Finite Group Databasebeta

← C127×#14000 #44577673

Subgroups — C127×#14000 #44577673

Order 32512.

1534 conjugacy classes of subgroups.

The subgroup lattice has 514 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×#384×C127C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
6C127×#1442C214yesmaximal
7C127×#1436C214yesmaximal
8C127×C4⋊#95C211yesmaximal, characteristic
9C4×#95×C127C211yesmaximal, characteristic
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2214yes—
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C42×C127C2211yescharacteristic
16C22×C42×C127C2211yescharacteristic
17C22×C42×C127C2211yescharacteristic
18C22×C42×C127C2212yes—
19#391×C127—24no—
20#391×C127—24no—
21#391×C127C418yescomplemented
22#384×C127—24no—
23C4×C4⋊C4×C127—24no—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2214yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2214yes—
30C2×#95×C127C2214yes—
31C2×#95×C127C2212yes—
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×C127C2311yescharacteristic
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2311yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C2×C4⋊C4×C127—22no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—22no—
52C2×C4⋊C4×C127—28no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—28no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—44no—
58C2×C4⋊C4×C127C2×C414yes—
59C2×C4⋊C4×C127D414yes—
60C2×C42×C127—22no—
61C2×C42×C127—22no—
62C2×C42×C127—22no—
63C2×C42×C127—22no—
64C2×C42×C127—24no—
65C2×C42×C127—22no—
66C2×C42×C127—22no—
67C2×C42×C127—22no—
68C2×C42×C127—44no—
69C2×C42×C127C2×C414yes—
70C2×C42×C127D414yes—
71#95×C127—24no—
72#95×C127—28no—
73#95×C127—24no—
74#95×C127—24no—
75#95×C127—24no—
76#95×C127—44no—
77#95×C127C2×C4116yes—
78#95×C127Q818yescomplemented
79C24×C127C2411yescharacteristic
80C2×Q8×C127—28no—
81C2×Q8×C127—28no—
82C2×Q8×C127—28no—
83C2×Q8×C127—44no—
84C2×Q8×C127—44no—
85C2×Q8×C127—44no—
86C2×Q8×C127—44no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—21no—
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—21no—
102C22×C4×C127—21no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—24no—
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—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×C127C22×C414yes—
124C22×C4×C127C22×C414yes—
125C22×C4×C127C22×C414yes—
126C22×C4×C127C22×C412yes—
127C22×C4×C127C2×D412yes—
128C22×C4×C127C2×D414yes—
129C22×C4×C127C2×D412yes—
130C22×C4×C127C2×D412yes—
131C22×C4×C127C2×D412yes—
132C22×C4×C127C2×Q814yes—
133C22×C4×C127C2×Q814yes—
134C22×C4×C127C2×Q814yes—
135C22×C4×C127#4114yes—
136C22×C4×C127#4112yes—
137C22×C4×C127#4112yes—
138C22×C4×C127#4112yes—
139C22×C4×C127#4112yes—
140C4⋊C4×C127—28no—
141C4⋊C4×C127—28no—
142C4⋊C4×C127—416no—
143C4⋊C4×C127—44no—
144C42×C127—28no—
145C42×C127—28no—
146C42×C127—48no—
147C42×C127—44no—
148C23×C127C23×C411yescharacteristic
149C23×C127C22×D411yescharacteristic
150C23×C127C22×D411yescharacteristic
151C23×C127C22×Q812yes—
152C23×C127C2×#4111yescharacteristic
153C23×C127C2×#4111yescharacteristic
154C23×C127C2×#4111yescharacteristic
155C23×C127C2×#4111yescharacteristic
156C23×C127C2×#4112yes—
157C23×C127H(5,𝔽2)12yes—
158C23×C1272−1+412yes—
159Q8×C127—416no—
160C2×C4×C127—24no—
161C2×C4×C127—24no—
162C2×C4×C127—22no—
163C2×C4×C127—22no—
164C2×C4×C127—24no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
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—28no—
175C2×C4×C127—24no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—24no—
179C2×C4×C127—22no—
180C2×C4×C127—28no—
181C2×C4×C127—24no—
182C2×C4×C127—24no—
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—44no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—44no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—44no—
203C2×C4×C127—44no—
204C2×C4×C127#11714yes—
205C2×C4×C127C4×D414yes—
206C2×C4×C127C4×D414yes—
207C2×C4×C127C4×Q818yes—
208C2×C4×C127#12114yes—
209C2×C4×C127#12314yes—
210C2×C4×C127#12414yes—
211C2×C4×C127#12614yes—
212C2×C4×C127C4⋊Q814yes—
213C22×C127C2×#11711yescharacteristic
214C22×C127C2×C4×D411yescharacteristic
215C22×C127C2×C4×D411yescharacteristic
216C22×C127C2×C4×Q812yes—
217C22×C127#52012yes—
218C22×C127C2×#12111yescharacteristic
219C22×C127C2×#12311yescharacteristic
220C22×C127C2×#12411yescharacteristic
221C22×C127C2×#12611yescharacteristic
222C22×C127C2×C4⋊Q811yescharacteristic
223C22×C127#53211yescharacteristic
224C22×C127#53312yes—
225C22×C127#53511yescharacteristic
226C22×C127#53611yescharacteristic
227C22×C127#54212yes—
228C22×C127#54612yes—
229C22×C127D4×Q812yes—
230C22×C127#55212yes—
231C22×C127#55412yes—
232C22×C127#55412yes—
233C22×C127#55612yes—
234C22×C127#55712yes—
235C22×C127#55912yes—
236C4×C127—28no—
237C4×C127—24no—
238C4×C127—44no—
239C4×C127—44no—
240C4×C127—42no—
241C4×C127—44no—
242C4×C127—44no—
243C4×C127—82no—
244C4×C127#38818yes—
245#14000C12711yesmaximal, characteristic, direct product factor, Sylow
246C2×C127C2×#38811yescharacteristic
247C2×C127C4×C4⋊Q811yescharacteristic
248C2×C127#232611yescharacteristic
249C2×C127#235512yes—
250C2×C127#236012yes—
251C2×C127#249212yes—
252C2×C127#249911yescharacteristic
253C2×C127#250211yescharacteristic
254C2×C127#251112yes—
255C2×C127#254411yescharacteristic
256C2×C127#254611yescharacteristic
257C2×#391C2×C12711yescharacteristic
258C2×#391C2×C12711yescharacteristic
259C2×#391C2×C12711yescharacteristic
260C2×#384C2×C12711yescharacteristic
261C2×C4×C4⋊C4C2×C12711yescharacteristic
262#1442C2×C12714yes—
263#1436C2×C12714yes—
264C4⋊#95C2×C12711yescharacteristic
265C4×#95C2×C12711yescharacteristic
266C127#1400011yescharacteristic, direct product factor, Sylow
267C23×Q8C22×C12711yescharacteristic
268C22×C4⋊C4C22×C12711yescharacteristic
269C22×C4⋊C4C22×C12714yes—
270C22×C4⋊C4C22×C12711yescharacteristic
271C22×C4⋊C4C22×C12711yescharacteristic
272C22×C42C22×C12711yescharacteristic
273C22×C42C22×C12711yescharacteristic
274C22×C42C22×C12711yescharacteristic
275C22×C42C22×C12712yes—
276#391—24no—
277#391—24no—
278#391C4×C12718yescomplemented
279#384—24no—
280C4×C4⋊C4—24no—
281C2×#95C22×C12712yes—
282C2×#95C22×C12712yes—
283C2×#95C22×C12714yes—
284C2×#95C22×C12712yes—
285C2×#95C22×C12712yes—
286C2×#95C22×C12714yes—
287C2×#95C22×C12714yes—
288C2×#95C22×C12712yes—
289C22×Q8—22no—
290C22×Q8—22no—
291C22×Q8—22no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—22no—
295C22×Q8C2×C4×C12714yes—
296C23×C4C23×C12712yes—
297C23×C4C23×C12712yes—
298C23×C4C23×C12712yes—
299C23×C4C23×C12712yes—
300C23×C4C23×C12711yescharacteristic
301C23×C4C23×C12712yes—
302C23×C4C23×C12712yes—
303C23×C4C23×C12711yescharacteristic
304C23×C4C23×C12711yescharacteristic
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4C2×C4×C12714yes—
316C2×C4⋊C4D4×C12714yes—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—24no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—22no—
325C2×C42—44no—
326C2×C42C2×C4×C12714yes—
327C2×C42D4×C12714yes—
328#95—24no—
329#95—28no—
330#95—24no—
331#95—24no—
332#95—24no—
333#95—44no—
334#95C2×C4×C127116yes—
335#95Q8×C12718yescomplemented
336C24C24×C12711yescharacteristic
337C2×Q8—28no—
338C2×Q8—28no—
339C2×Q8—28no—
340C2×Q8—44no—
341C2×Q8—44no—
342C2×Q8—44no—
343C2×Q8—44no—
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—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—24no—
379C22×C4—24no—
380C22×C4C22×C4×C12714yes—
381C22×C4C22×C4×C12714yes—
382C22×C4C22×C4×C12714yes—
383C22×C4C22×C4×C12712yes—
384C22×C4C2×D4×C12712yes—
385C22×C4C2×D4×C12714yes—
386C22×C4C2×D4×C12712yes—
387C22×C4C2×D4×C12712yes—
388C22×C4C2×D4×C12712yes—
389C22×C4C2×Q8×C12714yes—
390C22×C4C2×Q8×C12714yes—
391C22×C4C2×Q8×C12714yes—
392C22×C4#41×C12714yes—
393C22×C4#41×C12712yes—
394C22×C4#41×C12712yes—
395C22×C4#41×C12712yes—
396C22×C4#41×C12712yes—
397C4⋊C4—28no—
398C4⋊C4—28no—
399C4⋊C4—416no—
400C4⋊C4—44no—
401C42—28no—
402C42—28no—
403C42—48no—
404C42—44no—
405C23C23×C4×C12711yescharacteristic
406C23C22×D4×C12711yescharacteristic
407C23C22×D4×C12711yescharacteristic
408C23C22×Q8×C12712yes—
409C23C2×#41×C12711yescharacteristic
410C23C2×#41×C12711yescharacteristic
411C23C2×#41×C12711yescharacteristic
412C23C2×#41×C12711yescharacteristic
413C23C2×#41×C12712yes—
414C23H(5,𝔽2)×C12712yes—
415C232−1+4×C12712yes—
416Q8—416no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—28no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—28no—
438C2×C4—24no—
439C2×C4—24no—
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—44no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—44no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4#117×C12714yes—
462C2×C4C4×D4×C12714yes—
463C2×C4C4×D4×C12714yes—
464C2×C4C4×Q8×C12718yes—
465C2×C4#121×C12714yes—
466C2×C4#123×C12714yes—
467C2×C4#124×C12714yes—
468C2×C4#126×C12714yes—
469C2×C4C4⋊Q8×C12714yes—
470C22C2×#117×C12711yescharacteristic
471C22C2×C4×D4×C12711yescharacteristic
472C22C2×C4×D4×C12711yescharacteristic
473C22C2×C4×Q8×C12712yes—
474C22#520×C12712yes—
475C22C2×#121×C12711yescharacteristic
476C22C2×#123×C12711yescharacteristic
477C22C2×#124×C12711yescharacteristic
478C22C2×#126×C12711yescharacteristic
479C22C2×C4⋊Q8×C12711yescharacteristic
480C22#532×C12711yescharacteristic
481C22#533×C12712yes—
482C22#535×C12711yescharacteristic
483C22#536×C12711yescharacteristic
484C22#542×C12712yes—
485C22#546×C12712yes—
486C22D4×Q8×C12712yes—
487C22#552×C12712yes—
488C22#554×C12712yes—
489C22#554×C12712yes—
490C22#556×C12712yes—
491C22#557×C12712yes—
492C22#559×C12712yes—
493C4—28no—
494C4—24no—
495C4—44no—
496C4—44no—
497C4—42no—
498C4—44no—
499C4—44no—
500C4—82no—
501C4#388×C12718yes—
502C2C2×#388×C12711yescharacteristic
503C2C4×C4⋊Q8×C12711yescharacteristic
504C2C127×#232611yescharacteristic
505C2C127×#235512yes—
506C2C127×#236012yes—
507C2C127×#249212yes—
508C2C127×#249911yescharacteristic
509C2C127×#250211yescharacteristic
510C2C127×#251112yes—
511C2C127×#254411yescharacteristic
512C2C127×#254611yescharacteristic
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
21. #391×C127C4semidirect
78. #95×C127Q8semidirect
245. #14000C127direct (N × H)
266. C127#14000direct (N × H)
278. #391C4×C127semidirect
335. #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
C2×#384×C1272
C2×C4×C4⋊C4×C1272
C127×#14422
C127×#14362
C127×C4⋊#952
C4×#95×C1272
#14000127