Finite Group Databasebeta

← C127×#13815 #44577488

Subgroups — C127×#13815 #44577488

Order 32512.

1602 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#387×C127C212yesmaximal
2C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
4C2×#376×C127C211yesmaximal, characteristic
5C127×#1436C212yesmaximal
6C127×#1436C212yesmaximal
7C127×#1434C211yesmaximal, characteristic
8C127×#1434C211yesmaximal, characteristic
9C127×#1434C211yesmaximal, characteristic
10C4×#95×C127C211yesmaximal, characteristic
11C4×#95×C127C212yesmaximal
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C42×C127C2212yes—
16C22×C42×C127C2212yes—
17C22×C42×C127C2211yescharacteristic
18C22×C42×C127C2212yes—
19C22×C42×C127C2211yescharacteristic
20C22×C42×C127C2211yescharacteristic
21#387×C127C4116yescomplemented
22C4×C4⋊C4×C127—24no—
23C4×C4⋊C4×C127C418yescomplemented
24#376×C127—24no—
25C2×#95×C127C2211yescharacteristic
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2211yescharacteristic
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127C2×C414yes—
55C2×C4⋊C4×C127C2×C418yes—
56C2×C4⋊C4×C127C2×C414yes—
57C2×C4⋊C4×C127C2×C418yes—
58C2×C42×C127—22no—
59C2×C42×C127—24no—
60C2×C42×C127—22no—
61C2×C42×C127—24no—
62C2×C42×C127—22no—
63C2×C42×C127—22no—
64C2×C42×C127—24no—
65C2×C42×C127—24no—
66C2×C42×C127—24no—
67C2×C42×C127—24no—
68C2×C42×C127—24no—
69C2×C42×C127—42no—
70C2×C42×C127—42no—
71C2×C42×C127C2×C414yes—
72C2×C42×C127C2×C414yes—
73C2×C42×C127C2×C414yes—
74C2×C42×C127C2×C418yes—
75#95×C127—22no—
76#95×C127—24no—
77#95×C127—22no—
78#95×C127—24no—
79#95×C127—24no—
80#95×C127—22no—
81#95×C127—42no—
82#95×C127C2×C414yes—
83#95×C127C2×C414yes—
84#95×C127C2×C418yes—
85#95×C127C2×C418yes—
86#95×C127C2×C418yes—
87#95×C127C2×C418yes—
88#95×C127D414yes—
89C24×C127C2411yescharacteristic
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—21no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—21no—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—22no—
105C22×C4×C127—21no—
106C22×C4×C127—22no—
107C22×C4×C127—21no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
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—21no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—22no—
128C22×C4×C127—21no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—21no—
135C22×C4×C127—22no—
136C22×C4×C127C22×C414yes—
137C22×C4×C127C22×C414yes—
138C22×C4×C127C22×C414yes—
139C22×C4×C127C22×C412yes—
140C22×C4×C127C22×C414yes—
141C22×C4×C127C22×C412yes—
142C22×C4×C127C22×C412yes—
143C22×C4×C127C22×C414yes—
144C22×C4×C127C22×C414yes—
145C22×C4×C127C22×C412yes—
146C22×C4×C127C22×C412yes—
147C22×C4×C127C22×C412yes—
148C22×C4×C127C22×C414yes—
149C22×C4×C127C22×C412yes—
150C22×C4×C127C2×D412yes—
151C22×C4×C127C2×D414yes—
152C22×C4×C127#4112yes—
153C22×C4×C127#4114yes—
154C22×C4×C127#4112yes—
155C22×C4×C127#4112yes—
156C22×C4×C127#4114yes—
157C4⋊C4×C127—28no—
158C4⋊C4×C127—216no—
159C4⋊C4×C127C42116yescomplemented
160C42×C127—28no—
161C42×C127—28no—
162C42×C127—28no—
163C42×C127—216no—
164C42×C127—48no—
165C42×C127—48no—
166C23×C127C23×C411yescharacteristic
167C23×C127C23×C412yes—
168C23×C127C22×D411yescharacteristic
169C23×C127C2×#4111yescharacteristic
170C23×C127C2×#4112yes—
171C23×C127C2×#4111yescharacteristic
172C23×C127C2×#4112yes—
173C23×C127C2×#4111yescharacteristic
174C23×C127H(5,𝔽2)11yescharacteristic
175C23×C1272−1+412yes—
176C23×C1272−1+411yescharacteristic
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—22no—
186C2×C4×C127—24no—
187C2×C4×C127—24no—
188C2×C4×C127—24no—
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—22no—
196C2×C4×C127—24no—
197C2×C4×C127—22no—
198C2×C4×C127—24no—
199C2×C4×C127—24no—
200C2×C4×C127—24no—
201C2×C4×C127—22no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—22no—
207C2×C4×C127—24no—
208C2×C4×C127—22no—
209C2×C4×C127—22no—
210C2×C4×C127—22no—
211C2×C4×C127—24no—
212C2×C4×C127—24no—
213C2×C4×C127—24no—
214C2×C4×C127—24no—
215C2×C4×C127—24no—
216C2×C4×C127—24no—
217C2×C4×C127—24no—
218C2×C4×C127—22no—
219C2×C4×C127—24no—
220C2×C4×C127—24no—
221C2×C4×C127—42no—
222C2×C4×C127—41no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—41no—
226C2×C4×C127—42no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—41no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—41no—
234C2×C4×C127—42no—
235C2×C4×C127—42no—
236C2×C4×C127—42no—
237C2×C4×C127C2×C4214yes—
238C2×C4×C127C2×C4214yes—
239C2×C4×C127C2×C4214yes—
240C2×C4×C127#11714yes—
241C2×C4×C127#11714yes—
242C2×C4×C127C4×D414yes—
243C2×C4×C127C4×D418yes—
244C22×C127C22×C4211yescharacteristic
245C22×C127C2×#11711yescharacteristic
246C22×C127C2×#11711yescharacteristic
247C22×C127C2×C4×D411yescharacteristic
248C22×C127C2×C4×D412yes—
249C22×C127C4×#4111yescharacteristic
250C22×C127C4×#4112yes—
251C22×C127C4×#4112yes—
252C22×C127C4×#4112yes—
253C22×C127#51911yescharacteristic
254C22×C127#51912yes—
255C22×C127#52011yescharacteristic
256C22×C127#52012yes—
257C22×C127#54611yescharacteristic
258C22×C127#54712yes—
259C22×C127#54811yescharacteristic
260C22×C127#55112yes—
261C22×C127#55212yes—
262C22×C127#55212yes—
263C22×C127#55211yescharacteristic
264C22×C127#55212yes—
265C22×C127#55311yescharacteristic
266C22×C127#55612yes—
267C4×C127—24no—
268C4×C127—24no—
269C4×C127—24no—
270C4×C127—28no—
271C4×C127—24no—
272C4×C127—24no—
273C4×C127—24no—
274C4×C127—42no—
275C4×C127—44no—
276C4×C127—44no—
277C4×C127—44no—
278#13815C12711yesmaximal, characteristic, direct product factor, Sylow
279C2×C127C4×#11711yescharacteristic
280C2×C127C42×D411yescharacteristic
281C2×C127#227611yescharacteristic
282C2×C127#234311yescharacteristic
283C2×C127#234411yescharacteristic
284C2×C127#235211yescharacteristic
285C2×C127#235611yescharacteristic
286C2×C127#235912yes—
287C2×C127#236212yes—
288C2×C127#237112yes—
289C2×C127#237312yes—
290C2×#387C2×C12712yes—
291C2×C4×C4⋊C4C2×C12711yescharacteristic
292C2×C4×C4⋊C4C2×C12711yescharacteristic
293C2×#376C2×C12711yescharacteristic
294#1436C2×C12712yes—
295#1436C2×C12712yes—
296#1434C2×C12711yescharacteristic
297#1434C2×C12711yescharacteristic
298#1434C2×C12711yescharacteristic
299C4×#95C2×C12711yescharacteristic
300C4×#95C2×C12712yes—
301C127#1381511yescharacteristic, direct product factor, Sylow
302C22×C4⋊C4C22×C12711yescharacteristic
303C22×C4⋊C4C22×C12712yes—
304C22×C4⋊C4C22×C12711yescharacteristic
305C22×C42C22×C12712yes—
306C22×C42C22×C12712yes—
307C22×C42C22×C12711yescharacteristic
308C22×C42C22×C12712yes—
309C22×C42C22×C12711yescharacteristic
310C22×C42C22×C12711yescharacteristic
311#387C4×C127116yescomplemented
312C4×C4⋊C4—24no—
313C4×C4⋊C4C4×C12718yescomplemented
314#376—24no—
315C2×#95C22×C12711yescharacteristic
316C2×#95C22×C12712yes—
317C2×#95C22×C12712yes—
318C2×#95C22×C12711yescharacteristic
319C2×#95C22×C12711yescharacteristic
320C2×#95C22×C12712yes—
321C2×#95C22×C12712yes—
322C2×#95C22×C12711yescharacteristic
323C2×#95C22×C12712yes—
324C2×#95C22×C12712yes—
325C2×#95C22×C12712yes—
326C2×#95C22×C12712yes—
327C2×#95C22×C12711yescharacteristic
328C2×#95C22×C12711yescharacteristic
329C23×C4C23×C12711yescharacteristic
330C23×C4C23×C12712yes—
331C23×C4C23×C12712yes—
332C23×C4C23×C12712yes—
333C23×C4C23×C12711yescharacteristic
334C23×C4C23×C12711yescharacteristic
335C23×C4C23×C12711yescharacteristic
336C23×C4C23×C12712yes—
337C23×C4C23×C12711yescharacteristic
338C23×C4C23×C12711yescharacteristic
339C23×C4C23×C12711yescharacteristic
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4C2×C4×C12714yes—
345C2×C4⋊C4C2×C4×C12718yes—
346C2×C4⋊C4C2×C4×C12714yes—
347C2×C4⋊C4C2×C4×C12718yes—
348C2×C42—22no—
349C2×C42—24no—
350C2×C42—22no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—42no—
360C2×C42—42no—
361C2×C42C2×C4×C12714yes—
362C2×C42C2×C4×C12714yes—
363C2×C42C2×C4×C12714yes—
364C2×C42C2×C4×C12718yes—
365#95—22no—
366#95—24no—
367#95—22no—
368#95—24no—
369#95—24no—
370#95—22no—
371#95—42no—
372#95C2×C4×C12714yes—
373#95C2×C4×C12714yes—
374#95C2×C4×C12718yes—
375#95C2×C4×C12718yes—
376#95C2×C4×C12718yes—
377#95C2×C4×C12718yes—
378#95D4×C12714yes—
379C24C24×C12711yescharacteristic
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4C22×C4×C12714yes—
427C22×C4C22×C4×C12714yes—
428C22×C4C22×C4×C12714yes—
429C22×C4C22×C4×C12712yes—
430C22×C4C22×C4×C12714yes—
431C22×C4C22×C4×C12712yes—
432C22×C4C22×C4×C12712yes—
433C22×C4C22×C4×C12714yes—
434C22×C4C22×C4×C12714yes—
435C22×C4C22×C4×C12712yes—
436C22×C4C22×C4×C12712yes—
437C22×C4C22×C4×C12712yes—
438C22×C4C22×C4×C12714yes—
439C22×C4C22×C4×C12712yes—
440C22×C4C2×D4×C12712yes—
441C22×C4C2×D4×C12714yes—
442C22×C4#41×C12712yes—
443C22×C4#41×C12714yes—
444C22×C4#41×C12712yes—
445C22×C4#41×C12712yes—
446C22×C4#41×C12714yes—
447C4⋊C4—28no—
448C4⋊C4—216no—
449C4⋊C4C42×C127116yescomplemented
450C42—28no—
451C42—28no—
452C42—28no—
453C42—216no—
454C42—48no—
455C42—48no—
456C23C23×C4×C12711yescharacteristic
457C23C23×C4×C12712yes—
458C23C22×D4×C12711yescharacteristic
459C23C2×#41×C12711yescharacteristic
460C23C2×#41×C12712yes—
461C23C2×#41×C12711yescharacteristic
462C23C2×#41×C12712yes—
463C23C2×#41×C12711yescharacteristic
464C23H(5,𝔽2)×C12711yescharacteristic
465C232−1+4×C12712yes—
466C232−1+4×C12711yescharacteristic
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4C2×C42×C12714yes—
528C2×C4C2×C42×C12714yes—
529C2×C4C2×C42×C12714yes—
530C2×C4#117×C12714yes—
531C2×C4#117×C12714yes—
532C2×C4C4×D4×C12714yes—
533C2×C4C4×D4×C12718yes—
534C22C22×C42×C12711yescharacteristic
535C22C2×#117×C12711yescharacteristic
536C22C2×#117×C12711yescharacteristic
537C22C2×C4×D4×C12711yescharacteristic
538C22C2×C4×D4×C12712yes—
539C22C4×#41×C12711yescharacteristic
540C22C4×#41×C12712yes—
541C22C4×#41×C12712yes—
542C22C4×#41×C12712yes—
543C22#519×C12711yescharacteristic
544C22#519×C12712yes—
545C22#520×C12711yescharacteristic
546C22#520×C12712yes—
547C22#546×C12711yescharacteristic
548C22#547×C12712yes—
549C22#548×C12711yescharacteristic
550C22#551×C12712yes—
551C22#552×C12712yes—
552C22#552×C12712yes—
553C22#552×C12711yescharacteristic
554C22#552×C12712yes—
555C22#553×C12711yescharacteristic
556C22#556×C12712yes—
557C4—24no—
558C4—24no—
559C4—24no—
560C4—28no—
561C4—24no—
562C4—24no—
563C4—24no—
564C4—42no—
565C4—44no—
566C4—44no—
567C4—44no—
568C2C4×#117×C12711yescharacteristic
569C2C42×D4×C12711yescharacteristic
570C2C127×#227611yescharacteristic
571C2C127×#234311yescharacteristic
572C2C127×#234411yescharacteristic
573C2C127×#235211yescharacteristic
574C2C127×#235611yescharacteristic
575C2C127×#235912yes—
576C2C127×#236212yes—
577C2C127×#237112yes—
578C2C127×#237312yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
21. #387×C127C4semidirect
23. C4×C4⋊C4×C127C4semidirect
159. C4⋊C4×C127C42semidirect
278. #13815C127direct (N × H)
301. C127#13815direct (N × H)
311. #387C4×C127semidirect
313. C4×C4⋊C4C4×C127semidirect
449. C4⋊C4C42×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#387×C1272
C2×C4×C4⋊C4×C1272
C2×#376×C1272
C127×#14362
C127×#14342
C4×#95×C1272
#13815127