Finite Group Databasebeta

← C127×#14515 #44578188

Subgroups — C127×#14515 #44578188

Order 32512.

1406 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#385×C127C211yesmaximal, characteristic
2C127×#1445C212yesmaximal, complemented
3C127×#1443C212yesmaximal, complemented
4C127×#1440C212yesmaximal
5C127×#1437C211yesmaximal, characteristic
6C127×#1437C211yesmaximal, characteristic
7C127×#1436C212yesmaximal, complemented
8C127×#1434C212yesmaximal, complemented
9C127×C22⋊#95C212yesmaximal
10C24×C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C22⋊C4×C127C2212yes—
13C22×C22⋊C4×C127C2212yes—
14C22×C22⋊C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2211yescharacteristic
16C22×C42×C127C2211yescharacteristic
17C22×C42×C127C2211yescharacteristic
18#385×C127C418yescomplemented
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C25×C127C2311yescharacteristic
33C23×C4×C127—41no—
34C23×C4×C127—41no—
35C23×C4×C127—42no—
36C23×C4×C127—42no—
37C23×C4×C127C2×C414yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C2×C4⋊C4×C127—42no—
47C2×C4⋊C4×C127—42no—
48C2×C4⋊C4×C127C2×C418yes—
49C2×C22⋊C4×C127—24no—
50C2×C22⋊C4×C127—24no—
51C2×C22⋊C4×C127—24no—
52C2×C22⋊C4×C127—24no—
53C2×C22⋊C4×C127—24no—
54C2×C22⋊C4×C127—41no—
55C2×C22⋊C4×C127—41no—
56C2×C22⋊C4×C127—42no—
57C2×C22⋊C4×C127—42no—
58C2×C22⋊C4×C127C2×C414yes—
59C2×C22⋊C4×C127C2×C414yes—
60C2×C42×C127—24no—
61C2×C42×C127—41no—
62C2×C42×C127—41no—
63C2×C42×C127—42no—
64#95×C127—24no—
65#95×C127—24no—
66#95×C127—24no—
67#95×C127—42no—
68#95×C127—42no—
69#95×C127—42no—
70#95×C127—42no—
71#95×C127—42no—
72#95×C127—41no—
73#95×C127—41no—
74#95×C127—42no—
75#95×C127—42no—
76#95×C127C2×C418yes—
77C24×C127—22no—
78C24×C127—22no—
79C24×C127—21no—
80C24×C127—21no—
81C24×C127—22no—
82C24×C127—22no—
83C24×C127—22no—
84C24×C127C22×C412yes—
85C24×C127#4114yes—
86C24×C127C2411yescharacteristic
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—48no—
134C22×C4×C127—44no—
135C22×C4×C127—48no—
136C22×C4×C127—44no—
137C22×C4×C127—44no—
138C22×C4×C127C22×C412yes—
139C22×C4×C127C22×C414yes—
140C22×C4×C127C22×C414yes—
141C22×C4×C127C22×C412yes—
142C22×C4×C127#4114yes—
143C22×C4×C127#4114yes—
144C4⋊C4×C127—48no—
145C22⋊C4×C127—28no—
146C22⋊C4×C127—44no—
147C22⋊C4×C127—48no—
148C22⋊C4×C127—48no—
149C42×C127—44no—
150C42×C127—44no—
151C23×C127—24no—
152C23×C127—22no—
153C23×C127—24no—
154C23×C127—22no—
155C23×C127—24no—
156C23×C127—24no—
157C23×C127—24no—
158C23×C127—24no—
159C23×C127—24no—
160C23×C127—24no—
161C23×C127—42no—
162C23×C127—42no—
163C23×C127—42no—
164C23×C127—42no—
165C23×C127—41no—
166C23×C127—42no—
167C23×C127—41no—
168C23×C127—42no—
169C23×C127—41no—
170C23×C127—41no—
171C23×C127#11714yes—
172C23×C127C23×C411yescharacteristic
173C23×C127C2×#4112yes—
174C23×C127C2×#4112yes—
175C23×C127C2×#4112yes—
176C23×C127H(5,𝔽2)12yes—
177C23×C127H(5,𝔽2)11yescharacteristic
178C23×C127H(5,𝔽2)11yescharacteristic
179C23×C127H(5,𝔽2)12yes—
180C23×C1272−1+412yes—
181C2×C4×C127—24no—
182C2×C4×C127—24no—
183C2×C4×C127—24no—
184C2×C4×C127—22no—
185C2×C4×C127—22no—
186C2×C4×C127—24no—
187C2×C4×C127—24no—
188C2×C4×C127—24no—
189C2×C4×C127—24no—
190C2×C4×C127—24no—
191C2×C4×C127—24no—
192C2×C4×C127—24no—
193C2×C4×C127—24no—
194C2×C4×C127—24no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—416no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—41no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—41no—
211C2×C4×C127—42no—
212C2×C4×C127—41no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—41no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—42no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
233C2×C4×C127—42no—
234C22×C127—24no—
235C22×C127—28no—
236C22×C127—44no—
237C22×C127—42no—
238C22×C127—42no—
239C22×C127—44no—
240C22×C127—44no—
241C22×C127—44no—
242C22×C127—44no—
243C22×C127C2×#11711yescharacteristic
244C22×C127C4×#4112yes—
245C22×C127#51811yescharacteristic
246C22×C127#51812yes—
247C22×C127#51911yescharacteristic
248C22×C127#53912yes—
249C22×C127#53912yes—
250C22×C127#53912yes—
251C22×C127#53912yes—
252C22×C127#54212yes—
253C22×C127#54212yes—
254C22×C127#55112yes—
255C22×C127#55112yes—
256C22×C127#55111yescharacteristic
257C22×C127#55312yes—
258C22×C127#55312yes—
259C22×C127#55312yes—
260C22×C127#55911yescharacteristic
261C22×C127#56012yes—
262C22×C127#56011yescharacteristic
263C22×C127H(3,𝔽4)11yescharacteristic
264C4×C127—44no—
265C4×C127—42no—
266C4×C127—42no—
267C4×C127—44no—
268C4×C127—44no—
269C4×C127—44no—
270C4×C127—82no—
271C4×C127—82no—
272#14515C12711yesmaximal, characteristic, direct product factor, Sylow
273C2×C127—44no—
274C2×C127#231311yescharacteristic
275C2×C127#233212yes—
276C2×C127#235312yes—
277C2×C127#237411yescharacteristic
278C2×C127#237511yescharacteristic
279C2×C127#274612yes—
280C2×C127#275712yes—
281C2×C127#278212yes—
282C2×C127#279612yes—
283C2×#385C2×C12711yescharacteristic
284#1445C2×C12712yescomplemented
285#1443C2×C12712yescomplemented
286#1440C2×C12712yes—
287#1437C2×C12711yescharacteristic
288#1437C2×C12711yescharacteristic
289#1436C2×C12712yescomplemented
290#1434C2×C12712yescomplemented
291C22⋊#95C2×C12712yes—
292C127#1451511yescharacteristic, direct product factor, Sylow
293C24×C4C22×C12711yescharacteristic
294C22×C4⋊C4C22×C12712yes—
295C22×C22⋊C4C22×C12712yes—
296C22×C22⋊C4C22×C12712yes—
297C22×C22⋊C4C22×C12711yescharacteristic
298C22×C22⋊C4C22×C12711yescharacteristic
299C22×C42C22×C12711yescharacteristic
300C22×C42C22×C12711yescharacteristic
301#385C4×C12718yescomplemented
302C2×#95C22×C12712yes—
303C2×#95C22×C12712yes—
304C2×#95C22×C12712yes—
305C2×#95C22×C12712yes—
306C2×#95C22×C12712yes—
307C2×#95C22×C12712yes—
308C2×#95C22×C12712yes—
309C2×#95C22×C12712yes—
310C2×#95C22×C12712yes—
311C2×#95C22×C12711yescharacteristic
312C2×#95C22×C12711yescharacteristic
313C2×#95C22×C12712yes—
314C2×#95C22×C12712yes—
315C25C23×C12711yescharacteristic
316C23×C4—41no—
317C23×C4—41no—
318C23×C4—42no—
319C23×C4—42no—
320C23×C4C2×C4×C12714yes—
321C23×C4C23×C12712yes—
322C23×C4C23×C12712yes—
323C23×C4C23×C12711yescharacteristic
324C23×C4C23×C12712yes—
325C23×C4C23×C12711yescharacteristic
326C23×C4C23×C12712yes—
327C23×C4C23×C12712yes—
328C23×C4C23×C12712yes—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4C2×C4×C12718yes—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4C2×C4×C12714yes—
342C2×C22⋊C4C2×C4×C12714yes—
343C2×C42—24no—
344C2×C42—41no—
345C2×C42—41no—
346C2×C42—42no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—41no—
356#95—41no—
357#95—42no—
358#95—42no—
359#95C2×C4×C12718yes—
360C24—22no—
361C24—22no—
362C24—21no—
363C24—21no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24C22×C4×C12712yes—
368C24#41×C12714yes—
369C24C24×C12711yescharacteristic
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—48no—
417C22×C4—44no—
418C22×C4—48no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4C22×C4×C12712yes—
422C22×C4C22×C4×C12714yes—
423C22×C4C22×C4×C12714yes—
424C22×C4C22×C4×C12712yes—
425C22×C4#41×C12714yes—
426C22×C4#41×C12714yes—
427C4⋊C4—48no—
428C22⋊C4—28no—
429C22⋊C4—44no—
430C22⋊C4—48no—
431C22⋊C4—48no—
432C42—44no—
433C42—44no—
434C23—24no—
435C23—22no—
436C23—24no—
437C23—22no—
438C23—24no—
439C23—24no—
440C23—24no—
441C23—24no—
442C23—24no—
443C23—24no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—41no—
449C23—42no—
450C23—41no—
451C23—42no—
452C23—41no—
453C23—41no—
454C23#117×C12714yes—
455C23C23×C4×C12711yescharacteristic
456C23C2×#41×C12712yes—
457C23C2×#41×C12712yes—
458C23C2×#41×C12712yes—
459C23H(5,𝔽2)×C12712yes—
460C23H(5,𝔽2)×C12711yescharacteristic
461C23H(5,𝔽2)×C12711yescharacteristic
462C23H(5,𝔽2)×C12712yes—
463C232−1+4×C12712yes—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—416no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C22—24no—
518C22—28no—
519C22—44no—
520C22—42no—
521C22—42no—
522C22—44no—
523C22—44no—
524C22—44no—
525C22—44no—
526C22C2×#117×C12711yescharacteristic
527C22C4×#41×C12712yes—
528C22#518×C12711yescharacteristic
529C22#518×C12712yes—
530C22#519×C12711yescharacteristic
531C22#539×C12712yes—
532C22#539×C12712yes—
533C22#539×C12712yes—
534C22#539×C12712yes—
535C22#542×C12712yes—
536C22#542×C12712yes—
537C22#551×C12712yes—
538C22#551×C12712yes—
539C22#551×C12711yescharacteristic
540C22#553×C12712yes—
541C22#553×C12712yes—
542C22#553×C12712yes—
543C22#559×C12711yescharacteristic
544C22#560×C12712yes—
545C22#560×C12711yescharacteristic
546C22H(3,𝔽4)×C12711yescharacteristic
547C4—44no—
548C4—42no—
549C4—44no—
550C4—42no—
551C4—44no—
552C4—44no—
553C4—82no—
554C4—82no—
555C2—44no—
556C2C127×#231311yescharacteristic
557C2C127×#233212yes—
558C2C127×#235312yes—
559C2C127×#237411yescharacteristic
560C2C127×#237511yescharacteristic
561C2C127×#274612yes—
562C2C127×#275712yes—
563C2C127×#278212yes—
564C2C127×#279612yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1445C2semidirect
3. C127×#1443C2semidirect
7. C127×#1436C2semidirect
8. C127×#1434C2semidirect
18. #385×C127C4semidirect
272. #14515C127direct (N × H)
284. #1445C2×C127semidirect
285. #1443C2×C127semidirect
289. #1436C2×C127semidirect
290. #1434C2×C127semidirect
292. C127#14515direct (N × H)
301. #385C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#385×C1272
C127×#14452
C127×#14432
C127×#14402
C127×#14372
C127×#14362
C127×#14342
C127×C22⋊#952
#14515127