Finite Group Databasebeta

← C127×#13090 #44576763

Subgroups — C127×#13090 #44576763

Order 32512.

910 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C127C211yesmaximal, characteristic
2C127×#2435C211yesmaximal, characteristic
3C2×#354×C127C212yesmaximal, complemented
4C127×#1781C211yesmaximal, characteristic
5C127×#1393C212yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7C2×#124×C127C411yescharacteristic, complemented
8C2×#124×C127C2211yescharacteristic
9C2×C22⋊Q8×C127C411yescharacteristic, complemented
10C22×C22⋊C4×C127—21no—
11C2×#99×C127—21no—
12C2×#99×C127—24no—
13C2×#99×C127—21no—
14C2×#99×C127C2212yes—
15C2×#99×C127C2212yes—
16#394×C127—21no—
17#394×C127—21no—
18#390×C127C411yescharacteristic, complemented
19#390×C127C2211yescharacteristic
20#379×C127—21no—
21#379×C127—21no—
22#379×C127—21no—
23C4×C22⋊C4×C127C411yescharacteristic, complemented
24#354×C127—24no—
25C25×C127D411yescharacteristic
26C25×C127D411yescharacteristic
27C22×Q8×C127C2×C411yescharacteristic, complemented
28C22×D4×C127—22no—
29C22×D4×C127—22no—
30C22×D4×C127—41no—
31C22×D4×C127—41no—
32C22×D4×C127—42no—
33C22×D4×C127C2×C411yescharacteristic
34C22×D4×C127D411yescharacteristic
35C22×D4×C127D411yescharacteristic
36C22×D4×C127C2311yescharacteristic
37C23×C4×C127—41no—
38C23×C4×C127C2×C411yescharacteristic
39#124×C127—22no—
40#124×C127—22no—
41#124×C127—42no—
42C22⋊Q8×C127—41no—
43C22⋊Q8×C127—41no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127C2×C411yescharacteristic, complemented
46C2×C22⋊C4×C127—24no—
47C2×C22⋊C4×C127—22no—
48C2×C22⋊C4×C127—21no—
49C2×C22⋊C4×C127—21no—
50C2×C22⋊C4×C127—21no—
51C2×C22⋊C4×C127—21no—
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127—21no—
54C2×C22⋊C4×C127—22no—
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127—21no—
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—21no—
59C2×C22⋊C4×C127—41no—
60C2×C22⋊C4×C127—42no—
61C2×C22⋊C4×C127—41no—
62C2×C22⋊C4×C127—41no—
63C2×C42×C127C2×C411yescharacteristic, complemented
64C2×C42×C127C2×C411yescharacteristic, complemented
65#99×C127—24no—
66#99×C127—22no—
67#99×C127—22no—
68#99×C127—22no—
69#99×C127—42no—
70#99×C127D414yes—
71#95×C127—21no—
72C24×C127—21no—
73C24×C127—22no—
74C24×C127—21no—
75C24×C127—21no—
76C24×C127—21no—
77C24×C127—21no—
78C24×C127—21no—
79C24×C127—22no—
80C24×C127—41no—
81C24×C127—42no—
82C24×C127—42no—
83C24×C127—81no—
84C24×C127—81no—
85C24×C127C22⋊C411yescharacteristic
86C24×C127C22⋊C411yescharacteristic
87C24×C127C22⋊C411yescharacteristic
88C24×C127C2×D411yescharacteristic
89C24×C127C2×D411yescharacteristic
90C2×Q8×C127—22no—
91C2×Q8×C127—41no—
92C2×Q8×C127—41no—
93C2×D4×C127—22no—
94C2×D4×C127—22no—
95C2×D4×C127—21no—
96C2×D4×C127—22no—
97C2×D4×C127—21no—
98C2×D4×C127—22no—
99C2×D4×C127—41no—
100C2×D4×C127—41no—
101C2×D4×C127—41no—
102C2×D4×C127—41no—
103C2×D4×C127—41no—
104C2×D4×C127—41no—
105C2×D4×C127—44no—
106C2×D4×C127—44no—
107C2×D4×C127—44no—
108C2×D4×C127—44no—
109C2×D4×C127C2×D412yes—
110C2×D4×C127#4112yes—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
113C22×C4×C127—22no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—41no—
119C22×C4×C127—44no—
120C22×C4×C127—42no—
121C22×C4×C127—42no—
122C22×C4×C127—82no—
123C22×C4×C127—82no—
124C22×C4×C127C22⋊C411yescharacteristic
125C22×C4×C127C22×C411yescharacteristic
126C4⋊C4×C127—41no—
127C4⋊C4×C127—42no—
128C22⋊C4×C127—24no—
129C22⋊C4×C127—42no—
130C22⋊C4×C127—44no—
131C22⋊C4×C127—42no—
132C22⋊C4×C127—42no—
133C22⋊C4×C127—41no—
134C22⋊C4×C127—41no—
135C22⋊C4×C127—42no—
136C22⋊C4×C127—41no—
137C22⋊C4×C127—42no—
138C22⋊C4×C127—41no—
139C22⋊C4×C127—42no—
140C22⋊C4×C127—42no—
141C22⋊C4×C127—81no—
142C22⋊C4×C127—81no—
143C22⋊C4×C127—81no—
144C22⋊C4×C127—81no—
145C22⋊C4×C127—82no—
146C22⋊C4×C127—82no—
147C42×C127—22no—
148C42×C127—41no—
149C23×C127—22no—
150C23×C127—22no—
151C23×C127—22no—
152C23×C127—22no—
153C23×C127—22no—
154C23×C127—21no—
155C23×C127—21no—
156C23×C127—21no—
157C23×C127—21no—
158C23×C127—21no—
159C23×C127—21no—
160C23×C127—21no—
161C23×C127—21no—
162C23×C127—21no—
163C23×C127—21no—
164C23×C127—21no—
165C23×C127—41no—
166C23×C127—42no—
167C23×C127—42no—
168C23×C127—42no—
169C23×C127—41no—
170C23×C127—41no—
171C23×C127—41no—
172C23×C127—41no—
173C23×C127—41no—
174C23×C127—41no—
175C23×C127—41no—
176C23×C127—41no—
177C23×C127—42no—
178C23×C127—42no—
179C23×C127—42no—
180C23×C127—81no—
181C23×C127—81no—
182C23×C127—81no—
183C23×C127—81no—
184C23×C127—84no—
185C23×C127—82no—
186C23×C127—82no—
187C23×C127—84no—
188C23×C127—84no—
189C23×C127#9911yescharacteristic
190C23×C127#9911yescharacteristic
191C23×C127#9912yes—
192C23×C127C2×C22⋊C411yescharacteristic
193C23×C127#12011yescharacteristic
194C23×C127#12112yes—
195C23×C127#12311yescharacteristic
196Q8×C127—82no—
197D4×C127—42no—
198D4×C127—42no—
199D4×C127—44no—
200D4×C127—44no—
201D4×C127—42no—
202D4×C127—42no—
203C2×C4×C127—21no—
204C2×C4×C127—21no—
205C2×C4×C127—21no—
206C2×C4×C127—21no—
207C2×C4×C127—21no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—44no—
211C2×C4×C127—41no—
212C2×C4×C127—41no—
213C2×C4×C127—41no—
214C2×C4×C127—41no—
215C2×C4×C127—41no—
216C2×C4×C127—41no—
217C2×C4×C127—41no—
218C2×C4×C127—41no—
219C2×C4×C127—41no—
220C2×C4×C127—41no—
221C2×C4×C127—41no—
222C2×C4×C127—41no—
223C2×C4×C127—88no—
224C2×C4×C127—82no—
225C2×C4×C127—82no—
226C2×C4×C127—82no—
227C2×C4×C127—82no—
228C2×C4×C127—82no—
229C2×C4×C127C4×D412yes—
230C22×C127—21no—
231C22×C127—21no—
232C22×C127—21no—
233C22×C127—21no—
234C22×C127—21no—
235C22×C127—21no—
236C22×C127—21no—
237C22×C127—21no—
238C22×C127—22no—
239C22×C127—22no—
240C22×C127—21no—
241C22×C127—42no—
242C22×C127—42no—
243C22×C127—42no—
244C22×C127—41no—
245C22×C127—42no—
246C22×C127—41no—
247C22×C127—44no—
248C22×C127—44no—
249C22×C127—42no—
250C22×C127—41no—
251C22×C127—41no—
252C22×C127—41no—
253C22×C127—41no—
254C22×C127—41no—
255C22×C127—41no—
256C22×C127—41no—
257C22×C127—41no—
258C22×C127—41no—
259C22×C127—81no—
260C22×C127—81no—
261C22×C127—81no—
262C22×C127—84no—
263C22×C127—81no—
264C22×C127—82no—
265C22×C127—82no—
266C22×C127—84no—
267C22×C127#35412yescomplemented
268C22×C127#38611yescharacteristic
269C22×C127C2×#9911yescharacteristic
270C22×C127C2×#9911yescharacteristic
271C4×C127—22no—
272C4×C127—41no—
273C4×C127—81no—
274C4×C127—81no—
275C4×C127—84no—
276C4×C127—81no—
277C4×C127—81no—
278C4×C127—162no—
279#13090C12711yesmaximal, characteristic, direct product factor, Sylow
280C2×C127—21no—
281C2×C127—21no—
282C2×C127—22no—
283C2×C127—41no—
284C2×C127—42no—
285C2×C127—41no—
286C2×C127—42no—
287C2×C127—41no—
288C2×C127—81no—
289C2×C127#189811yescharacteristic
290C2×C127C2×#35411yescharacteristic
291C2×C127#212711yescharacteristic
292C22×#99C2×C12711yescharacteristic
293#2435C2×C12711yescharacteristic
294C2×#354C2×C12712yescomplemented
295#1781C2×C12711yescharacteristic
296#1393C2×C12712yescomplemented
297C127#1309011yescharacteristic, direct product factor, Sylow
298C23×D4C22×C12711yescharacteristic
299C2×#124C4×C12711yescharacteristic, complemented
300C2×#124C22×C12711yescharacteristic
301C2×C22⋊Q8C4×C12711yescharacteristic, complemented
302C22×C22⋊C4—21no—
303C2×#99—21no—
304C2×#99—24no—
305C2×#99—21no—
306C2×#99C22×C12712yes—
307C2×#99C22×C12712yes—
308#394—21no—
309#394—21no—
310#390C4×C12711yescharacteristic, complemented
311#390C22×C12711yescharacteristic
312#379—21no—
313#379—21no—
314#379—21no—
315C4×C22⋊C4C4×C12711yescharacteristic, complemented
316#354—24no—
317C25D4×C12711yescharacteristic
318C25D4×C12711yescharacteristic
319C22×Q8C2×C4×C12711yescharacteristic, complemented
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—41no—
323C22×D4—41no—
324C22×D4—42no—
325C22×D4C2×C4×C12711yescharacteristic
326C22×D4D4×C12711yescharacteristic
327C22×D4D4×C12711yescharacteristic
328C22×D4C23×C12711yescharacteristic
329C23×C4—41no—
330C23×C4C2×C4×C12711yescharacteristic
331#124—22no—
332#124—22no—
333#124—42no—
334C22⋊Q8—41no—
335C22⋊Q8—41no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4C2×C4×C12711yescharacteristic, complemented
338C2×C22⋊C4—24no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C42C2×C4×C12711yescharacteristic, complemented
356C2×C42C2×C4×C12711yescharacteristic, complemented
357#99—24no—
358#99—22no—
359#99—22no—
360#99—22no—
361#99—42no—
362#99D4×C12714yes—
363#95—21no—
364C24—21no—
365C24—22no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—22no—
372C24—41no—
373C24—42no—
374C24—42no—
375C24—81no—
376C24—81no—
377C24C22⋊C4×C12711yescharacteristic
378C24C22⋊C4×C12711yescharacteristic
379C24C22⋊C4×C12711yescharacteristic
380C24C2×D4×C12711yescharacteristic
381C24C2×D4×C12711yescharacteristic
382C2×Q8—22no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—44no—
400C2×D4—44no—
401C2×D4C2×D4×C12712yes—
402C2×D4#41×C12712yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—41no—
411C22×C4—44no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—82no—
415C22×C4—82no—
416C22×C4C22⋊C4×C12711yescharacteristic
417C22×C4C22×C4×C12711yescharacteristic
418C4⋊C4—41no—
419C4⋊C4—42no—
420C22⋊C4—24no—
421C22⋊C4—42no—
422C22⋊C4—44no—
423C22⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—42no—
428C22⋊C4—41no—
429C22⋊C4—42no—
430C22⋊C4—41no—
431C22⋊C4—42no—
432C22⋊C4—42no—
433C22⋊C4—81no—
434C22⋊C4—81no—
435C22⋊C4—81no—
436C22⋊C4—81no—
437C22⋊C4—82no—
438C22⋊C4—82no—
439C42—22no—
440C42—41no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—41no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23—84no—
477C23—82no—
478C23—82no—
479C23—84no—
480C23—84no—
481C23#99×C12711yescharacteristic
482C23#99×C12711yescharacteristic
483C23#99×C12712yes—
484C23C2×C22⋊C4×C12711yescharacteristic
485C23#120×C12711yescharacteristic
486C23#121×C12712yes—
487C23#123×C12711yescharacteristic
488Q8—82no—
489D4—42no—
490D4—42no—
491D4—44no—
492D4—44no—
493D4—42no—
494D4—42no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—88no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4C4×D4×C12712yes—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—22no—
531C22—22no—
532C22—21no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—44no—
540C22—44no—
541C22—42no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—84no—
555C22—81no—
556C22—82no—
557C22—82no—
558C22—84no—
559C22#354×C12712yescomplemented
560C22#386×C12711yescharacteristic
561C22C2×#99×C12711yescharacteristic
562C22C2×#99×C12711yescharacteristic
563C4—22no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—84no—
568C4—81no—
569C4—81no—
570C4—162no—
571C2—21no—
572C2—21no—
573C2—22no—
574C2—41no—
575C2—42no—
576C2—41no—
577C2—42no—
578C2—41no—
579C2—81no—
580C2C127×#189811yescharacteristic
581C2C2×#354×C12711yescharacteristic
582C2C127×#212711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC22×D4C23×C127
prime radicalC23×D4×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C23×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#354×C127C2semidirect
5. C127×#1393C2semidirect
7. C2×#124×C127C4semidirect
9. C2×C22⋊Q8×C127C4semidirect
18. #390×C127C4semidirect
23. C4×C22⋊C4×C127C4semidirect
27. C22×Q8×C127C2×C4semidirect
45. C2×C4⋊C4×C127C2×C4semidirect
63. C2×C42×C127C2×C4semidirect
64. C2×C42×C127C2×C4semidirect
267. C22×C127#354semidirect
279. #13090C127direct (N × H)
294. C2×#354C2×C127semidirect
296. #1393C2×C127semidirect
297. C127#13090direct (N × H)
299. C2×#124C4×C127semidirect
301. C2×C22⋊Q8C4×C127semidirect
310. #390C4×C127semidirect
315. C4×C22⋊C4C4×C127semidirect
319. C22×Q8C2×C4×C127semidirect
337. C2×C4⋊C4C2×C4×C127semidirect
355. C2×C42C2×C4×C127semidirect
356. C2×C42C2×C4×C127semidirect
559. C22#354×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C1272
C127×#24352
C2×#354×C1272
C127×#17812
C127×#13932
#13090127