Finite Group Databasebeta

← C127×#13787 #44577460

Subgroups — C127×#13787 #44577460

Order 32512.

1406 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×#387×C127C212yesmaximal
2C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
3C127×#1436C212yesmaximal
4C127×#1436C212yesmaximal
5C127×C4⋊#95C211yesmaximal, characteristic
6C127×#1434C211yesmaximal, characteristic
7C127×#1434C211yesmaximal, characteristic
8C127×#1434C212yesmaximal
9C127×#1434C211yesmaximal, characteristic
10C4×#95×C127C211yesmaximal, characteristic
11C4×#95×C127C211yesmaximal, characteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C42×C127C2211yescharacteristic
16C22×C42×C127C2212yes—
17C22×C42×C127C2211yescharacteristic
18C22×C42×C127C2212yes—
19C22×C42×C127C2211yescharacteristic
20#387×C127C4116yescomplemented
21C4×C4⋊C4×C127C418yescomplemented
22C2×#95×C127C2211yescharacteristic
23C2×#95×C127C2211yescharacteristic
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2211yescharacteristic
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2211yescharacteristic
37C23×C4×C127C2312yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—42no—
50C2×C4⋊C4×C127—42no—
51C2×C4⋊C4×C127C2×C414yes—
52C2×C4⋊C4×C127C2×C418yes—
53C2×C4⋊C4×C127C2×C414yes—
54C2×C4⋊C4×C127C2×C418yes—
55C2×C42×C127—22no—
56C2×C42×C127—22no—
57C2×C42×C127—24no—
58C2×C42×C127—42no—
59C2×C42×C127—42no—
60C2×C42×C127—42no—
61C2×C42×C127—42no—
62C2×C42×C127—42no—
63C2×C42×C127—42no—
64C2×C42×C127C2×C414yes—
65C2×C42×C127C2×C414yes—
66C2×C42×C127C2×C414yes—
67C2×C42×C127C2×C418yes—
68#95×C127—22no—
69#95×C127—22no—
70#95×C127—22no—
71#95×C127—22no—
72#95×C127—24no—
73#95×C127—42no—
74#95×C127—42no—
75#95×C127—42no—
76#95×C127—42no—
77#95×C127C2×C414yes—
78#95×C127C2×C414yes—
79#95×C127C2×C418yes—
80#95×C127C2×C418yes—
81#95×C127C2×C418yes—
82#95×C127C2×C418yes—
83C24×C127C2411yescharacteristic
84C22×C4×C127—21no—
85C22×C4×C127—21no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—21no—
90C22×C4×C127—22no—
91C22×C4×C127—21no—
92C22×C4×C127—22no—
93C22×C4×C127—21no—
94C22×C4×C127—22no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—21no—
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—21no—
105C22×C4×C127—21no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—21no—
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—21no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—21no—
130C22×C4×C127—21no—
131C22×C4×C127—22no—
132C22×C4×C127C22×C414yes—
133C22×C4×C127C22×C412yes—
134C22×C4×C127C22×C414yes—
135C22×C4×C127C22×C414yes—
136C22×C4×C127C22×C412yes—
137C22×C4×C127C22×C414yes—
138C22×C4×C127C22×C414yes—
139C22×C4×C127C22×C412yes—
140C22×C4×C127C22×C412yes—
141C22×C4×C127C22×C414yes—
142C22×C4×C127C22×C414yes—
143C22×C4×C127C22×C412yes—
144C22×C4×C127C22×C412yes—
145C22×C4×C127C22×C412yes—
146C22×C4×C127#4112yes—
147C22×C4×C127#4112yes—
148C22×C4×C127#4114yes—
149C4⋊C4×C127—28no—
150C4⋊C4×C127—48no—
151C4⋊C4×C127C42116yescomplemented
152C42×C127—28no—
153C42×C127—44no—
154C42×C127—44no—
155C42×C127—48no—
156C42×C127—48no—
157C23×C127C23×C411yescharacteristic
158C23×C127C23×C412yes—
159C23×C127C2×#4112yes—
160C23×C127C2×#4111yescharacteristic
161C23×C127C2×#4111yescharacteristic
162C23×C127H(5,𝔽2)12yes—
163C23×C127H(5,𝔽2)11yescharacteristic
164C23×C127H(5,𝔽2)11yescharacteristic
165C23×C1272−1+412yes—
166C23×C1272−1+411yescharacteristic
167C23×C1272−1+411yescharacteristic
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—24no—
177C2×C4×C127—24no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
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—22no—
189C2×C4×C127—22no—
190C2×C4×C127—24no—
191C2×C4×C127—24no—
192C2×C4×C127—24no—
193C2×C4×C127—24no—
194C2×C4×C127—24no—
195C2×C4×C127—22no—
196C2×C4×C127—24no—
197C2×C4×C127—24no—
198C2×C4×C127—24no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—42no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—41no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—41no—
220C2×C4×C127—42no—
221C2×C4×C127—41no—
222C2×C4×C127—41no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—42no—
227C2×C4×C127—42no—
228C2×C4×C127C2×C4214yes—
229C2×C4×C127C2×C4214yes—
230C2×C4×C127C2×C4214yes—
231C2×C4×C127#11714yes—
232C2×C4×C127#11714yes—
233C22×C127C22×C4211yescharacteristic
234C22×C127C2×#11711yescharacteristic
235C22×C127C2×#11711yescharacteristic
236C22×C127C4×#4112yes—
237C22×C127C4×#4112yes—
238C22×C127#51811yescharacteristic
239C22×C127#51812yes—
240C22×C127#51911yescharacteristic
241C22×C127#51912yes—
242C22×C127#52011yescharacteristic
243C22×C127#52011yescharacteristic
244C22×C127#52012yes—
245C22×C127#52012yes—
246C22×C127#53812yes—
247C22×C127#53912yes—
248C22×C127#53912yes—
249C22×C127#53912yes—
250C22×C127#54011yescharacteristic
251C22×C127#54111yescharacteristic
252C22×C127#54112yes—
253C22×C127#54211yescharacteristic
254C22×C127#54211yescharacteristic
255C22×C127#54212yes—
256C4×C127—24no—
257C4×C127—24no—
258C4×C127—24no—
259C4×C127—24no—
260C4×C127—24no—
261C4×C127—42no—
262C4×C127—42no—
263C4×C127—44no—
264C4×C127—44no—
265C4×C127—44no—
266C4×C127—44no—
267#13787C12711yesmaximal, characteristic, direct product factor, Sylow
268C2×C127C4×#11711yescharacteristic
269C2×C127#227511yescharacteristic
270C2×C127#227611yescharacteristic
271C2×C127#231311yescharacteristic
272C2×C127#231411yescharacteristic
273C2×C127#231811yescharacteristic
274C2×C127#232011yescharacteristic
275C2×C127#233212yes—
276C2×C127#233412yes—
277C2×C127#233512yes—
278C2×C127#233612yes—
279C2×#387C2×C12712yes—
280C2×C4×C4⋊C4C2×C12711yescharacteristic
281#1436C2×C12712yes—
282#1436C2×C12712yes—
283C4⋊#95C2×C12711yescharacteristic
284#1434C2×C12711yescharacteristic
285#1434C2×C12711yescharacteristic
286#1434C2×C12711yescharacteristic
287#1434C2×C12712yes—
288C4×#95C2×C12711yescharacteristic
289C4×#95C2×C12711yescharacteristic
290C127#1378711yescharacteristic, direct product factor, Sylow
291C22×C4⋊C4C22×C12711yescharacteristic
292C22×C4⋊C4C22×C12712yes—
293C22×C4⋊C4C22×C12711yescharacteristic
294C22×C42C22×C12711yescharacteristic
295C22×C42C22×C12712yes—
296C22×C42C22×C12711yescharacteristic
297C22×C42C22×C12712yes—
298C22×C42C22×C12711yescharacteristic
299#387C4×C127116yescomplemented
300C4×C4⋊C4C4×C12718yescomplemented
301C2×#95C22×C12711yescharacteristic
302C2×#95C22×C12711yescharacteristic
303C2×#95C22×C12711yescharacteristic
304C2×#95C22×C12711yescharacteristic
305C2×#95C22×C12712yes—
306C2×#95C22×C12712yes—
307C2×#95C22×C12712yes—
308C2×#95C22×C12712yes—
309C2×#95C22×C12712yes—
310C2×#95C22×C12712yes—
311C2×#95C22×C12711yescharacteristic
312C2×#95C22×C12712yes—
313C2×#95C22×C12712yes—
314C2×#95C22×C12712yes—
315C2×#95C22×C12711yescharacteristic
316C23×C4C23×C12712yes—
317C23×C4C23×C12712yes—
318C23×C4C23×C12711yescharacteristic
319C23×C4C23×C12712yes—
320C23×C4C23×C12712yes—
321C23×C4C23×C12711yescharacteristic
322C23×C4C23×C12711yescharacteristic
323C23×C4C23×C12711yescharacteristic
324C23×C4C23×C12711yescharacteristic
325C23×C4C23×C12711yescharacteristic
326C23×C4C23×C12711yescharacteristic
327C2×C4⋊C4—24no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4C2×C4×C12714yes—
331C2×C4⋊C4C2×C4×C12718yes—
332C2×C4⋊C4C2×C4×C12714yes—
333C2×C4⋊C4C2×C4×C12718yes—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—24no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42—42no—
342C2×C42—42no—
343C2×C42C2×C4×C12714yes—
344C2×C42C2×C4×C12714yes—
345C2×C42C2×C4×C12714yes—
346C2×C42C2×C4×C12718yes—
347#95—22no—
348#95—22no—
349#95—22no—
350#95—22no—
351#95—24no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95C2×C4×C12714yes—
357#95C2×C4×C12714yes—
358#95C2×C4×C12718yes—
359#95C2×C4×C12718yes—
360#95C2×C4×C12718yes—
361#95C2×C4×C12718yes—
362C24C24×C12711yescharacteristic
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
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—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4C22×C4×C12714yes—
412C22×C4C22×C4×C12712yes—
413C22×C4C22×C4×C12714yes—
414C22×C4C22×C4×C12714yes—
415C22×C4C22×C4×C12712yes—
416C22×C4C22×C4×C12714yes—
417C22×C4C22×C4×C12714yes—
418C22×C4C22×C4×C12712yes—
419C22×C4C22×C4×C12712yes—
420C22×C4C22×C4×C12714yes—
421C22×C4C22×C4×C12714yes—
422C22×C4C22×C4×C12712yes—
423C22×C4C22×C4×C12712yes—
424C22×C4C22×C4×C12712yes—
425C22×C4#41×C12712yes—
426C22×C4#41×C12712yes—
427C22×C4#41×C12714yes—
428C4⋊C4—28no—
429C4⋊C4—48no—
430C4⋊C4C42×C127116yescomplemented
431C42—28no—
432C42—44no—
433C42—44no—
434C42—48no—
435C42—48no—
436C23C23×C4×C12711yescharacteristic
437C23C23×C4×C12712yes—
438C23C2×#41×C12712yes—
439C23C2×#41×C12711yescharacteristic
440C23C2×#41×C12711yescharacteristic
441C23H(5,𝔽2)×C12712yes—
442C23H(5,𝔽2)×C12711yescharacteristic
443C23H(5,𝔽2)×C12711yescharacteristic
444C232−1+4×C12712yes—
445C232−1+4×C12711yescharacteristic
446C232−1+4×C12711yescharacteristic
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
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—22no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4C2×C42×C12714yes—
508C2×C4C2×C42×C12714yes—
509C2×C4C2×C42×C12714yes—
510C2×C4#117×C12714yes—
511C2×C4#117×C12714yes—
512C22C22×C42×C12711yescharacteristic
513C22C2×#117×C12711yescharacteristic
514C22C2×#117×C12711yescharacteristic
515C22C4×#41×C12712yes—
516C22C4×#41×C12712yes—
517C22#518×C12711yescharacteristic
518C22#518×C12712yes—
519C22#519×C12711yescharacteristic
520C22#519×C12712yes—
521C22#520×C12711yescharacteristic
522C22#520×C12711yescharacteristic
523C22#520×C12712yes—
524C22#520×C12712yes—
525C22#538×C12712yes—
526C22#539×C12712yes—
527C22#539×C12712yes—
528C22#539×C12712yes—
529C22#540×C12711yescharacteristic
530C22#541×C12711yescharacteristic
531C22#541×C12712yes—
532C22#542×C12711yescharacteristic
533C22#542×C12711yescharacteristic
534C22#542×C12712yes—
535C4—24no—
536C4—24no—
537C4—24no—
538C4—24no—
539C4—24no—
540C4—42no—
541C4—42no—
542C4—44no—
543C4—44no—
544C4—44no—
545C4—44no—
546C2C4×#117×C12711yescharacteristic
547C2C127×#227511yescharacteristic
548C2C127×#227611yescharacteristic
549C2C127×#231311yescharacteristic
550C2C127×#231411yescharacteristic
551C2C127×#231811yescharacteristic
552C2C127×#232011yescharacteristic
553C2C127×#233212yes—
554C2C127×#233412yes—
555C2C127×#233512yes—
556C2C127×#233612yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
20. #387×C127C4semidirect
21. C4×C4⋊C4×C127C4semidirect
151. C4⋊C4×C127C42semidirect
267. #13787C127direct (N × H)
290. C127#13787direct (N × H)
299. #387C4×C127semidirect
300. C4×C4⋊C4C4×C127semidirect
430. C4⋊C4C42×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#387×C1272
C2×C4×C4⋊C4×C1272
C127×#14362
C127×C4⋊#952
C127×#14342
C4×#95×C1272
#13787127