Finite Group Databasebeta

← C127×#15881 #44579554

Subgroups — C127×#15881 #44579554

Order 32512.

1370 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C127C211yesmaximal, characteristic
2C2×#400×C127C211yesmaximal, characteristic
3C2×#398×C127C211yesmaximal, characteristic
4C2×#382×C127C211yesmaximal, characteristic
5C127×#1445C211yesmaximal, characteristic
6C127×#1442C212yesmaximal
7C127×#1442C212yesmaximal
8C127×#1441C212yesmaximal
9C127×#1436C212yesmaximal
10C127×#1436C211yesmaximal, characteristic
11C127×#1436C211yesmaximal, characteristic
12C2×#125×C127—24no—
13C2×#125×C127—24no—
14C2×#125×C127—24no—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2212yes—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C4⋊C4×C127C2211yescharacteristic
22C22×C4⋊C4×C127C2211yescharacteristic
23C22×C42×C127C2211yescharacteristic
24C22×C42×C127C2211yescharacteristic
25#400×C127—24no—
26#398×C127—24no—
27#382×C127—24no—
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C2×#95×C127C2212yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2312yes—
49C23×C4×C127C2312yes—
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2311yescharacteristic
52#125×C127—232no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—22no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127—22no—
70C2×C4⋊C4×C127—24no—
71C2×C4⋊C4×C127—22no—
72C2×C4⋊C4×C127—24no—
73C2×C4⋊C4×C127—24no—
74C2×C4⋊C4×C127D414yes—
75C2×C4⋊C4×C127D414yes—
76C2×C4⋊C4×C127D414yes—
77C2×C42×C127—22no—
78C2×C42×C127—22no—
79C2×C42×C127—22no—
80C2×C42×C127—22no—
81C2×C42×C127—24no—
82#95×C127—24no—
83#95×C127—24no—
84#95×C127—22no—
85#95×C127—24no—
86#95×C127—22no—
87#95×C127—24no—
88#95×C127—24no—
89#95×C127—24no—
90#95×C127—24no—
91#95×C127—24no—
92#95×C127—24no—
93#95×C127—24no—
94#95×C127—24no—
95C24×C127C2411yescharacteristic
96C22×C4×C127—21no—
97C22×C4×C127—21no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—21no—
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127C2×D412yes—
148C22×C4×C127C2×D412yes—
149C22×C4×C127C2×D412yes—
150C22×C4×C127C2×D412yes—
151C22×C4×C127C2×D412yes—
152C22×C4×C127C2×D412yes—
153C22×C4×C127C2×D412yes—
154C22×C4×C127C2×D412yes—
155C22×C4×C127C2×D412yes—
156C22×C4×C127#4114yes—
157C22×C4×C127#4114yes—
158C22×C4×C127#4114yes—
159C4⋊C4×C127—28no—
160C4⋊C4×C127—28no—
161C4⋊C4×C127—28no—
162C4⋊C4×C127—28no—
163C4⋊C4×C127—28no—
164C4⋊C4×C127—28no—
165C4⋊C4×C127—44no—
166C4⋊C4×C127—48no—
167C42×C127—28no—
168C42×C127—28no—
169C23×C127C22×D411yescharacteristic
170C23×C127C22×D411yescharacteristic
171C23×C127C22×D411yescharacteristic
172C23×C127C2×#4112yes—
173C23×C127C2×#4112yes—
174C23×C127C2×#4112yes—
175C23×C1272−1+412yes—
176C23×C1272−1+412yes—
177C23×C1272−1+412yes—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—24no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—22no—
187C2×C4×C127—22no—
188C2×C4×C127—22no—
189C2×C4×C127—22no—
190C2×C4×C127—22no—
191C2×C4×C127—24no—
192C2×C4×C127—24no—
193C2×C4×C127—22no—
194C2×C4×C127—22no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—24no—
198C2×C4×C127—24no—
199C2×C4×C127—24no—
200C2×C4×C127—24no—
201C2×C4×C127—24no—
202C2×C4×C127—24no—
203C2×C4×C127—41no—
204C2×C4×C127—41no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
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—42no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—42no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—42no—
235C2×C4×C127—42no—
236C2×C4×C127—42no—
237C2×C4×C127—42no—
238C2×C4×C127—42no—
239C2×C4×C127#12014yes—
240C2×C4×C127#12414yes—
241C22×C127C2×#12011yescharacteristic
242C22×C127#52511yescharacteristic
243C22×C127C2×#12411yescharacteristic
244C22×C127#52912yes—
245C22×C127#53211yescharacteristic
246C22×C127#53611yescharacteristic
247C22×C127#53611yescharacteristic
248C22×C127#53611yescharacteristic
249C22×C127#54112yes—
250C22×C127#54112yes—
251C22×C127#54112yes—
252C22×C127#54712yes—
253C22×C127#54712yes—
254C22×C127#54712yes—
255C22×C127#54812yes—
256C22×C127#54812yes—
257C22×C127#54812yes—
258C22×C127#55212yes—
259C22×C127#55212yes—
260C22×C127#55212yes—
261C22×C127#56412yes—
262C4×C127—24no—
263C4×C127—24no—
264C4×C127—42no—
265C4×C127—42no—
266C4×C127—42no—
267C4×C127—42no—
268C4×C127—42no—
269C4×C127—44no—
270C4×C127—44no—
271C4×C127—82no—
272C4×C127—82no—
273#15881C12711yesmaximal, characteristic, direct product factor, Sylow
274C2×C127#240611yescharacteristic
275C2×C127#243211yescharacteristic
276C2×C127#243611yescharacteristic
277C2×C127#247512yes—
278C2×C127#248912yes—
279C2×C127#251912yes—
280C2×C127#271912yes—
281C2×C127#271912yes—
282C2×C127#271912yes—
283C22×#125C2×C12711yescharacteristic
284C2×#400C2×C12711yescharacteristic
285C2×#398C2×C12711yescharacteristic
286C2×#382C2×C12711yescharacteristic
287#1445C2×C12711yescharacteristic
288#1442C2×C12712yes—
289#1442C2×C12712yes—
290#1441C2×C12712yes—
291#1436C2×C12712yes—
292#1436C2×C12711yescharacteristic
293#1436C2×C12711yescharacteristic
294C127#1588111yescharacteristic, direct product factor, Sylow
295C2×#125—24no—
296C2×#125—24no—
297C2×#125—24no—
298C22×C4⋊C4C22×C12711yescharacteristic
299C22×C4⋊C4C22×C12712yes—
300C22×C4⋊C4C22×C12711yescharacteristic
301C22×C4⋊C4C22×C12711yescharacteristic
302C22×C4⋊C4C22×C12711yescharacteristic
303C22×C4⋊C4C22×C12711yescharacteristic
304C22×C4⋊C4C22×C12711yescharacteristic
305C22×C4⋊C4C22×C12711yescharacteristic
306C22×C42C22×C12711yescharacteristic
307C22×C42C22×C12711yescharacteristic
308#400—24no—
309#398—24no—
310#382—24no—
311C2×#95C22×C12711yescharacteristic
312C2×#95C22×C12712yes—
313C2×#95C22×C12712yes—
314C2×#95C22×C12711yescharacteristic
315C2×#95C22×C12712yes—
316C2×#95C22×C12712yes—
317C2×#95C22×C12712yes—
318C2×#95C22×C12712yes—
319C2×#95C22×C12712yes—
320C2×#95C22×C12712yes—
321C2×#95C22×C12712yes—
322C2×#95C22×C12712yes—
323C2×#95C22×C12712yes—
324C23×C4C23×C12712yes—
325C23×C4C23×C12712yes—
326C23×C4C23×C12711yescharacteristic
327C23×C4C23×C12711yescharacteristic
328C23×C4C23×C12711yescharacteristic
329C23×C4C23×C12711yescharacteristic
330C23×C4C23×C12711yescharacteristic
331C23×C4C23×C12712yes—
332C23×C4C23×C12712yes—
333C23×C4C23×C12711yescharacteristic
334C23×C4C23×C12711yescharacteristic
335#125—232no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4D4×C12714yes—
358C2×C4⋊C4D4×C12714yes—
359C2×C4⋊C4D4×C12714yes—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—24no—
365#95—24no—
366#95—24no—
367#95—22no—
368#95—24no—
369#95—22no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378C24C24×C12711yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4C2×D4×C12712yes—
431C22×C4C2×D4×C12712yes—
432C22×C4C2×D4×C12712yes—
433C22×C4C2×D4×C12712yes—
434C22×C4C2×D4×C12712yes—
435C22×C4C2×D4×C12712yes—
436C22×C4C2×D4×C12712yes—
437C22×C4C2×D4×C12712yes—
438C22×C4C2×D4×C12712yes—
439C22×C4#41×C12714yes—
440C22×C4#41×C12714yes—
441C22×C4#41×C12714yes—
442C4⋊C4—28no—
443C4⋊C4—28no—
444C4⋊C4—28no—
445C4⋊C4—28no—
446C4⋊C4—28no—
447C4⋊C4—28no—
448C4⋊C4—44no—
449C4⋊C4—48no—
450C42—28no—
451C42—28no—
452C23C22×D4×C12711yescharacteristic
453C23C22×D4×C12711yescharacteristic
454C23C22×D4×C12711yescharacteristic
455C23C2×#41×C12712yes—
456C23C2×#41×C12712yes—
457C23C2×#41×C12712yes—
458C232−1+4×C12712yes—
459C232−1+4×C12712yes—
460C232−1+4×C12712yes—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4#120×C12714yes—
523C2×C4#124×C12714yes—
524C22C2×#120×C12711yescharacteristic
525C22#525×C12711yescharacteristic
526C22C2×#124×C12711yescharacteristic
527C22#529×C12712yes—
528C22#532×C12711yescharacteristic
529C22#536×C12711yescharacteristic
530C22#536×C12711yescharacteristic
531C22#536×C12711yescharacteristic
532C22#541×C12712yes—
533C22#541×C12712yes—
534C22#541×C12712yes—
535C22#547×C12712yes—
536C22#547×C12712yes—
537C22#547×C12712yes—
538C22#548×C12712yes—
539C22#548×C12712yes—
540C22#548×C12712yes—
541C22#552×C12712yes—
542C22#552×C12712yes—
543C22#552×C12712yes—
544C22#564×C12712yes—
545C4—24no—
546C4—24no—
547C4—42no—
548C4—42no—
549C4—42no—
550C4—42no—
551C4—42no—
552C4—44no—
553C4—44no—
554C4—82no—
555C4—82no—
556C2C127×#240611yescharacteristic
557C2C127×#243211yescharacteristic
558C2C127×#243611yescharacteristic
559C2C127×#247512yes—
560C2C127×#248912yes—
561C2C127×#251912yes—
562C2C127×#271912yes—
563C2C127×#271912yes—
564C2C127×#271912yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
273. #15881C127direct (N × H)
294. C127#15881direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#125×C1272
C2×#400×C1272
C2×#398×C1272
C2×#382×C1272
C127×#14452
C127×#14422
C127×#14412
C127×#14362
#15881127