Finite Group Databasebeta

← C127×#14275 #44577948

Subgroups — C127×#14275 #44577948

Order 32512.

1926 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#385×C127C212yesmaximal
2C2×#380×C127C211yesmaximal, characteristic
3C2×#380×C127C211yesmaximal, characteristic
4C22×#95×C127C211yesmaximal, characteristic
5C127×#1444C212yesmaximal, complemented
6C127×#1442C212yesmaximal, complemented
7C127×#1441C214yesmaximal, complemented
8C127×C22⋊#95C212yesmaximal
9C24×C4×C127C2211yescharacteristic
10C24×C4×C127C2211yescharacteristic
11C24×C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2214yes—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2212yes—
18#385×C127—28no—
19#380×C127—24no—
20#380×C127C418yescomplemented
21C2×#95×C127—24no—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2214yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2214yes—
27C2×#95×C127C2214yes—
28C2×#95×C127C2212yes—
29C25×C127C2311yescharacteristic
30C23×C4×C127—22no—
31C23×C4×C127—22no—
32C23×C4×C127—22no—
33C23×C4×C127—22no—
34C23×C4×C127—42no—
35C23×C4×C127—42no—
36C23×C4×C127—42no—
37C23×C4×C127—42no—
38C23×C4×C127—42no—
39C23×C4×C127—42no—
40C23×C4×C127C2×C414yes—
41C23×C4×C127D414yes—
42C23×C4×C127D414yes—
43C23×C4×C127Q814yes—
44C23×C4×C127Q814yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2314yes—
48C23×C4×C127C2312yes—
49C23×C4×C127C2312yes—
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2311yescharacteristic
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—28no—
55C2×C4⋊C4×C127—42no—
56C2×C4⋊C4×C127—42no—
57C2×C4⋊C4×C127—42no—
58C2×C4⋊C4×C127—42no—
59C2×C4⋊C4×C127—44no—
60C2×C4⋊C4×C127—44no—
61C2×C4⋊C4×C127C2×C418yescomplemented
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—24no—
66C2×C22⋊C4×C127—24no—
67C2×C22⋊C4×C127C2×C418yes—
68#95×C127—24no—
69#95×C127—24no—
70#95×C127—24no—
71#95×C127—28no—
72#95×C127—44no—
73#95×C127—44no—
74#95×C127C2×C418yescomplemented
75C24×C127—22no—
76C24×C127—22no—
77C24×C127—22no—
78C24×C127—22no—
79C24×C127C22×C412yes—
80C24×C127C2×D412yes—
81C24×C127C2×D412yes—
82C24×C127C2×Q812yes—
83C24×C127C2×Q812yes—
84C24×C127#4112yes—
85C24×C127#4112yes—
86C24×C127C2411yescharacteristic
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—28no—
92C22×C4×C127—28no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—24no—
96C22×C4×C127—24no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—24no—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127—24no—
103C22×C4×C127—24no—
104C22×C4×C127—24no—
105C22×C4×C127—24no—
106C22×C4×C127—24no—
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—24no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127—24no—
117C22×C4×C127—48no—
118C22×C4×C127—44no—
119C22×C4×C127—44no—
120C22×C4×C127—48no—
121C22×C4×C127—48no—
122C22×C4×C127—48no—
123C22×C4×C127—44no—
124C22×C4×C127—44no—
125C22×C4×C127—44no—
126C22×C4×C127—44no—
127C22×C4×C127—48no—
128C22×C4×C127—48no—
129C22×C4×C127C4⋊C4116yescomplemented
130C22×C4×C127C22×C418yes—
131C22×C4×C127C22×C412yes—
132C22×C4×C127C22×C412yes—
133C22×C4×C127C2×D414yes—
134C22×C4×C127C2×D412yes—
135C22×C4×C127C2×D412yes—
136C22×C4×C127C2×Q814yes—
137C22×C4×C127C2×Q812yes—
138C22×C4×C127C2×Q812yes—
139C4⋊C4×C127—48no—
140C4⋊C4×C127—44no—
141C4⋊C4×C127—44no—
142C4⋊C4×C127—416no—
143C22⋊C4×C127—216no—
144C22⋊C4×C127—48no—
145C23×C127—24no—
146C23×C127—24no—
147C23×C127—22no—
148C23×C127—22no—
149C23×C127—24no—
150C23×C127—22no—
151C23×C127—22no—
152C23×C127—24no—
153C23×C127—24no—
154C23×C127—24no—
155C23×C127—24no—
156C23×C127—24no—
157C23×C127—24no—
158C23×C127—24no—
159C23×C127—24no—
160C23×C127—24no—
161C23×C127C2×C4⋊C414yes—
162C23×C127C4×D414yes—
163C23×C127C4×Q814yes—
164C23×C127#12114yes—
165C23×C127C22⋊Q814yes—
166C23×C127#12514yes—
167C23×C127C4⋊Q814yes—
168C23×C127C23×C411yescharacteristic
169C23×C127C22×D411yescharacteristic
170C23×C127C22×D411yescharacteristic
171C23×C127C22×Q811yescharacteristic
172C23×C127C22×Q811yescharacteristic
173C23×C127C2×#4111yescharacteristic
174C23×C127C2×#4111yescharacteristic
175C23×C127H(5,𝔽2)12yes—
176C23×C127H(5,𝔽2)12yes—
177C23×C127H(5,𝔽2)12yes—
178C23×C1272−1+412yes—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—22no—
182C2×C4×C127—22no—
183C2×C4×C127—22no—
184C2×C4×C127—22no—
185C2×C4×C127—24no—
186C2×C4×C127—24no—
187C2×C4×C127—28no—
188C2×C4×C127—28no—
189C2×C4×C127—28no—
190C2×C4×C127—24no—
191C2×C4×C127—24no—
192C2×C4×C127—28no—
193C2×C4×C127—28no—
194C2×C4×C127—416no—
195C2×C4×C127—416no—
196C2×C4×C127—416no—
197C2×C4×C127—44no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—44no—
203C2×C4×C127—44no—
204C2×C4×C127—44no—
205C2×C4×C127—44no—
206C2×C4×C127—44no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—44no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—44no—
215C2×C4×C127—44no—
216C2×C4×C127—44no—
217C2×C4×C127C2×C4⋊C414yes—
218C2×C4×C127C2×C4⋊C414yes—
219C22×C127—24no—
220C22×C127—24no—
221C22×C127—28no—
222C22×C127—28no—
223C22×C127—24no—
224C22×C127—24no—
225C22×C127—24no—
226C22×C127—24no—
227C22×C127—28no—
228C22×C127—28no—
229C22×C127#38918yes—
230C22×C127C22×C4⋊C411yescharacteristic
231C22×C127C2×C4×D411yescharacteristic
232C22×C127C2×C4×Q811yescharacteristic
233C22×C127#51812yes—
234C22×C127#52012yes—
235C22×C127C2×#12111yescharacteristic
236C22×C127C2×C22⋊Q811yescharacteristic
237C22×C127C2×#12511yescharacteristic
238C22×C127C2×C4⋊Q811yescharacteristic
239C22×C127#53411yescharacteristic
240C22×C127#53411yescharacteristic
241C22×C127#53412yes—
242C22×C127#53511yescharacteristic
243C22×C127#53611yescharacteristic
244C22×C127#53712yes—
245C22×C127#53812yes—
246C22×C127#53812yes—
247C22×C127#53912yes—
248C22×C127#53912yes—
249C22×C127#54312yes—
250C22×C127#54312yes—
251C22×C127#54412yes—
252C22×C127#54412yes—
253C4×C127—24no—
254C4×C127—24no—
255C4×C127—48no—
256C4×C127—44no—
257C4×C127—44no—
258C4×C127—82no—
259C4×C127—82no—
260#14275C12711yesmaximal, characteristic, direct product factor, Sylow
261C2×C127—28no—
262C2×C127C2×#38911yescharacteristic
263C2×C127#231511yescharacteristic
264C2×C127#231711yescharacteristic
265C2×C127#232512yes—
266C2×C127#232912yes—
267C2×C127#261711yescharacteristic
268C2×C127#261811yescharacteristic
269C2×C127#262611yescharacteristic
270C2×C127#262711yescharacteristic
271C2×C127#264612yes—
272C2×C127#265912yes—
273C2×#385C2×C12712yes—
274C2×#380C2×C12711yescharacteristic
275C2×#380C2×C12711yescharacteristic
276C22×#95C2×C12711yescharacteristic
277#1444C2×C12712yescomplemented
278#1442C2×C12712yescomplemented
279#1441C2×C12714yescomplemented
280C22⋊#95C2×C12712yes—
281C127#1427511yescharacteristic, direct product factor, Sylow
282C24×C4C22×C12711yescharacteristic
283C24×C4C22×C12711yescharacteristic
284C24×C4C22×C12711yescharacteristic
285C22×C4⋊C4C22×C12714yes—
286C22×C4⋊C4C22×C12711yescharacteristic
287C22×C4⋊C4C22×C12711yescharacteristic
288C22×C4⋊C4C22×C12712yes—
289C22×C22⋊C4C22×C12712yes—
290C22×C22⋊C4C22×C12712yes—
291#385—28no—
292#380—24no—
293#380C4×C12718yescomplemented
294C2×#95—24no—
295C2×#95C22×C12712yes—
296C2×#95C22×C12712yes—
297C2×#95C22×C12714yes—
298C2×#95C22×C12712yes—
299C2×#95C22×C12714yes—
300C2×#95C22×C12714yes—
301C2×#95C22×C12712yes—
302C25C23×C12711yescharacteristic
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—42no—
311C23×C4—42no—
312C23×C4—42no—
313C23×C4C2×C4×C12714yes—
314C23×C4D4×C12714yes—
315C23×C4D4×C12714yes—
316C23×C4Q8×C12714yes—
317C23×C4Q8×C12714yes—
318C23×C4C23×C12712yes—
319C23×C4C23×C12712yes—
320C23×C4C23×C12714yes—
321C23×C4C23×C12712yes—
322C23×C4C23×C12712yes—
323C23×C4C23×C12711yescharacteristic
324C23×C4C23×C12711yescharacteristic
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4C2×C4×C12718yescomplemented
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4C2×C4×C12718yes—
341#95—24no—
342#95—24no—
343#95—24no—
344#95—28no—
345#95—44no—
346#95—44no—
347#95C2×C4×C12718yescomplemented
348C24—22no—
349C24—22no—
350C24—22no—
351C24—22no—
352C24C22×C4×C12712yes—
353C24C2×D4×C12712yes—
354C24C2×D4×C12712yes—
355C24C2×Q8×C12712yes—
356C24C2×Q8×C12712yes—
357C24#41×C12712yes—
358C24#41×C12712yes—
359C24C24×C12711yescharacteristic
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—28no—
365C22×C4—28no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—48no—
391C22×C4—44no—
392C22×C4—44no—
393C22×C4—48no—
394C22×C4—48no—
395C22×C4—48no—
396C22×C4—44no—
397C22×C4—44no—
398C22×C4—44no—
399C22×C4—44no—
400C22×C4—48no—
401C22×C4—48no—
402C22×C4C4⋊C4×C127116yescomplemented
403C22×C4C22×C4×C12718yes—
404C22×C4C22×C4×C12712yes—
405C22×C4C22×C4×C12712yes—
406C22×C4C2×D4×C12714yes—
407C22×C4C2×D4×C12712yes—
408C22×C4C2×D4×C12712yes—
409C22×C4C2×Q8×C12714yes—
410C22×C4C2×Q8×C12712yes—
411C22×C4C2×Q8×C12712yes—
412C4⋊C4—48no—
413C4⋊C4—44no—
414C4⋊C4—44no—
415C4⋊C4—416no—
416C22⋊C4—216no—
417C22⋊C4—48no—
418C23—24no—
419C23—24no—
420C23—22no—
421C23—22no—
422C23—24no—
423C23—22no—
424C23—22no—
425C23—24no—
426C23—24no—
427C23—24no—
428C23—24no—
429C23—24no—
430C23—24no—
431C23—24no—
432C23—24no—
433C23—24no—
434C23C2×C4⋊C4×C12714yes—
435C23C4×D4×C12714yes—
436C23C4×Q8×C12714yes—
437C23#121×C12714yes—
438C23C22⋊Q8×C12714yes—
439C23#125×C12714yes—
440C23C4⋊Q8×C12714yes—
441C23C23×C4×C12711yescharacteristic
442C23C22×D4×C12711yescharacteristic
443C23C22×D4×C12711yescharacteristic
444C23C22×Q8×C12711yescharacteristic
445C23C22×Q8×C12711yescharacteristic
446C23C2×#41×C12711yescharacteristic
447C23C2×#41×C12711yescharacteristic
448C23H(5,𝔽2)×C12712yes—
449C23H(5,𝔽2)×C12712yes—
450C23H(5,𝔽2)×C12712yes—
451C232−1+4×C12712yes—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—28no—
461C2×C4—28no—
462C2×C4—28no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—28no—
466C2×C4—28no—
467C2×C4—416no—
468C2×C4—416no—
469C2×C4—416no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—44no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—44no—
479C2×C4—44no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—44no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4C2×C4⋊C4×C12714yes—
491C2×C4C2×C4⋊C4×C12714yes—
492C22—24no—
493C22—24no—
494C22—28no—
495C22—28no—
496C22—24no—
497C22—24no—
498C22—24no—
499C22—24no—
500C22—28no—
501C22—28no—
502C22#389×C12718yes—
503C22C22×C4⋊C4×C12711yescharacteristic
504C22C2×C4×D4×C12711yescharacteristic
505C22C2×C4×Q8×C12711yescharacteristic
506C22#518×C12712yes—
507C22#520×C12712yes—
508C22C2×#121×C12711yescharacteristic
509C22C2×C22⋊Q8×C12711yescharacteristic
510C22C2×#125×C12711yescharacteristic
511C22C2×C4⋊Q8×C12711yescharacteristic
512C22#534×C12711yescharacteristic
513C22#534×C12711yescharacteristic
514C22#534×C12712yes—
515C22#535×C12711yescharacteristic
516C22#536×C12711yescharacteristic
517C22#537×C12712yes—
518C22#538×C12712yes—
519C22#538×C12712yes—
520C22#539×C12712yes—
521C22#539×C12712yes—
522C22#543×C12712yes—
523C22#543×C12712yes—
524C22#544×C12712yes—
525C22#544×C12712yes—
526C4—24no—
527C4—24no—
528C4—48no—
529C4—44no—
530C4—44no—
531C4—82no—
532C4—82no—
533C2—28no—
534C2C2×#389×C12711yescharacteristic
535C2C127×#231511yescharacteristic
536C2C127×#231711yescharacteristic
537C2C127×#232512yes—
538C2C127×#232912yes—
539C2C127×#261711yescharacteristic
540C2C127×#261811yescharacteristic
541C2C127×#262611yescharacteristic
542C2C127×#262711yescharacteristic
543C2C127×#264612yes—
544C2C127×#265912yes—
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
5. C127×#1444C2semidirect
6. C127×#1442C2semidirect
7. C127×#1441C2semidirect
20. #380×C127C4semidirect
61. C2×C4⋊C4×C127C2×C4semidirect
74. #95×C127C2×C4semidirect
129. C22×C4×C127C4⋊C4semidirect
260. #14275C127direct (N × H)
277. #1444C2×C127semidirect
278. #1442C2×C127semidirect
279. #1441C2×C127semidirect
281. C127#14275direct (N × H)
293. #380C4×C127semidirect
334. C2×C4⋊C4C2×C4×C127semidirect
347. #95C2×C4×C127semidirect
402. C22×C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#385×C1272
C2×#380×C1272
C22×#95×C1272
C127×#14442
C127×#14422
C127×#14412
C127×C22⋊#952
#14275127