Finite Group Databasebeta

← C127×#16806 #44580479

Subgroups — C127×#16806 #44580479

Order 32512.

1294 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×#398×C127C211yesmaximal, characteristic
2C2×#395×C127C211yesmaximal, characteristic
3C2×#391×C127C211yesmaximal, characteristic
4C2×#387×C127C211yesmaximal, characteristic
5C127×#1446C211yesmaximal, characteristic
6C127×#1445C211yesmaximal, characteristic
7C127×#1442C212yesmaximal
8C127×#1441C212yesmaximal
9C127×#1441C212yesmaximal
10C127×#1441C212yesmaximal
11C127×C4⋊#95C211yesmaximal, characteristic
12C23×Q8×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2212yes—
17C22×C4⋊C4×C127C2211yescharacteristic
18C22×C4⋊C4×C127C2212yes—
19C22×C42×C127C2211yescharacteristic
20#398×C127—24no—
21#395×C127—24no—
22#391×C127—24no—
23#387×C127—24no—
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2212yes—
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2212yes—
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2211yescharacteristic
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2212yes—
38C2×#95×C127C2212yes—
39C22×Q8×C127—22no—
40C22×Q8×C127—22no—
41C22×Q8×C127—24no—
42C22×Q8×C127—22no—
43C22×Q8×C127—42no—
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2312yes—
51C23×C4×C127C2312yes—
52C23×C4×C127C2312yes—
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
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—22no—
64C2×C4⋊C4×C127—42no—
65C2×C4⋊C4×C127—42no—
66C2×C4⋊C4×C127—42no—
67C2×C4⋊C4×C127—42no—
68C2×C4⋊C4×C127—42no—
69C2×C4⋊C4×C127—42no—
70C2×C4⋊C4×C127D414yes—
71C2×C4⋊C4×C127Q818yescomplemented
72C2×C42×C127—42no—
73C2×C42×C127D414yes—
74#95×C127—22no—
75#95×C127—22no—
76#95×C127—22no—
77#95×C127—22no—
78#95×C127—24no—
79#95×C127—24no—
80#95×C127—22no—
81#95×C127—24no—
82#95×C127—22no—
83#95×C127—24no—
84#95×C127—24no—
85#95×C127—42no—
86#95×C127—42no—
87#95×C127—42no—
88#95×C127—42no—
89C24×C127C2411yescharacteristic
90C2×Q8×C127—28no—
91C2×Q8×C127—48no—
92C2×Q8×C127—48no—
93C2×Q8×C127—44no—
94C2×Q8×C127—44no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—21no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—21no—
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—21no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—22no—
129C22×C4×C127—21no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—21no—
133C22×C4×C127—22no—
134C22×C4×C127—21no—
135C22×C4×C127—22no—
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—22no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—21no—
148C22×C4×C127—21no—
149C22×C4×C127C2×D412yes—
150C22×C4×C127C2×D412yes—
151C22×C4×C127C2×D412yes—
152C22×C4×C127C2×D412yes—
153C22×C4×C127C2×D412yes—
154C22×C4×C127C2×D412yes—
155C22×C4×C127C2×Q814yes—
156C22×C4×C127C2×Q814yes—
157C22×C4×C127C2×Q814yes—
158C22×C4×C127#4114yes—
159C22×C4×C127#4112yes—
160C4⋊C4×C127—28no—
161C4⋊C4×C127—48no—
162C4⋊C4×C127—48no—
163C4⋊C4×C127—44no—
164C4⋊C4×C127—48no—
165C4⋊C4×C127—44no—
166C42×C127—44no—
167C23×C127C22×D411yescharacteristic
168C23×C127C22×D411yescharacteristic
169C23×C127C22×Q812yes—
170C23×C127C2×#4111yescharacteristic
171C23×C127C2×#4112yes—
172C23×C127H(5,𝔽2)12yes—
173C23×C127H(5,𝔽2)11yescharacteristic
174C23×C127H(5,𝔽2)11yescharacteristic
175C23×C1272−1+411yescharacteristic
176C23×C1272−1+411yescharacteristic
177C23×C1272−1+412yes—
178Q8×C127—416no—
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—24no—
186C2×C4×C127—24no—
187C2×C4×C127—22no—
188C2×C4×C127—22no—
189C2×C4×C127—24no—
190C2×C4×C127—22no—
191C2×C4×C127—22no—
192C2×C4×C127—22no—
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—24no—
200C2×C4×C127—24no—
201C2×C4×C127—24no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—42no—
205C2×C4×C127—41no—
206C2×C4×C127—41no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—41no—
213C2×C4×C127—41no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—41no—
227C2×C4×C127—41no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—41no—
231C2×C4×C127—41no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C2×C4×C127—41no—
235C2×C4×C127—41no—
236C2×C4×C127—42no—
237C2×C4×C127—42no—
238C2×C4×C127—42no—
239C2×C4×C127—42no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127#12114yes—
243C2×C4×C127C4⋊Q814yes—
244C22×C127C2×#12111yescharacteristic
245C22×C127#52511yescharacteristic
246C22×C127C2×C4⋊Q811yescharacteristic
247C22×C127#53411yescharacteristic
248C22×C127#53511yescharacteristic
249C22×C127#53611yescharacteristic
250C22×C127#53611yescharacteristic
251C22×C127#53711yescharacteristic
252C22×C127#53711yescharacteristic
253C22×C127#54112yes—
254C22×C127#54211yescharacteristic
255C22×C127#54211yescharacteristic
256C22×C127#54212yes—
257C22×C127#54312yes—
258C22×C127#54412yes—
259C22×C127#54612yes—
260C22×C127D4×Q812yes—
261C22×C127#55112yes—
262C22×C127#55412yes—
263C22×C127#55712yes—
264C22×C127#55712yes—
265C22×C127#56212yes—
266C22×C127#56312yes—
267C4×C127—24no—
268C4×C127—24no—
269C4×C127—42no—
270C4×C127—44no—
271C4×C127—44no—
272C4×C127—42no—
273C4×C127—44no—
274C4×C127—42no—
275C4×C127—82no—
276C4×C127—81no—
277C4×C127—81no—
278#16806C12711yesmaximal, characteristic, direct product factor, Sylow
279C2×C127#253411yescharacteristic
280C2×C127#254611yescharacteristic
281C2×C127#258411yescharacteristic
282C2×C127#262011yescharacteristic
283C2×C127#263711yescharacteristic
284C2×C127#265911yescharacteristic
285C2×C127#269212yes—
286C2×C127#271312yes—
287C2×C127#275512yes—
288C2×C127#279912yes—
289C2×C127#281411yescharacteristic
290C2×#398C2×C12711yescharacteristic
291C2×#395C2×C12711yescharacteristic
292C2×#391C2×C12711yescharacteristic
293C2×#387C2×C12711yescharacteristic
294#1446C2×C12711yescharacteristic
295#1445C2×C12711yescharacteristic
296#1442C2×C12712yes—
297#1441C2×C12712yes—
298#1441C2×C12712yes—
299#1441C2×C12712yes—
300C4⋊#95C2×C12711yescharacteristic
301C127#1680611yescharacteristic, direct product factor, Sylow
302C23×Q8C22×C12711yescharacteristic
303C22×C4⋊C4C22×C12711yescharacteristic
304C22×C4⋊C4C22×C12712yes—
305C22×C4⋊C4C22×C12711yescharacteristic
306C22×C4⋊C4C22×C12712yes—
307C22×C4⋊C4C22×C12711yescharacteristic
308C22×C4⋊C4C22×C12712yes—
309C22×C42C22×C12711yescharacteristic
310#398—24no—
311#395—24no—
312#391—24no—
313#387—24no—
314C2×#95C22×C12711yescharacteristic
315C2×#95C22×C12712yes—
316C2×#95C22×C12711yescharacteristic
317C2×#95C22×C12712yes—
318C2×#95C22×C12711yescharacteristic
319C2×#95C22×C12711yescharacteristic
320C2×#95C22×C12712yes—
321C2×#95C22×C12712yes—
322C2×#95C22×C12712yes—
323C2×#95C22×C12711yescharacteristic
324C2×#95C22×C12711yescharacteristic
325C2×#95C22×C12712yes—
326C2×#95C22×C12712yes—
327C2×#95C22×C12712yes—
328C2×#95C22×C12712yes—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—24no—
332C22×Q8—22no—
333C22×Q8—42no—
334C23×C4C23×C12712yes—
335C23×C4C23×C12711yescharacteristic
336C23×C4C23×C12711yescharacteristic
337C23×C4C23×C12711yescharacteristic
338C23×C4C23×C12711yescharacteristic
339C23×C4C23×C12711yescharacteristic
340C23×C4C23×C12712yes—
341C23×C4C23×C12712yes—
342C23×C4C23×C12712yes—
343C23×C4C23×C12711yescharacteristic
344C23×C4C23×C12711yescharacteristic
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4D4×C12714yes—
361C2×C4⋊C4Q8×C12718yescomplemented
362C2×C42—42no—
363C2×C42D4×C12714yes—
364#95—22no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—24no—
369#95—24no—
370#95—22no—
371#95—24no—
372#95—22no—
373#95—24no—
374#95—24no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379C24C24×C12711yescharacteristic
380C2×Q8—28no—
381C2×Q8—48no—
382C2×Q8—48no—
383C2×Q8—44no—
384C2×Q8—44no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4C2×D4×C12712yes—
440C22×C4C2×D4×C12712yes—
441C22×C4C2×D4×C12712yes—
442C22×C4C2×D4×C12712yes—
443C22×C4C2×D4×C12712yes—
444C22×C4C2×D4×C12712yes—
445C22×C4C2×Q8×C12714yes—
446C22×C4C2×Q8×C12714yes—
447C22×C4C2×Q8×C12714yes—
448C22×C4#41×C12714yes—
449C22×C4#41×C12712yes—
450C4⋊C4—28no—
451C4⋊C4—48no—
452C4⋊C4—48no—
453C4⋊C4—44no—
454C4⋊C4—48no—
455C4⋊C4—44no—
456C42—44no—
457C23C22×D4×C12711yescharacteristic
458C23C22×D4×C12711yescharacteristic
459C23C22×Q8×C12712yes—
460C23C2×#41×C12711yescharacteristic
461C23C2×#41×C12712yes—
462C23H(5,𝔽2)×C12712yes—
463C23H(5,𝔽2)×C12711yescharacteristic
464C23H(5,𝔽2)×C12711yescharacteristic
465C232−1+4×C12711yescharacteristic
466C232−1+4×C12711yescharacteristic
467C232−1+4×C12712yes—
468Q8—416no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4#121×C12714yes—
533C2×C4C4⋊Q8×C12714yes—
534C22C2×#121×C12711yescharacteristic
535C22#525×C12711yescharacteristic
536C22C2×C4⋊Q8×C12711yescharacteristic
537C22#534×C12711yescharacteristic
538C22#535×C12711yescharacteristic
539C22#536×C12711yescharacteristic
540C22#536×C12711yescharacteristic
541C22#537×C12711yescharacteristic
542C22#537×C12711yescharacteristic
543C22#541×C12712yes—
544C22#542×C12711yescharacteristic
545C22#542×C12711yescharacteristic
546C22#542×C12712yes—
547C22#543×C12712yes—
548C22#544×C12712yes—
549C22#546×C12712yes—
550C22D4×Q8×C12712yes—
551C22#551×C12712yes—
552C22#554×C12712yes—
553C22#557×C12712yes—
554C22#557×C12712yes—
555C22#562×C12712yes—
556C22#563×C12712yes—
557C4—24no—
558C4—24no—
559C4—42no—
560C4—44no—
561C4—44no—
562C4—44no—
563C4—42no—
564C4—42no—
565C4—82no—
566C4—81no—
567C4—81no—
568C2C127×#253411yescharacteristic
569C2C127×#254611yescharacteristic
570C2C127×#258411yescharacteristic
571C2C127×#262011yescharacteristic
572C2C127×#263711yescharacteristic
573C2C127×#265911yescharacteristic
574C2C127×#269212yes—
575C2C127×#271312yes—
576C2C127×#275512yes—
577C2C127×#279912yes—
578C2C127×#281411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
71. C2×C4⋊C4×C127Q8semidirect
278. #16806C127direct (N × H)
301. C127#16806direct (N × H)
361. C2×C4⋊C4Q8×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×#395×C1272
C2×#391×C1272
C2×#387×C1272
C127×#14462
C127×#14452
C127×#14422
C127×#14412
C127×C4⋊#952
#16806127