Finite Group Databasebeta

← C127×#13080 #44576753

Subgroups — C127×#13080 #44576753

Order 32512.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#100×C127C211yesmaximal, characteristic
2C127×#2405C211yesmaximal, characteristic
3C2×#352×C127C212yesmaximal, complemented
4C127×#1781C211yesmaximal, characteristic
5C127×#1390C212yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7C22×M16×C127—21no—
8C2×#123×C127C411yescharacteristic, complemented
9C2×#123×C127C2211yescharacteristic
10C22×C22⋊C4×C127C411yescharacteristic, complemented
11C2×#100×C127—21no—
12C2×#100×C127—24no—
13C2×#100×C127C2212yes—
14C2×#99×C127—21no—
15C2×#99×C127C2212yes—
16#394×C127—21no—
17#394×C127—21no—
18#386×C127C411yescharacteristic, complemented
19#386×C127C2211yescharacteristic
20#385×C127—21no—
21#379×C127—21no—
22#379×C127—21no—
23#379×C127C411yescharacteristic, complemented
24#352×C127—24no—
25C25×C127C2×C411yescharacteristic
26C25×C127D411yescharacteristic
27C22×D4×C127—22no—
28C22×D4×C127—22no—
29C22×D4×C127—42no—
30C22×D4×C127—41no—
31C22×D4×C127—41no—
32C22×D4×C127C2×C411yescharacteristic
33C22×D4×C127D411yescharacteristic
34C22×D4×C127D411yescharacteristic
35C22×D4×C127C2311yescharacteristic
36C23×C4×C127C2×C411yescharacteristic
37C23×C4×C127C2×C411yescharacteristic
38C23×C4×C127D411yescharacteristic
39C2×M16×C127—24no—
40C2×M16×C127—22no—
41C2×M16×C127—41no—
42C2×M16×C127—42no—
43C22×C8×C127—41no—
44#123×C127—22no—
45#123×C127—22no—
46#123×C127—42no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊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—41no—
59C2×C22⋊C4×C127—41no—
60C2×C22⋊C4×C127—41no—
61C2×C22⋊C4×C127—41no—
62C2×C22⋊C4×C127C2×C411yescharacteristic
63C2×C22⋊C4×C127C2×C411yescharacteristic
64#100×C127—24no—
65#100×C127—22no—
66#100×C127D414yes—
67#99×C127—22no—
68#99×C127—22no—
69#99×C127—42no—
70#95×C127—21no—
71#95×C127—21no—
72C24×C127—21no—
73C24×C127—21no—
74C24×C127—21no—
75C24×C127—21no—
76C24×C127—22no—
77C24×C127—22no—
78C24×C127—41no—
79C24×C127—41no—
80C24×C127—42no—
81C24×C127—42no—
82C24×C127—81no—
83C24×C127—81no—
84C24×C127C22⋊C411yescharacteristic
85C24×C127C22⋊C411yescharacteristic
86C24×C127C22⋊C411yescharacteristic
87C24×C127C22×C411yescharacteristic
88C24×C127C2×D411yescharacteristic
89C2×D4×C127—22no—
90C2×D4×C127—22no—
91C2×D4×C127—22no—
92C2×D4×C127—22no—
93C2×D4×C127—21no—
94C2×D4×C127—21no—
95C2×D4×C127—41no—
96C2×D4×C127—41no—
97C2×D4×C127—41no—
98C2×D4×C127—41no—
99C2×D4×C127—41no—
100C2×D4×C127—41no—
101C2×D4×C127—44no—
102C2×D4×C127—44no—
103C2×D4×C127—44no—
104C2×D4×C127—44no—
105C2×D4×C127C2×D412yes—
106C2×D4×C127#4112yes—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—22no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—22no—
117C22×C4×C127—41no—
118C22×C4×C127—41no—
119C22×C4×C127—41no—
120C22×C4×C127—42no—
121C22×C4×C127—81no—
122C22×C4×C127C22⋊C411yescharacteristic
123C22×C4×C127C2×D411yescharacteristic
124M16×C127—24no—
125M16×C127—44no—
126M16×C127—42no—
127C2×C8×C127—44no—
128C2×C8×C127—42no—
129C4⋊C4×C127—42no—
130C4⋊C4×C127—41no—
131C4⋊C4×C127—41no—
132C22⋊C4×C127—22no—
133C22⋊C4×C127—42no—
134C22⋊C4×C127—42no—
135C22⋊C4×C127—42no—
136C22⋊C4×C127—41no—
137C22⋊C4×C127—41no—
138C22⋊C4×C127—42no—
139C22⋊C4×C127—41no—
140C22⋊C4×C127—42no—
141C22⋊C4×C127—42no—
142C22⋊C4×C127—81no—
143C22⋊C4×C127—81no—
144C22⋊C4×C127—81no—
145C22⋊C4×C127—82no—
146C22⋊C4×C127—82no—
147C23×C127—22no—
148C23×C127—21no—
149C23×C127—21no—
150C23×C127—21no—
151C23×C127—21no—
152C23×C127—21no—
153C23×C127—21no—
154C23×C127—21no—
155C23×C127—21no—
156C23×C127—21no—
157C23×C127—21no—
158C23×C127—21no—
159C23×C127—21no—
160C23×C127—41no—
161C23×C127—42no—
162C23×C127—42no—
163C23×C127—42no—
164C23×C127—42no—
165C23×C127—41no—
166C23×C127—41no—
167C23×C127—41no—
168C23×C127—41no—
169C23×C127—41no—
170C23×C127—41no—
171C23×C127—42no—
172C23×C127—42no—
173C23×C127—41no—
174C23×C127—41no—
175C23×C127—42no—
176C23×C127—42no—
177C23×C127—81no—
178C23×C127—81no—
179C23×C127—81no—
180C23×C127—81no—
181C23×C127—84no—
182C23×C127—84no—
183C23×C127—84no—
184C23×C127—84no—
185C23×C127#9911yescharacteristic
186C23×C127#9911yescharacteristic
187C23×C127C2×C22⋊C411yescharacteristic
188C23×C127C4×D412yes—
189C23×C127#12112yes—
190D4×C127—42no—
191D4×C127—42no—
192D4×C127—44no—
193D4×C127—44no—
194D4×C127—42no—
195D4×C127—42no—
196C2×C4×C127—22no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—21no—
201C2×C4×C127—21no—
202C2×C4×C127—21no—
203C2×C4×C127—21no—
204C2×C4×C127—41no—
205C2×C4×C127—41no—
206C2×C4×C127—41no—
207C2×C4×C127—41no—
208C2×C4×C127—41no—
209C2×C4×C127—41no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—41no—
213C2×C4×C127—41no—
214C2×C4×C127—41no—
215C2×C4×C127—41no—
216C2×C4×C127—82no—
217C2×C4×C127—82no—
218C2×C4×C127—82no—
219C2×C4×C127—82no—
220C2×C4×C127—82no—
221C2×C4×C127#9912yes—
222C2×C4×C127#12011yescharacteristic
223C2×C4×C127#12311yescharacteristic
224C8×C127—44no—
225C22×C127—21no—
226C22×C127—21no—
227C22×C127—21no—
228C22×C127—21no—
229C22×C127—21no—
230C22×C127—21no—
231C22×C127—21no—
232C22×C127—22no—
233C22×C127—22no—
234C22×C127—42no—
235C22×C127—42no—
236C22×C127—42no—
237C22×C127—42no—
238C22×C127—42no—
239C22×C127—42no—
240C22×C127—41no—
241C22×C127—41no—
242C22×C127—41no—
243C22×C127—41no—
244C22×C127—41no—
245C22×C127—41no—
246C22×C127—41no—
247C22×C127—41no—
248C22×C127—41no—
249C22×C127—41no—
250C22×C127—81no—
251C22×C127—84no—
252C22×C127—84no—
253C22×C127—81no—
254C22×C127—81no—
255C22×C127—81no—
256C22×C127—84no—
257C22×C127—84no—
258C22×C127#35212yescomplemented
259C22×C127#38611yescharacteristic
260C22×C127C2×#9911yescharacteristic
261C22×C127C2×#9911yescharacteristic
262C4×C127—21no—
263C4×C127—22no—
264C4×C127—21no—
265C4×C127—81no—
266C4×C127—81no—
267C4×C127—81no—
268C4×C127—81no—
269C4×C127—162no—
270#13080C12711yesmaximal, characteristic, direct product factor, Sylow
271C2×C127—21no—
272C2×C127—21no—
273C2×C127—22no—
274C2×C127—42no—
275C2×C127—41no—
276C2×C127—42no—
277C2×C127—81no—
278C2×C127—81no—
279C2×C127#189811yescharacteristic
280C2×C127C2×#35211yescharacteristic
281C2×C127#212111yescharacteristic
282C22×#100C2×C12711yescharacteristic
283#2405C2×C12711yescharacteristic
284C2×#352C2×C12712yescomplemented
285#1781C2×C12711yescharacteristic
286#1390C2×C12712yescomplemented
287C127#1308011yescharacteristic, direct product factor, Sylow
288C23×D4C22×C12711yescharacteristic
289C22×M16—21no—
290C2×#123C4×C12711yescharacteristic, complemented
291C2×#123C22×C12711yescharacteristic
292C22×C22⋊C4C4×C12711yescharacteristic, complemented
293C2×#100—21no—
294C2×#100—24no—
295C2×#100C22×C12712yes—
296C2×#99—21no—
297C2×#99C22×C12712yes—
298#394—21no—
299#394—21no—
300#386C4×C12711yescharacteristic, complemented
301#386C22×C12711yescharacteristic
302#385—21no—
303#379—21no—
304#379—21no—
305#379C4×C12711yescharacteristic, complemented
306#352—24no—
307C25C2×C4×C12711yescharacteristic
308C25D4×C12711yescharacteristic
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—42no—
312C22×D4—41no—
313C22×D4—41no—
314C22×D4C2×C4×C12711yescharacteristic
315C22×D4D4×C12711yescharacteristic
316C22×D4D4×C12711yescharacteristic
317C22×D4C23×C12711yescharacteristic
318C23×C4C2×C4×C12711yescharacteristic
319C23×C4C2×C4×C12711yescharacteristic
320C23×C4D4×C12711yescharacteristic
321C2×M16—24no—
322C2×M16—22no—
323C2×M16—41no—
324C2×M16—42no—
325C22×C8—41no—
326#123—22no—
327#123—22no—
328#123—42no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4C2×C4×C12711yescharacteristic
345C2×C22⋊C4C2×C4×C12711yescharacteristic
346#100—24no—
347#100—22no—
348#100D4×C12714yes—
349#99—22no—
350#99—22no—
351#99—42no—
352#95—21no—
353#95—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—22no—
359C24—22no—
360C24—41no—
361C24—41no—
362C24—42no—
363C24—42no—
364C24—81no—
365C24—81no—
366C24C22⋊C4×C12711yescharacteristic
367C24C22⋊C4×C12711yescharacteristic
368C24C22⋊C4×C12711yescharacteristic
369C24C22×C4×C12711yescharacteristic
370C24C2×D4×C12711yescharacteristic
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4C2×D4×C12712yes—
388C2×D4#41×C12712yes—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—42no—
403C22×C4—81no—
404C22×C4C22⋊C4×C12711yescharacteristic
405C22×C4C2×D4×C12711yescharacteristic
406M16—24no—
407M16—44no—
408M16—42no—
409C2×C8—44no—
410C2×C8—42no—
411C4⋊C4—42no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C22⋊C4—22no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—81no—
427C22⋊C4—82no—
428C22⋊C4—82no—
429C23—22no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23#99×C12711yescharacteristic
468C23#99×C12711yescharacteristic
469C23C2×C22⋊C4×C12711yescharacteristic
470C23C4×D4×C12712yes—
471C23#121×C12712yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4#99×C12712yes—
504C2×C4#120×C12711yescharacteristic
505C2×C4#123×C12711yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22#352×C12712yescomplemented
541C22#386×C12711yescharacteristic
542C22C2×#99×C12711yescharacteristic
543C22C2×#99×C12711yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2C127×#189811yescharacteristic
561C2C2×#352×C12711yescharacteristic
562C2C127×#212111yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC24C22×C4×C127
Frattini, cosocleC22×D4C23×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ 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×#352×C127C2semidirect
5. C127×#1390C2semidirect
8. C2×#123×C127C4semidirect
10. C22×C22⋊C4×C127C4semidirect
18. #386×C127C4semidirect
23. #379×C127C4semidirect
258. C22×C127#352semidirect
270. #13080C127direct (N × H)
284. C2×#352C2×C127semidirect
286. #1390C2×C127semidirect
287. C127#13080direct (N × H)
290. C2×#123C4×C127semidirect
292. C22×C22⋊C4C4×C127semidirect
300. #386C4×C127semidirect
305. #379C4×C127semidirect
540. C22#352×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#100×C1272
C127×#24052
C2×#352×C1272
C127×#17812
C127×#13902
#13080127