Finite Group Databasebeta

← C127×#14244 #44577917

Subgroups — C127×#14244 #44577917

Order 32512.

1362 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C127C211yesmaximal, characteristic
2C2×#387×C127C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
4C127×#1445C211yesmaximal, characteristic
5C127×#1444C211yesmaximal, characteristic
6C127×#1441C211yesmaximal, characteristic
7C127×#1436C212yesmaximal
8C127×#1436C212yesmaximal
9C127×#1436C212yesmaximal
10C127×C4⋊#95C212yesmaximal
11C4×#95×C127C211yesmaximal, characteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2212yes—
18C22×C42×C127C2212yes—
19C22×C42×C127C2211yescharacteristic
20C22×C42×C127C2212yes—
21#398×C127C418yescomplemented
22#387×C127—24no—
23C4×C4⋊C4×C127—24no—
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2211yescharacteristic
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C23×C4×C127C2311yescharacteristic
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2312yes—
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127—24no—
59C2×C4⋊C4×C127—42no—
60C2×C4⋊C4×C127—42no—
61C2×C4⋊C4×C127—42no—
62C2×C4⋊C4×C127C2×C414yes—
63C2×C4⋊C4×C127C2×C414yes—
64C2×C4⋊C4×C127C2×C418yes—
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×C127—42no—
72C2×C42×C127D414yes—
73#95×C127—24no—
74#95×C127—22no—
75#95×C127—22no—
76#95×C127—22no—
77#95×C127—22no—
78#95×C127—24no—
79#95×C127—22no—
80#95×C127—24no—
81#95×C127—42no—
82#95×C127—42no—
83#95×C127—42no—
84#95×C127C2×C418yes—
85#95×C127C2×C414yes—
86#95×C127Q818yes—
87C24×C127C2411yescharacteristic
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—21no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—21no—
111C22×C4×C127—22no—
112C22×C4×C127—21no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—21no—
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—21no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—21no—
128C22×C4×C127—21no—
129C22×C4×C127—21no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—21no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—21no—
138C22×C4×C127C22×C412yes—
139C22×C4×C127C22×C414yes—
140C22×C4×C127C22×C412yes—
141C22×C4×C127C22×C412yes—
142C22×C4×C127C22×C414yes—
143C22×C4×C127C2×D412yes—
144C22×C4×C127C2×D412yes—
145C22×C4×C127C2×D412yes—
146C22×C4×C127C2×Q814yes—
147C22×C4×C127C2×Q814yes—
148C22×C4×C127C2×Q814yes—
149C22×C4×C127#4114yes—
150C22×C4×C127#4112yes—
151C22×C4×C127#4114yes—
152C22×C4×C127#4114yes—
153C4⋊C4×C127—28no—
154C4⋊C4×C127—28no—
155C4⋊C4×C127—28no—
156C4⋊C4×C127—48no—
157C4⋊C4×C127—48no—
158C4⋊C4×C127—44no—
159C42×C127—28no—
160C42×C127—48no—
161C42×C127—48no—
162C23×C127C23×C411yescharacteristic
163C23×C127C22×D411yescharacteristic
164C23×C127C22×Q812yes—
165C23×C127C2×#4111yescharacteristic
166C23×C127C2×#4112yes—
167C23×C127C2×#4112yes—
168C23×C127C2×#4112yes—
169C23×C127H(5,𝔽2)11yescharacteristic
170C23×C127H(5,𝔽2)11yescharacteristic
171C23×C127H(5,𝔽2)11yescharacteristic
172C23×C1272−1+411yescharacteristic
173C2×C4×C127—24no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—24no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—24no—
187C2×C4×C127—24no—
188C2×C4×C127—24no—
189C2×C4×C127—24no—
190C2×C4×C127—24no—
191C2×C4×C127—22no—
192C2×C4×C127—24no—
193C2×C4×C127—22no—
194C2×C4×C127—24no—
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—24no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—41no—
206C2×C4×C127—41no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—42no—
211C2×C4×C127—42no—
212C2×C4×C127—41no—
213C2×C4×C127—41no—
214C2×C4×C127—42no—
215C2×C4×C127—41no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—41no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—41no—
225C2×C4×C127—41no—
226C2×C4×C127—41no—
227C2×C4×C127—41no—
228C2×C4×C127—41no—
229C2×C4×C127—41no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127C4×D414yes—
235C2×C4×C127C4×Q818yes—
236C2×C4×C127#12314yes—
237C2×C4×C127C4⋊Q814yes—
238C22×C127C2×C4×D411yescharacteristic
239C22×C127C2×C4×Q812yes—
240C22×C127C4×#4112yes—
241C22×C127#51811yescharacteristic
242C22×C127#52011yescharacteristic
243C22×C127C2×#12311yescharacteristic
244C22×C127#52511yescharacteristic
245C22×C127#52912yes—
246C22×C127C2×C4⋊Q811yescharacteristic
247C22×C127#53211yescharacteristic
248C22×C127#53312yes—
249C22×C127#53511yescharacteristic
250C22×C127#53711yescharacteristic
251C22×C127#54011yescharacteristic
252C22×C127#54211yescharacteristic
253C22×C127#55112yes—
254C22×C127#55112yes—
255C22×C127#55212yes—
256C22×C127#55312yes—
257C22×C127#55412yes—
258C22×C127#55412yes—
259C22×C127#55412yes—
260C22×C127#55712yes—
261C4×C127—28no—
262C4×C127—24no—
263C4×C127—24no—
264C4×C127—24no—
265C4×C127—42no—
266C4×C127—44no—
267C4×C127—44no—
268C4×C127—44no—
269C4×C127—42no—
270C4×C127—81no—
271C4×C127—81no—
272#14244C12711yesmaximal, characteristic, direct product factor, Sylow
273C2×C127C4×#12311yescharacteristic
274C2×C127C4×C4⋊Q811yescharacteristic
275C2×C127#232411yescharacteristic
276C2×C127#236812yes—
277C2×C127#237012yes—
278C2×C127#249811yescharacteristic
279C2×C127#250211yescharacteristic
280C2×C127#252012yes—
281C2×C127#252212yes—
282C2×C127#258411yescharacteristic
283C2×C127#260311yescharacteristic
284C2×#398C2×C12711yescharacteristic
285C2×#387C2×C12711yescharacteristic
286C2×C4×C4⋊C4C2×C12711yescharacteristic
287#1445C2×C12711yescharacteristic
288#1444C2×C12711yescharacteristic
289#1441C2×C12711yescharacteristic
290#1436C2×C12712yes—
291#1436C2×C12712yes—
292#1436C2×C12712yes—
293C4⋊#95C2×C12712yes—
294C4×#95C2×C12711yescharacteristic
295C127#1424411yescharacteristic, direct product factor, Sylow
296C22×C4⋊C4C22×C12711yescharacteristic
297C22×C4⋊C4C22×C12711yescharacteristic
298C22×C4⋊C4C22×C12712yes—
299C22×C4⋊C4C22×C12711yescharacteristic
300C22×C4⋊C4C22×C12711yescharacteristic
301C22×C4⋊C4C22×C12712yes—
302C22×C42C22×C12712yes—
303C22×C42C22×C12711yescharacteristic
304C22×C42C22×C12712yes—
305#398C4×C12718yescomplemented
306#387—24no—
307C4×C4⋊C4—24no—
308C2×#95C22×C12711yescharacteristic
309C2×#95C22×C12711yescharacteristic
310C2×#95C22×C12712yes—
311C2×#95C22×C12712yes—
312C2×#95C22×C12712yes—
313C2×#95C22×C12711yescharacteristic
314C2×#95C22×C12711yescharacteristic
315C2×#95C22×C12711yescharacteristic
316C2×#95C22×C12712yes—
317C2×#95C22×C12712yes—
318C2×#95C22×C12712yes—
319C2×#95C22×C12711yescharacteristic
320C2×#95C22×C12712yes—
321C2×#95C22×C12712yes—
322C23×C4C23×C12711yescharacteristic
323C23×C4C23×C12711yescharacteristic
324C23×C4C23×C12711yescharacteristic
325C23×C4C23×C12711yescharacteristic
326C23×C4C23×C12712yes—
327C23×C4C23×C12712yes—
328C23×C4C23×C12712yes—
329C23×C4C23×C12711yescharacteristic
330C23×C4C23×C12712yes—
331C23×C4C23×C12711yescharacteristic
332C23×C4C23×C12711yescharacteristic
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4C2×C4×C12714yes—
347C2×C4⋊C4C2×C4×C12714yes—
348C2×C4⋊C4C2×C4×C12718yes—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—42no—
354C2×C42—42no—
355C2×C42—42no—
356C2×C42D4×C12714yes—
357#95—24no—
358#95—22no—
359#95—22no—
360#95—22no—
361#95—22no—
362#95—24no—
363#95—22no—
364#95—24no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95C2×C4×C12718yes—
369#95C2×C4×C12714yes—
370#95Q8×C12718yes—
371C24C24×C12711yescharacteristic
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4C22×C4×C12712yes—
423C22×C4C22×C4×C12714yes—
424C22×C4C22×C4×C12712yes—
425C22×C4C22×C4×C12712yes—
426C22×C4C22×C4×C12714yes—
427C22×C4C2×D4×C12712yes—
428C22×C4C2×D4×C12712yes—
429C22×C4C2×D4×C12712yes—
430C22×C4C2×Q8×C12714yes—
431C22×C4C2×Q8×C12714yes—
432C22×C4C2×Q8×C12714yes—
433C22×C4#41×C12714yes—
434C22×C4#41×C12712yes—
435C22×C4#41×C12714yes—
436C22×C4#41×C12714yes—
437C4⋊C4—28no—
438C4⋊C4—28no—
439C4⋊C4—28no—
440C4⋊C4—48no—
441C4⋊C4—48no—
442C4⋊C4—44no—
443C42—28no—
444C42—48no—
445C42—48no—
446C23C23×C4×C12711yescharacteristic
447C23C22×D4×C12711yescharacteristic
448C23C22×Q8×C12712yes—
449C23C2×#41×C12711yescharacteristic
450C23C2×#41×C12712yes—
451C23C2×#41×C12712yes—
452C23C2×#41×C12712yes—
453C23H(5,𝔽2)×C12711yescharacteristic
454C23H(5,𝔽2)×C12711yescharacteristic
455C23H(5,𝔽2)×C12711yescharacteristic
456C232−1+4×C12711yescharacteristic
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4C4×D4×C12714yes—
519C2×C4C4×Q8×C12718yes—
520C2×C4#123×C12714yes—
521C2×C4C4⋊Q8×C12714yes—
522C22C2×C4×D4×C12711yescharacteristic
523C22C2×C4×Q8×C12712yes—
524C22C4×#41×C12712yes—
525C22#518×C12711yescharacteristic
526C22#520×C12711yescharacteristic
527C22C2×#123×C12711yescharacteristic
528C22#525×C12711yescharacteristic
529C22#529×C12712yes—
530C22C2×C4⋊Q8×C12711yescharacteristic
531C22#532×C12711yescharacteristic
532C22#533×C12712yes—
533C22#535×C12711yescharacteristic
534C22#537×C12711yescharacteristic
535C22#540×C12711yescharacteristic
536C22#542×C12711yescharacteristic
537C22#551×C12712yes—
538C22#551×C12712yes—
539C22#552×C12712yes—
540C22#553×C12712yes—
541C22#554×C12712yes—
542C22#554×C12712yes—
543C22#554×C12712yes—
544C22#557×C12712yes—
545C4—28no—
546C4—24no—
547C4—24no—
548C4—24no—
549C4—42no—
550C4—44no—
551C4—44no—
552C4—44no—
553C4—42no—
554C4—81no—
555C4—81no—
556C2C4×#123×C12711yescharacteristic
557C2C4×C4⋊Q8×C12711yescharacteristic
558C2C127×#232411yescharacteristic
559C2C127×#236812yes—
560C2C127×#237012yes—
561C2C127×#249811yescharacteristic
562C2C127×#250211yescharacteristic
563C2C127×#252012yes—
564C2C127×#252212yes—
565C2C127×#258411yescharacteristic
566C2C127×#260311yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
21. #398×C127C4semidirect
272. #14244C127direct (N × H)
295. C127#14244direct (N × H)
305. #398C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1272
C2×#387×C1272
C2×C4×C4⋊C4×C1272
C127×#14452
C127×#14442
C127×#14412
C127×#14362
C127×C4⋊#952
C4×#95×C1272
#14244127