Finite Group Databasebeta

← C127×#14469 #44578142

Subgroups — C127×#14469 #44578142

Order 32512.

1210 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C211yesmaximal, characteristic
2C127×#1446C212yesmaximal
3C127×#1443C212yesmaximal
4C127×#1442C212yesmaximal
5C127×#1436C212yesmaximal
6C127×#1436C212yesmaximal
7C127×C4⋊#95C211yesmaximal, characteristic
8C127×#1434C212yesmaximal
9C127×#1434C211yesmaximal, characteristic
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C42×C127C2212yes—
14C22×C42×C127C2211yescharacteristic
15#391×C127C418yescomplemented
16C2×#95×C127C2212yes—
17C2×#95×C127C2212yes—
18C2×#95×C127C2211yescharacteristic
19C2×#95×C127C2212yes—
20C2×#95×C127C2211yescharacteristic
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C22×Q8×C127—22no—
33C22×Q8×C127—22no—
34C22×Q8×C127—42no—
35C22×Q8×C127—42no—
36C22×Q8×C127C2×C414yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—42no—
49C2×C4⋊C4×C127—42no—
50C2×C4⋊C4×C127C2×C414yes—
51C2×C42×C127—24no—
52C2×C42×C127—42no—
53C2×C42×C127—42no—
54C2×C42×C127—42no—
55C2×C42×C127C2×C414yes—
56#95×C127—24no—
57#95×C127—24no—
58#95×C127—24no—
59#95×C127—22no—
60#95×C127—41no—
61#95×C127—42no—
62#95×C127—42no—
63#95×C127—41no—
64#95×C127—42no—
65#95×C127—42no—
66#95×C127—42no—
67#95×C127—42no—
68#95×C127—42no—
69#95×C127C2×C418yes—
70#95×C127C2×C418yes—
71#95×C127Q814yescomplemented
72C24×C127C2411yescharacteristic
73C2×Q8×C127—28no—
74C2×Q8×C127—44no—
75C2×Q8×C127—44no—
76C2×Q8×C127—48no—
77C2×Q8×C127—48no—
78C22×C4×C127—22no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
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—21no—
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—21no—
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×C127C22×C412yes—
125C22×C4×C127C22×C414yes—
126C22×C4×C127C22×C414yes—
127C22×C4×C127C22×C412yes—
128C22×C4×C127C22×C412yes—
129C22×C4×C127C2×Q814yes—
130C22×C4×C127C2×Q812yes—
131C22×C4×C127#4114yes—
132C22×C4×C127#4112yes—
133C22×C4×C127#4112yes—
134C22×C4×C127#4112yes—
135C4⋊C4×C127—44no—
136C4⋊C4×C127—48no—
137C42×C127—44no—
138C42×C127—48no—
139C23×C127C23×C411yescharacteristic
140C23×C127C22×Q811yescharacteristic
141C23×C127C2×#4111yescharacteristic
142C23×C127C2×#4111yescharacteristic
143C23×C127C2×#4111yescharacteristic
144C23×C127C2×#4112yes—
145C23×C127H(5,𝔽2)12yes—
146C23×C127H(5,𝔽2)12yes—
147C23×C127H(5,𝔽2)11yescharacteristic
148C23×C1272−1+412yes—
149C23×C1272−1+411yescharacteristic
150Q8×C127—416no—
151C2×C4×C127—22no—
152C2×C4×C127—22no—
153C2×C4×C127—22no—
154C2×C4×C127—22no—
155C2×C4×C127—24no—
156C2×C4×C127—24no—
157C2×C4×C127—24no—
158C2×C4×C127—24no—
159C2×C4×C127—24no—
160C2×C4×C127—24no—
161C2×C4×C127—22no—
162C2×C4×C127—24no—
163C2×C4×C127—24no—
164C2×C4×C127—24no—
165C2×C4×C127—22no—
166C2×C4×C127—24no—
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—42no—
175C2×C4×C127—42no—
176C2×C4×C127—42no—
177C2×C4×C127—42no—
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#11714yes—
207C2×C4×C127C4×Q814yes—
208C22×C127C2×#11711yescharacteristic
209C22×C127C2×C4×Q811yescharacteristic
210C22×C127C4×#4111yescharacteristic
211C22×C127#51811yescharacteristic
212C22×C127#51811yescharacteristic
213C22×C127#51911yescharacteristic
214C22×C127#52011yescharacteristic
215C22×C127#53812yes—
216C22×C127#53812yes—
217C22×C127#53812yes—
218C22×C127#54212yes—
219C22×C127#54212yes—
220C22×C127#54412yes—
221C22×C127#55112yes—
222C22×C127#55212yes—
223C22×C127#55411yescharacteristic
224C22×C127#55412yes—
225C22×C127#55611yescharacteristic
226C22×C127#55612yes—
227C22×C127#55711yescharacteristic
228C22×C127#55911yescharacteristic
229C22×C127#56212yes—
230C22×C127#56312yes—
231C4×C127—24no—
232C4×C127—24no—
233C4×C127—44no—
234C4×C127—44no—
235C4×C127—42no—
236C4×C127—44no—
237C4×C127—44no—
238C4×C127—82no—
239C4×C127—82no—
240#14469C12711yesmaximal, characteristic, direct product factor, Sylow
241C2×C127#231211yescharacteristic
242C2×C127#233111yescharacteristic
243C2×C127#233711yescharacteristic
244C2×C127#235511yescharacteristic
245C2×C127#235611yescharacteristic
246C2×C127#236811yescharacteristic
247C2×C127#237811yescharacteristic
248C2×C127#275112yes—
249C2×C127#275912yes—
250C2×C127#277412yes—
251C2×C127#278812yes—
252C2×#391C2×C12711yescharacteristic
253#1446C2×C12712yes—
254#1443C2×C12712yes—
255#1442C2×C12712yes—
256#1436C2×C12712yes—
257#1436C2×C12712yes—
258C4⋊#95C2×C12711yescharacteristic
259#1434C2×C12712yes—
260#1434C2×C12711yescharacteristic
261C127#1446911yescharacteristic, direct product factor, Sylow
262C23×Q8C22×C12711yescharacteristic
263C22×C4⋊C4C22×C12712yes—
264C22×C4⋊C4C22×C12711yescharacteristic
265C22×C42C22×C12712yes—
266C22×C42C22×C12711yescharacteristic
267#391C4×C12718yescomplemented
268C2×#95C22×C12712yes—
269C2×#95C22×C12712yes—
270C2×#95C22×C12711yescharacteristic
271C2×#95C22×C12712yes—
272C2×#95C22×C12711yescharacteristic
273C2×#95C22×C12712yes—
274C2×#95C22×C12712yes—
275C2×#95C22×C12712yes—
276C2×#95C22×C12711yescharacteristic
277C2×#95C22×C12712yes—
278C2×#95C22×C12712yes—
279C2×#95C22×C12712yes—
280C2×#95C22×C12712yes—
281C2×#95C22×C12712yes—
282C2×#95C22×C12712yes—
283C2×#95C22×C12711yescharacteristic
284C22×Q8—22no—
285C22×Q8—22no—
286C22×Q8—42no—
287C22×Q8—42no—
288C22×Q8C2×C4×C12714yes—
289C23×C4C23×C12712yes—
290C23×C4C23×C12712yes—
291C23×C4C23×C12712yes—
292C23×C4C23×C12712yes—
293C23×C4C23×C12711yescharacteristic
294C23×C4C23×C12712yes—
295C23×C4C23×C12712yes—
296C23×C4C23×C12711yescharacteristic
297C23×C4C23×C12711yescharacteristic
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4C2×C4×C12714yes—
303C2×C42—24no—
304C2×C42—42no—
305C2×C42—42no—
306C2×C42—42no—
307C2×C42C2×C4×C12714yes—
308#95—24no—
309#95—24no—
310#95—24no—
311#95—22no—
312#95—41no—
313#95—42no—
314#95—42no—
315#95—41no—
316#95—42no—
317#95—42no—
318#95—42no—
319#95—42no—
320#95—42no—
321#95C2×C4×C12718yes—
322#95C2×C4×C12718yes—
323#95Q8×C12714yescomplemented
324C24C24×C12711yescharacteristic
325C2×Q8—28no—
326C2×Q8—44no—
327C2×Q8—44no—
328C2×Q8—48no—
329C2×Q8—48no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
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×C4C22×C4×C12712yes—
377C22×C4C22×C4×C12714yes—
378C22×C4C22×C4×C12714yes—
379C22×C4C22×C4×C12712yes—
380C22×C4C22×C4×C12712yes—
381C22×C4C2×Q8×C12714yes—
382C22×C4C2×Q8×C12712yes—
383C22×C4#41×C12714yes—
384C22×C4#41×C12712yes—
385C22×C4#41×C12712yes—
386C22×C4#41×C12712yes—
387C4⋊C4—44no—
388C4⋊C4—48no—
389C42—44no—
390C42—48no—
391C23C23×C4×C12711yescharacteristic
392C23C22×Q8×C12711yescharacteristic
393C23C2×#41×C12711yescharacteristic
394C23C2×#41×C12711yescharacteristic
395C23C2×#41×C12711yescharacteristic
396C23C2×#41×C12712yes—
397C23H(5,𝔽2)×C12712yes—
398C23H(5,𝔽2)×C12712yes—
399C23H(5,𝔽2)×C12711yescharacteristic
400C232−1+4×C12712yes—
401C232−1+4×C12711yescharacteristic
402Q8—416no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
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#117×C12714yes—
459C2×C4C4×Q8×C12714yes—
460C22C2×#117×C12711yescharacteristic
461C22C2×C4×Q8×C12711yescharacteristic
462C22C4×#41×C12711yescharacteristic
463C22#518×C12711yescharacteristic
464C22#518×C12711yescharacteristic
465C22#519×C12711yescharacteristic
466C22#520×C12711yescharacteristic
467C22#538×C12712yes—
468C22#538×C12712yes—
469C22#538×C12712yes—
470C22#542×C12712yes—
471C22#542×C12712yes—
472C22#544×C12712yes—
473C22#551×C12712yes—
474C22#552×C12712yes—
475C22#554×C12711yescharacteristic
476C22#554×C12712yes—
477C22#556×C12711yescharacteristic
478C22#556×C12712yes—
479C22#557×C12711yescharacteristic
480C22#559×C12711yescharacteristic
481C22#562×C12712yes—
482C22#563×C12712yes—
483C4—24no—
484C4—24no—
485C4—44no—
486C4—44no—
487C4—42no—
488C4—44no—
489C4—44no—
490C4—82no—
491C4—82no—
492C2C127×#231211yescharacteristic
493C2C127×#233111yescharacteristic
494C2C127×#233711yescharacteristic
495C2C127×#235511yescharacteristic
496C2C127×#235611yescharacteristic
497C2C127×#236811yescharacteristic
498C2C127×#237811yescharacteristic
499C2C127×#275112yes—
500C2C127×#275912yes—
501C2C127×#277412yes—
502C2C127×#278812yes—
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
15. #391×C127C4semidirect
71. #95×C127Q8semidirect
240. #14469C127direct (N × H)
261. C127#14469direct (N × H)
267. #391C4×C127semidirect
323. #95Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C127×#14462
C127×#14432
C127×#14422
C127×#14362
C127×C4⋊#952
C127×#14342
#14469127