Finite Group Databasebeta

← C127×#21816 #44585489

Subgroups — C127×#21816 #44585489

Order 32512.

1352 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C127C211yesmaximal, characteristic
2C127×#2920C211yesmaximal, characteristic, complemented
3C127×#2283C211yesmaximal, characteristic, complemented
4C127×#1980C214yesmaximal, complemented
5C127×#1963C214yesmaximal, 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—
23C22×C42×C127C2211yescharacteristic
24#432×C127—21no—
25#432×C127—21no—
26#431×C127—21no—
27#431×C127—21no—
28#423×C127C2212yescomplemented
29C2×#104×C127C22116yescomplemented
30#407×C127C2212yes—
31C4×M16×C127C2212yescomplemented
32#383×C127—21no—
33#382×C127—21no—
34#381×C127—21no—
35#380×C127—21no—
36C4×C4⋊C4×C127C2212yescomplemented
37C4×C22⋊C4×C127C2212yes—
38#376×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—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127—21no—
84C2×C4⋊C4×C127—22no—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—22no—
88C2×C42×C127C2×C411yescharacteristic
89C2×C42×C127C2×C411yescharacteristic
90C2×C42×C127C2×C411yescharacteristic
91C2×C42×C127C2×C411yescharacteristic
92C2×C42×C127D411yescharacteristic
93C2×C42×C127D411yescharacteristic
94C2×C42×C127D411yescharacteristic
95C2×C42×C127D411yescharacteristic
96C2×C42×C127D411yescharacteristic
97C2×C42×C127D411yescharacteristic
98C2×C42×C127C2314yes—
99C2×C42×C127C2311yescharacteristic
100C2×C42×C127C2311yescharacteristic
101C4⋊C8×C127—22no—
102C4⋊C8×C127—22no—
103#104×C127—416no—
104C22⋊C8×C127—22no—
105C22⋊C8×C127—22no—
106#97×C127—22no—
107C4×C8×C127—22no—
108#95×C127—22no—
109#95×C127—22no—
110#95×C127—22no—
111#95×C127—22no—
112C24×C127—22no—
113C24×C127C2×D411yescharacteristic
114#41×C127—216no—
115#41×C127—48no—
116#41×C127—48no—
117#41×C127—48no—
118C2×Q8×C127—22no—
119C2×Q8×C127—44no—
120C2×Q8×C127C22×C414yes—
121C2×D4×C127—24no—
122C2×D4×C127—24no—
123C2×D4×C127—22no—
124C2×D4×C127—22no—
125C2×D4×C127—22no—
126C2×D4×C127—22no—
127C2×D4×C127—22no—
128C2×D4×C127—44no—
129C2×D4×C127—44no—
130C2×D4×C127—44no—
131C2×D4×C127—48no—
132C2×D4×C127C22×C414yes—
133C22×C4×C127—24no—
134C22×C4×C127—22no—
135C22×C4×C127—24no—
136C22×C4×C127—24no—
137C22×C4×C127—24no—
138C22×C4×C127—42no—
139C22×C4×C127—42no—
140C22×C4×C127—48no—
141C22×C4×C127C22⋊C411yescharacteristic
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×C127C2×D411yescharacteristic
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×C127C2411yescharacteristic
159M16×C127—28no—
160C2×C8×C127—24no—
161C4⋊C4×C127—22no—
162C4⋊C4×C127—22no—
163C4⋊C4×C127—22no—
164C4⋊C4×C127—22no—
165C4⋊C4×C127—44no—
166C22⋊C4×C127—24no—
167C22⋊C4×C127—24no—
168C22⋊C4×C127—24no—
169C22⋊C4×C127—24no—
170C22⋊C4×C127—44no—
171C42×C127—28no—
172C42×C127C22⋊C411yescharacteristic
173C42×C127C22⋊C411yescharacteristic
174C42×C127C22⋊C411yescharacteristic
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×C127C2×D411yescharacteristic
185C42×C127C2×D411yescharacteristic
186C42×C127C2×D411yescharacteristic
187C42×C127C2×D411yescharacteristic
188C23×C127—22no—
189C23×C127—22no—
190C23×C127—24no—
191C23×C127—41no—
192C23×C127—44no—
193C23×C127—44no—
194C23×C127—44no—
195C23×C127C2×C22⋊C411yescharacteristic
196C23×C127C2×C22⋊C411yescharacteristic
197C23×C127C22×D411yescharacteristic
198Q8×C127—28no—
199Q8×C127—44no—
200D4×C127—28no—
201D4×C127—44no—
202D4×C127—44no—
203D4×C127—44no—
204D4×C127—44no—
205D4×C127—48no—
206D4×C127—48no—
207D4×C127—44no—
208C2×C4×C127—22no—
209C2×C4×C127—22no—
210C2×C4×C127—22no—
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—24no—
219C2×C4×C127—41no—
220C2×C4×C127—41no—
221C2×C4×C127—41no—
222C2×C4×C127—41no—
223C2×C4×C127—41no—
224C2×C4×C127—41no—
225C2×C4×C127—41no—
226C2×C4×C127—48no—
227C2×C4×C127—44no—
228C2×C4×C127—48no—
229C2×C4×C127—44no—
230C2×C4×C127—44no—
231C2×C4×C127—44no—
232C2×C4×C127C2×C22⋊C411yescharacteristic
233C2×C4×C127C2×C22⋊C411yescharacteristic
234C2×C4×C127C2×C22⋊C411yescharacteristic
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×C127C23×C411yescharacteristic
243C2×C4×C127C22×D411yescharacteristic
244C2×C4×C127H(5,𝔽2)14yes—
245C8×C127—44no—
246C22×C127—21no—
247C22×C127—21no—
248C22×C127—21no—
249C22×C127—21no—
250C22×C127—21no—
251C22×C127—21no—
252C22×C127—21no—
253C22×C127—44no—
254C22×C127—44no—
255C22×C127—44no—
256C22×C127—44no—
257C22×C127—88no—
258C22×C127#42112yes—
259C22×C127C22×C22⋊C411yescharacteristic
260C22×C127#53512yes—
261C4×C127—21no—
262C4×C127—21no—
263C4×C127—21no—
264C4×C127—21no—
265C4×C127—21no—
266C4×C127—21no—
267C4×C127—21no—
268C4×C127—21no—
269C4×C127—21no—
270C4×C127—44no—
271C4×C127—84no—
272C4×C127#42112yes—
273C4×C127#51812yes—
274C4×C127#53512yes—
275#21816C12711yesmaximal, characteristic, direct product factor, Sylow
276C2×C127—22no—
277C2×C127—22no—
278C2×C127—41no—
279C2×C127—84no—
280C2×C127#230911yescharacteristic
281C2×C127C2×#42111yescharacteristic
282C2×C127C2×#42111yescharacteristic
283C2×#532C2×C12711yescharacteristic
284#2920C2×C12711yescharacteristic, complemented
285#2283C2×C12711yescharacteristic, complemented
286#1980C2×C12714yescomplemented
287#1963C2×C12714yescomplemented
288#1789C2×C12714yescomplemented
289C127#2181611yescharacteristic, direct product factor, Sylow
290C22×#41C22×C12712yes—
291#532—21no—
292#532—21no—
293#532—21no—
294#532—21no—
295#532C4×C12712yescomplemented
296#532C4×C12712yescomplemented
297#532C22×C12712yes—
298#532C22×C12712yes—
299C2×C4⋊Q8C4×C12711yescharacteristic, complemented
300C2×#127C4×C12711yescharacteristic, complemented
301C2×#124C4×C12712yescomplemented
302C2×#121—21no—
303C2×#121—21no—
304C2×C4×D4—21no—
305C2×C4×D4—21no—
306C22×C42C22×C12711yescharacteristic
307#432—21no—
308#432—21no—
309#431—21no—
310#431—21no—
311#423C22×C12712yescomplemented
312C2×#104C22×C127116yescomplemented
313#407C22×C12712yes—
314C4×M16C22×C12712yescomplemented
315#383—21no—
316#382—21no—
317#381—21no—
318#380—21no—
319C4×C4⋊C4C22×C12712yescomplemented
320C4×C22⋊C4C22×C12712yes—
321#376C22×C12712yescomplemented
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—48no—
325C2×#41C2×C4×C12714yes—
326C2×#41C23×C12714yes—
327C22×Q8C2×C4×C12712yes—
328C22×D4—22no—
329C22×D4—21no—
330C22×D4—21no—
331C22×D4C2×C4×C12712yes—
332C23×C4—22no—
333C23×C4D4×C12711yescharacteristic
334C23×C4D4×C12711yescharacteristic
335C23×C4C23×C12711yescharacteristic
336C2×M16C23×C12714yes—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8C2×C4×C12712yes—
340C4⋊Q8C2×C4×C12712yes—
341#127—21no—
342#127—21no—
343#127C2×C4×C12712yes—
344#127C2×C4×C12712yes—
345#124—22no—
346#124—22no—
347#124C2×C4×C12714yes—
348#124C2×C4×C12714yes—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—22no—
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C42C2×C4×C12711yescharacteristic
372C2×C42C2×C4×C12711yescharacteristic
373C2×C42C2×C4×C12711yescharacteristic
374C2×C42C2×C4×C12711yescharacteristic
375C2×C42D4×C12711yescharacteristic
376C2×C42D4×C12711yescharacteristic
377C2×C42D4×C12711yescharacteristic
378C2×C42D4×C12711yescharacteristic
379C2×C42D4×C12711yescharacteristic
380C2×C42D4×C12711yescharacteristic
381C2×C42C23×C12714yes—
382C2×C42C23×C12711yescharacteristic
383C2×C42C23×C12711yescharacteristic
384C4⋊C8—22no—
385C4⋊C8—22no—
386#104—416no—
387C22⋊C8—22no—
388C22⋊C8—22no—
389#97—22no—
390C4×C8—22no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—22no—
395C24—22no—
396C24C2×D4×C12711yescharacteristic
397#41—216no—
398#41—48no—
399#41—48no—
400#41—48no—
401C2×Q8—22no—
402C2×Q8—44no—
403C2×Q8C22×C4×C12714yes—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—44no—
414C2×D4—48no—
415C2×D4C22×C4×C12714yes—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—48no—
424C22×C4C22⋊C4×C12711yescharacteristic
425C22×C4C22⋊C4×C12711yescharacteristic
426C22×C4C22⋊C4×C12711yescharacteristic
427C22×C4C22⋊C4×C12711yescharacteristic
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×C4C2×D4×C12711yescharacteristic
435C22×C4C2×D4×C12711yescharacteristic
436C22×C4C2×D4×C12711yescharacteristic
437C22×C4C2×D4×C12711yescharacteristic
438C22×C4C2×D4×C12711yescharacteristic
439C22×C4C2×D4×C12711yescharacteristic
440C22×C4C2×D4×C12711yescharacteristic
441C22×C4C24×C12711yescharacteristic
442M16—28no—
443C2×C8—24no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—44no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—24no—
453C22⋊C4—44no—
454C42—28no—
455C42C22⋊C4×C12711yescharacteristic
456C42C22⋊C4×C12711yescharacteristic
457C42C22⋊C4×C12711yescharacteristic
458C42C22⋊C4×C12711yescharacteristic
459C42C22⋊C4×C12711yescharacteristic
460C42C22⋊C4×C12711yescharacteristic
461C42C22⋊C4×C12711yescharacteristic
462C42C22⋊C4×C12711yescharacteristic
463C42C22×C4×C12711yescharacteristic
464C42C22×C4×C12711yescharacteristic
465C42C22×C4×C12711yescharacteristic
466C42C22×C4×C12711yescharacteristic
467C42C2×D4×C12711yescharacteristic
468C42C2×D4×C12711yescharacteristic
469C42C2×D4×C12711yescharacteristic
470C42C2×D4×C12711yescharacteristic
471C23—22no—
472C23—22no—
473C23—24no—
474C23—41no—
475C23—44no—
476C23—44no—
477C23—44no—
478C23C2×C22⋊C4×C12711yescharacteristic
479C23C2×C22⋊C4×C12711yescharacteristic
480C23C22×D4×C12711yescharacteristic
481Q8—28no—
482Q8—44no—
483D4—28no—
484D4—44no—
485D4—44no—
486D4—44no—
487D4—44no—
488D4—48no—
489D4—48no—
490D4—44no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—48no—
510C2×C4—44no—
511C2×C4—48no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4C2×C22⋊C4×C12711yescharacteristic
516C2×C4C2×C22⋊C4×C12711yescharacteristic
517C2×C4C2×C22⋊C4×C12711yescharacteristic
518C2×C4C2×C22⋊C4×C12711yescharacteristic
519C2×C4C2×C22⋊C4×C12711yescharacteristic
520C2×C4C2×C22⋊C4×C12711yescharacteristic
521C2×C4C2×C22⋊C4×C12711yescharacteristic
522C2×C4C2×C22⋊C4×C12711yescharacteristic
523C2×C4C2×C22⋊C4×C12711yescharacteristic
524C2×C4C2×C22⋊C4×C12711yescharacteristic
525C2×C4C23×C4×C12711yescharacteristic
526C2×C4C22×D4×C12711yescharacteristic
527C2×C4H(5,𝔽2)×C12714yes—
528C8—44no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—44no—
537C22—44no—
538C22—44no—
539C22—44no—
540C22—88no—
541C22#421×C12712yes—
542C22C22×C22⋊C4×C12711yescharacteristic
543C22#535×C12712yes—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—44no—
554C4—84no—
555C4#421×C12712yes—
556C4#518×C12712yes—
557C4#535×C12712yes—
558C2—22no—
559C2—22no—
560C2—41no—
561C2—84no—
562C2C127×#230911yescharacteristic
563C2C2×#421×C12711yescharacteristic
564C2C2×#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. C127×#2283C2semidirect
4. C127×#1980C2semidirect
5. C127×#1963C2semidirect
6. C127×#1789C2semidirect
12. #532×C127C4semidirect
13. #532×C127C4semidirect
16. C2×C4⋊Q8×C127C4semidirect
17. C2×#127×C127C4semidirect
18. C2×#124×C127C4semidirect
28. #423×C127C22semidirect
29. C2×#104×C127C22semidirect
31. C4×M16×C127C22semidirect
36. C4×C4⋊C4×C127C22semidirect
38. #376×C127C22semidirect
275. #21816C127direct (N × H)
284. #2920C2×C127semidirect
285. #2283C2×C127semidirect
286. #1980C2×C127semidirect
287. #1963C2×C127semidirect
288. #1789C2×C127semidirect
289. C127#21816direct (N × H)
295. #532C4×C127semidirect
296. #532C4×C127semidirect
299. C2×C4⋊Q8C4×C127semidirect
300. C2×#127C4×C127semidirect
301. C2×#124C4×C127semidirect
311. #423C22×C127semidirect
312. C2×#104C22×C127semidirect
314. C4×M16C22×C127semidirect
319. C4×C4⋊C4C22×C127semidirect
321. #376C22×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
C127×#22832
C127×#19802
C127×#19632
C127×#17892
#21816127