Finite Group Databasebeta

← C127×#11009 #44574682

Subgroups — C127×#11009 #44574682

Order 32512.

1558 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C127C211yesmaximal, characteristic
2C22×#103×C127C212yesmaximal, complemented
3C22×#102×C127C212yesmaximal
4C2×#336×C127C211yesmaximal, characteristic, complemented
5C127×C4⋊#95C211yesmaximal, characteristic, complemented
6C23×Q8×C127C2211yescharacteristic
7C23×D4×C127C2211yescharacteristic
8C23×C8×C127C2212yes—
9C2×#124×C127—24no—
10C2×#124×C127—24no—
11C2×#124×C127—22no—
12C2×#124×C127C414yescomplemented
13C22×C4⋊C4×C127C2212yes—
14C22×C22⋊C4×C127—22no—
15C22×C42×C127C2211yescharacteristic
16C2×#103×C127—24no—
17C2×#103×C127—24no—
18C2×#103×C127—24no—
19C2×#102×C127—24no—
20C2×#102×C127—24no—
21C2×#102×C127—24no—
22C2×#95×C127—22no—
23#336×C127—22no—
24C25×C127—21no—
25C22×Q8×C127—21no—
26C22×Q8×C127—22no—
27C22×Q8×C127—22no—
28C22×Q8×C127—22no—
29C22×Q8×C127—22no—
30C22×Q8×C127—22no—
31C22×Q8×C127C2×C412yes—
32C22×Q8×C127D414yes—
33C22×D4×C127—22no—
34C22×D4×C127—22no—
35C22×D4×C127—22no—
36C22×D4×C127—21no—
37C22×D4×C127—22no—
38C22×D4×C127—22no—
39C22×D4×C127C2×C412yes—
40C22×D4×C127D414yes—
41C23×C4×C127—21no—
42C23×C4×C127—22no—
43C23×C4×C127D412yes—
44C23×C4×C127C2311yescharacteristic
45C22×C8×C127—22no—
46C22×C8×C127—22no—
47C22×C8×C127—22no—
48C22×C8×C127—22no—
49C22×C8×C127—22no—
50C22×C8×C127—22no—
51C22×C8×C127D414yes—
52#124×C127—216no—
53#124×C127—28no—
54#124×C127—28no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127D414yes—
61C2×C22⋊C4×C127—216no—
62C2×C22⋊C4×C127—28no—
63C2×C42×C127—22no—
64C2×C42×C127—22no—
65C2×C42×C127C2×C412yes—
66C2×C42×C127D412yes—
67#103×C127—216no—
68#102×C127—216no—
69#95×C127—44no—
70C24×C127—22no—
71C24×C127—24no—
72C24×C127—42no—
73C24×C127—41no—
74C24×C127—41no—
75C24×C127—44no—
76C24×C127—42no—
77C24×C127—42no—
78C24×C127C2×D411yescharacteristic
79C2×Q8×C127—22no—
80C2×Q8×C127—24no—
81C2×Q8×C127—24no—
82C2×Q8×C127—24no—
83C2×Q8×C127—24no—
84C2×Q8×C127—24no—
85C2×Q8×C127—24no—
86C2×Q8×C127—24no—
87C2×Q8×C127—42no—
88C2×Q8×C127—42no—
89C2×Q8×C127—42no—
90C2×Q8×C127—42no—
91C2×Q8×C127—42no—
92C2×Q8×C127—41no—
93C2×Q8×C127—41no—
94C2×Q8×C127C22⋊C414yes—
95C2×D4×C127—22no—
96C2×D4×C127—24no—
97C2×D4×C127—24no—
98C2×D4×C127—24no—
99C2×D4×C127—24no—
100C2×D4×C127—24no—
101C2×D4×C127—24no—
102C2×D4×C127—24no—
103C2×D4×C127—42no—
104C2×D4×C127—42no—
105C2×D4×C127—42no—
106C2×D4×C127—42no—
107C2×D4×C127—42no—
108C2×D4×C127—41no—
109C2×D4×C127—41no—
110C2×D4×C127C22⋊C414yes—
111C22×C4×C127—22no—
112C22×C4×C127—24no—
113C22×C4×C127—24no—
114C22×C4×C127—24no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—24no—
118C22×C4×C127—42no—
119C22×C4×C127—41no—
120C22×C4×C127—41no—
121C22×C4×C127—42no—
122C22×C4×C127—42no—
123C22×C4×C127—44no—
124C22×C4×C127—44no—
125C22×C4×C127C22⋊C414yes—
126C22×C4×C127C22×C411yescharacteristic
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D412yes—
129C22×C4×C127C2×D412yes—
130C22×C4×C127C2×D412yes—
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127#4112yes—
133C22×C4×C127#4112yes—
134C2×C8×C127—24no—
135C2×C8×C127—24no—
136C2×C8×C127—24no—
137C2×C8×C127—42no—
138C2×C8×C127—42no—
139C2×C8×C127—42no—
140C2×C8×C127—42no—
141C4⋊C4×C127—24no—
142C4⋊C4×C127—24no—
143C4⋊C4×C127—42no—
144C4⋊C4×C127—42no—
145C22⋊C4×C127—232no—
146C42×C127—22no—
147C42×C127—22no—
148C42×C127—24no—
149C23×C127—24no—
150C23×C127—42no—
151C23×C127—42no—
152C23×C127—44no—
153C23×C127—44no—
154C23×C127—44no—
155C23×C127—44no—
156C23×C127—48no—
157C23×C127—48no—
158C23×C127—84no—
159C23×C127—84no—
160C23×C127—82no—
161C23×C127—82no—
162C23×C127—82no—
163C23×C127—81no—
164C23×C127—81no—
165C23×C127C2×C22⋊C411yescharacteristic
166C23×C127#12012yes—
167C23×C127#12112yes—
168C23×C127#12411yescharacteristic
169C23×C127#12711yescharacteristic
170C23×C127#13514yes—
171C23×C127AGL(1,ℤ/8)12yes—
172C23×C127#13712yes—
173Q8×C127—28no—
174Q8×C127—44no—
175Q8×C127—44no—
176Q8×C127—44no—
177D4×C127—28no—
178D4×C127—44no—
179D4×C127—44no—
180D4×C127—44no—
181C2×C4×C127—24no—
182C2×C4×C127—24no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—44no—
188C2×C4×C127—44no—
189C2×C4×C127—44no—
190C2×C4×C127—44no—
191C2×C4×C127—44no—
192C2×C4×C127—48no—
193C2×C4×C127—84no—
194C2×C4×C127—82no—
195C2×C4×C127—82no—
196C2×C4×C127C2×C22⋊C411yescharacteristic
197C2×C4×C127C2×C22⋊C411yescharacteristic
198C2×C4×C127C4×D412yes—
199C2×C4×C127C4×D412yes—
200C2×C4×C127#12012yes—
201C2×C4×C127#12012yes—
202C2×C4×C127#12012yes—
203C2×C4×C127#12112yes—
204C2×C4×C127#12112yes—
205C2×C4×C127#12112yes—
206C2×C4×C127#12112yes—
207C2×C4×C127#12112yes—
208C2×C4×C127#12312yes—
209C2×C4×C127#12312yes—
210C2×C4×C127#12411yescharacteristic
211C2×C4×C127#12711yescharacteristic
212C8×C127—44no—
213C22×C127—44no—
214C22×C127—48no—
215C22×C127—82no—
216C22×C127—82no—
217C22×C127—84no—
218C22×C127—84no—
219C22×C127—84no—
220C22×C127—88no—
221C22×C127#37911yescharacteristic
222C22×C127#39011yescharacteristic
223C22×C127#39011yescharacteristic
224C22×C127#39212yes—
225C22×C127#39412yes—
226C22×C127#41612yes—
227C22×C127#41712yes—
228C22×C127#44914yes—
229C22×C127#45214yes—
230C22×C127#46314yes—
231C22×C127#46414yes—
232C22×C127#48812yes—
233C22×C127#48912yes—
234C22×C127#49512yes—
235C22×C127#49611yescharacteristic
236C22×C127#49711yescharacteristic
237C4×C127—44no—
238C4×C127—44no—
239C4×C127—84no—
240C4×C127#38612yes—
241C4×C127#38612yes—
242C4×C127#39212yes—
243C4×C127#39412yes—
244#11009C12711yesmaximal, characteristic, direct product factor, Sylow
245C2×C127—84no—
246C2×C127#143811yescharacteristic
247C2×C127#178812yes—
248C2×C127#195811yescharacteristic
249C2×C127#195911yescharacteristic
250C2×C127#198312yes—
251C2×C127#201212yes—
252C2×C127#201512yes—
253C2×C127#204214yes—
254C22×#124C2×C12711yescharacteristic
255C22×#103C2×C12712yescomplemented
256C22×#102C2×C12712yes—
257C2×#336C2×C12711yescharacteristic, complemented
258C4⋊#95C2×C12711yescharacteristic, complemented
259C127#1100911yescharacteristic, direct product factor, Sylow
260C23×Q8C22×C12711yescharacteristic
261C23×D4C22×C12711yescharacteristic
262C23×C8C22×C12712yes—
263C2×#124—24no—
264C2×#124—24no—
265C2×#124—22no—
266C2×#124C4×C12714yescomplemented
267C22×C4⋊C4C22×C12712yes—
268C22×C22⋊C4—22no—
269C22×C42C22×C12711yescharacteristic
270C2×#103—24no—
271C2×#103—24no—
272C2×#103—24no—
273C2×#102—24no—
274C2×#102—24no—
275C2×#102—24no—
276C2×#95—22no—
277#336—22no—
278C25—21no—
279C22×Q8—21no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—22no—
284C22×Q8—22no—
285C22×Q8C2×C4×C12712yes—
286C22×Q8D4×C12714yes—
287C22×D4—22no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—21no—
291C22×D4—22no—
292C22×D4—22no—
293C22×D4C2×C4×C12712yes—
294C22×D4D4×C12714yes—
295C23×C4—21no—
296C23×C4—22no—
297C23×C4D4×C12712yes—
298C23×C4C23×C12711yescharacteristic
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8D4×C12714yes—
306#124—216no—
307#124—28no—
308#124—28no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4D4×C12714yes—
315C2×C22⋊C4—216no—
316C2×C22⋊C4—28no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42C2×C4×C12712yes—
320C2×C42D4×C12712yes—
321#103—216no—
322#102—216no—
323#95—44no—
324C24—22no—
325C24—24no—
326C24—42no—
327C24—41no—
328C24—41no—
329C24—44no—
330C24—42no—
331C24—42no—
332C24C2×D4×C12711yescharacteristic
333C2×Q8—22no—
334C2×Q8—24no—
335C2×Q8—24no—
336C2×Q8—24no—
337C2×Q8—24no—
338C2×Q8—24no—
339C2×Q8—24no—
340C2×Q8—24no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8—42no—
344C2×Q8—42no—
345C2×Q8—42no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8C22⋊C4×C12714yes—
349C2×D4—22no—
350C2×D4—24no—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—24no—
354C2×D4—24no—
355C2×D4—24no—
356C2×D4—24no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4C22⋊C4×C12714yes—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—42no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—44no—
378C22×C4—44no—
379C22×C4C22⋊C4×C12714yes—
380C22×C4C22×C4×C12711yescharacteristic
381C22×C4C2×D4×C12712yes—
382C22×C4C2×D4×C12712yes—
383C22×C4C2×D4×C12712yes—
384C22×C4C2×D4×C12712yes—
385C22×C4C2×D4×C12711yescharacteristic
386C22×C4#41×C12712yes—
387C22×C4#41×C12712yes—
388C2×C8—24no—
389C2×C8—24no—
390C2×C8—24no—
391C2×C8—42no—
392C2×C8—42no—
393C2×C8—42no—
394C2×C8—42no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C22⋊C4—232no—
400C42—22no—
401C42—22no—
402C42—24no—
403C23—24no—
404C23—42no—
405C23—42no—
406C23—44no—
407C23—44no—
408C23—44no—
409C23—44no—
410C23—48no—
411C23—48no—
412C23—81no—
413C23—81no—
414C23—84no—
415C23—84no—
416C23—82no—
417C23—82no—
418C23—82no—
419C23C2×C22⋊C4×C12711yescharacteristic
420C23#120×C12712yes—
421C23#121×C12712yes—
422C23#124×C12711yescharacteristic
423C23#127×C12711yescharacteristic
424C23#135×C12714yes—
425C23AGL(1,ℤ/8)×C12712yes—
426C23#137×C12712yes—
427Q8—28no—
428Q8—44no—
429Q8—44no—
430Q8—44no—
431D4—28no—
432D4—44no—
433D4—44no—
434D4—44no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—48no—
447C2×C4—82no—
448C2×C4—84no—
449C2×C4—82no—
450C2×C4C2×C22⋊C4×C12711yescharacteristic
451C2×C4C2×C22⋊C4×C12711yescharacteristic
452C2×C4C4×D4×C12712yes—
453C2×C4C4×D4×C12712yes—
454C2×C4#120×C12712yes—
455C2×C4#120×C12712yes—
456C2×C4#120×C12712yes—
457C2×C4#121×C12712yes—
458C2×C4#121×C12712yes—
459C2×C4#121×C12712yes—
460C2×C4#121×C12712yes—
461C2×C4#121×C12712yes—
462C2×C4#123×C12712yes—
463C2×C4#123×C12712yes—
464C2×C4#124×C12711yescharacteristic
465C2×C4#127×C12711yescharacteristic
466C8—44no—
467C22—44no—
468C22—48no—
469C22—82no—
470C22—82no—
471C22—84no—
472C22—84no—
473C22—84no—
474C22—88no—
475C22#379×C12711yescharacteristic
476C22#390×C12711yescharacteristic
477C22#390×C12711yescharacteristic
478C22#392×C12712yes—
479C22#394×C12712yes—
480C22#416×C12712yes—
481C22#417×C12712yes—
482C22#449×C12714yes—
483C22#452×C12714yes—
484C22#463×C12714yes—
485C22#464×C12714yes—
486C22#488×C12712yes—
487C22#489×C12712yes—
488C22#495×C12712yes—
489C22#496×C12711yescharacteristic
490C22#497×C12711yescharacteristic
491C4—44no—
492C4—44no—
493C4—84no—
494C4#386×C12712yes—
495C4#386×C12712yes—
496C4#392×C12712yes—
497C4#394×C12712yes—
498C2—84no—
499C2C127×#143811yescharacteristic
500C2C127×#178812yes—
501C2C127×#195811yescharacteristic
502C2C127×#195911yescharacteristic
503C2C127×#198312yes—
504C2C127×#201212yes—
505C2C127×#201512yes—
506C2C127×#204214yes—
subgroupG/H
center, socleC24×C127C2×D4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC23×D4×C127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#103×C127C2semidirect
4. C2×#336×C127C2semidirect
5. C127×C4⋊#95C2semidirect
12. C2×#124×C127C4semidirect
244. #11009C127direct (N × H)
255. C22×#103C2×C127semidirect
257. C2×#336C2×C127semidirect
258. C4⋊#95C2×C127semidirect
259. C127#11009direct (N × H)
266. C2×#124C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1272
C22×#103×C1272
C22×#102×C1272
C2×#336×C1272
C127×C4⋊#952
#11009127