Finite Group Databasebeta

← C127×#21424 #44585097

Subgroups — C127×#21424 #44585097

Order 32512.

1380 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C127C211yesmaximal, characteristic
2C127×#2920C211yesmaximal, characteristic, complemented
3C2×C4×M16×C127C211yesmaximal, characteristic, complemented
4C127×#1997C212yesmaximal, complemented
5C127×#1965C212yesmaximal, complemented
6C127×#1900C214yesmaximal, complemented
7C4×#100×C127C214yesmaximal, complemented
8C22×#41×C127C412yes—
9C22×M16×C127C2212yes—
10#532×C127—21no—
11#532×C127—21no—
12#532×C127—21no—
13#532×C127—21no—
14#532×C127—21no—
15#532×C127—21no—
16#532×C127—21no—
17#532×C127—21no—
18C2×C4⋊Q8×C127C2211yescharacteristic
19C2×#127×C127C2211yescharacteristic
20C2×#124×C127C412yes—
21C2×#121×C127C412yes—
22C2×#121×C127C2212yes—
23C2×C4×D4×C127C412yes—
24C2×C4×D4×C127C2212yes—
25C22×C42×C127C2211yescharacteristic
26#432×C127—21no—
27#432×C127—21no—
28#431×C127—21no—
29#431×C127—21no—
30#423×C127C2212yes—
31C2×#100×C127C2218yes—
32#407×C127C2212yes—
33C4×M16×C127—21no—
34C4×M16×C127—21no—
35C4×M16×C127C2212yes—
36C4×M16×C127C2212yes—
37C4×M16×C127C2212yes—
38C2×#97×C127—21no—
39C2×C4×C8×C127—21no—
40#343×C127C2218yes—
41C2×#41×C127—22no—
42C2×#41×C127—22no—
43C2×#41×C127—22no—
44C2×#41×C127—22no—
45C2×#41×C127—48no—
46C22×Q8×C127C2×C412yes—
47C22×D4×C127C2×C412yes—
48C22×D4×C127C2×C414yes—
49C22×D4×C127C2×C412yes—
50C22×D4×C127C2312yes—
51C23×C4×C127C2×C411yescharacteristic
52C23×C4×C127C2×C414yes—
53C23×C4×C127C2×C411yescharacteristic
54C23×C4×C127C2311yescharacteristic
55C2×M16×C127—22no—
56C2×M16×C127—28no—
57C2×M16×C127C2314yes—
58C2×M16×C127C2314yes—
59C22×C8×C127—22no—
60C4⋊Q8×C127—21no—
61C4⋊Q8×C127—21no—
62C4⋊Q8×C127—21no—
63C4⋊Q8×C127—21no—
64#127×C127—21no—
65#127×C127—21no—
66#127×C127—21no—
67#127×C127—21no—
68#124×C127—22no—
69#124×C127—22no—
70#124×C127—22no—
71#124×C127—22no—
72#121×C127—22no—
73#121×C127—22no—
74#121×C127—22no—
75#121×C127—22no—
76#121×C127—22no—
77#121×C127—22no—
78#121×C127—22no—
79#121×C127—22no—
80C4×D4×C127—22no—
81C4×D4×C127—22no—
82C4×D4×C127—22no—
83C4×D4×C127—22no—
84C4×D4×C127—22no—
85C4×D4×C127—22no—
86C4×D4×C127—22no—
87C4×D4×C127—22no—
88C2×C4⋊C4×C127C2×C412yes—
89C2×C4⋊C4×C127C2312yes—
90C2×C22⋊C4×C127C2×C414yes—
91C2×C22⋊C4×C127C2×C414yes—
92C2×C42×C127C2×C411yescharacteristic
93C2×C42×C127C2×C411yescharacteristic
94C2×C42×C127D411yescharacteristic
95C2×C42×C127D411yescharacteristic
96C2×C42×C127D411yescharacteristic
97C2×C42×C127D411yescharacteristic
98C2×C42×C127D411yescharacteristic
99C2×C42×C127D411yescharacteristic
100C2×C42×C127D411yescharacteristic
101C2×C42×C127D411yescharacteristic
102C2×C42×C127C2311yescharacteristic
103C2×C42×C127C2311yescharacteristic
104C4⋊C8×C127—22no—
105C4⋊C8×C127—22no—
106#100×C127—216no—
107C22⋊C8×C127—22no—
108C22⋊C8×C127—22no—
109#97×C127—22no—
110#97×C127—22no—
111#97×C127—22no—
112C4×C8×C127—22no—
113C4×C8×C127—22no—
114C4×C8×C127—22no—
115C24×C127C22×C411yescharacteristic
116C24×C127C22×C414yes—
117#41×C127—48no—
118#41×C127—48no—
119#41×C127—48no—
120#41×C127—48no—
121C2×Q8×C127—22no—
122C2×Q8×C127—22no—
123C2×Q8×C127—44no—
124C2×D4×C127—24no—
125C2×D4×C127—24no—
126C2×D4×C127—22no—
127C2×D4×C127—22no—
128C2×D4×C127—22no—
129C2×D4×C127—22no—
130C2×D4×C127—22no—
131C2×D4×C127—22no—
132C2×D4×C127—28no—
133C2×D4×C127—44no—
134C2×D4×C127—44no—
135C2×D4×C127—48no—
136C22×C4×C127—24no—
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×C127C22×C411yescharacteristic
153C22×C4×C127C22×C411yescharacteristic
154C22×C4×C127C22×C414yes—
155C22×C4×C127C22×C411yescharacteristic
156C22×C4×C127C2×D411yescharacteristic
157C22×C4×C127C2×D411yescharacteristic
158C22×C4×C127C2×D411yescharacteristic
159C22×C4×C127C2×D411yescharacteristic
160C22×C4×C127C2411yescharacteristic
161M16×C127—28no—
162M16×C127—24no—
163M16×C127—28no—
164M16×C127#4118yescomplemented
165C2×C8×C127—28no—
166C2×C8×C127—24no—
167C2×C8×C127—24no—
168C4⋊C4×C127—22no—
169C4⋊C4×C127—22no—
170C4⋊C4×C127—22no—
171C4⋊C4×C127—22no—
172C22⋊C4×C127—24no—
173C22⋊C4×C127—24no—
174C22⋊C4×C127—24no—
175C22⋊C4×C127—24no—
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
188C42×C127C2×D411yescharacteristic
189C42×C127C2×D411yescharacteristic
190C42×C127C2×D411yescharacteristic
191C42×C127C2×D411yescharacteristic
192C23×C127—22no—
193C23×C127—22no—
194C23×C127—24no—
195C23×C127—28no—
196C23×C127—41no—
197C23×C127—44no—
198C23×C127—44no—
199C23×C127C2×C22⋊C411yescharacteristic
200C23×C127C2×C22⋊C411yescharacteristic
201C23×C127C23×C411yescharacteristic
202Q8×C127—44no—
203Q8×C127—44no—
204D4×C127—44no—
205D4×C127—44no—
206D4×C127—48no—
207D4×C127—48no—
208D4×C127—44no—
209D4×C127—44no—
210D4×C127—44no—
211D4×C127—44no—
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—22no—
225C2×C4×C127—24no—
226C2×C4×C127—41no—
227C2×C4×C127—41no—
228C2×C4×C127—41no—
229C2×C4×C127—48no—
230C2×C4×C127—48no—
231C2×C4×C127—44no—
232C2×C4×C127#10014yescomplemented
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×C127C2×C22⋊C411yescharacteristic
243C2×C4×C127C22×D411yescharacteristic
244C2×C4×C127C22×D411yescharacteristic
245C2×C4×C127C2×#4114yes—
246C8×C127—28no—
247C8×C127—44no—
248C22×C127—21no—
249C22×C127—21no—
250C22×C127—21no—
251C22×C127—21no—
252C22×C127—21no—
253C22×C127—21no—
254C22×C127—21no—
255C22×C127—44no—
256C22×C127—44no—
257C22×C127—44no—
258C22×C127—44no—
259C22×C127—88no—
260C22×C127C2×#10012yes—
261C22×C127C22×C22⋊C411yescharacteristic
262C22×C127C4×#4112yes—
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×C127C2×#10012yes—
272C4×C127C2×#10012yes—
273C4×C127#41312yes—
274C4×C127#52512yes—
275C4×C127#53212yes—
276#21424C12711yesmaximal, characteristic, direct product factor, Sylow
277C2×C127—22no—
278C2×C127—22no—
279C2×C127—41no—
280C2×C127—84no—
281C2×C127#229711yescharacteristic
282C2×C127C22×#10011yescharacteristic
283C2×C127C2×#41311yescharacteristic
284C2×#532C2×C12711yescharacteristic
285#2920C2×C12711yescharacteristic, complemented
286C2×C4×M16C2×C12711yescharacteristic, complemented
287#1997C2×C12712yescomplemented
288#1965C2×C12712yescomplemented
289#1900C2×C12714yescomplemented
290C4×#100C2×C12714yescomplemented
291C127#2142411yescharacteristic, direct product factor, Sylow
292C22×#41C4×C12712yes—
293C22×M16C22×C12712yes—
294#532—21no—
295#532—21no—
296#532—21no—
297#532—21no—
298#532—21no—
299#532—21no—
300#532—21no—
301#532—21no—
302C2×C4⋊Q8C22×C12711yescharacteristic
303C2×#127C22×C12711yescharacteristic
304C2×#124C4×C12712yes—
305C2×#121C4×C12712yes—
306C2×#121C22×C12712yes—
307C2×C4×D4C4×C12712yes—
308C2×C4×D4C22×C12712yes—
309C22×C42C22×C12711yescharacteristic
310#432—21no—
311#432—21no—
312#431—21no—
313#431—21no—
314#423C22×C12712yes—
315C2×#100C22×C12718yes—
316#407C22×C12712yes—
317C4×M16—21no—
318C4×M16—21no—
319C4×M16C22×C12712yes—
320C4×M16C22×C12712yes—
321C4×M16C22×C12712yes—
322C2×#97—21no—
323C2×C4×C8—21no—
324#343C22×C12718yes—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—48no—
330C22×Q8C2×C4×C12712yes—
331C22×D4C2×C4×C12712yes—
332C22×D4C2×C4×C12714yes—
333C22×D4C2×C4×C12712yes—
334C22×D4C23×C12712yes—
335C23×C4C2×C4×C12711yescharacteristic
336C23×C4C2×C4×C12714yes—
337C23×C4C2×C4×C12711yescharacteristic
338C23×C4C23×C12711yescharacteristic
339C2×M16—22no—
340C2×M16—28no—
341C2×M16C23×C12714yes—
342C2×M16C23×C12714yes—
343C22×C8—22no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348#127—21no—
349#127—21no—
350#127—21no—
351#127—21no—
352#124—22no—
353#124—22no—
354#124—22no—
355#124—22no—
356#121—22no—
357#121—22no—
358#121—22no—
359#121—22no—
360#121—22no—
361#121—22no—
362#121—22no—
363#121—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—22no—
372C2×C4⋊C4C2×C4×C12712yes—
373C2×C4⋊C4C23×C12712yes—
374C2×C22⋊C4C2×C4×C12714yes—
375C2×C22⋊C4C2×C4×C12714yes—
376C2×C42C2×C4×C12711yescharacteristic
377C2×C42C2×C4×C12711yescharacteristic
378C2×C42D4×C12711yescharacteristic
379C2×C42D4×C12711yescharacteristic
380C2×C42D4×C12711yescharacteristic
381C2×C42D4×C12711yescharacteristic
382C2×C42D4×C12711yescharacteristic
383C2×C42D4×C12711yescharacteristic
384C2×C42D4×C12711yescharacteristic
385C2×C42D4×C12711yescharacteristic
386C2×C42C23×C12711yescharacteristic
387C2×C42C23×C12711yescharacteristic
388C4⋊C8—22no—
389C4⋊C8—22no—
390#100—216no—
391C22⋊C8—22no—
392C22⋊C8—22no—
393#97—22no—
394#97—22no—
395#97—22no—
396C4×C8—22no—
397C4×C8—22no—
398C4×C8—22no—
399C24C22×C4×C12711yescharacteristic
400C24C22×C4×C12714yes—
401#41—48no—
402#41—48no—
403#41—48no—
404#41—48no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—44no—
408C2×D4—24no—
409C2×D4—24no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—28no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—48no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—42no—
425C22×C4—48no—
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×C4C22×C4×C12711yescharacteristic
435C22×C4C22×C4×C12711yescharacteristic
436C22×C4C22×C4×C12711yescharacteristic
437C22×C4C22×C4×C12711yescharacteristic
438C22×C4C22×C4×C12714yes—
439C22×C4C22×C4×C12711yescharacteristic
440C22×C4C2×D4×C12711yescharacteristic
441C22×C4C2×D4×C12711yescharacteristic
442C22×C4C2×D4×C12711yescharacteristic
443C22×C4C2×D4×C12711yescharacteristic
444C22×C4C24×C12711yescharacteristic
445M16—28no—
446M16—24no—
447M16—28no—
448M16#41×C12718yescomplemented
449C2×C8—28no—
450C2×C8—24no—
451C2×C8—24no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C42C22⋊C4×C12711yescharacteristic
461C42C22⋊C4×C12711yescharacteristic
462C42C22⋊C4×C12711yescharacteristic
463C42C22⋊C4×C12711yescharacteristic
464C42C22⋊C4×C12711yescharacteristic
465C42C22⋊C4×C12711yescharacteristic
466C42C22⋊C4×C12711yescharacteristic
467C42C22⋊C4×C12711yescharacteristic
468C42C2×D4×C12711yescharacteristic
469C42C2×D4×C12711yescharacteristic
470C42C2×D4×C12711yescharacteristic
471C42C2×D4×C12711yescharacteristic
472C42C2×D4×C12711yescharacteristic
473C42C2×D4×C12711yescharacteristic
474C42C2×D4×C12711yescharacteristic
475C42C2×D4×C12711yescharacteristic
476C23—22no—
477C23—22no—
478C23—24no—
479C23—28no—
480C23—41no—
481C23—44no—
482C23—44no—
483C23C2×C22⋊C4×C12711yescharacteristic
484C23C2×C22⋊C4×C12711yescharacteristic
485C23C23×C4×C12711yescharacteristic
486Q8—44no—
487Q8—44no—
488D4—44no—
489D4—44no—
490D4—48no—
491D4—48no—
492D4—44no—
493D4—44no—
494D4—44no—
495D4—44no—
496C2×C4—22no—
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—24no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—48no—
514C2×C4—48no—
515C2×C4—44no—
516C2×C4#100×C12714yescomplemented
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×C4C2×C22⋊C4×C12711yescharacteristic
526C2×C4C2×C22⋊C4×C12711yescharacteristic
527C2×C4C22×D4×C12711yescharacteristic
528C2×C4C22×D4×C12711yescharacteristic
529C2×C4C2×#41×C12714yes—
530C8—28no—
531C8—44no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—44no—
543C22—88no—
544C22C2×#100×C12712yes—
545C22C22×C22⋊C4×C12711yescharacteristic
546C22C4×#41×C12712yes—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—44no—
555C4C2×#100×C12712yes—
556C4C2×#100×C12712yes—
557C4#413×C12712yes—
558C4#525×C12712yes—
559C4#532×C12712yes—
560C2—22no—
561C2—22no—
562C2—41no—
563C2—84no—
564C2C127×#229711yescharacteristic
565C2C22×#100×C12711yescharacteristic
566C2C2×#413×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC2×#532×C127C2
LCSG ▷ C23 ▷ 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. C2×C4×M16×C127C2semidirect
4. C127×#1997C2semidirect
5. C127×#1965C2semidirect
6. C127×#1900C2semidirect
7. C4×#100×C127C2semidirect
164. M16×C127#41semidirect
232. C2×C4×C127#100semidirect
276. #21424C127direct (N × H)
285. #2920C2×C127semidirect
286. C2×C4×M16C2×C127semidirect
287. #1997C2×C127semidirect
288. #1965C2×C127semidirect
289. #1900C2×C127semidirect
290. C4×#100C2×C127semidirect
291. C127#21424direct (N × H)
448. M16#41×C127semidirect
516. C2×C4#100×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
C2×C4×M16×C1272
C127×#19972
C127×#19652
C127×#19002
C4×#100×C1272
#21424127