Finite Group Databasebeta

← C127×#13825 #44577498

Subgroups — C127×#13825 #44577498

Order 32512.

1630 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C127C211yesmaximal, characteristic
2C2×#387×C127C212yesmaximal
3C2×C4×C4⋊C4×C127C212yesmaximal
4C127×#1436C212yesmaximal
5C127×#1436C212yesmaximal
6C127×#1436C212yesmaximal
7C4×#95×C127C211yesmaximal, characteristic
8C4×#95×C127C212yesmaximal
9C4×#95×C127C211yesmaximal, characteristic
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C42×C127C2212yes—
15C22×C42×C127C2212yes—
16C22×C42×C127C2212yes—
17C22×C42×C127C2212yes—
18C22×C42×C127C2211yescharacteristic
19#389×C127C418yescomplemented
20#387×C127C4116yescomplemented
21C4×C4⋊C4×C127—28no—
22C2×#95×C127C2212yes—
23C2×#95×C127C2211yescharacteristic
24C2×#95×C127C2211yescharacteristic
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2211yescharacteristic
33C2×#95×C127C2211yescharacteristic
34C23×C4×C127C2312yes—
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2311yescharacteristic
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2311yescharacteristic
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—42no—
48C2×C4⋊C4×C127C2×C418yes—
49C2×C4⋊C4×C127C2×C418yes—
50C2×C4⋊C4×C127C2×C414yes—
51C2×C4⋊C4×C127C2×C418yes—
52C2×C4⋊C4×C127C2×C414yes—
53C2×C42×C127—24no—
54C2×C42×C127—24no—
55C2×C42×C127—24no—
56C2×C42×C127—24no—
57C2×C42×C127—24no—
58C2×C42×C127—24no—
59C2×C42×C127—24no—
60C2×C42×C127—24no—
61C2×C42×C127—42no—
62C2×C42×C127—42no—
63C2×C42×C127—42no—
64C2×C42×C127—42no—
65C2×C42×C127C2×C418yes—
66C2×C42×C127C2×C414yes—
67#95×C127—24no—
68#95×C127—22no—
69#95×C127—24no—
70#95×C127—22no—
71#95×C127—42no—
72#95×C127C2×C418yes—
73#95×C127C2×C418yes—
74#95×C127C2×C418yes—
75#95×C127C2×C418yes—
76#95×C127C2×C418yes—
77#95×C127D414yes—
78#95×C127Q814yes—
79C24×C127C2411yescharacteristic
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
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—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127C22×C414yes—
118C22×C4×C127C22×C414yes—
119C22×C4×C127C22×C414yes—
120C22×C4×C127C22×C414yes—
121C22×C4×C127C22×C414yes—
122C22×C4×C127C22×C414yes—
123C22×C4×C127C22×C414yes—
124C22×C4×C127C22×C412yes—
125C22×C4×C127C22×C414yes—
126C22×C4×C127C22×C412yes—
127C22×C4×C127C22×C414yes—
128C22×C4×C127C22×C412yes—
129C22×C4×C127C2×D414yes—
130C22×C4×C127C2×D412yes—
131C22×C4×C127C2×Q814yes—
132C22×C4×C127C2×Q812yes—
133C22×C4×C127#4112yes—
134C22×C4×C127#4114yes—
135C22×C4×C127#4114yes—
136C22×C4×C127#4112yes—
137C4⋊C4×C127—216no—
138C4⋊C4×C127—216no—
139C4⋊C4×C127—44no—
140C4⋊C4×C127C42116yescomplemented
141C42×C127—216no—
142C42×C127—44no—
143C42×C127—48no—
144C42×C127—48no—
145C42×C127—48no—
146C23×C127C23×C411yescharacteristic
147C23×C127C23×C412yes—
148C23×C127C22×D411yescharacteristic
149C23×C127C22×Q811yescharacteristic
150C23×C127C2×#4112yes—
151C23×C127C2×#4111yescharacteristic
152C23×C127C2×#4112yes—
153C23×C127C2×#4111yescharacteristic
154C23×C127H(5,𝔽2)12yes—
155C23×C1272−1+411yescharacteristic
156C23×C1272−1+411yescharacteristic
157C2×C4×C127—24no—
158C2×C4×C127—24no—
159C2×C4×C127—24no—
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—22no—
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—22no—
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—24no—
178C2×C4×C127—24no—
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—24no—
191C2×C4×C127—24no—
192C2×C4×C127—24no—
193C2×C4×C127—24no—
194C2×C4×C127—24no—
195C2×C4×C127—24no—
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—42no—
207C2×C4×C127—42no—
208C2×C4×C127C2×C4218yes—
209C2×C4×C127C2×C4214yes—
210C2×C4×C127C4×D418yes—
211C2×C4×C127C4×D414yes—
212C2×C4×C127C4×Q818yes—
213C2×C4×C127C4×Q814yes—
214C22×C127C22×C4211yescharacteristic
215C22×C127C2×C4×D412yes—
216C22×C127C2×C4×D411yescharacteristic
217C22×C127C2×C4×Q812yes—
218C22×C127C2×C4×Q811yescharacteristic
219C22×C127C4×#4112yes—
220C22×C127C4×#4111yescharacteristic
221C22×C127C4×#4111yescharacteristic
222C22×C127C4×#4112yes—
223C22×C127#51811yescharacteristic
224C22×C127#51911yescharacteristic
225C22×C127#52012yes—
226C22×C127#52012yes—
227C22×C127#54612yes—
228C22×C127#54711yescharacteristic
229C22×C127D4×Q811yescharacteristic
230C22×C127#55112yes—
231C22×C127#55212yes—
232C22×C127#55212yes—
233C22×C127#55312yes—
234C22×C127#55412yes—
235C22×C127#55611yescharacteristic
236C22×C127#55711yescharacteristic
237C4×C127—28no—
238C4×C127—28no—
239C4×C127—24no—
240C4×C127—24no—
241C4×C127—28no—
242C4×C127—24no—
243C4×C127—44no—
244C4×C127—44no—
245C4×C127—44no—
246#13825C12711yesmaximal, characteristic, direct product factor, Sylow
247C2×C127C42×D411yescharacteristic
248C2×C127C42×Q811yescharacteristic
249C2×C127#227411yescharacteristic
250C2×C127#235912yes—
251C2×C127#236012yes—
252C2×C127#236411yescharacteristic
253C2×C127#236511yescharacteristic
254C2×C127#236811yescharacteristic
255C2×C127#237012yes—
256C2×C127#237111yescharacteristic
257C2×C127#237312yes—
258C2×#389C2×C12711yescharacteristic
259C2×#387C2×C12712yes—
260C2×C4×C4⋊C4C2×C12712yes—
261#1436C2×C12712yes—
262#1436C2×C12712yes—
263#1436C2×C12712yes—
264C4×#95C2×C12711yescharacteristic
265C4×#95C2×C12711yescharacteristic
266C4×#95C2×C12712yes—
267C127#1382511yescharacteristic, direct product factor, Sylow
268C22×C4⋊C4C22×C12712yes—
269C22×C4⋊C4C22×C12712yes—
270C22×C4⋊C4C22×C12711yescharacteristic
271C22×C4⋊C4C22×C12711yescharacteristic
272C22×C42C22×C12712yes—
273C22×C42C22×C12712yes—
274C22×C42C22×C12712yes—
275C22×C42C22×C12712yes—
276C22×C42C22×C12711yescharacteristic
277#389C4×C12718yescomplemented
278#387C4×C127116yescomplemented
279C4×C4⋊C4—28no—
280C2×#95C22×C12712yes—
281C2×#95C22×C12711yescharacteristic
282C2×#95C22×C12711yescharacteristic
283C2×#95C22×C12712yes—
284C2×#95C22×C12712yes—
285C2×#95C22×C12712yes—
286C2×#95C22×C12712yes—
287C2×#95C22×C12712yes—
288C2×#95C22×C12712yes—
289C2×#95C22×C12712yes—
290C2×#95C22×C12711yescharacteristic
291C2×#95C22×C12711yescharacteristic
292C23×C4C23×C12712yes—
293C23×C4C23×C12712yes—
294C23×C4C23×C12712yes—
295C23×C4C23×C12712yes—
296C23×C4C23×C12711yescharacteristic
297C23×C4C23×C12711yescharacteristic
298C23×C4C23×C12712yes—
299C23×C4C23×C12712yes—
300C23×C4C23×C12711yescharacteristic
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4C2×C4×C12718yes—
307C2×C4⋊C4C2×C4×C12718yes—
308C2×C4⋊C4C2×C4×C12714yes—
309C2×C4⋊C4C2×C4×C12718yes—
310C2×C4⋊C4C2×C4×C12714yes—
311C2×C42—24no—
312C2×C42—24no—
313C2×C42—24no—
314C2×C42—24no—
315C2×C42—24no—
316C2×C42—24no—
317C2×C42—24no—
318C2×C42—24no—
319C2×C42—42no—
320C2×C42—42no—
321C2×C42—42no—
322C2×C42—42no—
323C2×C42C2×C4×C12718yes—
324C2×C42C2×C4×C12714yes—
325#95—24no—
326#95—22no—
327#95—24no—
328#95—22no—
329#95—42no—
330#95C2×C4×C12718yes—
331#95C2×C4×C12718yes—
332#95C2×C4×C12718yes—
333#95C2×C4×C12718yes—
334#95C2×C4×C12718yes—
335#95D4×C12714yes—
336#95Q8×C12714yes—
337C24C24×C12711yescharacteristic
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
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—22no—
374C22×C4—22no—
375C22×C4C22×C4×C12714yes—
376C22×C4C22×C4×C12714yes—
377C22×C4C22×C4×C12714yes—
378C22×C4C22×C4×C12714yes—
379C22×C4C22×C4×C12714yes—
380C22×C4C22×C4×C12714yes—
381C22×C4C22×C4×C12714yes—
382C22×C4C22×C4×C12712yes—
383C22×C4C22×C4×C12714yes—
384C22×C4C22×C4×C12712yes—
385C22×C4C22×C4×C12714yes—
386C22×C4C22×C4×C12712yes—
387C22×C4C2×D4×C12714yes—
388C22×C4C2×D4×C12712yes—
389C22×C4C2×Q8×C12714yes—
390C22×C4C2×Q8×C12712yes—
391C22×C4#41×C12712yes—
392C22×C4#41×C12714yes—
393C22×C4#41×C12714yes—
394C22×C4#41×C12712yes—
395C4⋊C4—216no—
396C4⋊C4—216no—
397C4⋊C4—44no—
398C4⋊C4C42×C127116yescomplemented
399C42—216no—
400C42—44no—
401C42—48no—
402C42—48no—
403C42—48no—
404C23C23×C4×C12711yescharacteristic
405C23C23×C4×C12712yes—
406C23C22×D4×C12711yescharacteristic
407C23C22×Q8×C12711yescharacteristic
408C23C2×#41×C12712yes—
409C23C2×#41×C12711yescharacteristic
410C23C2×#41×C12712yes—
411C23C2×#41×C12711yescharacteristic
412C23H(5,𝔽2)×C12712yes—
413C232−1+4×C12711yescharacteristic
414C232−1+4×C12711yescharacteristic
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
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—24no—
439C2×C4—24no—
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—24no—
452C2×C4—24no—
453C2×C4—24no—
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×C4C2×C42×C12718yes—
467C2×C4C2×C42×C12714yes—
468C2×C4C4×D4×C12718yes—
469C2×C4C4×D4×C12714yes—
470C2×C4C4×Q8×C12718yes—
471C2×C4C4×Q8×C12714yes—
472C22C22×C42×C12711yescharacteristic
473C22C2×C4×D4×C12712yes—
474C22C2×C4×D4×C12711yescharacteristic
475C22C2×C4×Q8×C12712yes—
476C22C2×C4×Q8×C12711yescharacteristic
477C22C4×#41×C12712yes—
478C22C4×#41×C12711yescharacteristic
479C22C4×#41×C12711yescharacteristic
480C22C4×#41×C12712yes—
481C22#518×C12711yescharacteristic
482C22#519×C12711yescharacteristic
483C22#520×C12712yes—
484C22#520×C12712yes—
485C22#546×C12712yes—
486C22#547×C12711yescharacteristic
487C22D4×Q8×C12711yescharacteristic
488C22#551×C12712yes—
489C22#552×C12712yes—
490C22#552×C12712yes—
491C22#553×C12712yes—
492C22#554×C12712yes—
493C22#556×C12711yescharacteristic
494C22#557×C12711yescharacteristic
495C4—28no—
496C4—28no—
497C4—24no—
498C4—24no—
499C4—28no—
500C4—24no—
501C4—44no—
502C4—44no—
503C4—44no—
504C2C42×D4×C12711yescharacteristic
505C2C42×Q8×C12711yescharacteristic
506C2C127×#227411yescharacteristic
507C2C127×#235912yes—
508C2C127×#236012yes—
509C2C127×#236411yescharacteristic
510C2C127×#236511yescharacteristic
511C2C127×#236811yescharacteristic
512C2C127×#237012yes—
513C2C127×#237111yescharacteristic
514C2C127×#237312yes—
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
19. #389×C127C4semidirect
20. #387×C127C4semidirect
140. C4⋊C4×C127C42semidirect
246. #13825C127direct (N × H)
267. C127#13825direct (N × H)
277. #389C4×C127semidirect
278. #387C4×C127semidirect
398. C4⋊C4C42×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1272
C2×#387×C1272
C2×C4×C4⋊C4×C1272
C127×#14362
C4×#95×C1272
#13825127