Finite Group Databasebeta

← C127×#21815 #44585488

Subgroups — C127×#21815 #44585488

Order 32512.

1444 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C127C211yesmaximal, characteristic
2C127×#2920C211yesmaximal, characteristic, complemented
3C4×#117×C127C211yesmaximal, characteristic, complemented
4C127×#1980C214yesmaximal, complemented
5C127×#1962C214yesmaximal, complemented
6C127×#1789C214yesmaximal, complemented
7C22×#41×C127C2212yes—
8#532×C127—21no—
9#532×C127—21no—
10#532×C127—21no—
11#532×C127—21no—
12#532×C127C412yescomplemented
13#532×C127C412yescomplemented
14#532×C127C2212yes—
15#532×C127C2212yes—
16C2×C4⋊Q8×C127C411yescharacteristic, complemented
17C2×#127×C127C411yescharacteristic, complemented
18C2×#124×C127C412yescomplemented
19C2×#121×C127—21no—
20C2×#121×C127—21no—
21C2×C4×D4×C127—21no—
22C2×C4×D4×C127—21no—
23C2×#117×C127—21no—
24C22×C42×C127C2211yescharacteristic
25#432×C127—21no—
26#432×C127—21no—
27#431×C127—21no—
28#431×C127—21no—
29#423×C127C2212yescomplemented
30C2×#104×C127C22116yescomplemented
31#407×C127C2212yes—
32C4×M16×C127C2212yescomplemented
33C4×C4⋊C4×C127—21no—
34C4×C4⋊C4×C127C2212yescomplemented
35C4×C22⋊C4×C127—21no—
36C4×C22⋊C4×C127C2212yes—
37#376×C127—21no—
38C43×C127C2212yescomplemented
39C2×#41×C127—22no—
40C2×#41×C127—22no—
41C2×#41×C127—48no—
42C2×#41×C127C2×C414yes—
43C2×#41×C127C2314yes—
44C22×Q8×C127C2×C412yes—
45C22×D4×C127—22no—
46C22×D4×C127—21no—
47C22×D4×C127—21no—
48C22×D4×C127C2×C412yes—
49C23×C4×C127—22no—
50C23×C4×C127D411yescharacteristic
51C23×C4×C127D411yescharacteristic
52C23×C4×C127C2311yescharacteristic
53C2×M16×C127C2314yes—
54C4⋊Q8×C127—21no—
55C4⋊Q8×C127—21no—
56C4⋊Q8×C127C2×C412yes—
57C4⋊Q8×C127C2×C412yes—
58#127×C127—21no—
59#127×C127—21no—
60#127×C127C2×C412yes—
61#127×C127C2×C412yes—
62#124×C127—22no—
63#124×C127—22no—
64#124×C127C2×C414yes—
65#124×C127C2×C414yes—
66#121×C127—22no—
67#121×C127—22no—
68#121×C127—22no—
69#121×C127—22no—
70#121×C127—22no—
71#121×C127—22no—
72#121×C127—22no—
73#121×C127—22no—
74C4×D4×C127—22no—
75C4×D4×C127—22no—
76C4×D4×C127—22no—
77C4×D4×C127—22no—
78C4×D4×C127—22no—
79C4×D4×C127—22no—
80C4×D4×C127—22no—
81C4×D4×C127—22no—
82#117×C127—28no—
83C2×C4⋊C4×C127—21no—
84C2×C4⋊C4×C127—21no—
85C2×C4⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—22no—
89C2×C42×C127—22no—
90C2×C42×C127—22no—
91C2×C42×C127C2×C411yescharacteristic
92C2×C42×C127C2×C411yescharacteristic
93C2×C42×C127C2×C411yescharacteristic
94C2×C42×C127C2×C411yescharacteristic
95C2×C42×C127D411yescharacteristic
96C2×C42×C127D411yescharacteristic
97C2×C42×C127D411yescharacteristic
98C2×C42×C127D411yescharacteristic
99C2×C42×C127D411yescharacteristic
100C2×C42×C127D411yescharacteristic
101C2×C42×C127C2314yes—
102C2×C42×C127C2311yescharacteristic
103C2×C42×C127C2311yescharacteristic
104C4⋊C8×C127—22no—
105C4⋊C8×C127—22no—
106#104×C127—416no—
107C22⋊C8×C127—22no—
108C22⋊C8×C127—22no—
109#97×C127—22no—
110C4×C8×C127—22no—
111#95×C127—22no—
112#95×C127—22no—
113C24×C127—22no—
114C24×C127C2×D411yescharacteristic
115#41×C127—216no—
116#41×C127—48no—
117#41×C127—48no—
118#41×C127—48no—
119C2×Q8×C127—22no—
120C2×Q8×C127—44no—
121C2×Q8×C127C22×C414yes—
122C2×D4×C127—24no—
123C2×D4×C127—24no—
124C2×D4×C127—22no—
125C2×D4×C127—22no—
126C2×D4×C127—22no—
127C2×D4×C127—22no—
128C2×D4×C127—22no—
129C2×D4×C127—44no—
130C2×D4×C127—44no—
131C2×D4×C127—48no—
132C2×D4×C127—44no—
133C2×D4×C127C22×C414yes—
134C22×C4×C127—24no—
135C22×C4×C127—24no—
136C22×C4×C127—22no—
137C22×C4×C127—24no—
138C22×C4×C127—24no—
139C22×C4×C127—24no—
140C22×C4×C127—42no—
141C22×C4×C127—48no—
142C22×C4×C127C22⋊C411yescharacteristic
143C22×C4×C127C22⋊C411yescharacteristic
144C22×C4×C127C22⋊C411yescharacteristic
145C22×C4×C127C22⋊C411yescharacteristic
146C22×C4×C127C22⋊C411yescharacteristic
147C22×C4×C127C22⋊C411yescharacteristic
148C22×C4×C127C22⋊C411yescharacteristic
149C22×C4×C127C22⋊C411yescharacteristic
150C22×C4×C127C22×C411yescharacteristic
151C22×C4×C127C22×C411yescharacteristic
152C22×C4×C127C2×D411yescharacteristic
153C22×C4×C127C2×D411yescharacteristic
154C22×C4×C127C2×D411yescharacteristic
155C22×C4×C127C2×D411yescharacteristic
156C22×C4×C127C2×D411yescharacteristic
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127C2411yescharacteristic
160M16×C127—28no—
161C2×C8×C127—24no—
162C4⋊C4×C127—28no—
163C4⋊C4×C127—22no—
164C4⋊C4×C127—22no—
165C4⋊C4×C127—22no—
166C4⋊C4×C127—22no—
167C22⋊C4×C127—28no—
168C22⋊C4×C127—24no—
169C22⋊C4×C127—24no—
170C22⋊C4×C127—24no—
171C22⋊C4×C127—24no—
172C42×C127—28no—
173C42×C127—28no—
174C42×C127—44no—
175C42×C127C22⋊C411yescharacteristic
176C42×C127C22⋊C411yescharacteristic
177C42×C127C22⋊C411yescharacteristic
178C42×C127C22⋊C411yescharacteristic
179C42×C127C22⋊C411yescharacteristic
180C42×C127C22⋊C411yescharacteristic
181C42×C127C22⋊C411yescharacteristic
182C42×C127C22⋊C411yescharacteristic
183C42×C127C22×C411yescharacteristic
184C42×C127C22×C411yescharacteristic
185C42×C127C22×C411yescharacteristic
186C42×C127C22×C411yescharacteristic
187C42×C127C2×D411yescharacteristic
188C42×C127C2×D411yescharacteristic
189C42×C127C2×D411yescharacteristic
190C42×C127C2×D411yescharacteristic
191C23×C127—22no—
192C23×C127—22no—
193C23×C127—24no—
194C23×C127—41no—
195C23×C127—44no—
196C23×C127—44no—
197C23×C127—44no—
198C23×C127C2×C22⋊C411yescharacteristic
199C23×C127C2×C22⋊C411yescharacteristic
200C23×C127C22×D411yescharacteristic
201Q8×C127—28no—
202Q8×C127—44no—
203D4×C127—28no—
204D4×C127—44no—
205D4×C127—44no—
206D4×C127—48no—
207D4×C127—48no—
208D4×C127—44no—
209D4×C127—44no—
210D4×C127—44no—
211C2×C4×C127—22no—
212C2×C4×C127—22no—
213C2×C4×C127—22no—
214C2×C4×C127—22no—
215C2×C4×C127—22no—
216C2×C4×C127—22no—
217C2×C4×C127—22no—
218C2×C4×C127—22no—
219C2×C4×C127—22no—
220C2×C4×C127—22no—
221C2×C4×C127—22no—
222C2×C4×C127—22no—
223C2×C4×C127—22no—
224C2×C4×C127—28no—
225C2×C4×C127—24no—
226C2×C4×C127—41no—
227C2×C4×C127—41no—
228C2×C4×C127—41no—
229C2×C4×C127—48no—
230C2×C4×C127—44no—
231C2×C4×C127—44no—
232C2×C4×C127—44no—
233C2×C4×C127—48no—
234C2×C4×C127#10414yescomplemented
235C2×C4×C127C2×C22⋊C411yescharacteristic
236C2×C4×C127C2×C22⋊C411yescharacteristic
237C2×C4×C127C2×C22⋊C411yescharacteristic
238C2×C4×C127C2×C22⋊C411yescharacteristic
239C2×C4×C127C2×C22⋊C411yescharacteristic
240C2×C4×C127C2×C22⋊C411yescharacteristic
241C2×C4×C127C2×C22⋊C411yescharacteristic
242C2×C4×C127C2×C22⋊C411yescharacteristic
243C2×C4×C127C2×C22⋊C411yescharacteristic
244C2×C4×C127C2×C22⋊C411yescharacteristic
245C2×C4×C127C23×C411yescharacteristic
246C2×C4×C127C22×D411yescharacteristic
247C2×C4×C127H(5,𝔽2)14yes—
248C8×C127—44no—
249C22×C127—21no—
250C22×C127—21no—
251C22×C127—21no—
252C22×C127—21no—
253C22×C127—21no—
254C22×C127—21no—
255C22×C127—21no—
256C22×C127—44no—
257C22×C127—44no—
258C22×C127—44no—
259C22×C127—44no—
260C22×C127—88no—
261C22×C127C2×#10412yes—
262C22×C127C22×C22⋊C411yescharacteristic
263C22×C127#53512yes—
264C4×C127—21no—
265C4×C127—21no—
266C4×C127—21no—
267C4×C127—21no—
268C4×C127—21no—
269C4×C127—21no—
270C4×C127—21no—
271C4×C127—48no—
272C4×C127—44no—
273C4×C127C2×#10412yes—
274C4×C127C2×#10412yes—
275C4×C127#42112yes—
276C4×C127#51812yes—
277C4×C127#53512yes—
278#21815C12711yesmaximal, characteristic, direct product factor, Sylow
279C2×C127—22no—
280C2×C127—22no—
281C2×C127—41no—
282C2×C127—84no—
283C2×C127#230911yescharacteristic
284C2×C127C22×#10411yescharacteristic
285C2×C127C2×#42111yescharacteristic
286C2×#532C2×C12711yescharacteristic
287#2920C2×C12711yescharacteristic, complemented
288C4×#117C2×C12711yescharacteristic, complemented
289#1980C2×C12714yescomplemented
290#1962C2×C12714yescomplemented
291#1789C2×C12714yescomplemented
292C127#2181511yescharacteristic, direct product factor, Sylow
293C22×#41C22×C12712yes—
294#532—21no—
295#532—21no—
296#532—21no—
297#532—21no—
298#532C4×C12712yescomplemented
299#532C4×C12712yescomplemented
300#532C22×C12712yes—
301#532C22×C12712yes—
302C2×C4⋊Q8C4×C12711yescharacteristic, complemented
303C2×#127C4×C12711yescharacteristic, complemented
304C2×#124C4×C12712yescomplemented
305C2×#121—21no—
306C2×#121—21no—
307C2×C4×D4—21no—
308C2×C4×D4—21no—
309C2×#117—21no—
310C22×C42C22×C12711yescharacteristic
311#432—21no—
312#432—21no—
313#431—21no—
314#431—21no—
315#423C22×C12712yescomplemented
316C2×#104C22×C127116yescomplemented
317#407C22×C12712yes—
318C4×M16C22×C12712yescomplemented
319C4×C4⋊C4—21no—
320C4×C4⋊C4C22×C12712yescomplemented
321C4×C22⋊C4—21no—
322C4×C22⋊C4C22×C12712yes—
323#376—21no—
324C43C22×C12712yescomplemented
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—48no—
328C2×#41C2×C4×C12714yes—
329C2×#41C23×C12714yes—
330C22×Q8C2×C4×C12712yes—
331C22×D4—22no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4C2×C4×C12712yes—
335C23×C4—22no—
336C23×C4D4×C12711yescharacteristic
337C23×C4D4×C12711yescharacteristic
338C23×C4C23×C12711yescharacteristic
339C2×M16C23×C12714yes—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8C2×C4×C12712yes—
343C4⋊Q8C2×C4×C12712yes—
344#127—21no—
345#127—21no—
346#127C2×C4×C12712yes—
347#127C2×C4×C12712yes—
348#124—22no—
349#124—22no—
350#124C2×C4×C12714yes—
351#124C2×C4×C12714yes—
352#121—22no—
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368#117—28no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42C2×C4×C12711yescharacteristic
378C2×C42C2×C4×C12711yescharacteristic
379C2×C42C2×C4×C12711yescharacteristic
380C2×C42C2×C4×C12711yescharacteristic
381C2×C42D4×C12711yescharacteristic
382C2×C42D4×C12711yescharacteristic
383C2×C42D4×C12711yescharacteristic
384C2×C42D4×C12711yescharacteristic
385C2×C42D4×C12711yescharacteristic
386C2×C42D4×C12711yescharacteristic
387C2×C42C23×C12714yes—
388C2×C42C23×C12711yescharacteristic
389C2×C42C23×C12711yescharacteristic
390C4⋊C8—22no—
391C4⋊C8—22no—
392#104—416no—
393C22⋊C8—22no—
394C22⋊C8—22no—
395#97—22no—
396C4×C8—22no—
397#95—22no—
398#95—22no—
399C24—22no—
400C24C2×D4×C12711yescharacteristic
401#41—216no—
402#41—48no—
403#41—48no—
404#41—48no—
405C2×Q8—22no—
406C2×Q8—44no—
407C2×Q8C22×C4×C12714yes—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4—48no—
418C2×D4—44no—
419C2×D4C22×C4×C12714yes—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—42no—
427C22×C4—48no—
428C22×C4C22⋊C4×C12711yescharacteristic
429C22×C4C22⋊C4×C12711yescharacteristic
430C22×C4C22⋊C4×C12711yescharacteristic
431C22×C4C22⋊C4×C12711yescharacteristic
432C22×C4C22⋊C4×C12711yescharacteristic
433C22×C4C22⋊C4×C12711yescharacteristic
434C22×C4C22⋊C4×C12711yescharacteristic
435C22×C4C22⋊C4×C12711yescharacteristic
436C22×C4C22×C4×C12711yescharacteristic
437C22×C4C22×C4×C12711yescharacteristic
438C22×C4C2×D4×C12711yescharacteristic
439C22×C4C2×D4×C12711yescharacteristic
440C22×C4C2×D4×C12711yescharacteristic
441C22×C4C2×D4×C12711yescharacteristic
442C22×C4C2×D4×C12711yescharacteristic
443C22×C4C2×D4×C12711yescharacteristic
444C22×C4C2×D4×C12711yescharacteristic
445C22×C4C24×C12711yescharacteristic
446M16—28no—
447C2×C8—24no—
448C4⋊C4—28no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C22⋊C4—28no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C42—28no—
459C42—28no—
460C42—44no—
461C42C22⋊C4×C12711yescharacteristic
462C42C22⋊C4×C12711yescharacteristic
463C42C22⋊C4×C12711yescharacteristic
464C42C22⋊C4×C12711yescharacteristic
465C42C22⋊C4×C12711yescharacteristic
466C42C22⋊C4×C12711yescharacteristic
467C42C22⋊C4×C12711yescharacteristic
468C42C22⋊C4×C12711yescharacteristic
469C42C22×C4×C12711yescharacteristic
470C42C22×C4×C12711yescharacteristic
471C42C22×C4×C12711yescharacteristic
472C42C22×C4×C12711yescharacteristic
473C42C2×D4×C12711yescharacteristic
474C42C2×D4×C12711yescharacteristic
475C42C2×D4×C12711yescharacteristic
476C42C2×D4×C12711yescharacteristic
477C23—22no—
478C23—22no—
479C23—24no—
480C23—41no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23C2×C22⋊C4×C12711yescharacteristic
485C23C2×C22⋊C4×C12711yescharacteristic
486C23C22×D4×C12711yescharacteristic
487Q8—28no—
488Q8—44no—
489D4—28no—
490D4—44no—
491D4—44no—
492D4—48no—
493D4—48no—
494D4—44no—
495D4—44no—
496D4—44no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—28no—
511C2×C4—24no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—48no—
516C2×C4—44no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—48no—
520C2×C4#104×C12714yescomplemented
521C2×C4C2×C22⋊C4×C12711yescharacteristic
522C2×C4C2×C22⋊C4×C12711yescharacteristic
523C2×C4C2×C22⋊C4×C12711yescharacteristic
524C2×C4C2×C22⋊C4×C12711yescharacteristic
525C2×C4C2×C22⋊C4×C12711yescharacteristic
526C2×C4C2×C22⋊C4×C12711yescharacteristic
527C2×C4C2×C22⋊C4×C12711yescharacteristic
528C2×C4C2×C22⋊C4×C12711yescharacteristic
529C2×C4C2×C22⋊C4×C12711yescharacteristic
530C2×C4C2×C22⋊C4×C12711yescharacteristic
531C2×C4C23×C4×C12711yescharacteristic
532C2×C4C22×D4×C12711yescharacteristic
533C2×C4H(5,𝔽2)×C12714yes—
534C8—44no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—88no—
547C22C2×#104×C12712yes—
548C22C22×C22⋊C4×C12711yescharacteristic
549C22#535×C12712yes—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—48no—
558C4—44no—
559C4C2×#104×C12712yes—
560C4C2×#104×C12712yes—
561C4#421×C12712yes—
562C4#518×C12712yes—
563C4#535×C12712yes—
564C2—22no—
565C2—22no—
566C2—41no—
567C2—84no—
568C2C127×#230911yescharacteristic
569C2C22×#104×C12711yescharacteristic
570C2C2×#421×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC2×#532×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2920C2semidirect
3. C4×#117×C127C2semidirect
4. C127×#1980C2semidirect
5. C127×#1962C2semidirect
6. C127×#1789C2semidirect
12. #532×C127C4semidirect
13. #532×C127C4semidirect
16. C2×C4⋊Q8×C127C4semidirect
17. C2×#127×C127C4semidirect
18. C2×#124×C127C4semidirect
29. #423×C127C22semidirect
30. C2×#104×C127C22semidirect
32. C4×M16×C127C22semidirect
34. C4×C4⋊C4×C127C22semidirect
38. C43×C127C22semidirect
234. C2×C4×C127#104semidirect
278. #21815C127direct (N × H)
287. #2920C2×C127semidirect
288. C4×#117C2×C127semidirect
289. #1980C2×C127semidirect
290. #1962C2×C127semidirect
291. #1789C2×C127semidirect
292. C127#21815direct (N × H)
298. #532C4×C127semidirect
299. #532C4×C127semidirect
302. C2×C4⋊Q8C4×C127semidirect
303. C2×#127C4×C127semidirect
304. C2×#124C4×C127semidirect
315. #423C22×C127semidirect
316. C2×#104C22×C127semidirect
318. C4×M16C22×C127semidirect
320. C4×C4⋊C4C22×C127semidirect
324. C43C22×C127semidirect
520. C2×C4#104×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#532×C1272
C127×#29202
C4×#117×C1272
C127×#19802
C127×#19622
C127×#17892
#21815127