Finite Group Databasebeta

← C127×#14255 #44577928

Subgroups — C127×#14255 #44577928

Order 32512.

3930 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C127C211yesmaximal, characteristic
2C23×C22⋊C4×C127C211yesmaximal, characteristic, complemented
3C2×#386×C127C212yesmaximal, complemented
4C2×#379×C127C211yesmaximal, characteristic, complemented
5C127×#1440C214yesmaximal, complemented
6C127×#1438C214yesmaximal, complemented
7C127×C22⋊#95C212yesmaximal, complemented
8C26×C127C2211yescharacteristic
9C23×D4×C127C2211yescharacteristic
10C23×D4×C127C2212yes—
11C24×C4×C127C2212yes—
12C2×#120×C127—24no—
13C2×#120×C127—24no—
14C2×#120×C127C418yescomplemented
15C22×C22⋊C4×C127—24no—
16C22×C22⋊C4×C127—28no—
17C22×C22⋊C4×C127C2214yes—
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2214yes—
22C22×C22⋊C4×C127C2214yescomplemented
23#386×C127—28no—
24#379×C127—24no—
25C2×#95×C127C2214yescomplemented
26C2×#95×C127C2218yescomplemented
27C25×C127—24no—
28C25×C127—24no—
29C25×C127—48no—
30C25×C127C2×C414yes—
31C25×C127D414yes—
32C25×C127D414yes—
33C25×C127C2311yescharacteristic
34C25×C127C2312yes—
35C25×C127C2311yescharacteristic
36C22×D4×C127—22no—
37C22×D4×C127—22no—
38C22×D4×C127—24no—
39C22×D4×C127—24no—
40C22×D4×C127—24no—
41C22×D4×C127—24no—
42C22×D4×C127—48no—
43C22×D4×C127C2×C414yes—
44C22×D4×C127C2×C418yescomplemented
45C23×C4×C127—24no—
46C23×C4×C127—24no—
47C23×C4×C127—48no—
48C23×C4×C127D418yescomplemented
49C23×C4×C127C2314yes—
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2312yes—
52C23×C4×C127C2314yes—
53#120×C127—232no—
54C2×C22⋊C4×C127—232no—
55C2×C22⋊C4×C127—28no—
56C2×C22⋊C4×C127—22no—
57C2×C22⋊C4×C127—22no—
58C2×C22⋊C4×C127—24no—
59C2×C22⋊C4×C127—24no—
60C2×C22⋊C4×C127—216no—
61C2×C22⋊C4×C127—28no—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—28no—
66C2×C22⋊C4×C127—48no—
67C2×C22⋊C4×C127—48no—
68C2×C22⋊C4×C127C2×C414yes—
69C2×C22⋊C4×C127C2×C418yescomplemented
70#95×C127—28no—
71#95×C127—48no—
72C24×C127—28no—
73C24×C127—216no—
74C24×C127—28no—
75C24×C127—216no—
76C24×C127—28no—
77C24×C127—24no—
78C24×C127—24no—
79C24×C127—28no—
80C24×C127—28no—
81C24×C127—22no—
82C24×C127—21no—
83C24×C127—21no—
84C24×C127—22no—
85C24×C127—28no—
86C24×C127—416no—
87C24×C127—416no—
88C24×C127—416no—
89C24×C127—416no—
90C24×C127—416no—
91C24×C127—432no—
92C24×C127C22⋊C4116yescomplemented
93C24×C127C22×C412yes—
94C24×C127C22×C414yes—
95C24×C127C22×C412yes—
96C24×C127C2×D414yes—
97C24×C127C2×D414yes—
98C24×C127C2×D412yes—
99C24×C127C2×D412yes—
100C24×C127C2×D414yes—
101C24×C127#4114yes—
102C24×C127C2411yescharacteristic
103C2×D4×C127—28no—
104C2×D4×C127—216no—
105C2×D4×C127—216no—
106C2×D4×C127—416no—
107C2×D4×C127—416no—
108C2×D4×C127—416no—
109C2×D4×C127—44no—
110C2×D4×C127—48no—
111C2×D4×C127—44no—
112C22×C4×C127—216no—
113C22×C4×C127—22no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—28no—
122C22×C4×C127—28no—
123C22×C4×C127—28no—
124C22×C4×C127—24no—
125C22×C4×C127—24no—
126C22×C4×C127—24no—
127C22×C4×C127—28no—
128C22×C4×C127—28no—
129C22×C4×C127—416no—
130C22×C4×C127—416no—
131C22×C4×C127—416no—
132C22×C4×C127C22×C414yes—
133C22×C4×C127C22×C412yes—
134C22×C4×C127C2×D418yes—
135C22⋊C4×C127—232no—
136C22⋊C4×C127—28no—
137C22⋊C4×C127—216no—
138C22⋊C4×C127—416no—
139C22⋊C4×C127—416no—
140C22⋊C4×C127—48no—
141C23×C127—28no—
142C23×C127—28no—
143C23×C127—28no—
144C23×C127—28no—
145C23×C127—28no—
146C23×C127—216no—
147C23×C127—28no—
148C23×C127—28no—
149C23×C127—28no—
150C23×C127—24no—
151C23×C127—28no—
152C23×C127—24no—
153C23×C127—28no—
154C23×C127—28no—
155C23×C127—28no—
156C23×C127—28no—
157C23×C127—232no—
158C23×C127—22no—
159C23×C127—24no—
160C23×C127—28no—
161C23×C127—432no—
162C23×C127—464no—
163C23×C127—432no—
164C23×C127—464no—
165C23×C127—432no—
166C23×C127—48no—
167C23×C127—48no—
168C23×C127—416no—
169C23×C127—41no—
170C23×C127—42no—
171C23×C127—41no—
172C23×C127—44no—
173C23×C127—44no—
174C23×C127—44no—
175C23×C127—44no—
176C23×C127—48no—
177C23×C127C2×C22⋊C418yes—
178C23×C127C2×C22⋊C414yes—
179C23×C127C4×D418yes—
180C23×C127#12014yes—
181C23×C127#12118yes—
182C23×C127#12314yes—
183C23×C127C23×C411yescharacteristic
184C23×C127C22×D411yescharacteristic
185C23×C127C22×D411yescharacteristic
186C23×C127C22×D412yes—
187C23×C127C2×#4112yes—
188C23×C127H(5,𝔽2)18yes—
189D4×C127—432no—
190D4×C127—416no—
191C2×C4×C127—24no—
192C2×C4×C127—22no—
193C2×C4×C127—24no—
194C2×C4×C127—28no—
195C2×C4×C127—28no—
196C2×C4×C127—28no—
197C2×C4×C127—28no—
198C2×C4×C127—432no—
199C2×C4×C127—41no—
200C2×C4×C127—42no—
201C2×C4×C127—41no—
202C2×C4×C127—48no—
203C2×C4×C127—44no—
204C2×C4×C127—44no—
205C2×C4×C127—48no—
206C2×C4×C127—44no—
207C2×C4×C127—48no—
208C2×C4×C127—44no—
209C2×C4×C127—44no—
210C2×C4×C127—48no—
211C22×C127—28no—
212C22×C127—216no—
213C22×C127—28no—
214C22×C127—216no—
215C22×C127—28no—
216C22×C127—28no—
217C22×C127—28no—
218C22×C127—28no—
219C22×C127—464no—
220C22×C127—416no—
221C22×C127—48no—
222C22×C127—416no—
223C22×C127—48no—
224C22×C127—44no—
225C22×C127—48no—
226C22×C127—42no—
227C22×C127—82no—
228C22×C127—84no—
229C22×C127—82no—
230C22×C127#38618yes—
231C22×C127C22×C22⋊C411yescharacteristic
232C22×C127C2×C4×D412yes—
233C22×C127#51814yes—
234C22×C127C2×#12011yescharacteristic
235C22×C127C2×#12112yes—
236C22×C127C2×#12311yescharacteristic
237C22×C127#53414yes—
238C22×C127#53414yes—
239C22×C127#53414yes—
240C22×C127#53514yes—
241C22×C127#53818yes—
242C4×C127—44no—
243C4×C127—48no—
244C4×C127—42no—
245C4×C127—84no—
246#14255C12711yesmaximal, characteristic, direct product factor, Sylow
247C2×C127—28no—
248C2×C127—48no—
249C2×C127—82no—
250C2×C127C2×#38611yescharacteristic
251C2×C127#230812yes—
252C2×C127#232114yes—
253C2×C127#261312yes—
254C2×C127#261714yes—
255C2×C127#262212yes—
256C22×#120C2×C12711yescharacteristic
257C23×C22⋊C4C2×C12711yescharacteristic, complemented
258C2×#386C2×C12712yescomplemented
259C2×#379C2×C12711yescharacteristic, complemented
260#1440C2×C12714yescomplemented
261#1438C2×C12714yescomplemented
262C22⋊#95C2×C12712yescomplemented
263C127#1425511yescharacteristic, direct product factor, Sylow
264C26C22×C12711yescharacteristic
265C23×D4C22×C12711yescharacteristic
266C23×D4C22×C12712yes—
267C24×C4C22×C12712yes—
268C2×#120—24no—
269C2×#120—24no—
270C2×#120C4×C12718yescomplemented
271C22×C22⋊C4—24no—
272C22×C22⋊C4—28no—
273C22×C22⋊C4C22×C12714yes—
274C22×C22⋊C4C22×C12712yes—
275C22×C22⋊C4C22×C12711yescharacteristic
276C22×C22⋊C4C22×C12712yes—
277C22×C22⋊C4C22×C12714yes—
278C22×C22⋊C4C22×C12714yescomplemented
279#386—28no—
280#379—24no—
281C2×#95C22×C12714yescomplemented
282C2×#95C22×C12718yescomplemented
283C25—24no—
284C25—24no—
285C25—48no—
286C25C2×C4×C12714yes—
287C25D4×C12714yes—
288C25D4×C12714yes—
289C25C23×C12711yescharacteristic
290C25C23×C12712yes—
291C25C23×C12711yescharacteristic
292C22×D4—22no—
293C22×D4—22no—
294C22×D4—24no—
295C22×D4—24no—
296C22×D4—24no—
297C22×D4—24no—
298C22×D4—48no—
299C22×D4C2×C4×C12714yes—
300C22×D4C2×C4×C12718yescomplemented
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—48no—
304C23×C4D4×C12718yescomplemented
305C23×C4C23×C12714yes—
306C23×C4C23×C12711yescharacteristic
307C23×C4C23×C12712yes—
308C23×C4C23×C12714yes—
309#120—232no—
310C2×C22⋊C4—232no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—216no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—48no—
323C2×C22⋊C4—48no—
324C2×C22⋊C4C2×C4×C12714yes—
325C2×C22⋊C4C2×C4×C12718yescomplemented
326#95—28no—
327#95—48no—
328C24—28no—
329C24—216no—
330C24—28no—
331C24—216no—
332C24—28no—
333C24—24no—
334C24—24no—
335C24—28no—
336C24—28no—
337C24—22no—
338C24—21no—
339C24—21no—
340C24—22no—
341C24—28no—
342C24—416no—
343C24—416no—
344C24—416no—
345C24—416no—
346C24—416no—
347C24—432no—
348C24C22⋊C4×C127116yescomplemented
349C24C22×C4×C12712yes—
350C24C22×C4×C12714yes—
351C24C22×C4×C12712yes—
352C24C2×D4×C12714yes—
353C24C2×D4×C12714yes—
354C24C2×D4×C12712yes—
355C24C2×D4×C12712yes—
356C24C2×D4×C12714yes—
357C24#41×C12714yes—
358C24C24×C12711yescharacteristic
359C2×D4—28no—
360C2×D4—216no—
361C2×D4—216no—
362C2×D4—416no—
363C2×D4—416no—
364C2×D4—416no—
365C2×D4—44no—
366C2×D4—48no—
367C2×D4—44no—
368C22×C4—216no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—28no—
378C22×C4—28no—
379C22×C4—28no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—28no—
384C22×C4—28no—
385C22×C4—416no—
386C22×C4—416no—
387C22×C4—416no—
388C22×C4C22×C4×C12714yes—
389C22×C4C22×C4×C12712yes—
390C22×C4C2×D4×C12718yes—
391C22⋊C4—232no—
392C22⋊C4—28no—
393C22⋊C4—216no—
394C22⋊C4—416no—
395C22⋊C4—416no—
396C22⋊C4—48no—
397C23—28no—
398C23—28no—
399C23—28no—
400C23—28no—
401C23—28no—
402C23—216no—
403C23—28no—
404C23—28no—
405C23—28no—
406C23—24no—
407C23—28no—
408C23—24no—
409C23—28no—
410C23—28no—
411C23—28no—
412C23—28no—
413C23—232no—
414C23—22no—
415C23—24no—
416C23—28no—
417C23—432no—
418C23—464no—
419C23—432no—
420C23—464no—
421C23—432no—
422C23—48no—
423C23—48no—
424C23—416no—
425C23—41no—
426C23—42no—
427C23—41no—
428C23—44no—
429C23—44no—
430C23—44no—
431C23—44no—
432C23—48no—
433C23C2×C22⋊C4×C12718yes—
434C23C2×C22⋊C4×C12714yes—
435C23C4×D4×C12718yes—
436C23#120×C12714yes—
437C23#121×C12718yes—
438C23#123×C12714yes—
439C23C23×C4×C12711yescharacteristic
440C23C22×D4×C12711yescharacteristic
441C23C22×D4×C12711yescharacteristic
442C23C22×D4×C12712yes—
443C23C2×#41×C12712yes—
444C23H(5,𝔽2)×C12718yes—
445D4—432no—
446D4—416no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—28no—
451C2×C4—28no—
452C2×C4—28no—
453C2×C4—28no—
454C2×C4—432no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—41no—
458C2×C4—48no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—48no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—48no—
465C2×C4—44no—
466C2×C4—48no—
467C22—216no—
468C22—28no—
469C22—216no—
470C22—28no—
471C22—28no—
472C22—28no—
473C22—28no—
474C22—28no—
475C22—464no—
476C22—416no—
477C22—48no—
478C22—416no—
479C22—48no—
480C22—48no—
481C22—42no—
482C22—44no—
483C22—82no—
484C22—84no—
485C22—82no—
486C22#386×C12718yes—
487C22C22×C22⋊C4×C12711yescharacteristic
488C22C2×C4×D4×C12712yes—
489C22#518×C12714yes—
490C22C2×#120×C12711yescharacteristic
491C22C2×#121×C12712yes—
492C22C2×#123×C12711yescharacteristic
493C22#534×C12714yes—
494C22#534×C12714yes—
495C22#534×C12714yes—
496C22#535×C12714yes—
497C22#538×C12718yes—
498C4—48no—
499C4—42no—
500C4—44no—
501C4—84no—
502C2—28no—
503C2—48no—
504C2—82no—
505C2C2×#386×C12711yescharacteristic
506C2C127×#230812yes—
507C2C127×#232114yes—
508C2C127×#261312yes—
509C2C127×#261714yes—
510C2C127×#262212yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC22×#120×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C127C2semidirect
3. C2×#386×C127C2semidirect
4. C2×#379×C127C2semidirect
5. C127×#1440C2semidirect
6. C127×#1438C2semidirect
7. C127×C22⋊#95C2semidirect
14. C2×#120×C127C4semidirect
22. C22×C22⋊C4×C127C22semidirect
25. C2×#95×C127C22semidirect
26. C2×#95×C127C22semidirect
44. C22×D4×C127C2×C4semidirect
48. C23×C4×C127D4semidirect
69. C2×C22⋊C4×C127C2×C4semidirect
92. C24×C127C22⋊C4semidirect
246. #14255C127direct (N × H)
257. C23×C22⋊C4C2×C127semidirect
258. C2×#386C2×C127semidirect
259. C2×#379C2×C127semidirect
260. #1440C2×C127semidirect
261. #1438C2×C127semidirect
262. C22⋊#95C2×C127semidirect
263. C127#14255direct (N × H)
270. C2×#120C4×C127semidirect
278. C22×C22⋊C4C22×C127semidirect
281. C2×#95C22×C127semidirect
282. C2×#95C22×C127semidirect
300. C22×D4C2×C4×C127semidirect
304. C23×C4D4×C127semidirect
325. C2×C22⋊C4C2×C4×C127semidirect
348. C24C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1272
C23×C22⋊C4×C1272
C2×#386×C1272
C2×#379×C1272
C127×#14402
C127×#14382
C127×C22⋊#952
#14255127