Finite Group Databasebeta

← C127×#15856 #44579529

Subgroups — C127×#15856 #44579529

Order 32512.

1418 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C127C211yesmaximal, characteristic
2C2×#395×C127C212yesmaximal
3C2×#391×C127C211yesmaximal, characteristic
4C2×#387×C127C212yesmaximal
5C127×#1445C212yesmaximal
6C127×#1445C212yesmaximal
7C127×#1444C212yesmaximal
8C127×#1436C211yesmaximal, characteristic
9C127×C4⋊#95C212yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C42×C127C2211yescharacteristic
18C22×C42×C127C2211yescharacteristic
19#398×C127—24no—
20#395×C127—28no—
21#391×C127—24no—
22#387×C127—28no—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2211yescharacteristic
34C2×#95×C127C2212yes—
35C22×Q8×C127—22no—
36C22×Q8×C127—24no—
37C22×Q8×C127—24no—
38C22×Q8×C127—41no—
39C22×Q8×C127—41no—
40C23×C4×C127C2312yes—
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C23×C4×C127C2312yes—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—24no—
58C2×C4⋊C4×C127—24no—
59C2×C4⋊C4×C127—41no—
60C2×C4⋊C4×C127—41no—
61C2×C4⋊C4×C127—42no—
62C2×C4⋊C4×C127—42no—
63C2×C4⋊C4×C127—41no—
64C2×C4⋊C4×C127—41no—
65C2×C4⋊C4×C127D414yes—
66C2×C4⋊C4×C127Q818yescomplemented
67C2×C42×C127—24no—
68C2×C42×C127—22no—
69C2×C42×C127—24no—
70C2×C42×C127—41no—
71#95×C127—24no—
72#95×C127—24no—
73#95×C127—24no—
74#95×C127—24no—
75#95×C127—24no—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—22no—
79#95×C127—24no—
80#95×C127—24no—
81#95×C127—41no—
82#95×C127D418yes—
83C24×C127C2411yescharacteristic
84C2×Q8×C127—28no—
85C2×Q8×C127—48no—
86C2×Q8×C127—48no—
87C2×Q8×C127—44no—
88C2×Q8×C127—44no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—21no—
94C22×C4×C127—21no—
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—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—21no—
113C22×C4×C127—22no—
114C22×C4×C127—21no—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
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—22no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127C2×D412yes—
136C22×C4×C127C2×D414yes—
137C22×C4×C127C2×D412yes—
138C22×C4×C127C2×D414yes—
139C22×C4×C127C2×D414yes—
140C22×C4×C127C2×D412yes—
141C22×C4×C127C2×Q814yes—
142C22×C4×C127C2×Q814yes—
143C22×C4×C127C2×Q814yes—
144C22×C4×C127#4114yes—
145C22×C4×C127#4114yes—
146C4⋊C4×C127—216no—
147C4⋊C4×C127—44no—
148C4⋊C4×C127—48no—
149C4⋊C4×C127—48no—
150C4⋊C4×C127—44no—
151C4⋊C4×C127—48no—
152C42×C127—44no—
153C42×C127—44no—
154C23×C127C22×D412yes—
155C23×C127C22×D411yescharacteristic
156C23×C127C22×Q812yes—
157C23×C127C2×#4112yes—
158C23×C127C2×#4112yes—
159C23×C127H(5,𝔽2)11yescharacteristic
160C23×C127H(5,𝔽2)11yescharacteristic
161C23×C1272−1+412yes—
162C23×C1272−1+412yes—
163Q8×C127—416no—
164C2×C4×C127—22no—
165C2×C4×C127—24no—
166C2×C4×C127—22no—
167C2×C4×C127—24no—
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—22no—
178C2×C4×C127—22no—
179C2×C4×C127—24no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
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—24no—
189C2×C4×C127—24no—
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—41no—
207C2×C4×C127—41no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127C22⋊Q818yes—
220C2×C4×C127#12714yes—
221C22×C127C2×C22⋊Q812yes—
222C22×C127#52511yescharacteristic
223C22×C127C2×#12711yescharacteristic
224C22×C127#53312yes—
225C22×C127#53411yescharacteristic
226C22×C127#53612yes—
227C22×C127#54112yes—
228C22×C127#54212yes—
229C22×C127#54412yes—
230C22×C127#54612yes—
231C22×C127#54612yes—
232C22×C127#54712yes—
233C22×C127#54712yes—
234C22×C127D4×Q812yes—
235C22×C127D4×Q812yes—
236C22×C127#55111yescharacteristic
237C22×C127#55212yes—
238C22×C127#55712yes—
239C22×C127Q8211yescharacteristic
240C22×C127#56311yescharacteristic
241C22×C127#56311yescharacteristic
242C4×C127—28no—
243C4×C127—24no—
244C4×C127—44no—
245C4×C127—42no—
246C4×C127—42no—
247C4×C127—44no—
248C4×C127—44no—
249C4×C127—44no—
250C4×C127—82no—
251#15856C12711yesmaximal, characteristic, direct product factor, Sylow
252C2×C127#243812yes—
253C2×C127#245112yes—
254C2×C127#246212yes—
255C2×C127#253911yescharacteristic
256C2×C127#254212yes—
257C2×C127#269812yes—
258C2×C127#271312yes—
259C2×C127#271711yescharacteristic
260C2×C127#273411yescharacteristic
261C2×#398C2×C12711yescharacteristic
262C2×#395C2×C12712yes—
263C2×#391C2×C12711yescharacteristic
264C2×#387C2×C12712yes—
265#1445C2×C12712yes—
266#1445C2×C12712yes—
267#1444C2×C12712yes—
268#1436C2×C12711yescharacteristic
269C4⋊#95C2×C12712yes—
270C127#1585611yescharacteristic, direct product factor, Sylow
271C23×Q8C22×C12711yescharacteristic
272C22×C4⋊C4C22×C12712yes—
273C22×C4⋊C4C22×C12712yes—
274C22×C4⋊C4C22×C12712yes—
275C22×C4⋊C4C22×C12712yes—
276C22×C4⋊C4C22×C12711yescharacteristic
277C22×C4⋊C4C22×C12711yescharacteristic
278C22×C42C22×C12711yescharacteristic
279C22×C42C22×C12711yescharacteristic
280#398—24no—
281#395—28no—
282#391—24no—
283#387—28no—
284C2×#95C22×C12712yes—
285C2×#95C22×C12712yes—
286C2×#95C22×C12712yes—
287C2×#95C22×C12711yescharacteristic
288C2×#95C22×C12712yes—
289C2×#95C22×C12712yes—
290C2×#95C22×C12712yes—
291C2×#95C22×C12712yes—
292C2×#95C22×C12712yes—
293C2×#95C22×C12712yes—
294C2×#95C22×C12711yescharacteristic
295C2×#95C22×C12712yes—
296C22×Q8—22no—
297C22×Q8—24no—
298C22×Q8—24no—
299C22×Q8—41no—
300C22×Q8—41no—
301C23×C4C23×C12712yes—
302C23×C4C23×C12711yescharacteristic
303C23×C4C23×C12712yes—
304C23×C4C23×C12711yescharacteristic
305C23×C4C23×C12712yes—
306C23×C4C23×C12712yes—
307C23×C4C23×C12712yes—
308C23×C4C23×C12711yescharacteristic
309C23×C4C23×C12712yes—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4D4×C12714yes—
327C2×C4⋊C4Q8×C12718yescomplemented
328C2×C42—24no—
329C2×C42—22no—
330C2×C42—24no—
331C2×C42—41no—
332#95—24no—
333#95—24no—
334#95—24no—
335#95—24no—
336#95—24no—
337#95—24no—
338#95—24no—
339#95—22no—
340#95—24no—
341#95—24no—
342#95—41no—
343#95D4×C12718yes—
344C24C24×C12711yescharacteristic
345C2×Q8—28no—
346C2×Q8—48no—
347C2×Q8—48no—
348C2×Q8—44no—
349C2×Q8—44no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
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—21no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4C2×D4×C12712yes—
397C22×C4C2×D4×C12714yes—
398C22×C4C2×D4×C12712yes—
399C22×C4C2×D4×C12714yes—
400C22×C4C2×D4×C12714yes—
401C22×C4C2×D4×C12712yes—
402C22×C4C2×Q8×C12714yes—
403C22×C4C2×Q8×C12714yes—
404C22×C4C2×Q8×C12714yes—
405C22×C4#41×C12714yes—
406C22×C4#41×C12714yes—
407C4⋊C4—216no—
408C4⋊C4—44no—
409C4⋊C4—48no—
410C4⋊C4—48no—
411C4⋊C4—44no—
412C4⋊C4—48no—
413C42—44no—
414C42—44no—
415C23C22×D4×C12712yes—
416C23C22×D4×C12711yescharacteristic
417C23C22×Q8×C12712yes—
418C23C2×#41×C12712yes—
419C23C2×#41×C12712yes—
420C23H(5,𝔽2)×C12711yescharacteristic
421C23H(5,𝔽2)×C12711yescharacteristic
422C232−1+4×C12712yes—
423C232−1+4×C12712yes—
424Q8—416no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
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—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4C22⋊Q8×C12718yes—
481C2×C4#127×C12714yes—
482C22C2×C22⋊Q8×C12712yes—
483C22#525×C12711yescharacteristic
484C22C2×#127×C12711yescharacteristic
485C22#533×C12712yes—
486C22#534×C12711yescharacteristic
487C22#536×C12712yes—
488C22#541×C12712yes—
489C22#542×C12712yes—
490C22#544×C12712yes—
491C22#546×C12712yes—
492C22#546×C12712yes—
493C22#547×C12712yes—
494C22#547×C12712yes—
495C22D4×Q8×C12712yes—
496C22D4×Q8×C12712yes—
497C22#551×C12711yescharacteristic
498C22#552×C12712yes—
499C22#557×C12712yes—
500C22Q82×C12711yescharacteristic
501C22#563×C12711yescharacteristic
502C22#563×C12711yescharacteristic
503C4—28no—
504C4—24no—
505C4—44no—
506C4—42no—
507C4—42no—
508C4—44no—
509C4—44no—
510C4—44no—
511C4—82no—
512C2C127×#243812yes—
513C2C127×#245112yes—
514C2C127×#246212yes—
515C2C127×#253911yescharacteristic
516C2C127×#254212yes—
517C2C127×#269812yes—
518C2C127×#271312yes—
519C2C127×#271711yescharacteristic
520C2C127×#273411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
66. C2×C4⋊C4×C127Q8semidirect
251. #15856C127direct (N × H)
270. C127#15856direct (N × H)
327. C2×C4⋊C4Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1272
C2×#395×C1272
C2×#391×C1272
C2×#387×C1272
C127×#14452
C127×#14442
C127×#14362
C127×C4⋊#952
#15856127