Finite Group Databasebeta

← C127×#10735 #44574408

Subgroups — C127×#10735 #44574408

Order 32512.

3062 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C2×#379×C127C211yesmaximal, characteristic
3C2×#379×C127C211yesmaximal, characteristic
4C2×#342×C127C214yesmaximal, complemented
5C26×C127C2211yescharacteristic
6C24×C4×C127—21no—
7C22×C22⋊C4×C127—21no—
8C22×C22⋊C4×C127—22no—
9C22×C22⋊C4×C127—28no—
10C22×C22⋊C4×C127—22no—
11C22×C22⋊C4×C127C414yescomplemented
12C22×C22⋊C4×C127C414yescomplemented
13C22×C22⋊C4×C127C2212yes—
14C22×C22⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2212yes—
16#379×C127—22no—
17#379×C127—21no—
18#379×C127—22no—
19#379×C127—21no—
20#379×C127C414yescomplemented
21#342×C127—28no—
22C25×C127—24no—
23C25×C127—24no—
24C25×C127—48no—
25C25×C127C2×C412yes—
26C25×C127C2×C412yes—
27C25×C127C2×C412yes—
28C25×C127D411yescharacteristic
29C25×C127D412yes—
30C25×C127D412yes—
31C25×C127D411yescharacteristic
32C25×C127Q812yes—
33C25×C127C2311yescharacteristic
34C23×C4×C127—28no—
35C23×C4×C127—24no—
36C23×C4×C127—22no—
37C23×C4×C127—22no—
38C23×C4×C127—48no—
39C23×C4×C127C2×C414yescomplemented
40C2×C22⋊C4×C127—28no—
41C2×C22⋊C4×C127—216no—
42C2×C22⋊C4×C127—24no—
43C2×C22⋊C4×C127—24no—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—216no—
46C2×C22⋊C4×C127—24no—
47C2×C22⋊C4×C127—24no—
48C2×C22⋊C4×C127—28no—
49C2×C22⋊C4×C127—24no—
50C2×C22⋊C4×C127—24no—
51C2×C22⋊C4×C127—24no—
52C2×C22⋊C4×C127—22no—
53C2×C22⋊C4×C127—22no—
54C2×C22⋊C4×C127—22no—
55C2×C22⋊C4×C127—24no—
56C2×C22⋊C4×C127—48no—
57C2×C22⋊C4×C127—48no—
58C2×C22⋊C4×C127C2×C414yes—
59C2×C22⋊C4×C127C2×C414yescomplemented
60C2×C22⋊C4×C127D418yes—
61C24×C127—28no—
62C24×C127—22no—
63C24×C127—22no—
64C24×C127—28no—
65C24×C127—28no—
66C24×C127—24no—
67C24×C127—24no—
68C24×C127—28no—
69C24×C127—28no—
70C24×C127—24no—
71C24×C127—22no—
72C24×C127—28no—
73C24×C127—28no—
74C24×C127—24no—
75C24×C127—22no—
76C24×C127—48no—
77C24×C127—48no—
78C24×C127—44no—
79C24×C127—48no—
80C24×C127—44no—
81C24×C127—44no—
82C24×C127—48no—
83C24×C127—44no—
84C24×C127—432no—
85C24×C127—432no—
86C24×C127C4214yes—
87C24×C127C22⋊C412yes—
88C24×C127C22⋊C412yes—
89C24×C127C22⋊C414yes—
90C24×C127C22⋊C412yes—
91C24×C127C22⋊C412yes—
92C24×C127C4⋊C412yes—
93C24×C127C4⋊C414yes—
94C24×C127C4⋊C414yes—
95C24×C127C4⋊C412yes—
96C24×C127C22×C411yescharacteristic
97C24×C127C22×C411yescharacteristic
98C24×C127C22×C411yescharacteristic
99C24×C127C2×D411yescharacteristic
100C24×C127C2×D411yescharacteristic
101C24×C127C2×D411yescharacteristic
102C24×C127C2×D414yes—
103C24×C127C2×Q811yescharacteristic
104C24×C127#4114yes—
105C22×C4×C127—216no—
106C22×C4×C127—24no—
107C22×C4×C127—28no—
108C22×C4×C127—24no—
109C22×C4×C127—24no—
110C22×C4×C127—28no—
111C22×C4×C127—432no—
112C22×C4×C127—416no—
113C22×C4×C127—48no—
114C22×C4×C127—48no—
115C22×C4×C127—44no—
116C22×C4×C127—48no—
117C22⋊C4×C127—216no—
118C22⋊C4×C127—24no—
119C22⋊C4×C127—28no—
120C22⋊C4×C127—28no—
121C22⋊C4×C127—416no—
122C22⋊C4×C127—48no—
123C22⋊C4×C127—48no—
124C22⋊C4×C127—42no—
125C22⋊C4×C127—42no—
126C22⋊C4×C127—44no—
127C22⋊C4×C127—42no—
128C22⋊C4×C127—42no—
129C22⋊C4×C127C22⋊C418yescomplemented
130C23×C127—216no—
131C23×C127—216no—
132C23×C127—28no—
133C23×C127—28no—
134C23×C127—22no—
135C23×C127—22no—
136C23×C127—24no—
137C23×C127—24no—
138C23×C127—24no—
139C23×C127—24no—
140C23×C127—24no—
141C23×C127—24no—
142C23×C127—28no—
143C23×C127—28no—
144C23×C127—28no—
145C23×C127—28no—
146C23×C127—28no—
147C23×C127—22no—
148C23×C127—28no—
149C23×C127—22no—
150C23×C127—28no—
151C23×C127—24no—
152C23×C127—28no—
153C23×C127—24no—
154C23×C127—24no—
155C23×C127—24no—
156C23×C127—44no—
157C23×C127—44no—
158C23×C127—44no—
159C23×C127—44no—
160C23×C127—44no—
161C23×C127—44no—
162C23×C127—42no—
163C23×C127—42no—
164C23×C127—48no—
165C23×C127—42no—
166C23×C127—42no—
167C23×C127—48no—
168C23×C127—432no—
169C23×C127—432no—
170C23×C127—416no—
171C23×C127—416no—
172C23×C127—416no—
173C23×C127—432no—
174C23×C127—432no—
175C23×C127—416no—
176C23×C127—48no—
177C23×C127—48no—
178C23×C127#9514yes—
179C23×C127#9514yes—
180C23×C127#9918yes—
181C23×C127C2×C4211yescharacteristic
182C23×C127C2×C22⋊C411yescharacteristic
183C23×C127C2×C22⋊C411yescharacteristic
184C23×C127C2×C22⋊C412yes—
185C23×C127C2×C22⋊C411yescharacteristic
186C23×C127C2×C4⋊C411yescharacteristic
187C23×C127C2×C4⋊C411yescharacteristic
188C23×C127C2×C4⋊C411yescharacteristic
189C23×C127#11712yes—
190C23×C127C4×D414yes—
191C23×C127C4×D414yes—
192C23×C127#12012yes—
193C23×C127#12012yes—
194C23×C127#12114yes—
195C23×C127C22⋊Q814yes—
196C23×C127#12312yes—
197C23×C127#12312yes—
198C2×C4×C127—28no—
199C2×C4×C127—432no—
200C2×C4×C127—416no—
201C2×C4×C127—48no—
202C2×C4×C127—48no—
203C2×C4×C127—44no—
204C2×C4×C127—44no—
205C2×C4×C127—48no—
206C2×C4×C127—88no—
207C2×C4×C127—88no—
208C22×C127—28no—
209C22×C127—28no—
210C22×C127—216no—
211C22×C127—24no—
212C22×C127—28no—
213C22×C127—28no—
214C22×C127—216no—
215C22×C127—24no—
216C22×C127—24no—
217C22×C127—22no—
218C22×C127—22no—
219C22×C127—24no—
220C22×C127—22no—
221C22×C127—22no—
222C22×C127—22no—
223C22×C127—22no—
224C22×C127—24no—
225C22×C127—24no—
226C22×C127—24no—
227C22×C127—42no—
228C22×C127—42no—
229C22×C127—44no—
230C22×C127—42no—
231C22×C127—44no—
232C22×C127—42no—
233C22×C127—416no—
234C22×C127—416no—
235C22×C127—416no—
236C22×C127—416no—
237C22×C127—44no—
238C22×C127—44no—
239C22×C127—48no—
240C22×C127—48no—
241C22×C127#34218yescomplemented
242C22×C127C2×#9511yescharacteristic
243C22×C127C4×C22⋊C412yes—
244C22×C127#37911yescharacteristic
245C22×C127#38012yes—
246C22×C127#38111yescharacteristic
247C22×C127#38512yes—
248C22×C127#38512yes—
249C22×C127#38612yes—
250C22×C127#38612yes—
251C22×C127C2×#9914yes—
252C4×C127—48no—
253C4×C127—84no—
254C4×C127—84no—
255#10735C12711yesmaximal, characteristic, direct product factor, Sylow
256C2×C127—21no—
257C2×C127—22no—
258C2×C127—28no—
259C2×C127—21no—
260C2×C127—22no—
261C2×C127—22no—
262C2×C127—22no—
263C2×C127—22no—
264C2×C127—44no—
265C2×C127C22⋊#9511yescharacteristic
266C2×C127C2×#34212yes—
267C2×C127#189814yes—
268C23×C22⋊C4C2×C12711yescharacteristic
269C2×#379C2×C12711yescharacteristic
270C2×#379C2×C12711yescharacteristic
271C2×#342C2×C12714yescomplemented
272C127#1073511yescharacteristic, direct product factor, Sylow
273C26C22×C12711yescharacteristic
274C24×C4—21no—
275C22×C22⋊C4—21no—
276C22×C22⋊C4—22no—
277C22×C22⋊C4—28no—
278C22×C22⋊C4—22no—
279C22×C22⋊C4C4×C12714yescomplemented
280C22×C22⋊C4C4×C12714yescomplemented
281C22×C22⋊C4C22×C12712yes—
282C22×C22⋊C4C22×C12712yes—
283C22×C22⋊C4C22×C12712yes—
284#379—22no—
285#379—21no—
286#379—22no—
287#379—21no—
288#379C4×C12714yescomplemented
289#342—28no—
290C25—24no—
291C25—24no—
292C25—48no—
293C25C2×C4×C12712yes—
294C25C2×C4×C12712yes—
295C25C2×C4×C12712yes—
296C25D4×C12711yescharacteristic
297C25D4×C12712yes—
298C25D4×C12711yescharacteristic
299C25D4×C12712yes—
300C25Q8×C12712yes—
301C25C23×C12711yescharacteristic
302C23×C4—28no—
303C23×C4—24no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—48no—
307C23×C4C2×C4×C12714yescomplemented
308C2×C22⋊C4—28no—
309C2×C22⋊C4—216no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—216no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—48no—
325C2×C22⋊C4—48no—
326C2×C22⋊C4C2×C4×C12714yes—
327C2×C22⋊C4C2×C4×C12714yescomplemented
328C2×C22⋊C4D4×C12718yes—
329C24—28no—
330C24—22no—
331C24—22no—
332C24—28no—
333C24—28no—
334C24—24no—
335C24—24no—
336C24—28no—
337C24—28no—
338C24—24no—
339C24—22no—
340C24—28no—
341C24—28no—
342C24—24no—
343C24—22no—
344C24—48no—
345C24—48no—
346C24—44no—
347C24—48no—
348C24—44no—
349C24—44no—
350C24—48no—
351C24—44no—
352C24—432no—
353C24—432no—
354C24C42×C12714yes—
355C24C22⋊C4×C12712yes—
356C24C22⋊C4×C12712yes—
357C24C22⋊C4×C12714yes—
358C24C22⋊C4×C12712yes—
359C24C22⋊C4×C12712yes—
360C24C4⋊C4×C12712yes—
361C24C4⋊C4×C12714yes—
362C24C4⋊C4×C12714yes—
363C24C4⋊C4×C12712yes—
364C24C22×C4×C12711yescharacteristic
365C24C22×C4×C12711yescharacteristic
366C24C22×C4×C12711yescharacteristic
367C24C2×D4×C12711yescharacteristic
368C24C2×D4×C12711yescharacteristic
369C24C2×D4×C12711yescharacteristic
370C24C2×D4×C12714yes—
371C24C2×Q8×C12711yescharacteristic
372C24#41×C12714yes—
373C22×C4—216no—
374C22×C4—24no—
375C22×C4—28no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—28no—
379C22×C4—432no—
380C22×C4—416no—
381C22×C4—48no—
382C22×C4—48no—
383C22×C4—44no—
384C22×C4—48no—
385C22⋊C4—216no—
386C22⋊C4—24no—
387C22⋊C4—28no—
388C22⋊C4—28no—
389C22⋊C4—416no—
390C22⋊C4—48no—
391C22⋊C4—48no—
392C22⋊C4—42no—
393C22⋊C4—42no—
394C22⋊C4—44no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4C22⋊C4×C12718yescomplemented
398C23—216no—
399C23—216no—
400C23—28no—
401C23—28no—
402C23—22no—
403C23—22no—
404C23—24no—
405C23—24no—
406C23—24no—
407C23—24no—
408C23—24no—
409C23—24no—
410C23—28no—
411C23—28no—
412C23—28no—
413C23—28no—
414C23—28no—
415C23—22no—
416C23—28no—
417C23—22no—
418C23—28no—
419C23—24no—
420C23—28no—
421C23—24no—
422C23—24no—
423C23—24no—
424C23—44no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—42no—
431C23—42no—
432C23—48no—
433C23—42no—
434C23—42no—
435C23—48no—
436C23—432no—
437C23—432no—
438C23—416no—
439C23—416no—
440C23—416no—
441C23—432no—
442C23—432no—
443C23—416no—
444C23—48no—
445C23—48no—
446C23#95×C12714yes—
447C23#95×C12714yes—
448C23#99×C12718yes—
449C23C2×C42×C12711yescharacteristic
450C23C2×C22⋊C4×C12711yescharacteristic
451C23C2×C22⋊C4×C12711yescharacteristic
452C23C2×C22⋊C4×C12712yes—
453C23C2×C22⋊C4×C12711yescharacteristic
454C23C2×C4⋊C4×C12711yescharacteristic
455C23C2×C4⋊C4×C12711yescharacteristic
456C23C2×C4⋊C4×C12711yescharacteristic
457C23#117×C12712yes—
458C23C4×D4×C12714yes—
459C23C4×D4×C12714yes—
460C23#120×C12712yes—
461C23#120×C12712yes—
462C23#121×C12714yes—
463C23C22⋊Q8×C12714yes—
464C23#123×C12712yes—
465C23#123×C12712yes—
466C2×C4—28no—
467C2×C4—432no—
468C2×C4—416no—
469C2×C4—48no—
470C2×C4—48no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—88no—
475C2×C4—88no—
476C22—28no—
477C22—28no—
478C22—216no—
479C22—24no—
480C22—28no—
481C22—28no—
482C22—216no—
483C22—24no—
484C22—24no—
485C22—22no—
486C22—22no—
487C22—24no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—24no—
493C22—24no—
494C22—24no—
495C22—42no—
496C22—42no—
497C22—44no—
498C22—42no—
499C22—44no—
500C22—42no—
501C22—416no—
502C22—416no—
503C22—416no—
504C22—416no—
505C22—44no—
506C22—44no—
507C22—48no—
508C22—48no—
509C22#342×C12718yescomplemented
510C22C2×#95×C12711yescharacteristic
511C22C4×C22⋊C4×C12712yes—
512C22#379×C12711yescharacteristic
513C22#380×C12712yes—
514C22#381×C12711yescharacteristic
515C22#385×C12712yes—
516C22#385×C12712yes—
517C22#386×C12712yes—
518C22#386×C12712yes—
519C22C2×#99×C12714yes—
520C4—48no—
521C4—84no—
522C4—84no—
523C2—21no—
524C2—22no—
525C2—28no—
526C2—21no—
527C2—22no—
528C2—22no—
529C2—22no—
530C2—22no—
531C2—44no—
532C2C127×C22⋊#9511yescharacteristic
533C2C2×#342×C12712yes—
534C2C127×#189814yes—
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC23C2×C42×C127
Frattini, cosocleC25C23×C127
prime radicalC26×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C26×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#342×C127C2semidirect
11. C22×C22⋊C4×C127C4semidirect
12. C22×C22⋊C4×C127C4semidirect
20. #379×C127C4semidirect
39. C23×C4×C127C2×C4semidirect
59. C2×C22⋊C4×C127C2×C4semidirect
129. C22⋊C4×C127C22⋊C4semidirect
241. C22×C127#342semidirect
255. #10735C127direct (N × H)
271. C2×#342C2×C127semidirect
272. C127#10735direct (N × H)
279. C22×C22⋊C4C4×C127semidirect
280. C22×C22⋊C4C4×C127semidirect
288. #379C4×C127semidirect
307. C23×C4C2×C4×C127semidirect
327. C2×C22⋊C4C2×C4×C127semidirect
397. C22⋊C4C22⋊C4×C127semidirect
509. C22#342×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1272
C2×#379×C1272
C2×#342×C1272
#10735127