C4C2×D4×C12711yescharacteristic
461C22×C4#41×C12711yescharacteristic
462Q16—42no—
463SD16—42no—
464SD16—42no—
465SD16—42no—
466SD16—42no—
467D8—42no—
468M16—42no—
469M16—42no—
470C2×C8—22no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—41no—
478C2×C8—42no—
479C2×C8—42no—
480C2×C8C2×D4×C12711yescharacteristic
481C2×C8C2×D4×C12711yescharacteristic
482C2×C8C2×D4×C12711yescharacteristic
483C2×C8C2×D4×C12711yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4C2×D4×C12711yescharacteristic
495C4⋊C4C2×D4×C12711yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—41no—
506C42C2×D4×C12711yescharacteristic
507C42C2×D4×C12711yescharacteristic
508C42#41×C12711yescharacteristic
509C42C24×C12711yescharacteristic
510C23—21no—
511C23—41no—
512C23#121×C12711yescharacteristic
513Q8—21no—
514Q8—21no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—81no—
520D4—21no—
521D4—21no—
522D4—42no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—81no—
528D4—82no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4#121×C12711yescharacteristic
544C2×C4#121×C12711yescharacteristic
545C2×C4#121×C12711yescharacteristic
546C2×C4AGL(1,ℤ/8)×C12712yes—
547C2×C4#137×C12712yes—
548C2×C4C22×D4×C12711yescharacteristic
549C2×C4C22×D4×C12711yescharacteristic
550C2×C4C2×#41×C12711yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8#135×C12712yescomplemented
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#468×C12712yes—
570C22C2×#121×C12711yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4#468×C12712yes—
581C4C2×#135×C12711yescharacteristic
582C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
583C4C2×#137×C12711yescharacteristic
584C4#575×C12711yescharacteristic
585C2—22no—
586C2—81no—
587C2—161no—
588C2C127×#303511yescharacteristic
589C2C2×#468×C12711yescharacteristic
590C2C127×#306711yescharacteristic
subgroupG/H
centerC2×C4×C127#121
commutator, Frattini, cosocleC42C24×C127
socleC22×C127C2×#121
prime radicalC127×#3035C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3167C2semidirect
2. C127×#3076C2semidirect
4. C127×#2965C2semidirect
5. C127×#1700C2semidirect
6. C127×#1699C2semidirect
7. C127×#1698C2semidirect
8. C127×#1697C2semidirect
9. C127×#1692C2semidirect
10. C127×#1691C2semidirect
11. C127×#1686C2semidirect
12. C127×#1685C2semidirect
13. C2×#335×C127C2semidirect
14. C127×#1542C2semidirect
15. C127×#1540C2semidirect
264. C8×C127#135semidirect
289. #19156C127direct (N × H)
296. #3167C2×C127semidirect
297. #3076C2×C127semidirect
299. #2965C2×C127semidirect
300. #1700C2×C127semidirect
301. #1699C2×C127semidirect
302. #1698C2×C127semidirect
303. #1697C2×C127semidirect
304. #1692C2×C127semidirect
305. #1691C2×C127semidirect
306. #1686C2×C127semidirect
307. #1685C2×C127semidirect
308. C2×#335C2×C127semidirect
309. #1542C2×C127semidirect
310. #1540C2×C127semidirect
311. C127#19156direct (N × H)
560. C8#135×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31672
C127×#30762
C127×#30352
C127×#29652
C127×#17002
C127×#16992
C127×#16982
C127×#16972
C127×#16922
C127×#16912
C127×#16862
C127×#16852
C2×#335×C1272
C127×#15422
C127×#15402
#19156127