Finite Group Databasebeta

← C127×#8352 #44572025

Subgroups — C127×#8352 #44572025

Order 32512.

860 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3505C211yesmaximal, characteristic
2C127×#1893C211yesmaximal, characteristic, complemented
3C127×#1892C211yesmaximal, characteristic, complemented
4C127×#1869C211yesmaximal, characteristic, complemented
5C127×#1799C211yesmaximal, characteristic, complemented
6C127×#1520C211yesmaximal, characteristic, complemented
7C127×#1519C211yesmaximal, characteristic, complemented
8C23×C8×C127C2211yescharacteristic
9#553×C127—22no—
10#553×C127—21no—
11#552×C127—21no—
12#551×C127—22no—
13#548×C127—21no—
14#546×C127—21no—
15#539×C127C412yescomplemented
16#538×C127C412yescomplemented
17#534×C127—21no—
18#529×C127—21no—
19#525×C127—21no—
20C2×C22⋊Q8×C127C2211yescharacteristic
21C2×#121×C127C2211yescharacteristic
22#518×C127—21no—
23C2×C4×D4×C127C2211yescharacteristic
24C2×#103×C127—21no—
25C2×#102×C127—21no—
26C2×#99×C127—21no—
27C2×C22⋊C8×C127—21no—
28C2×C22⋊C8×C127C2211yescharacteristic
29#380×C127C2211yescharacteristic
30#380×C127C2211yescharacteristic
31#342×C127—21no—
32#340×C127—21no—
33#340×C127—21no—
34#336×C127—21no—
35#328×C127—22no—
36#327×C127—22no—
37C2×#41×C127—21no—
38C22×Q8×C127D411yescharacteristic
39C22×D4×C127—21no—
40C22×D4×C127D411yescharacteristic
41C22×D4×C127D411yescharacteristic
42C23×C4×C127D411yescharacteristic
43C23×C4×C127C2311yescharacteristic
44C22×C8×C127—21no—
45C22×C8×C127—21no—
46C22×C8×C127—21no—
47C22×C8×C127—21no—
48C22×C8×C127—42no—
49#126×C127—22no—
50#126×C127—22no—
51#126×C127—22no—
52#125×C127—21no—
53#125×C127—22no—
54#124×C127—21no—
55#124×C127—22no—
56#123×C127—22no—
57#123×C127—22no—
58#123×C127—22no—
59#123×C127—22no—
60#123×C127—22no—
61C22⋊Q8×C127—21no—
62C22⋊Q8×C127—22no—
63C22⋊Q8×C127—21no—
64C22⋊Q8×C127—21no—
65C22⋊Q8×C127C2×C412yes—
66C22⋊Q8×C127D412yes—
67#121×C127—21no—
68#121×C127—22no—
69#121×C127—22no—
70#121×C127—22no—
71#121×C127—21no—
72#121×C127—21no—
73#121×C127C2×C412yes—
74#121×C127D412yes—
75#120×C127—22no—
76#120×C127—22no—
77C4×Q8×C127—21no—
78C4×D4×C127—22no—
79C4×D4×C127—22no—
80C4×D4×C127—22no—
81C4×D4×C127—21no—
82C4×D4×C127—22no—
83C4×D4×C127—22no—
84C4×D4×C127—21no—
85C4×D4×C127—21no—
86C4×D4×C127—21no—
87C4×D4×C127—21no—
88#117×C127—22no—
89#117×C127—21no—
90#117×C127—22no—
91C2×C4⋊C4×C127—21no—
92C2×C4⋊C4×C127—21no—
93C2×C4⋊C4×C127—21no—
94C2×C4⋊C4×C127C2×C411yescharacteristic
95C2×C4⋊C4×C127D411yescharacteristic
96C2×C4⋊C4×C127D411yescharacteristic
97C2×C22⋊C4×C127—22no—
98C2×C22⋊C4×C127—21no—
99C2×C22⋊C4×C127—21no—
100C2×C22⋊C4×C127—21no—
101C2×C22⋊C4×C127—21no—
102C2×C22⋊C4×C127C2×C411yescharacteristic
103C2×C22⋊C4×C127D411yescharacteristic
104C2×C42×C127D411yescharacteristic
105#103×C127—42no—
106#102×C127—42no—
107#99×C127—42no—
108C22⋊C8×C127—21no—
109C22⋊C8×C127—21no—
110C22⋊C8×C127—42no—
111#95×C127—21no—
112#95×C127—21no—
113C24×C127—21no—
114C24×C127C22⋊C411yescharacteristic
115C24×C127C2×D411yescharacteristic
116#41×C127—81no—
117#41×C127—81no—
118C2×Q8×C127—21no—
119C2×Q8×C127—41no—
120C2×Q8×C127—41no—
121C2×Q8×C127C22⋊C412yes—
122C2×D4×C127—22no—
123C2×D4×C127—21no—
124C2×D4×C127—21no—
125C2×D4×C127—22no—
126C2×D4×C127—21no—
127C2×D4×C127—21no—
128C2×D4×C127—21no—
129C2×D4×C127—21no—
130C2×D4×C127—22no—
131C2×D4×C127—22no—
132C2×D4×C127—21no—
133C2×D4×C127—41no—
134C2×D4×C127—41no—
135C2×D4×C127—41no—
136C2×D4×C127—41no—
137C2×D4×C127—41no—
138C2×D4×C127—41no—
139C2×D4×C127C22⋊C412yes—
140C22×C4×C127—21no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—21no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—41no—
148C22×C4×C127—41no—
149C22×C4×C127—41no—
150C22×C4×C127—41no—
151C22×C4×C127—41no—
152C22×C4×C127—41no—
153C22×C4×C127C22⋊C411yescharacteristic
154C22×C4×C127C22⋊C411yescharacteristic
155C22×C4×C127C22⋊C411yescharacteristic
156C22×C4×C127C22×C411yescharacteristic
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127C2×D411yescharacteristic
160C22×C4×C127C2×D411yescharacteristic
161C22×C4×C127C2×D411yescharacteristic
162C2×C8×C127—22no—
163C2×C8×C127—22no—
164C2×C8×C127—22no—
165C2×C8×C127—41no—
166C2×C8×C127—41no—
167C2×C8×C127—41no—
168C2×C8×C127—41no—
169C2×C8×C127—41no—
170C2×C8×C127—41no—
171C2×C8×C127—41no—
172C4⋊C4×C127—22no—
173C4⋊C4×C127—22no—
174C4⋊C4×C127—22no—
175C4⋊C4×C127—22no—
176C4⋊C4×C127—22no—
177C4⋊C4×C127—21no—
178C4⋊C4×C127—21no—
179C4⋊C4×C127—22no—
180C4⋊C4×C127—21no—
181C4⋊C4×C127—21no—
182C4⋊C4×C127—41no—
183C4⋊C4×C127—41no—
184C4⋊C4×C127—41no—
185C4⋊C4×C127—41no—
186C4⋊C4×C127C22⋊C412yes—
187C4⋊C4×C127C22⋊C412yes—
188C22⋊C4×C127—22no—
189C22⋊C4×C127—22no—
190C22⋊C4×C127—22no—
191C22⋊C4×C127—22no—
192C22⋊C4×C127—22no—
193C22⋊C4×C127—22no—
194C22⋊C4×C127—22no—
195C22⋊C4×C127—21no—
196C22⋊C4×C127—22no—
197C22⋊C4×C127—21no—
198C22⋊C4×C127—22no—
199C22⋊C4×C127—21no—
200C22⋊C4×C127—21no—
201C22⋊C4×C127—22no—
202C22⋊C4×C127—41no—
203C22⋊C4×C127—41no—
204C22⋊C4×C127—41no—
205C22⋊C4×C127—41no—
206C42×C127—22no—
207C42×C127—22no—
208C42×C127—21no—
209C42×C127—21no—
210C23×C127—21no—
211C23×C127—22no—
212C23×C127—21no—
213C23×C127—21no—
214C23×C127—41no—
215C23×C127—41no—
216C23×C127—41no—
217C23×C127—41no—
218C23×C127—41no—
219C23×C127—41no—
220C23×C127—81no—
221C23×C127—81no—
222C23×C127C2×C22⋊C411yescharacteristic
223C23×C127#12011yescharacteristic
224C23×C127#12011yescharacteristic
225C23×C127#13511yescharacteristic
226C23×C127#13511yescharacteristic
227C23×C127AGL(1,ℤ/8)11yescharacteristic
228C23×C127#13711yescharacteristic
229Q8×C127—42no—
230Q8×C127—41no—
231Q8×C127—41no—
232D4×C127—42no—
233D4×C127—42no—
234D4×C127—42no—
235D4×C127—41no—
236D4×C127—41no—
237D4×C127—42no—
238D4×C127—41no—
239D4×C127—41no—
240D4×C127—42no—
241D4×C127—41no—
242D4×C127—41no—
243D4×C127—82no—
244D4×C127—82no—
245C2×C4×C127—21no—
246C2×C4×C127—21no—
247C2×C4×C127—21no—
248C2×C4×C127—21no—
249C2×C4×C127—21no—
250C2×C4×C127—21no—
251C2×C4×C127—21no—
252C2×C4×C127—21no—
253C2×C4×C127—22no—
254C2×C4×C127—21no—
255C2×C4×C127—22no—
256C2×C4×C127—22no—
257C2×C4×C127—21no—
258C2×C4×C127—21no—
259C2×C4×C127—41no—
260C2×C4×C127—41no—
261C2×C4×C127—41no—
262C2×C4×C127—41no—
263C2×C4×C127—41no—
264C2×C4×C127—41no—
265C2×C4×C127—41no—
266C2×C4×C127—41no—
267C2×C4×C127—41no—
268C2×C4×C127—81no—
269C2×C4×C127—81no—
270C2×C4×C127—81no—
271C2×C4×C127—82no—
272C2×C4×C127—82no—
273C2×C4×C127—81no—
274C2×C4×C127—81no—
275C2×C4×C127—81no—
276C2×C4×C127—81no—
277C2×C4×C127—81no—
278C2×C4×C127—81no—
279C2×C4×C127C2×C22⋊C411yescharacteristic
280C2×C4×C127C2×C22⋊C411yescharacteristic
281C2×C4×C127#12011yescharacteristic
282C2×C4×C127#12011yescharacteristic
283C8×C127—42no—
284C8×C127—81no—
285C22×C127—21no—
286C22×C127—21no—
287C22×C127—21no—
288C22×C127—21no—
289C22×C127—21no—
290C22×C127—21no—
291C22×C127—41no—
292C22×C127—41no—
293C22×C127—41no—
294C22×C127—41no—
295C22×C127—42no—
296C22×C127—42no—
297C22×C127—41no—
298C22×C127—41no—
299C22×C127—42no—
300C22×C127—41no—
301C22×C127—42no—
302C22×C127—81no—
303C22×C127—161no—
304C22×C127—161no—
305C22×C127#37911yescharacteristic
306C22×C127#41611yescharacteristic
307C22×C127#41711yescharacteristic
308C22×C127#44911yescharacteristic
309C22×C127#44911yescharacteristic
310C22×C127#45211yescharacteristic
311C22×C127#45211yescharacteristic
312C4×C127—21no—
313C4×C127—21no—
314C4×C127—21no—
315C4×C127—41no—
316C4×C127—42no—
317C4×C127—41no—
318C4×C127—42no—
319C4×C127—41no—
320C4×C127—42no—
321C4×C127—161no—
322C4×C127—161no—
323C4×C127B(4,𝔽2)11yescharacteristic
324C4×C127#45811yescharacteristic
325#8352C12711yesmaximal, characteristic, direct product factor, Sylow
326C2×C127—21no—
327C2×C127—21no—
328C2×C127—21no—
329C2×C127—21no—
330C2×C127—21no—
331C2×C127—21no—
332C2×C127—81no—
333C2×C127—82no—
334C2×C127#178811yescharacteristic
335C2×C127#179011yescharacteristic
336C2×C127#179411yescharacteristic
337#3505C2×C12711yescharacteristic
338#1893C2×C12711yescharacteristic, complemented
339#1892C2×C12711yescharacteristic, complemented
340#1869C2×C12711yescharacteristic, complemented
341#1799C2×C12711yescharacteristic, complemented
342#1520C2×C12711yescharacteristic, complemented
343#1519C2×C12711yescharacteristic, complemented
344C127#835211yescharacteristic, direct product factor, Sylow
345C23×C8C22×C12711yescharacteristic
346#553—22no—
347#553—21no—
348#552—21no—
349#551—22no—
350#548—21no—
351#546—21no—
352#539C4×C12712yescomplemented
353#538C4×C12712yescomplemented
354#534—21no—
355#529—21no—
356#525—21no—
357C2×C22⋊Q8C22×C12711yescharacteristic
358C2×#121C22×C12711yescharacteristic
359#518—21no—
360C2×C4×D4C22×C12711yescharacteristic
361C2×#103—21no—
362C2×#102—21no—
363C2×#99—21no—
364C2×C22⋊C8—21no—
365C2×C22⋊C8C22×C12711yescharacteristic
366#380C22×C12711yescharacteristic
367#380C22×C12711yescharacteristic
368#342—21no—
369#340—21no—
370#340—21no—
371#336—21no—
372#328—22no—
373#327—22no—
374C2×#41—21no—
375C22×Q8D4×C12711yescharacteristic
376C22×D4—21no—
377C22×D4D4×C12711yescharacteristic
378C22×D4D4×C12711yescharacteristic
379C23×C4D4×C12711yescharacteristic
380C23×C4C23×C12711yescharacteristic
381C22×C8—21no—
382C22×C8—21no—
383C22×C8—21no—
384C22×C8—21no—
385C22×C8—42no—
386#126—22no—
387#126—22no—
388#126—22no—
389#125—21no—
390#125—22no—
391#124—21no—
392#124—22no—
393#123—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8C2×C4×C12712yes—
403C22⋊Q8D4×C12712yes—
404#121—21no—
405#121—22no—
406#121—22no—
407#121—22no—
408#121—21no—
409#121—21no—
410#121C2×C4×C12712yes—
411#121D4×C12712yes—
412#120—22no—
413#120—22no—
414C4×Q8—21no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425#117—22no—
426#117—21no—
427#117—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4C2×C4×C12711yescharacteristic
432C2×C4⋊C4D4×C12711yescharacteristic
433C2×C4⋊C4D4×C12711yescharacteristic
434C2×C22⋊C4—22no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4C2×C4×C12711yescharacteristic
440C2×C22⋊C4D4×C12711yescharacteristic
441C2×C42D4×C12711yescharacteristic
442#103—42no—
443#102—42no—
444#99—42no—
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—42no—
448#95—21no—
449#95—21no—
450C24—21no—
451C24C22⋊C4×C12711yescharacteristic
452C24C2×D4×C12711yescharacteristic
453#41—81no—
454#41—81no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8—41no—
458C2×Q8C22⋊C4×C12712yes—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C22⋊C4×C12712yes—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4C22⋊C4×C12711yescharacteristic
491C22×C4C22⋊C4×C12711yescharacteristic
492C22×C4C22⋊C4×C12711yescharacteristic
493C22×C4C22×C4×C12711yescharacteristic
494C22×C4C2×D4×C12711yescharacteristic
495C22×C4C2×D4×C12711yescharacteristic
496C22×C4C2×D4×C12711yescharacteristic
497C22×C4C2×D4×C12711yescharacteristic
498C22×C4C2×D4×C12711yescharacteristic
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4C22⋊C4×C12712yes—
524C4⋊C4C22⋊C4×C12712yes—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C42—22no—
544C42—22no—
545C42—21no—
546C42—21no—
547C23—21no—
548C23—22no—
549C23—21no—
550C23—21no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—81no—
558C23—81no—
559C23C2×C22⋊C4×C12711yescharacteristic
560C23#120×C12711yescharacteristic
561C23#120×C12711yescharacteristic
562C23#135×C12711yescharacteristic
563C23#135×C12711yescharacteristic
564C23AGL(1,ℤ/8)×C12711yescharacteristic
565C23#137×C12711yescharacteristic
566Q8—42no—
567Q8—41no—
568Q8—41no—
569D4—42no—
570D4—42no—
571D4—42no—
572D4—41no—
573D4—41no—
574D4—42no—
575D4—41no—
576D4—41no—
577D4—42no—
578D4—41no—
579D4—41no—
580D4—82no—
581D4—82no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—82no—
609C2×C4—82no—
610C2×C4—81no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4C2×C22⋊C4×C12711yescharacteristic
617C2×C4C2×C22⋊C4×C12711yescharacteristic
618C2×C4#120×C12711yescharacteristic
619C2×C4#120×C12711yescharacteristic
620C8—42no—
621C8—81no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—42no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—41no—
639C22—81no—
640C22—161no—
641C22—161no—
642C22#379×C12711yescharacteristic
643C22#416×C12711yescharacteristic
644C22#417×C12711yescharacteristic
645C22#449×C12711yescharacteristic
646C22#449×C12711yescharacteristic
647C22#452×C12711yescharacteristic
648C22#452×C12711yescharacteristic
649C4—21no—
650C4—21no—
651C4—21no—
652C4—41no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—42no—
658C4—161no—
659C4—161no—
660C4B(4,𝔽2)×C12711yescharacteristic
661C4#458×C12711yescharacteristic
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—81no—
669C2—82no—
670C2C127×#178811yescharacteristic
671C2C127×#179011yescharacteristic
672C2C127×#179411yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC127×#3505C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1893C2semidirect
3. C127×#1892C2semidirect
4. C127×#1869C2semidirect
5. C127×#1799C2semidirect
6. C127×#1520C2semidirect
7. C127×#1519C2semidirect
15. #539×C127C4semidirect
16. #538×C127C4semidirect
325. #8352C127direct (N × H)
338. #1893C2×C127semidirect
339. #1892C2×C127semidirect
340. #1869C2×C127semidirect
341. #1799C2×C127semidirect
342. #1520C2×C127semidirect
343. #1519C2×C127semidirect
344. C127#8352direct (N × H)
352. #539C4×C127semidirect
353. #538C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35052
C127×#18932
C127×#18922
C127×#18692
C127×#17992
C127×#15202
C127×#15192
#8352127