Finite Group Databasebeta

← C127×#14286 #44577959

Subgroups — C127×#14286 #44577959

Order 32512.

1146 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
1C2×#389×C127C211yesmaximal, characteristic
2C127×#1445C212yesmaximal
3C127×#1445C212yesmaximal
4C127×#1441C212yesmaximal
5C127×#1441C212yesmaximal
6C127×#1436C212yesmaximal
7C127×#1434C211yesmaximal, characteristic
8C127×#1434C212yesmaximal
9C4×#95×C127C211yesmaximal, characteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C42×C127C2211yescharacteristic
15C22×C42×C127C2211yescharacteristic
16C22×C42×C127C2211yescharacteristic
17#389×C127C418yescomplemented
18C2×#95×C127C2212yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2211yescharacteristic
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C23×C4×C127C2312yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2311yescharacteristic
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2311yescharacteristic
41C2×C4⋊C4×C127—24no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—41no—
44C2×C4⋊C4×C127—41no—
45C2×C4⋊C4×C127—42no—
46C2×C4⋊C4×C127—42no—
47C2×C4⋊C4×C127—42no—
48C2×C4⋊C4×C127—42no—
49C2×C4⋊C4×C127C2×C414yes—
50C2×C4⋊C4×C127C2×C418yes—
51C2×C4⋊C4×C127C2×C414yes—
52C2×C42×C127—22no—
53C2×C42×C127—41no—
54C2×C42×C127—41no—
55C2×C42×C127—41no—
56C2×C42×C127—41no—
57C2×C42×C127—41no—
58C2×C42×C127—41no—
59C2×C42×C127C2×C414yes—
60C2×C42×C127Q814yes—
61#95×C127—24no—
62#95×C127—24no—
63#95×C127—24no—
64#95×C127—24no—
65#95×C127—24no—
66#95×C127—42no—
67#95×C127—42no—
68#95×C127—42no—
69#95×C127—42no—
70#95×C127—42no—
71#95×C127—41no—
72#95×C127—41no—
73#95×C127—42no—
74#95×C127C2×C418yes—
75C24×C127C2411yescharacteristic
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—22no—
82C22×C4×C127—21no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
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—21no—
95C22×C4×C127—21no—
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—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×C127C22×C414yes—
126C22×C4×C127C22×C414yes—
127C22×C4×C127C22×C412yes—
128C22×C4×C127C22×C412yes—
129C22×C4×C127C22×C412yes—
130C22×C4×C127C2×Q814yes—
131C22×C4×C127C2×Q812yes—
132C22×C4×C127#4114yes—
133C22×C4×C127#4114yes—
134C22×C4×C127#4112yes—
135C4⋊C4×C127—28no—
136C4⋊C4×C127—44no—
137C4⋊C4×C127—48no—
138C4⋊C4×C127—48no—
139C42×C127—44no—
140C42×C127—44no—
141C42×C127—44no—
142C23×C127C23×C411yescharacteristic
143C23×C127C22×Q811yescharacteristic
144C23×C127C2×#4112yes—
145C23×C127C2×#4111yescharacteristic
146C23×C127C2×#4112yes—
147C23×C127H(5,𝔽2)11yescharacteristic
148C23×C127H(5,𝔽2)12yes—
149C23×C127H(5,𝔽2)11yescharacteristic
150C23×C127H(5,𝔽2)11yescharacteristic
151C23×C1272−1+412yes—
152C23×C1272−1+411yescharacteristic
153C2×C4×C127—22no—
154C2×C4×C127—22no—
155C2×C4×C127—22no—
156C2×C4×C127—22no—
157C2×C4×C127—22no—
158C2×C4×C127—24no—
159C2×C4×C127—24no—
160C2×C4×C127—22no—
161C2×C4×C127—22no—
162C2×C4×C127—22no—
163C2×C4×C127—24no—
164C2×C4×C127—22no—
165C2×C4×C127—24no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
168C2×C4×C127—24no—
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—24no—
173C2×C4×C127—24no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—24no—
177C2×C4×C127—24no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—42no—
181C2×C4×C127—42no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
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—42no—
209C2×C4×C127—42no—
210C2×C4×C127#11714yes—
211C2×C4×C127C4×Q814yes—
212C22×C127C2×#11711yescharacteristic
213C22×C127C2×C4×Q811yescharacteristic
214C22×C127C4×#4111yescharacteristic
215C22×C127#51811yescharacteristic
216C22×C127#51811yescharacteristic
217C22×C127#51911yescharacteristic
218C22×C127#52011yescharacteristic
219C22×C127#52912yes—
220C22×C127#53312yes—
221C22×C127#53811yescharacteristic
222C22×C127#53812yes—
223C22×C127#53912yes—
224C22×C127#53912yes—
225C22×C127#53911yescharacteristic
226C22×C127#53912yes—
227C22×C127#54012yes—
228C22×C127#54012yes—
229C22×C127#54112yes—
230C22×C127#54212yes—
231C22×C127#54212yes—
232C22×C127#54311yescharacteristic
233C22×C127#54411yescharacteristic
234C22×C127#54412yes—
235C4×C127—24no—
236C4×C127—24no—
237C4×C127—44no—
238C4×C127—42no—
239C4×C127—44no—
240C4×C127—44no—
241C4×C127—44no—
242C4×C127—82no—
243C4×C127—82no—
244#14286C12711yesmaximal, characteristic, direct product factor, Sylow
245C2×C127#229511yescharacteristic
246C2×C127#231311yescharacteristic
247C2×C127#231911yescharacteristic
248C2×C127#232911yescharacteristic
249C2×C127#233111yescharacteristic
250C2×C127#233311yescharacteristic
251C2×C127#233611yescharacteristic
252C2×C127#264912yes—
253C2×C127#265412yes—
254C2×C127#266612yes—
255C2×C127#266712yes—
256C2×#389C2×C12711yescharacteristic
257#1445C2×C12712yes—
258#1445C2×C12712yes—
259#1441C2×C12712yes—
260#1441C2×C12712yes—
261#1436C2×C12712yes—
262#1434C2×C12711yescharacteristic
263#1434C2×C12712yes—
264C4×#95C2×C12711yescharacteristic
265C127#1428611yescharacteristic, direct product factor, Sylow
266C22×C4⋊C4C22×C12711yescharacteristic
267C22×C4⋊C4C22×C12712yes—
268C22×C4⋊C4C22×C12711yescharacteristic
269C22×C4⋊C4C22×C12712yes—
270C22×C42C22×C12711yescharacteristic
271C22×C42C22×C12711yescharacteristic
272C22×C42C22×C12711yescharacteristic
273#389C4×C12718yescomplemented
274C2×#95C22×C12712yes—
275C2×#95C22×C12712yes—
276C2×#95C22×C12712yes—
277C2×#95C22×C12712yes—
278C2×#95C22×C12712yes—
279C2×#95C22×C12711yescharacteristic
280C2×#95C22×C12712yes—
281C2×#95C22×C12712yes—
282C2×#95C22×C12712yes—
283C2×#95C22×C12711yescharacteristic
284C2×#95C22×C12712yes—
285C2×#95C22×C12712yes—
286C2×#95C22×C12712yes—
287C2×#95C22×C12712yes—
288C23×C4C23×C12712yes—
289C23×C4C23×C12712yes—
290C23×C4C23×C12712yes—
291C23×C4C23×C12712yes—
292C23×C4C23×C12711yescharacteristic
293C23×C4C23×C12712yes—
294C23×C4C23×C12712yes—
295C23×C4C23×C12711yescharacteristic
296C23×C4C23×C12711yescharacteristic
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4C2×C4×C12714yes—
306C2×C4⋊C4C2×C4×C12718yes—
307C2×C4⋊C4C2×C4×C12714yes—
308C2×C42—22no—
309C2×C42—41no—
310C2×C42—41no—
311C2×C42—41no—
312C2×C42—41no—
313C2×C42—41no—
314C2×C42—41no—
315C2×C42C2×C4×C12714yes—
316C2×C42Q8×C12714yes—
317#95—24no—
318#95—24no—
319#95—24no—
320#95—24no—
321#95—24no—
322#95—42no—
323#95—42no—
324#95—42no—
325#95—42no—
326#95—42no—
327#95—41no—
328#95—41no—
329#95—42no—
330#95C2×C4×C12718yes—
331C24C24×C12711yescharacteristic
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
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×C4C22×C4×C12714yes—
382C22×C4C22×C4×C12714yes—
383C22×C4C22×C4×C12712yes—
384C22×C4C22×C4×C12712yes—
385C22×C4C22×C4×C12712yes—
386C22×C4C2×Q8×C12714yes—
387C22×C4C2×Q8×C12712yes—
388C22×C4#41×C12714yes—
389C22×C4#41×C12714yes—
390C22×C4#41×C12712yes—
391C4⋊C4—28no—
392C4⋊C4—44no—
393C4⋊C4—48no—
394C4⋊C4—48no—
395C42—44no—
396C42—44no—
397C42—44no—
398C23C23×C4×C12711yescharacteristic
399C23C22×Q8×C12711yescharacteristic
400C23C2×#41×C12712yes—
401C23C2×#41×C12711yescharacteristic
402C23C2×#41×C12712yes—
403C23H(5,𝔽2)×C12711yescharacteristic
404C23H(5,𝔽2)×C12712yes—
405C23H(5,𝔽2)×C12711yescharacteristic
406C23H(5,𝔽2)×C12711yescharacteristic
407C232−1+4×C12712yes—
408C232−1+4×C12711yescharacteristic
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4#117×C12714yes—
467C2×C4C4×Q8×C12714yes—
468C22C2×#117×C12711yescharacteristic
469C22C2×C4×Q8×C12711yescharacteristic
470C22C4×#41×C12711yescharacteristic
471C22#518×C12711yescharacteristic
472C22#518×C12711yescharacteristic
473C22#519×C12711yescharacteristic
474C22#520×C12711yescharacteristic
475C22#529×C12712yes—
476C22#533×C12712yes—
477C22#538×C12711yescharacteristic
478C22#538×C12712yes—
479C22#539×C12712yes—
480C22#539×C12712yes—
481C22#539×C12711yescharacteristic
482C22#539×C12712yes—
483C22#540×C12712yes—
484C22#540×C12712yes—
485C22#541×C12712yes—
486C22#542×C12712yes—
487C22#542×C12712yes—
488C22#543×C12711yescharacteristic
489C22#544×C12711yescharacteristic
490C22#544×C12712yes—
491C4—24no—
492C4—24no—
493C4—44no—
494C4—42no—
495C4—44no—
496C4—44no—
497C4—44no—
498C4—82no—
499C4—82no—
500C2C127×#229511yescharacteristic
501C2C127×#231311yescharacteristic
502C2C127×#231911yescharacteristic
503C2C127×#232911yescharacteristic
504C2C127×#233111yescharacteristic
505C2C127×#233311yescharacteristic
506C2C127×#233611yescharacteristic
507C2C127×#264912yes—
508C2C127×#265412yes—
509C2C127×#266612yes—
510C2C127×#266712yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
17. #389×C127C4semidirect
244. #14286C127direct (N × H)
265. C127#14286direct (N × H)
273. #389C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C127×#14452
C127×#14412
C127×#14362
C127×#14342
C4×#95×C1272
#14286127