Finite Group Databasebeta

← C127×#14186 #44577859

Subgroups — C127×#14186 #44577859

Order 32512.

1786 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C127C211yesmaximal, characteristic
2C2×#395×C127C211yesmaximal, characteristic
3C2×#389×C127C212yesmaximal
4C2×#387×C127C211yesmaximal, characteristic
5C127×#1446C211yesmaximal, characteristic
6C127×#1444C211yesmaximal, characteristic
7C127×#1441C211yesmaximal, characteristic
8C127×#1436C212yesmaximal
9C127×#1436C212yesmaximal
10C127×#1436C212yesmaximal
11C4×#95×C127C211yesmaximal, characteristic
12C23×Q8×C127C2211yescharacteristic
13C2×C4×Q8×C127—28no—
14C2×C4×Q8×C127—24no—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2212yes—
18C22×C4⋊C4×C127C2212yes—
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2212yes—
21C22×C42×C127C2212yes—
22C22×C42×C127C2212yes—
23C22×C42×C127C2211yescharacteristic
24#395×C127C418yescomplemented
25#389×C127—28no—
26#387×C127—24no—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2211yescharacteristic
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C2×#95×C127C2212yes—
39C2×#95×C127C2212yes—
40C22×Q8×C127—24no—
41C22×Q8×C127—22no—
42C22×Q8×C127—22no—
43C22×Q8×C127—24no—
44C22×Q8×C127C2×C414yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2312yes—
50C23×C4×C127C2312yes—
51C23×C4×C127C2312yes—
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2312yes—
54C23×C4×C127C2311yescharacteristic
55C23×C4×C127C2311yescharacteristic
56C4×Q8×C127—232no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—24no—
60C2×C4⋊C4×C127—24no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127—24no—
63C2×C4⋊C4×C127—24no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—24no—
67C2×C4⋊C4×C127—24no—
68C2×C4⋊C4×C127—24no—
69C2×C4⋊C4×C127—42no—
70C2×C4⋊C4×C127C2×C414yes—
71C2×C4⋊C4×C127C2×C418yes—
72C2×C4⋊C4×C127D418yes—
73C2×C42×C127—24no—
74C2×C42×C127—24no—
75C2×C42×C127—24no—
76C2×C42×C127—24no—
77C2×C42×C127—24no—
78C2×C42×C127—24no—
79C2×C42×C127—42no—
80C2×C42×C127D414yes—
81#95×C127—22no—
82#95×C127—22no—
83#95×C127—22no—
84#95×C127—22no—
85#95×C127—24no—
86#95×C127—24no—
87#95×C127—22no—
88#95×C127—24no—
89#95×C127—24no—
90#95×C127—42no—
91#95×C127C2×C418yes—
92#95×C127C2×C414yes—
93#95×C127Q818yescomplemented
94C24×C127C2411yescharacteristic
95C2×Q8×C127—28no—
96C2×Q8×C127—28no—
97C2×Q8×C127—216no—
98C2×Q8×C127—28no—
99C2×Q8×C127—216no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
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—22no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—22no—
117C22×C4×C127—21no—
118C22×C4×C127—21no—
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—21no—
127C22×C4×C127—22no—
128C22×C4×C127—21no—
129C22×C4×C127—22no—
130C22×C4×C127—21no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—21no—
134C22×C4×C127—21no—
135C22×C4×C127—21no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—21no—
139C22×C4×C127—21no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127—22no—
144C22×C4×C127—21no—
145C22×C4×C127—21no—
146C22×C4×C127—21no—
147C22×C4×C127—21no—
148C22×C4×C127C22×C412yes—
149C22×C4×C127C22×C412yes—
150C22×C4×C127C22×C414yes—
151C22×C4×C127C22×C412yes—
152C22×C4×C127C22×C414yes—
153C22×C4×C127C2×D414yes—
154C22×C4×C127C2×D414yes—
155C22×C4×C127C2×D412yes—
156C22×C4×C127C2×D412yes—
157C22×C4×C127C2×D414yes—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×Q814yes—
160C22×C4×C127C2×Q814yes—
161C22×C4×C127C2×Q814yes—
162C22×C4×C127#4112yes—
163C22×C4×C127#4114yes—
164C22×C4×C127#4114yes—
165C4⋊C4×C127—28no—
166C4⋊C4×C127—216no—
167C4⋊C4×C127—28no—
168C4⋊C4×C127—216no—
169C4⋊C4×C127—48no—
170C4⋊C4×C127—44no—
171C42×C127—216no—
172C42×C127—28no—
173C42×C127—48no—
174C23×C127C23×C411yescharacteristic
175C23×C127C22×D411yescharacteristic
176C23×C127C22×D412yes—
177C23×C127C22×Q812yes—
178C23×C127C2×#4111yescharacteristic
179C23×C127C2×#4112yes—
180C23×C127C2×#4112yes—
181C23×C127H(5,𝔽2)11yescharacteristic
182C23×C1272−1+411yescharacteristic
183C23×C1272−1+411yescharacteristic
184C23×C1272−1+411yescharacteristic
185Q8×C127—232no—
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—22no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—24no—
198C2×C4×C127—24no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—24no—
207C2×C4×C127—24no—
208C2×C4×C127—24no—
209C2×C4×C127—24no—
210C2×C4×C127—22no—
211C2×C4×C127—22no—
212C2×C4×C127—24no—
213C2×C4×C127—22no—
214C2×C4×C127—22no—
215C2×C4×C127—24no—
216C2×C4×C127—24no—
217C2×C4×C127—24no—
218C2×C4×C127—24no—
219C2×C4×C127—24no—
220C2×C4×C127—24no—
221C2×C4×C127—41no—
222C2×C4×C127—42no—
223C2×C4×C127—41no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—41no—
227C2×C4×C127—41no—
228C2×C4×C127—42no—
229C2×C4×C127—41no—
230C2×C4×C127—41no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—42no—
235C2×C4×C127—42no—
236C2×C4×C127—41no—
237C2×C4×C127—41no—
238C2×C4×C127—41no—
239C2×C4×C127—41no—
240C2×C4×C127—41no—
241C2×C4×C127—41no—
242C2×C4×C127—42no—
243C2×C4×C127—42no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127C4×D414yes—
247C2×C4×C127C4×D418yes—
248C2×C4×C127C4×Q818yescomplemented
249C2×C4×C127#12014yes—
250C2×C4×C127C4⋊Q814yes—
251C22×C127C2×C4×D411yescharacteristic
252C22×C127C2×C4×D412yes—
253C22×C127C2×C4×Q812yes—
254C22×C127#51911yescharacteristic
255C22×C127#52011yescharacteristic
256C22×C127C2×#12011yescharacteristic
257C22×C127#52511yescharacteristic
258C22×C127#52512yes—
259C22×C127C2×C4⋊Q811yescharacteristic
260C22×C127#53211yescharacteristic
261C22×C127#53312yes—
262C22×C127#53611yescharacteristic
263C22×C127#53711yescharacteristic
264C22×C127#54111yescharacteristic
265C22×C127#54211yescharacteristic
266C22×C127#54612yes—
267C22×C127#54712yes—
268C22×C127D4×Q812yes—
269C22×C127D4×Q812yes—
270C22×C127#55212yes—
271C22×C127#55412yes—
272C22×C127#55612yes—
273C22×C127#55712yes—
274C4×C127—28no—
275C4×C127—24no—
276C4×C127—24no—
277C4×C127—28no—
278C4×C127—24no—
279C4×C127—42no—
280C4×C127—44no—
281C4×C127—44no—
282C4×C127—42no—
283C4×C127—81no—
284C4×C127—81no—
285#14186C12711yesmaximal, characteristic, direct product factor, Sylow
286C2×C127C4×#12011yescharacteristic
287C2×C127C4×C4⋊Q811yescharacteristic
288C2×C127#232311yescharacteristic
289C2×C127#236012yes—
290C2×C127#236512yes—
291C2×C127#243011yescharacteristic
292C2×C127#243411yescharacteristic
293C2×C127#246212yes—
294C2×C127#246512yes—
295C2×C127#258411yescharacteristic
296C2×C127#260411yescharacteristic
297C22×C4×Q8C2×C12711yescharacteristic
298C2×#395C2×C12711yescharacteristic
299C2×#389C2×C12712yes—
300C2×#387C2×C12711yescharacteristic
301#1446C2×C12711yescharacteristic
302#1444C2×C12711yescharacteristic
303#1441C2×C12711yescharacteristic
304#1436C2×C12712yes—
305#1436C2×C12712yes—
306#1436C2×C12712yes—
307C4×#95C2×C12711yescharacteristic
308C127#1418611yescharacteristic, direct product factor, Sylow
309C23×Q8C22×C12711yescharacteristic
310C2×C4×Q8—28no—
311C2×C4×Q8—24no—
312C22×C4⋊C4C22×C12711yescharacteristic
313C22×C4⋊C4C22×C12711yescharacteristic
314C22×C4⋊C4C22×C12712yes—
315C22×C4⋊C4C22×C12712yes—
316C22×C4⋊C4C22×C12711yescharacteristic
317C22×C4⋊C4C22×C12712yes—
318C22×C42C22×C12712yes—
319C22×C42C22×C12712yes—
320C22×C42C22×C12711yescharacteristic
321#395C4×C12718yescomplemented
322#389—28no—
323#387—24no—
324C2×#95C22×C12711yescharacteristic
325C2×#95C22×C12712yes—
326C2×#95C22×C12712yes—
327C2×#95C22×C12711yescharacteristic
328C2×#95C22×C12711yescharacteristic
329C2×#95C22×C12711yescharacteristic
330C2×#95C22×C12712yes—
331C2×#95C22×C12712yes—
332C2×#95C22×C12711yescharacteristic
333C2×#95C22×C12712yes—
334C2×#95C22×C12711yescharacteristic
335C2×#95C22×C12712yes—
336C2×#95C22×C12712yes—
337C22×Q8—24no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—24no—
341C22×Q8C2×C4×C12714yes—
342C23×C4C23×C12711yescharacteristic
343C23×C4C23×C12711yescharacteristic
344C23×C4C23×C12711yescharacteristic
345C23×C4C23×C12711yescharacteristic
346C23×C4C23×C12712yes—
347C23×C4C23×C12712yes—
348C23×C4C23×C12712yes—
349C23×C4C23×C12711yescharacteristic
350C23×C4C23×C12712yes—
351C23×C4C23×C12711yescharacteristic
352C23×C4C23×C12711yescharacteristic
353C4×Q8—232no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4C2×C4×C12714yes—
368C2×C4⋊C4C2×C4×C12718yes—
369C2×C4⋊C4D4×C12718yes—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—42no—
377C2×C42D4×C12714yes—
378#95—22no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—24no—
383#95—24no—
384#95—22no—
385#95—24no—
386#95—24no—
387#95—42no—
388#95C2×C4×C12718yes—
389#95C2×C4×C12714yes—
390#95Q8×C12718yescomplemented
391C24C24×C12711yescharacteristic
392C2×Q8—28no—
393C2×Q8—28no—
394C2×Q8—216no—
395C2×Q8—28no—
396C2×Q8—216no—
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—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C22×C4×C12712yes—
446C22×C4C22×C4×C12712yes—
447C22×C4C22×C4×C12714yes—
448C22×C4C22×C4×C12712yes—
449C22×C4C22×C4×C12714yes—
450C22×C4C2×D4×C12714yes—
451C22×C4C2×D4×C12714yes—
452C22×C4C2×D4×C12712yes—
453C22×C4C2×D4×C12712yes—
454C22×C4C2×D4×C12714yes—
455C22×C4C2×D4×C12712yes—
456C22×C4C2×Q8×C12714yes—
457C22×C4C2×Q8×C12714yes—
458C22×C4C2×Q8×C12714yes—
459C22×C4#41×C12712yes—
460C22×C4#41×C12714yes—
461C22×C4#41×C12714yes—
462C4⋊C4—28no—
463C4⋊C4—216no—
464C4⋊C4—28no—
465C4⋊C4—216no—
466C4⋊C4—48no—
467C4⋊C4—44no—
468C42—216no—
469C42—28no—
470C42—48no—
471C23C23×C4×C12711yescharacteristic
472C23C22×D4×C12711yescharacteristic
473C23C22×D4×C12712yes—
474C23C22×Q8×C12712yes—
475C23C2×#41×C12711yescharacteristic
476C23C2×#41×C12712yes—
477C23C2×#41×C12712yes—
478C23H(5,𝔽2)×C12711yescharacteristic
479C232−1+4×C12711yescharacteristic
480C232−1+4×C12711yescharacteristic
481C232−1+4×C12711yescharacteristic
482Q8—232no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4C4×D4×C12714yes—
544C2×C4C4×D4×C12718yes—
545C2×C4C4×Q8×C12718yescomplemented
546C2×C4#120×C12714yes—
547C2×C4C4⋊Q8×C12714yes—
548C22C2×C4×D4×C12711yescharacteristic
549C22C2×C4×D4×C12712yes—
550C22C2×C4×Q8×C12712yes—
551C22#519×C12711yescharacteristic
552C22#520×C12711yescharacteristic
553C22C2×#120×C12711yescharacteristic
554C22#525×C12711yescharacteristic
555C22#525×C12712yes—
556C22C2×C4⋊Q8×C12711yescharacteristic
557C22#532×C12711yescharacteristic
558C22#533×C12712yes—
559C22#536×C12711yescharacteristic
560C22#537×C12711yescharacteristic
561C22#541×C12711yescharacteristic
562C22#542×C12711yescharacteristic
563C22#546×C12712yes—
564C22#547×C12712yes—
565C22D4×Q8×C12712yes—
566C22D4×Q8×C12712yes—
567C22#552×C12712yes—
568C22#554×C12712yes—
569C22#556×C12712yes—
570C22#557×C12712yes—
571C4—28no—
572C4—24no—
573C4—24no—
574C4—28no—
575C4—24no—
576C4—42no—
577C4—44no—
578C4—44no—
579C4—42no—
580C4—81no—
581C4—81no—
582C2C4×#120×C12711yescharacteristic
583C2C4×C4⋊Q8×C12711yescharacteristic
584C2C127×#232311yescharacteristic
585C2C127×#236012yes—
586C2C127×#236512yes—
587C2C127×#243011yescharacteristic
588C2C127×#243411yescharacteristic
589C2C127×#246212yes—
590C2C127×#246512yes—
591C2C127×#258411yescharacteristic
592C2C127×#260411yescharacteristic
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
24. #395×C127C4semidirect
93. #95×C127Q8semidirect
248. C2×C4×C127C4×Q8semidirect
285. #14186C127direct (N × H)
308. C127#14186direct (N × H)
321. #395C4×C127semidirect
390. #95Q8×C127semidirect
545. C2×C4C4×Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C1272
C2×#395×C1272
C2×#389×C1272
C2×#387×C1272
C127×#14462
C127×#14442
C127×#14412
C127×#14362
C4×#95×C1272
#14186127