Finite Group Databasebeta

← C127×#14261 #44577934

Subgroups — C127×#14261 #44577934

Order 32512.

1382 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C211yesmaximal, characteristic
2C2×#391×C127C211yesmaximal, characteristic
3C2×#391×C127C211yesmaximal, characteristic
4C2×#389×C127C211yesmaximal, characteristic
5C2×#376×C127C211yesmaximal, characteristic
6C127×#1443C214yesmaximal
7C127×#1442C214yesmaximal
8C127×C4⋊#95C211yesmaximal, characteristic
9C127×C4⋊#95C211yesmaximal, characteristic
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2212yes—
15C22×C42×C127C2211yescharacteristic
16C22×C42×C127C2211yescharacteristic
17C22×C42×C127C2211yescharacteristic
18#391×C127—24no—
19#391×C127—24no—
20#391×C127C418yescomplemented
21#389×C127—24no—
22#376×C127—24no—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2214yes—
30C2×#95×C127C2214yes—
31C2×#95×C127C2214yes—
32C22×Q8×C127—22no—
33C22×Q8×C127—22no—
34C22×Q8×C127—22no—
35C22×Q8×C127—22no—
36C22×Q8×C127—22no—
37C22×Q8×C127—22no—
38C22×Q8×C127C2×C414yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C2×C4⋊C4×C127—22no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—44no—
58C2×C4⋊C4×C127C2×C414yes—
59C2×C42×C127—22no—
60C2×C42×C127—22no—
61C2×C42×C127—22no—
62C2×C42×C127—22no—
63C2×C42×C127—22no—
64C2×C42×C127—22no—
65C2×C42×C127C2×C414yes—
66C2×C42×C127D414yes—
67C2×C42×C127D414yes—
68#95×C127—24no—
69#95×C127—24no—
70#95×C127—24no—
71#95×C127—28no—
72#95×C127—24no—
73#95×C127—24no—
74#95×C127—44no—
75#95×C127—44no—
76#95×C127C2×C4116yes—
77C24×C127C2411yescharacteristic
78C2×Q8×C127—28no—
79C2×Q8×C127—28no—
80C2×Q8×C127—28no—
81C2×Q8×C127—44no—
82C2×Q8×C127—44no—
83C2×Q8×C127—44no—
84C2×Q8×C127—44no—
85C22×C4×C127—22no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—21no—
93C22×C4×C127—21no—
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—24no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—24no—
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—24no—
122C22×C4×C127—24no—
123C22×C4×C127—24no—
124C22×C4×C127—24no—
125C22×C4×C127C22×C414yes—
126C22×C4×C127C22×C414yes—
127C22×C4×C127C22×C414yes—
128C22×C4×C127C22×C412yes—
129C22×C4×C127C2×D412yes—
130C22×C4×C127C2×D414yes—
131C22×C4×C127C2×D412yes—
132C22×C4×C127C2×D412yes—
133C22×C4×C127C2×D412yes—
134C22×C4×C127#4112yes—
135C22×C4×C127#4112yes—
136C22×C4×C127#4112yes—
137C22×C4×C127#4112yes—
138C4⋊C4×C127—28no—
139C4⋊C4×C127—48no—
140C4⋊C4×C127—44no—
141C4⋊C4×C127—44no—
142C42×C127—28no—
143C42×C127—28no—
144C42×C127—28no—
145C23×C127C23×C411yescharacteristic
146C23×C127C22×D411yescharacteristic
147C23×C127C22×D411yescharacteristic
148C23×C127C2×#4111yescharacteristic
149C23×C127C2×#4111yescharacteristic
150C23×C127C2×#4111yescharacteristic
151C23×C127C2×#4111yescharacteristic
152C23×C127H(5,𝔽2)12yes—
153C23×C1272−1+412yes—
154C23×C1272−1+412yes—
155C23×C1272−1+412yes—
156Q8×C127—416no—
157C2×C4×C127—24no—
158C2×C4×C127—24no—
159C2×C4×C127—24no—
160C2×C4×C127—24no—
161C2×C4×C127—24no—
162C2×C4×C127—24no—
163C2×C4×C127—24no—
164C2×C4×C127—28no—
165C2×C4×C127—22no—
166C2×C4×C127—22no—
167C2×C4×C127—24no—
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
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—44no—
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—44no—
200C2×C4×C127—44no—
201C2×C4×C127—44no—
202C2×C4×C127—44no—
203C2×C4×C127#11714yes—
204C2×C4×C127C4×D414yes—
205C2×C4×C127C4×D414yes—
206C2×C4×C127#12114yes—
207C2×C4×C127#12314yes—
208C2×C4×C127#12414yes—
209C2×C4×C127#12614yes—
210C22×C127C2×#11711yescharacteristic
211C22×C127C2×C4×D411yescharacteristic
212C22×C127C2×C4×D411yescharacteristic
213C22×C127#51912yes—
214C22×C127#52012yes—
215C22×C127C2×#12111yescharacteristic
216C22×C127C2×#12311yescharacteristic
217C22×C127C2×#12411yescharacteristic
218C22×C127C2×#12611yescharacteristic
219C22×C127#53511yescharacteristic
220C22×C127#53612yes—
221C22×C127#53611yescharacteristic
222C22×C127#53611yescharacteristic
223C22×C127#53611yescharacteristic
224C22×C127#53712yes—
225C22×C127#54112yes—
226C22×C127#54112yes—
227C22×C127#54112yes—
228C22×C127#54112yes—
229C22×C127#54212yes—
230C22×C127#54212yes—
231C22×C127#54212yes—
232C22×C127#54212yes—
233C4×C127—44no—
234C4×C127—44no—
235C4×C127—42no—
236C4×C127—42no—
237C4×C127—44no—
238C4×C127—44no—
239C4×C127—82no—
240C4×C127—82no—
241C4×C127#38818yes—
242#14261C12711yesmaximal, characteristic, direct product factor, Sylow
243C2×C127C2×#38811yescharacteristic
244C2×C127#232012yes—
245C2×C127#232312yes—
246C2×C127#232611yescharacteristic
247C2×C127#232711yescharacteristic
248C2×C127#262011yescharacteristic
249C2×C127#262111yescharacteristic
250C2×C127#262512yes—
251C2×C127#264011yescharacteristic
252C2×C127#264211yescharacteristic
253C2×C127#264512yes—
254C2×#391C2×C12711yescharacteristic
255C2×#391C2×C12711yescharacteristic
256C2×#391C2×C12711yescharacteristic
257C2×#389C2×C12711yescharacteristic
258C2×#376C2×C12711yescharacteristic
259#1443C2×C12714yes—
260#1442C2×C12714yes—
261C4⋊#95C2×C12711yescharacteristic
262C4⋊#95C2×C12711yescharacteristic
263C127#1426111yescharacteristic, direct product factor, Sylow
264C23×Q8C22×C12711yescharacteristic
265C22×C4⋊C4C22×C12711yescharacteristic
266C22×C4⋊C4C22×C12711yescharacteristic
267C22×C4⋊C4C22×C12711yescharacteristic
268C22×C4⋊C4C22×C12712yes—
269C22×C42C22×C12711yescharacteristic
270C22×C42C22×C12711yescharacteristic
271C22×C42C22×C12711yescharacteristic
272#391—24no—
273#391—24no—
274#391C4×C12718yescomplemented
275#389—24no—
276#376—24no—
277C2×#95C22×C12712yes—
278C2×#95C22×C12712yes—
279C2×#95C22×C12714yes—
280C2×#95C22×C12712yes—
281C2×#95C22×C12712yes—
282C2×#95C22×C12712yes—
283C2×#95C22×C12714yes—
284C2×#95C22×C12714yes—
285C2×#95C22×C12714yes—
286C22×Q8—22no—
287C22×Q8—22no—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8C2×C4×C12714yes—
293C23×C4C23×C12712yes—
294C23×C4C23×C12712yes—
295C23×C4C23×C12712yes—
296C23×C4C23×C12712yes—
297C23×C4C23×C12712yes—
298C23×C4C23×C12711yescharacteristic
299C23×C4C23×C12711yescharacteristic
300C23×C4C23×C12712yes—
301C23×C4C23×C12711yescharacteristic
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4C2×C4×C12714yes—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42C2×C4×C12714yes—
320C2×C42D4×C12714yes—
321C2×C42D4×C12714yes—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—28no—
326#95—24no—
327#95—24no—
328#95—44no—
329#95—44no—
330#95C2×C4×C127116yes—
331C24C24×C12711yescharacteristic
332C2×Q8—28no—
333C2×Q8—28no—
334C2×Q8—28no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8—44no—
338C2×Q8—44no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
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—24no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—24no—
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—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4C22×C4×C12714yes—
380C22×C4C22×C4×C12714yes—
381C22×C4C22×C4×C12714yes—
382C22×C4C22×C4×C12712yes—
383C22×C4C2×D4×C12712yes—
384C22×C4C2×D4×C12714yes—
385C22×C4C2×D4×C12712yes—
386C22×C4C2×D4×C12712yes—
387C22×C4C2×D4×C12712yes—
388C22×C4#41×C12712yes—
389C22×C4#41×C12712yes—
390C22×C4#41×C12712yes—
391C22×C4#41×C12712yes—
392C4⋊C4—28no—
393C4⋊C4—48no—
394C4⋊C4—44no—
395C4⋊C4—44no—
396C42—28no—
397C42—28no—
398C42—28no—
399C23C23×C4×C12711yescharacteristic
400C23C22×D4×C12711yescharacteristic
401C23C22×D4×C12711yescharacteristic
402C23C2×#41×C12711yescharacteristic
403C23C2×#41×C12711yescharacteristic
404C23C2×#41×C12711yescharacteristic
405C23C2×#41×C12711yescharacteristic
406C23H(5,𝔽2)×C12712yes—
407C232−1+4×C12712yes—
408C232−1+4×C12712yes—
409C232−1+4×C12712yes—
410Q8—416no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—28no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—24no—
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—44no—
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—44no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—44no—
457C2×C4#117×C12714yes—
458C2×C4C4×D4×C12714yes—
459C2×C4C4×D4×C12714yes—
460C2×C4#121×C12714yes—
461C2×C4#123×C12714yes—
462C2×C4#124×C12714yes—
463C2×C4#126×C12714yes—
464C22C2×#117×C12711yescharacteristic
465C22C2×C4×D4×C12711yescharacteristic
466C22C2×C4×D4×C12711yescharacteristic
467C22#519×C12712yes—
468C22#520×C12712yes—
469C22C2×#121×C12711yescharacteristic
470C22C2×#123×C12711yescharacteristic
471C22C2×#124×C12711yescharacteristic
472C22C2×#126×C12711yescharacteristic
473C22#535×C12711yescharacteristic
474C22#536×C12712yes—
475C22#536×C12711yescharacteristic
476C22#536×C12711yescharacteristic
477C22#536×C12711yescharacteristic
478C22#537×C12712yes—
479C22#541×C12712yes—
480C22#541×C12712yes—
481C22#541×C12712yes—
482C22#541×C12712yes—
483C22#542×C12712yes—
484C22#542×C12712yes—
485C22#542×C12712yes—
486C22#542×C12712yes—
487C4—44no—
488C4—44no—
489C4—42no—
490C4—42no—
491C4—44no—
492C4—44no—
493C4—82no—
494C4—82no—
495C4#388×C12718yes—
496C2C2×#388×C12711yescharacteristic
497C2C127×#232012yes—
498C2C127×#232312yes—
499C2C127×#232611yescharacteristic
500C2C127×#232711yescharacteristic
501C2C127×#262011yescharacteristic
502C2C127×#262111yescharacteristic
503C2C127×#262512yes—
504C2C127×#264011yescharacteristic
505C2C127×#264211yescharacteristic
506C2C127×#264512yes—
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
20. #391×C127C4semidirect
242. #14261C127direct (N × H)
263. C127#14261direct (N × H)
274. #391C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C2×#389×C1272
C2×#376×C1272
C127×#14432
C127×#14422
C127×C4⋊#952
#14261127