Finite Group Databasebeta

← C127×#14257 #44577930

Subgroups — C127×#14257 #44577930

Order 32512.

2662 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×#121×C127C211yesmaximal, characteristic
2C22×#117×C127C211yesmaximal, characteristic, complemented
3C2×#390×C127C212yesmaximal, complemented
4C2×#380×C127C211yesmaximal, characteristic, complemented
5C127×#1439C214yesmaximal, complemented
6C127×#1438C214yesmaximal, complemented
7C127×C4⋊#95C212yesmaximal, complemented
8C23×D4×C127C2211yescharacteristic
9C23×D4×C127C2212yes—
10C24×C4×C127C2211yescharacteristic
11C2×#121×C127—24no—
12C2×#121×C127—24no—
13C2×#121×C127C418yescomplemented
14C2×#117×C127—24no—
15C2×#117×C127—28no—
16C22×C4⋊C4×C127C2212yes—
17C22×C4⋊C4×C127C2212yes—
18C22×C4⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2212yes—
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2218yes—
23C22×C42×C127C2212yes—
24#390×C127—28no—
25#380×C127—24no—
26C2×#95×C127C2212yes—
27C2×#95×C127C2218yes—
28C25×C127C2312yes—
29C25×C127C2311yescharacteristic
30C22×D4×C127—24no—
31C22×D4×C127—24no—
32C22×D4×C127—22no—
33C22×D4×C127—22no—
34C22×D4×C127—24no—
35C22×D4×C127—24no—
36C22×D4×C127—48no—
37C22×D4×C127C2×C414yes—
38C22×D4×C127C2×C418yes—
39C23×C4×C127—24no—
40C23×C4×C127—24no—
41C23×C4×C127C2×C414yes—
42C23×C4×C127D414yes—
43C23×C4×C127D414yes—
44C23×C4×C127C2314yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2314yes—
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2311yescharacteristic
49#121×C127—232no—
50#117×C127—232no—
51C2×C4⋊C4×C127—28no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—24no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127C2×C414yes—
59C2×C22⋊C4×C127—24no—
60C2×C22⋊C4×C127—28no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—216no—
65C2×C22⋊C4×C127—48no—
66C2×C22⋊C4×C127—48no—
67C2×C22⋊C4×C127—44no—
68C2×C22⋊C4×C127C2×C418yes—
69C2×C42×C127—24no—
70C2×C42×C127—24no—
71C2×C42×C127D418yescomplemented
72#95×C127—24no—
73#95×C127—48no—
74C24×C127—22no—
75C24×C127—22no—
76C24×C127—22no—
77C24×C127—24no—
78C24×C127—22no—
79C24×C127—24no—
80C24×C127—22no—
81C24×C127—22no—
82C24×C127—24no—
83C24×C127—24no—
84C24×C127—28no—
85C24×C127—24no—
86C24×C127C22×C414yes—
87C24×C127C22×C412yes—
88C24×C127C2×D412yes—
89C24×C127C2×D412yes—
90C24×C127C2411yescharacteristic
91C2×D4×C127—216no—
92C2×D4×C127—28no—
93C2×D4×C127—216no—
94C2×D4×C127—416no—
95C2×D4×C127—416no—
96C2×D4×C127—416no—
97C2×D4×C127—44no—
98C2×D4×C127—48no—
99C2×D4×C127—44no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—216no—
103C22×C4×C127—28no—
104C22×C4×C127—216no—
105C22×C4×C127—28no—
106C22×C4×C127—24no—
107C22×C4×C127—24no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—24no—
111C22×C4×C127—28no—
112C22×C4×C127—24no—
113C22×C4×C127—24no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127—24no—
117C22×C4×C127—24no—
118C22×C4×C127—28no—
119C22×C4×C127—28no—
120C22×C4×C127C22⋊C4116yescomplemented
121C22×C4×C127C22×C414yes—
122C22×C4×C127C22×C412yes—
123C22×C4×C127C22×C412yes—
124C22×C4×C127C2×D418yes—
125C22×C4×C127C2×D412yes—
126C22×C4×C127C2×D412yes—
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D412yes—
129C22×C4×C127C2×D414yes—
130C22×C4×C127#4114yes—
131C4⋊C4×C127—216no—
132C4⋊C4×C127—28no—
133C4⋊C4×C127—48no—
134C22⋊C4×C127—216no—
135C22⋊C4×C127—216no—
136C22⋊C4×C127—432no—
137C22⋊C4×C127—48no—
138C42×C127—216no—
139C23×C127—24no—
140C23×C127—24no—
141C23×C127—24no—
142C23×C127—22no—
143C23×C127—24no—
144C23×C127—22no—
145C23×C127—22no—
146C23×C127—24no—
147C23×C127—24no—
148C23×C127—22no—
149C23×C127—24no—
150C23×C127—24no—
151C23×C127—28no—
152C23×C127—28no—
153C23×C127—28no—
154C23×C127—44no—
155C23×C127—44no—
156C23×C127—44no—
157C23×C127—44no—
158C23×C127—42no—
159C23×C127—44no—
160C23×C127—42no—
161C23×C127—48no—
162C23×C127—44no—
163C23×C127—44no—
164C23×C127—42no—
165C23×C127—42no—
166C23×C127—44no—
167C23×C127—48no—
168C23×C127—48no—
169C23×C127—48no—
170C23×C127C2×C22⋊C414yes—
171C23×C127C23×C411yescharacteristic
172C23×C127C22×D411yescharacteristic
173C23×C127C22×D411yescharacteristic
174C23×C127C22×D412yes—
175C23×C127C2×#4112yes—
176C23×C127H(5,𝔽2)14yes—
177C23×C127H(5,𝔽2)12yes—
178C23×C1272−1+412yes—
179D4×C127—432no—
180D4×C127—416no—
181C2×C4×C127—24no—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—22no—
185C2×C4×C127—232no—
186C2×C4×C127—24no—
187C2×C4×C127—28no—
188C2×C4×C127—28no—
189C2×C4×C127—28no—
190C2×C4×C127—28no—
191C2×C4×C127—44no—
192C2×C4×C127—44no—
193C2×C4×C127—44no—
194C2×C4×C127—44no—
195C2×C4×C127—44no—
196C2×C4×C127—44no—
197C2×C4×C127—44no—
198C2×C4×C127—44no—
199C2×C4×C127—48no—
200C2×C4×C127—44no—
201C2×C4×C127—48no—
202C2×C4×C127C2×C22⋊C414yes—
203C2×C4×C127C2×C22⋊C414yes—
204C2×C4×C127C4×D418yes—
205C2×C4×C127#12014yes—
206C2×C4×C127#12118yes—
207C2×C4×C127#12314yes—
208C22×C127—24no—
209C22×C127—24no—
210C22×C127—24no—
211C22×C127—48no—
212C22×C127—44no—
213C22×C127—44no—
214C22×C127—44no—
215C22×C127—44no—
216C22×C127—44no—
217C22×C127—44no—
218C22×C127—416no—
219C22×C127—44no—
220C22×C127—84no—
221C22×C127—84no—
222C22×C127—84no—
223C22×C127—84no—
224C22×C127C22×C22⋊C411yescharacteristic
225C22×C127C2×C4×D412yes—
226C22×C127#51812yes—
227C22×C127#52012yes—
228C22×C127C2×#12011yescharacteristic
229C22×C127C2×#12112yes—
230C22×C127C2×#12311yescharacteristic
231C22×C127#53512yes—
232C22×C127#53512yes—
233C22×C127#53511yescharacteristic
234C22×C127#53514yes—
235C22×C127#53611yescharacteristic
236C22×C127#53712yes—
237C22×C127#53714yes—
238C22×C127#54014yes—
239C22×C127#54214yes—
240C4×C127—24no—
241C4×C127—44no—
242C4×C127—48no—
243C4×C127—84no—
244C4×C127#38618yes—
245#14257C12711yesmaximal, characteristic, direct product factor, Sylow
246C2×C127—44no—
247C2×C127—84no—
248C2×C127C2×#38611yescharacteristic
249C2×C127#230911yescharacteristic
250C2×C127#231111yescharacteristic
251C2×C127#232414yes—
252C2×C127#261512yes—
253C2×C127#261912yes—
254C2×C127#262012yes—
255C2×C127#262412yes—
256C22×#121C2×C12711yescharacteristic
257C22×#117C2×C12711yescharacteristic, complemented
258C2×#390C2×C12712yescomplemented
259C2×#380C2×C12711yescharacteristic, complemented
260#1439C2×C12714yescomplemented
261#1438C2×C12714yescomplemented
262C4⋊#95C2×C12712yescomplemented
263C127#1425711yescharacteristic, direct product factor, Sylow
264C23×D4C22×C12711yescharacteristic
265C23×D4C22×C12712yes—
266C24×C4C22×C12711yescharacteristic
267C2×#121—24no—
268C2×#121—24no—
269C2×#121C4×C12718yescomplemented
270C2×#117—24no—
271C2×#117—28no—
272C22×C4⋊C4C22×C12712yes—
273C22×C4⋊C4C22×C12712yes—
274C22×C4⋊C4C22×C12711yescharacteristic
275C22×C22⋊C4C22×C12712yes—
276C22×C22⋊C4C22×C12712yes—
277C22×C22⋊C4C22×C12712yes—
278C22×C22⋊C4C22×C12718yes—
279C22×C42C22×C12712yes—
280#390—28no—
281#380—24no—
282C2×#95C22×C12712yes—
283C2×#95C22×C12718yes—
284C25C23×C12712yes—
285C25C23×C12711yescharacteristic
286C22×D4—24no—
287C22×D4—24no—
288C22×D4—22no—
289C22×D4—22no—
290C22×D4—24no—
291C22×D4—24no—
292C22×D4—48no—
293C22×D4C2×C4×C12714yes—
294C22×D4C2×C4×C12718yes—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4C2×C4×C12714yes—
298C23×C4D4×C12714yes—
299C23×C4D4×C12714yes—
300C23×C4C23×C12714yes—
301C23×C4C23×C12712yes—
302C23×C4C23×C12714yes—
303C23×C4C23×C12711yescharacteristic
304C23×C4C23×C12711yescharacteristic
305#121—232no—
306#117—232no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4C2×C4×C12714yes—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—216no—
321C2×C22⋊C4—48no—
322C2×C22⋊C4—48no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4C2×C4×C12718yes—
325C2×C42—24no—
326C2×C42—24no—
327C2×C42D4×C12718yescomplemented
328#95—24no—
329#95—48no—
330C24—22no—
331C24—22no—
332C24—22no—
333C24—24no—
334C24—22no—
335C24—24no—
336C24—22no—
337C24—22no—
338C24—24no—
339C24—24no—
340C24—28no—
341C24—24no—
342C24C22×C4×C12714yes—
343C24C22×C4×C12712yes—
344C24C2×D4×C12712yes—
345C24C2×D4×C12712yes—
346C24C24×C12711yescharacteristic
347C2×D4—216no—
348C2×D4—28no—
349C2×D4—216no—
350C2×D4—416no—
351C2×D4—416no—
352C2×D4—416no—
353C2×D4—44no—
354C2×D4—48no—
355C2×D4—44no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—216no—
359C22×C4—28no—
360C22×C4—216no—
361C22×C4—28no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—24no—
367C22×C4—28no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—28no—
375C22×C4—28no—
376C22×C4C22⋊C4×C127116yescomplemented
377C22×C4C22×C4×C12714yes—
378C22×C4C22×C4×C12712yes—
379C22×C4C22×C4×C12712yes—
380C22×C4C2×D4×C12718yes—
381C22×C4C2×D4×C12712yes—
382C22×C4C2×D4×C12712yes—
383C22×C4C2×D4×C12712yes—
384C22×C4C2×D4×C12712yes—
385C22×C4C2×D4×C12714yes—
386C22×C4#41×C12714yes—
387C4⋊C4—216no—
388C4⋊C4—28no—
389C4⋊C4—48no—
390C22⋊C4—216no—
391C22⋊C4—216no—
392C22⋊C4—432no—
393C22⋊C4—48no—
394C42—216no—
395C23—24no—
396C23—24no—
397C23—24no—
398C23—22no—
399C23—24no—
400C23—22no—
401C23—22no—
402C23—24no—
403C23—24no—
404C23—22no—
405C23—24no—
406C23—24no—
407C23—28no—
408C23—28no—
409C23—28no—
410C23—44no—
411C23—44no—
412C23—44no—
413C23—44no—
414C23—42no—
415C23—44no—
416C23—42no—
417C23—48no—
418C23—44no—
419C23—44no—
420C23—42no—
421C23—42no—
422C23—48no—
423C23—44no—
424C23—48no—
425C23—48no—
426C23C2×C22⋊C4×C12714yes—
427C23C23×C4×C12711yescharacteristic
428C23C22×D4×C12711yescharacteristic
429C23C22×D4×C12711yescharacteristic
430C23C22×D4×C12712yes—
431C23C2×#41×C12712yes—
432C23H(5,𝔽2)×C12714yes—
433C23H(5,𝔽2)×C12712yes—
434C232−1+4×C12712yes—
435D4—432no—
436D4—416no—
437C2×C4—24no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—232no—
442C2×C4—24no—
443C2×C4—28no—
444C2×C4—28no—
445C2×C4—28no—
446C2×C4—28no—
447C2×C4—44no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—48no—
455C2×C4—44no—
456C2×C4—44no—
457C2×C4—48no—
458C2×C4C2×C22⋊C4×C12714yes—
459C2×C4C2×C22⋊C4×C12714yes—
460C2×C4C4×D4×C12718yes—
461C2×C4#120×C12714yes—
462C2×C4#121×C12718yes—
463C2×C4#123×C12714yes—
464C22—24no—
465C22—24no—
466C22—24no—
467C22—48no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22—44no—
472C22—416no—
473C22—44no—
474C22—44no—
475C22—44no—
476C22—84no—
477C22—84no—
478C22—84no—
479C22—84no—
480C22C22×C22⋊C4×C12711yescharacteristic
481C22C2×C4×D4×C12712yes—
482C22#518×C12712yes—
483C22#520×C12712yes—
484C22C2×#120×C12711yescharacteristic
485C22C2×#121×C12712yes—
486C22C2×#123×C12711yescharacteristic
487C22#535×C12714yes—
488C22#535×C12712yes—
489C22#535×C12711yescharacteristic
490C22#535×C12712yes—
491C22#536×C12711yescharacteristic
492C22#537×C12714yes—
493C22#537×C12712yes—
494C22#540×C12714yes—
495C22#542×C12714yes—
496C4—24no—
497C4—48no—
498C4—44no—
499C4—84no—
500C4#386×C12718yes—
501C2—44no—
502C2—84no—
503C2C2×#386×C12711yescharacteristic
504C2C127×#230911yescharacteristic
505C2C127×#231111yescharacteristic
506C2C127×#232414yes—
507C2C127×#261512yes—
508C2C127×#261912yes—
509C2C127×#262012yes—
510C2C127×#262412yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC22×#121×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#117×C127C2semidirect
3. C2×#390×C127C2semidirect
4. C2×#380×C127C2semidirect
5. C127×#1439C2semidirect
6. C127×#1438C2semidirect
7. C127×C4⋊#95C2semidirect
13. C2×#121×C127C4semidirect
71. C2×C42×C127D4semidirect
120. C22×C4×C127C22⋊C4semidirect
245. #14257C127direct (N × H)
257. C22×#117C2×C127semidirect
258. C2×#390C2×C127semidirect
259. C2×#380C2×C127semidirect
260. #1439C2×C127semidirect
261. #1438C2×C127semidirect
262. C4⋊#95C2×C127semidirect
263. C127#14257direct (N × H)
269. C2×#121C4×C127semidirect
327. C2×C42D4×C127semidirect
376. C22×C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1272
C22×#117×C1272
C2×#390×C1272
C2×#380×C1272
C127×#14392
C127×#14382
C127×C4⋊#952
#14257127