Finite Group Databasebeta

← C127×#14253 #44577926

Subgroups — C127×#14253 #44577926

Order 32512.

1354 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C127C211yesmaximal, characteristic
2C127×#1443C212yesmaximal, complemented
3C127×#1440C211yesmaximal, characteristic
4C127×#1437C211yesmaximal, characteristic
5C127×#1437C212yesmaximal
6C127×#1437C212yesmaximal
7C127×#1436C212yesmaximal, complemented
8C127×#1434C212yesmaximal, complemented
9C4×#95×C127C212yesmaximal, complemented
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C22⋊C4×C127C2212yes—
12C22×C22⋊C4×C127C2211yescharacteristic
13C22×C22⋊C4×C127C2211yescharacteristic
14C22×C22⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2211yescharacteristic
16C22×C42×C127C2211yescharacteristic
17C22×C42×C127C2212yes—
18C22×C42×C127C2212yes—
19#397×C127C418yescomplemented
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×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C25×C127C2311yescharacteristic
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2311yescharacteristic
36C23×C4×C127C2312yes—
37C23×C4×C127C2311yescharacteristic
38C23×C4×C127C2312yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2312yes—
41C2×C4⋊C4×C127—41no—
42C2×C4⋊C4×C127—41no—
43C2×C4⋊C4×C127C2×C414yes—
44C2×C22⋊C4×C127—24no—
45C2×C22⋊C4×C127—24no—
46C2×C22⋊C4×C127—24no—
47C2×C22⋊C4×C127—24no—
48C2×C22⋊C4×C127—24no—
49C2×C22⋊C4×C127—42no—
50C2×C22⋊C4×C127—42no—
51C2×C22⋊C4×C127—41no—
52C2×C22⋊C4×C127—41no—
53C2×C22⋊C4×C127—41no—
54C2×C22⋊C4×C127—41no—
55C2×C22⋊C4×C127C2×C418yes—
56C2×C22⋊C4×C127C2×C414yes—
57C2×C42×C127—24no—
58C2×C42×C127—24no—
59C2×C42×C127—24no—
60C2×C42×C127—24no—
61C2×C42×C127—41no—
62C2×C42×C127—42no—
63C2×C42×C127—42no—
64C2×C42×C127—42no—
65#95×C127—24no—
66#95×C127—24no—
67#95×C127—24no—
68#95×C127—24no—
69#95×C127—24no—
70#95×C127—24no—
71#95×C127—42no—
72#95×C127—42no—
73#95×C127—42no—
74#95×C127—41no—
75#95×C127C2×C418yes—
76#95×C127C2×C414yes—
77C24×C127—22no—
78C24×C127—22no—
79C24×C127—22no—
80C24×C127—22no—
81C24×C127—22no—
82C24×C127—22no—
83C24×C127—21no—
84C24×C127—21no—
85C24×C127C22×C412yes—
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—22no—
102C22×C4×C127—22no—
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—22no—
112C22×C4×C127—22no—
113C22×C4×C127—21no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—21no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
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×C127C22×C412yes—
131C22×C4×C127C22×C414yes—
132C22×C4×C127C22×C412yes—
133C22×C4×C127C22×C414yes—
134C22×C4×C127#4114yes—
135C22×C4×C127#4114yes—
136C22×C4×C127#4114yes—
137C22×C4×C127#4114yes—
138C22×C4×C127#4114yes—
139C4⋊C4×C127—44no—
140C22⋊C4×C127—44no—
141C22⋊C4×C127—48no—
142C22⋊C4×C127—44no—
143C22⋊C4×C127—44no—
144C22⋊C4×C127—48no—
145C42×C127—44no—
146C42×C127—48no—
147C42×C127—48no—
148C23×C127—22no—
149C23×C127—24no—
150C23×C127—24no—
151C23×C127—22no—
152C23×C127—22no—
153C23×C127—42no—
154C23×C127—42no—
155C23×C127—42no—
156C23×C127—42no—
157C23×C127—42no—
158C23×C127—42no—
159C23×C127—41no—
160C23×C127—41no—
161C23×C127—41no—
162C23×C127—42no—
163C23×C127—42no—
164C23×C127—42no—
165C23×C127—42no—
166C23×C127—42no—
167C23×C127—42no—
168C23×C127—41no—
169C23×C127C23×C411yescharacteristic
170C23×C127C2×#4112yes—
171C23×C127C2×#4112yes—
172C23×C127C2×#4112yes—
173C23×C127C2×#4112yes—
174C23×C127C2×#4112yes—
175C23×C127H(5,𝔽2)11yescharacteristic
176C23×C127H(5,𝔽2)12yes—
177C23×C127H(5,𝔽2)11yescharacteristic
178C2×C4×C127—24no—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
182C2×C4×C127—24no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—24no—
187C2×C4×C127—24no—
188C2×C4×C127—24no—
189C2×C4×C127—22no—
190C2×C4×C127—24no—
191C2×C4×C127—22no—
192C2×C4×C127—24no—
193C2×C4×C127—24no—
194C2×C4×C127—24no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—24no—
198C2×C4×C127—24no—
199C2×C4×C127—24no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—41no—
209C2×C4×C127—42no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—41no—
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#12618yes—
230C22×C127—44no—
231C22×C127—42no—
232C22×C127—42no—
233C22×C127—44no—
234C22×C127—42no—
235C22×C127—82no—
236C22×C127—82no—
237C22×C127—82no—
238C22×C127—82no—
239C22×C127C4×#4111yescharacteristic
240C22×C127C4×#4112yes—
241C22×C127C4×#4112yes—
242C22×C127#51811yescharacteristic
243C22×C127#51811yescharacteristic
244C22×C127C2×#12612yes—
245C22×C127#52912yes—
246C22×C127#52912yes—
247C22×C127#52912yes—
248C22×C127#53812yes—
249C22×C127#54012yes—
250C22×C127#55111yescharacteristic
251C22×C127#55111yescharacteristic
252C22×C127#55112yes—
253C22×C127#55111yescharacteristic
254C22×C127#55312yes—
255C22×C127#55312yes—
256C22×C127#55312yes—
257C22×C127#55512yes—
258C22×C127#55912yes—
259C22×C127#55911yescharacteristic
260C4×C127—28no—
261C4×C127—44no—
262C4×C127—44no—
263C4×C127—42no—
264C4×C127—42no—
265C4×C127—44no—
266C4×C127—44no—
267C4×C127—82no—
268#14253C12711yesmaximal, characteristic, direct product factor, Sylow
269C2×C127—82no—
270C2×C127C4×#12612yes—
271C2×C127#233311yescharacteristic
272C2×C127#237211yescharacteristic
273C2×C127#237412yes—
274C2×C127#237411yescharacteristic
275C2×C127#251012yes—
276C2×C127#251312yes—
277C2×C127#252612yes—
278C2×C127#259512yes—
279C2×#397C2×C12711yescharacteristic
280#1443C2×C12712yescomplemented
281#1440C2×C12711yescharacteristic
282#1437C2×C12711yescharacteristic
283#1437C2×C12712yes—
284#1437C2×C12712yes—
285#1436C2×C12712yescomplemented
286#1434C2×C12712yescomplemented
287C4×#95C2×C12712yescomplemented
288C127#1425311yescharacteristic, direct product factor, Sylow
289C22×C4⋊C4C22×C12711yescharacteristic
290C22×C22⋊C4C22×C12712yes—
291C22×C22⋊C4C22×C12711yescharacteristic
292C22×C22⋊C4C22×C12711yescharacteristic
293C22×C22⋊C4C22×C12712yes—
294C22×C22⋊C4C22×C12711yescharacteristic
295C22×C42C22×C12711yescharacteristic
296C22×C42C22×C12712yes—
297C22×C42C22×C12712yes—
298#397C4×C12718yescomplemented
299C2×#95C22×C12712yes—
300C2×#95C22×C12712yes—
301C2×#95C22×C12712yes—
302C2×#95C22×C12712yes—
303C2×#95C22×C12712yes—
304C2×#95C22×C12712yes—
305C2×#95C22×C12712yes—
306C2×#95C22×C12712yes—
307C2×#95C22×C12712yes—
308C2×#95C22×C12711yescharacteristic
309C2×#95C22×C12712yes—
310C2×#95C22×C12711yescharacteristic
311C25C23×C12711yescharacteristic
312C23×C4C23×C12712yes—
313C23×C4C23×C12711yescharacteristic
314C23×C4C23×C12712yes—
315C23×C4C23×C12712yes—
316C23×C4C23×C12711yescharacteristic
317C23×C4C23×C12712yes—
318C23×C4C23×C12712yes—
319C23×C4C23×C12712yes—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4C2×C4×C12714yes—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—41no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4C2×C4×C12718yes—
335C2×C22⋊C4C2×C4×C12714yes—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—41no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42—42no—
344#95—24no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—41no—
354#95C2×C4×C12718yes—
355#95C2×C4×C12714yes—
356C24—22no—
357C24—22no—
358C24—22no—
359C24—22no—
360C24—22no—
361C24—22no—
362C24—21no—
363C24—21no—
364C24C22×C4×C12712yes—
365C24C24×C12711yescharacteristic
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
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—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4C22×C4×C12712yes—
410C22×C4C22×C4×C12714yes—
411C22×C4C22×C4×C12712yes—
412C22×C4C22×C4×C12714yes—
413C22×C4#41×C12714yes—
414C22×C4#41×C12714yes—
415C22×C4#41×C12714yes—
416C22×C4#41×C12714yes—
417C22×C4#41×C12714yes—
418C4⋊C4—44no—
419C22⋊C4—44no—
420C22⋊C4—48no—
421C22⋊C4—44no—
422C22⋊C4—44no—
423C22⋊C4—48no—
424C42—44no—
425C42—48no—
426C42—48no—
427C23—22no—
428C23—24no—
429C23—24no—
430C23—22no—
431C23—22no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23C23×C4×C12711yescharacteristic
449C23C2×#41×C12712yes—
450C23C2×#41×C12712yes—
451C23C2×#41×C12712yes—
452C23C2×#41×C12712yes—
453C23C2×#41×C12712yes—
454C23H(5,𝔽2)×C12711yescharacteristic
455C23H(5,𝔽2)×C12712yes—
456C23H(5,𝔽2)×C12711yescharacteristic
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—22no—
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—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
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#126×C12718yes—
509C22—42no—
510C22—42no—
511C22—44no—
512C22—42no—
513C22—44no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22C4×#41×C12711yescharacteristic
519C22C4×#41×C12712yes—
520C22C4×#41×C12712yes—
521C22#518×C12711yescharacteristic
522C22#518×C12711yescharacteristic
523C22C2×#126×C12712yes—
524C22#529×C12712yes—
525C22#529×C12712yes—
526C22#529×C12712yes—
527C22#538×C12712yes—
528C22#540×C12712yes—
529C22#551×C12711yescharacteristic
530C22#551×C12711yescharacteristic
531C22#551×C12712yes—
532C22#551×C12711yescharacteristic
533C22#553×C12712yes—
534C22#553×C12712yes—
535C22#553×C12712yes—
536C22#555×C12712yes—
537C22#559×C12712yes—
538C22#559×C12711yescharacteristic
539C4—28no—
540C4—44no—
541C4—44no—
542C4—42no—
543C4—42no—
544C4—44no—
545C4—44no—
546C4—82no—
547C2—82no—
548C2C4×#126×C12712yes—
549C2C127×#233311yescharacteristic
550C2C127×#237211yescharacteristic
551C2C127×#237412yes—
552C2C127×#237411yescharacteristic
553C2C127×#251012yes—
554C2C127×#251312yes—
555C2C127×#252612yes—
556C2C127×#259512yes—
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×#1443C2semidirect
7. C127×#1436C2semidirect
8. C127×#1434C2semidirect
9. C4×#95×C127C2semidirect
19. #397×C127C4semidirect
268. #14253C127direct (N × H)
280. #1443C2×C127semidirect
285. #1436C2×C127semidirect
286. #1434C2×C127semidirect
287. C4×#95C2×C127semidirect
288. C127#14253direct (N × H)
298. #397C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1272
C127×#14432
C127×#14402
C127×#14372
C127×#14362
C127×#14342
C4×#95×C1272
#14253127