Finite Group Databasebeta

← C127×#17005 #44580678

Subgroups — C127×#17005 #44580678

Order 32512.

1362 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#385×C127C211yesmaximal, characteristic
2C2×#380×C127C211yesmaximal, characteristic
3C127×#1443C212yesmaximal, complemented
4C127×#1442C211yesmaximal, characteristic, complemented
5C127×#1442C211yesmaximal, characteristic, complemented
6C127×#1442C212yesmaximal, complemented
7C127×#1441C211yesmaximal, characteristic, complemented
8C127×#1441C211yesmaximal, characteristic, complemented
9C127×#1440C212yesmaximal
10C127×#1440C212yesmaximal
11C127×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2211yescharacteristic
21#385×C127—24no—
22#380×C127—24no—
23C2×#95×C127C2211yescharacteristic
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C25×C127C2311yescharacteristic
38C23×C4×C127—22no—
39C23×C4×C127—22no—
40C23×C4×C127—42no—
41C23×C4×C127—42no—
42C23×C4×C127D414yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2312yes—
48C23×C4×C127C2312yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2311yescharacteristic
52C23×C4×C127C2311yescharacteristic
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—42no—
60C2×C4⋊C4×C127—42no—
61C2×C4⋊C4×C127—42no—
62C2×C22⋊C4×C127—22no—
63C2×C22⋊C4×C127—22no—
64C2×C22⋊C4×C127—22no—
65C2×C22⋊C4×C127—24no—
66C2×C22⋊C4×C127—22no—
67C2×C22⋊C4×C127—24no—
68C2×C22⋊C4×C127—24no—
69C2×C22⋊C4×C127—24no—
70C2×C22⋊C4×C127—42no—
71C2×C22⋊C4×C127—42no—
72C2×C22⋊C4×C127—42no—
73#95×C127—24no—
74#95×C127—22no—
75#95×C127—22no—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—22no—
79#95×C127—22no—
80#95×C127—42no—
81#95×C127—42no—
82#95×C127—42no—
83#95×C127—42no—
84#95×C127—42no—
85#95×C127—42no—
86#95×C127—42no—
87C24×C127—21no—
88C24×C127—21no—
89C24×C127—21no—
90C24×C127—21no—
91C24×C127—21no—
92C24×C127—22no—
93C24×C127—22no—
94C24×C127—22no—
95C24×C127—21no—
96C24×C127C2×D412yes—
97C24×C127#4114yes—
98C24×C127C2411yescharacteristic
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
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—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—21no—
115C22×C4×C127—28no—
116C22×C4×C127—21no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—21no—
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—21no—
133C22×C4×C127—21no—
134C22×C4×C127—22no—
135C22×C4×C127—21no—
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×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—21no—
152C22×C4×C127—22no—
153C22×C4×C127—22no—
154C22×C4×C127—44no—
155C22×C4×C127—44no—
156C22×C4×C127—48no—
157C22×C4×C127—48no—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D412yes—
160C22×C4×C127#4112yes—
161C22×C4×C127#4112yes—
162C22×C4×C127#4112yes—
163C22×C4×C127#4112yes—
164C4⋊C4×C127—44no—
165C4⋊C4×C127—44no—
166C4⋊C4×C127—44no—
167C4⋊C4×C127—44no—
168C22⋊C4×C127—28no—
169C22⋊C4×C127—44no—
170C22⋊C4×C127—48no—
171C22⋊C4×C127—48no—
172C23×C127—22no—
173C23×C127—22no—
174C23×C127—22no—
175C23×C127—22no—
176C23×C127—22no—
177C23×C127—22no—
178C23×C127—24no—
179C23×C127—24no—
180C23×C127—24no—
181C23×C127—24no—
182C23×C127—24no—
183C23×C127—24no—
184C23×C127—42no—
185C23×C127—42no—
186C23×C127—42no—
187C23×C127—42no—
188C23×C127—41no—
189C23×C127—41no—
190C23×C127—41no—
191C23×C127—41no—
192C23×C127—42no—
193C23×C127—42no—
194C23×C127#12414yes—
195C23×C127C22×D411yescharacteristic
196C23×C127C2×#4111yescharacteristic
197C23×C127C2×#4111yescharacteristic
198C23×C127C2×#4111yescharacteristic
199C23×C127C2×#4111yescharacteristic
200C23×C127C2×#4112yes—
201C23×C127H(5,𝔽2)12yes—
202C23×C127H(5,𝔽2)12yes—
203C23×C127H(5,𝔽2)11yescharacteristic
204C23×C1272−1+412yes—
205C23×C1272−1+411yescharacteristic
206C2×C4×C127—22no—
207C2×C4×C127—22no—
208C2×C4×C127—24no—
209C2×C4×C127—24no—
210C2×C4×C127—22no—
211C2×C4×C127—22no—
212C2×C4×C127—22no—
213C2×C4×C127—22no—
214C2×C4×C127—22no—
215C2×C4×C127—24no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—416no—
219C2×C4×C127—41no—
220C2×C4×C127—41no—
221C2×C4×C127—41no—
222C2×C4×C127—41no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—41no—
227C2×C4×C127—41no—
228C2×C4×C127—41no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—41no—
233C2×C4×C127—41no—
234C2×C4×C127—42no—
235C2×C4×C127—41no—
236C2×C4×C127—42no—
237C2×C4×C127—41no—
238C2×C4×C127—42no—
239C2×C4×C127—41no—
240C2×C4×C127—42no—
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—42no—
248C2×C4×C127—42no—
249C2×C4×C127—42no—
250C2×C4×C127—42no—
251C2×C4×C127—42no—
252C2×C4×C127—42no—
253C2×C4×C127—42no—
254C2×C4×C127—42no—
255C2×C4×C127—42no—
256C2×C4×C127—42no—
257C2×C4×C127—42no—
258C2×C4×C127—42no—
259C2×C4×C127—42no—
260C2×C4×C127—42no—
261C2×C4×C127—42no—
262C2×C4×C127—42no—
263C2×C4×C127—42no—
264C2×C4×C127—42no—
265C2×C4×C127—42no—
266C2×C4×C127#12314yes—
267C22×C127—24no—
268C22×C127—24no—
269C22×C127—24no—
270C22×C127—42no—
271C22×C127—42no—
272C22×C127—42no—
273C22×C127—44no—
274C22×C127—44no—
275C22×C127—44no—
276C22×C127—44no—
277C22×C127—42no—
278C22×C127C2×#12311yescharacteristic
279C22×C127#52511yescharacteristic
280C22×C127C2×#12411yescharacteristic
281C22×C127#53411yescharacteristic
282C22×C127#53411yescharacteristic
283C22×C127#53611yescharacteristic
284C22×C127#53711yescharacteristic
285C22×C127#53812yes—
286C22×C127#53812yes—
287C22×C127#53812yes—
288C22×C127#53912yes—
289C22×C127#53912yes—
290C22×C127#54212yes—
291C22×C127#55211yescharacteristic
292C22×C127#55212yes—
293C22×C127#55212yes—
294C22×C127#55312yes—
295C22×C127#55312yes—
296C22×C127#55311yescharacteristic
297C22×C127#55511yescharacteristic
298C22×C127#55611yescharacteristic
299C22×C127#56212yes—
300C22×C127#56312yes—
301C4×C127—24no—
302C4×C127—42no—
303C4×C127—42no—
304C4×C127—42no—
305C4×C127—82no—
306C4×C127—81no—
307C4×C127—82no—
308C4×C127—82no—
309C4×C127—82no—
310C4×C127—81no—
311#17005C12711yesmaximal, characteristic, direct product factor, Sylow
312C2×C127—44no—
313C2×C127#248511yescharacteristic
314C2×C127#250311yescharacteristic
315C2×C127#259111yescharacteristic
316C2×C127#262211yescharacteristic
317C2×C127#263811yescharacteristic
318C2×C127#263911yescharacteristic
319C2×C127#277012yes—
320C2×C127#277912yes—
321C2×C127#278112yes—
322C2×C127#278712yes—
323C2×C127#281411yescharacteristic
324C2×#385C2×C12711yescharacteristic
325C2×#380C2×C12711yescharacteristic
326#1443C2×C12712yescomplemented
327#1442C2×C12711yescharacteristic, complemented
328#1442C2×C12711yescharacteristic, complemented
329#1442C2×C12712yescomplemented
330#1441C2×C12711yescharacteristic, complemented
331#1441C2×C12711yescharacteristic, complemented
332#1440C2×C12712yes—
333#1440C2×C12712yes—
334C22⋊#95C2×C12711yescharacteristic
335C127#1700511yescharacteristic, direct product factor, Sylow
336C24×C4C22×C12711yescharacteristic
337C22×C4⋊C4C22×C12711yescharacteristic
338C22×C4⋊C4C22×C12711yescharacteristic
339C22×C4⋊C4C22×C12711yescharacteristic
340C22×C4⋊C4C22×C12711yescharacteristic
341C22×C22⋊C4C22×C12712yes—
342C22×C22⋊C4C22×C12711yescharacteristic
343C22×C22⋊C4C22×C12712yes—
344C22×C22⋊C4C22×C12711yescharacteristic
345#385—24no—
346#380—24no—
347C2×#95C22×C12711yescharacteristic
348C2×#95C22×C12711yescharacteristic
349C2×#95C22×C12712yes—
350C2×#95C22×C12712yes—
351C2×#95C22×C12711yescharacteristic
352C2×#95C22×C12712yes—
353C2×#95C22×C12711yescharacteristic
354C2×#95C22×C12712yes—
355C2×#95C22×C12712yes—
356C2×#95C22×C12712yes—
357C2×#95C22×C12712yes—
358C2×#95C22×C12712yes—
359C2×#95C22×C12712yes—
360C2×#95C22×C12712yes—
361C25C23×C12711yescharacteristic
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4D4×C12714yes—
367C23×C4C23×C12711yescharacteristic
368C23×C4C23×C12712yes—
369C23×C4C23×C12712yes—
370C23×C4C23×C12711yescharacteristic
371C23×C4C23×C12712yes—
372C23×C4C23×C12712yes—
373C23×C4C23×C12711yescharacteristic
374C23×C4C23×C12711yescharacteristic
375C23×C4C23×C12711yescharacteristic
376C23×C4C23×C12711yescharacteristic
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397#95—24no—
398#95—22no—
399#95—22no—
400#95—24no—
401#95—24no—
402#95—22no—
403#95—22no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24C2×D4×C12712yes—
421C24#41×C12714yes—
422C24C24×C12711yescharacteristic
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—28no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—48no—
481C22×C4—48no—
482C22×C4C2×D4×C12712yes—
483C22×C4C2×D4×C12712yes—
484C22×C4#41×C12712yes—
485C22×C4#41×C12712yes—
486C22×C4#41×C12712yes—
487C22×C4#41×C12712yes—
488C4⋊C4—44no—
489C4⋊C4—44no—
490C4⋊C4—44no—
491C4⋊C4—44no—
492C22⋊C4—28no—
493C22⋊C4—44no—
494C22⋊C4—48no—
495C22⋊C4—48no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23#124×C12714yes—
519C23C22×D4×C12711yescharacteristic
520C23C2×#41×C12711yescharacteristic
521C23C2×#41×C12711yescharacteristic
522C23C2×#41×C12711yescharacteristic
523C23C2×#41×C12711yescharacteristic
524C23C2×#41×C12712yes—
525C23H(5,𝔽2)×C12712yes—
526C23H(5,𝔽2)×C12712yes—
527C23H(5,𝔽2)×C12711yescharacteristic
528C232−1+4×C12712yes—
529C232−1+4×C12711yescharacteristic
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—416no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4#123×C12714yes—
591C22—24no—
592C22—24no—
593C22—24no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—42no—
602C22C2×#123×C12711yescharacteristic
603C22#525×C12711yescharacteristic
604C22C2×#124×C12711yescharacteristic
605C22#534×C12711yescharacteristic
606C22#534×C12711yescharacteristic
607C22#536×C12711yescharacteristic
608C22#537×C12711yescharacteristic
609C22#538×C12712yes—
610C22#538×C12712yes—
611C22#538×C12712yes—
612C22#539×C12712yes—
613C22#539×C12712yes—
614C22#542×C12712yes—
615C22#552×C12711yescharacteristic
616C22#552×C12712yes—
617C22#552×C12712yes—
618C22#553×C12712yes—
619C22#553×C12712yes—
620C22#553×C12711yescharacteristic
621C22#555×C12711yescharacteristic
622C22#556×C12711yescharacteristic
623C22#562×C12712yes—
624C22#563×C12712yes—
625C4—24no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—82no—
630C4—81no—
631C4—82no—
632C4—82no—
633C4—82no—
634C4—81no—
635C2—44no—
636C2C127×#248511yescharacteristic
637C2C127×#250311yescharacteristic
638C2C127×#259111yescharacteristic
639C2C127×#262211yescharacteristic
640C2C127×#263811yescharacteristic
641C2C127×#263911yescharacteristic
642C2C127×#277012yes—
643C2C127×#277912yes—
644C2C127×#278112yes—
645C2C127×#278712yes—
646C2C127×#281411yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1443C2semidirect
4. C127×#1442C2semidirect
5. C127×#1442C2semidirect
6. C127×#1442C2semidirect
7. C127×#1441C2semidirect
8. C127×#1441C2semidirect
311. #17005C127direct (N × H)
326. #1443C2×C127semidirect
327. #1442C2×C127semidirect
328. #1442C2×C127semidirect
329. #1442C2×C127semidirect
330. #1441C2×C127semidirect
331. #1441C2×C127semidirect
335. C127#17005direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#385×C1272
C2×#380×C1272
C127×#14432
C127×#14422
C127×#14412
C127×#14402
C127×C22⋊#952
#17005127