Finite Group Databasebeta

← C127×#15011 #44578684

Subgroups — C127×#15011 #44578684

Order 32512.

1466 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×#395×C127C212yesmaximal
2C2×#391×C127C212yesmaximal
3C127×#1446C212yesmaximal
4C127×#1442C212yesmaximal
5C127×#1441C212yesmaximal
6C127×#1436C212yesmaximal
7C127×C4⋊#95C211yesmaximal, characteristic
8C127×#1434C211yesmaximal, characteristic
9C4×#95×C127C211yesmaximal, characteristic
10C23×Q8×C127C2212yes—
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2212yes—
14C22×C42×C127C2212yes—
15C22×C42×C127C2211yescharacteristic
16#395×C127—28no—
17#391×C127—28no—
18C2×#95×C127C2212yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2211yescharacteristic
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2211yescharacteristic
33C22×Q8×C127—24no—
34C22×Q8×C127—24no—
35C22×Q8×C127—24no—
36C22×Q8×C127—24no—
37C22×Q8×C127—24no—
38C22×Q8×C127—42no—
39C22×Q8×C127—42no—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2311yescharacteristic
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—24no—
56C2×C4⋊C4×C127—42no—
57C2×C4⋊C4×C127—42no—
58C2×C42×C127—24no—
59C2×C42×C127—24no—
60C2×C42×C127—42no—
61C2×C42×C127—42no—
62C2×C42×C127Q814yescomplemented
63#95×C127—24no—
64#95×C127—24no—
65#95×C127—24no—
66#95×C127—24no—
67#95×C127—24no—
68#95×C127—24no—
69#95×C127—24no—
70#95×C127—42no—
71#95×C127—42no—
72#95×C127—41no—
73#95×C127—41no—
74#95×C127D414yes—
75#95×C127D414yes—
76#95×C127Q814yescomplemented
77#95×C127Q814yescomplemented
78C24×C127C2411yescharacteristic
79C2×Q8×C127—216no—
80C2×Q8×C127—48no—
81C2×Q8×C127—48no—
82C2×Q8×C127—48no—
83C2×Q8×C127—48no—
84C2×Q8×C127—48no—
85C2×Q8×C127—48no—
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—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—21no—
112C22×C4×C127—22no—
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—21no—
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×C127C2×D414yes—
130C22×C4×C127C2×D414yes—
131C22×C4×C127C2×D412yes—
132C22×C4×C127C2×D412yes—
133C22×C4×C127C2×Q814yes—
134C22×C4×C127C2×Q814yes—
135C22×C4×C127C2×Q812yes—
136C22×C4×C127C2×Q812yes—
137C22×C4×C127C2×Q812yes—
138C22×C4×C127C2×Q812yes—
139C22×C4×C127C2×Q812yes—
140C22×C4×C127#4114yes—
141C22×C4×C127#4114yes—
142C22×C4×C127#4114yes—
143C4⋊C4×C127—48no—
144C4⋊C4×C127—48no—
145C4⋊C4×C127—48no—
146C42×C127—44no—
147C42×C127—48no—
148C23×C127C22×D411yescharacteristic
149C23×C127C22×D411yescharacteristic
150C23×C127C22×Q811yescharacteristic
151C23×C127C22×Q811yescharacteristic
152C23×C127C22×Q811yescharacteristic
153C23×C127C2×#4112yes—
154C23×C127C2×#4112yes—
155C23×C127C2×#4112yes—
156C23×C127H(5,𝔽2)11yescharacteristic
157C23×C127H(5,𝔽2)12yes—
158C23×C1272−1+411yescharacteristic
159Q8×C127—432no—
160C2×C4×C127—24no—
161C2×C4×C127—22no—
162C2×C4×C127—22no—
163C2×C4×C127—24no—
164C2×C4×C127—22no—
165C2×C4×C127—22no—
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—24no—
175C2×C4×C127—24no—
176C2×C4×C127—22no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
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—42no—
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—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#12418yes—
215C2×C4×C127C4⋊Q814yes—
216C2×C4×C127C4⋊Q814yes—
217C22×C127#52512yes—
218C22×C127C2×#12412yes—
219C22×C127C2×C4⋊Q811yescharacteristic
220C22×C127C2×C4⋊Q811yescharacteristic
221C22×C127#53312yes—
222C22×C127#53312yes—
223C22×C127#53311yescharacteristic
224C22×C127#53311yescharacteristic
225C22×C127#53311yescharacteristic
226C22×C127#53812yes—
227C22×C127#54212yes—
228C22×C127#54311yescharacteristic
229C22×C127#54411yescharacteristic
230C22×C127D4211yescharacteristic
231C22×C127#54612yes—
232C22×C127#54612yes—
233C22×C127D4×Q811yescharacteristic
234C22×C127D4×Q811yescharacteristic
235C22×C127#55112yes—
236C22×C127#55412yes—
237C22×C127#55412yes—
238C22×C127#55612yes—
239C22×C127Q8211yescharacteristic
240C4×C127—28no—
241C4×C127—24no—
242C4×C127—24no—
243C4×C127—42no—
244C4×C127—44no—
245C4×C127—44no—
246C4×C127—44no—
247C4×C127—44no—
248C4×C127—82no—
249#15011C12711yesmaximal, characteristic, direct product factor, Sylow
250C2×C127#239911yescharacteristic
251C2×C127#246512yes—
252C2×C127#247212yes—
253C2×C127#249212yes—
254C2×C127#254911yescharacteristic
255C2×C127#254911yescharacteristic
256C2×C127#255111yescharacteristic
257C2×C127#258612yes—
258C2×C127#260511yescharacteristic
259C2×C127#266511yescharacteristic
260C2×C127#286211yescharacteristic
261C2×#395C2×C12712yes—
262C2×#391C2×C12712yes—
263#1446C2×C12712yes—
264#1442C2×C12712yes—
265#1441C2×C12712yes—
266#1436C2×C12712yes—
267C4⋊#95C2×C12711yescharacteristic
268#1434C2×C12711yescharacteristic
269C4×#95C2×C12711yescharacteristic
270C127#1501111yescharacteristic, direct product factor, Sylow
271C23×Q8C22×C12712yes—
272C22×C4⋊C4C22×C12712yes—
273C22×C4⋊C4C22×C12712yes—
274C22×C4⋊C4C22×C12712yes—
275C22×C42C22×C12712yes—
276C22×C42C22×C12711yescharacteristic
277#395—28no—
278#391—28no—
279C2×#95C22×C12712yes—
280C2×#95C22×C12712yes—
281C2×#95C22×C12712yes—
282C2×#95C22×C12712yes—
283C2×#95C22×C12712yes—
284C2×#95C22×C12712yes—
285C2×#95C22×C12712yes—
286C2×#95C22×C12712yes—
287C2×#95C22×C12711yescharacteristic
288C2×#95C22×C12711yescharacteristic
289C2×#95C22×C12712yes—
290C2×#95C22×C12711yescharacteristic
291C2×#95C22×C12711yescharacteristic
292C2×#95C22×C12711yescharacteristic
293C2×#95C22×C12711yescharacteristic
294C22×Q8—24no—
295C22×Q8—24no—
296C22×Q8—24no—
297C22×Q8—24no—
298C22×Q8—24no—
299C22×Q8—42no—
300C22×Q8—42no—
301C23×C4C23×C12712yes—
302C23×C4C23×C12712yes—
303C23×C4C23×C12712yes—
304C23×C4C23×C12712yes—
305C23×C4C23×C12711yescharacteristic
306C23×C4C23×C12712yes—
307C23×C4C23×C12711yescharacteristic
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—24no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C42—24no—
320C2×C42—24no—
321C2×C42—42no—
322C2×C42—42no—
323C2×C42Q8×C12714yescomplemented
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—24no—
329#95—24no—
330#95—24no—
331#95—42no—
332#95—42no—
333#95—41no—
334#95—41no—
335#95D4×C12714yes—
336#95D4×C12714yes—
337#95Q8×C12714yescomplemented
338#95Q8×C12714yescomplemented
339C24C24×C12711yescharacteristic
340C2×Q8—216no—
341C2×Q8—48no—
342C2×Q8—48no—
343C2×Q8—48no—
344C2×Q8—48no—
345C2×Q8—48no—
346C2×Q8—48no—
347C22×C4—22no—
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—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—21no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
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×C4C2×D4×C12714yes—
391C22×C4C2×D4×C12714yes—
392C22×C4C2×D4×C12712yes—
393C22×C4C2×D4×C12712yes—
394C22×C4C2×Q8×C12714yes—
395C22×C4C2×Q8×C12714yes—
396C22×C4C2×Q8×C12712yes—
397C22×C4C2×Q8×C12712yes—
398C22×C4C2×Q8×C12712yes—
399C22×C4C2×Q8×C12712yes—
400C22×C4C2×Q8×C12712yes—
401C22×C4#41×C12714yes—
402C22×C4#41×C12714yes—
403C22×C4#41×C12714yes—
404C4⋊C4—48no—
405C4⋊C4—48no—
406C4⋊C4—48no—
407C42—44no—
408C42—48no—
409C23C22×D4×C12711yescharacteristic
410C23C22×D4×C12711yescharacteristic
411C23C22×Q8×C12711yescharacteristic
412C23C22×Q8×C12711yescharacteristic
413C23C22×Q8×C12711yescharacteristic
414C23C2×#41×C12712yes—
415C23C2×#41×C12712yes—
416C23C2×#41×C12712yes—
417C23H(5,𝔽2)×C12711yescharacteristic
418C23H(5,𝔽2)×C12712yes—
419C232−1+4×C12711yescharacteristic
420Q8—432no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
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—22no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
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—42no—
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—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4#124×C12718yes—
476C2×C4C4⋊Q8×C12714yes—
477C2×C4C4⋊Q8×C12714yes—
478C22#525×C12712yes—
479C22C2×#124×C12712yes—
480C22C2×C4⋊Q8×C12711yescharacteristic
481C22C2×C4⋊Q8×C12711yescharacteristic
482C22#533×C12712yes—
483C22#533×C12712yes—
484C22#533×C12711yescharacteristic
485C22#533×C12711yescharacteristic
486C22#533×C12711yescharacteristic
487C22#538×C12712yes—
488C22#542×C12712yes—
489C22#543×C12711yescharacteristic
490C22#544×C12711yescharacteristic
491C22D42×C12711yescharacteristic
492C22#546×C12712yes—
493C22#546×C12712yes—
494C22D4×Q8×C12711yescharacteristic
495C22D4×Q8×C12711yescharacteristic
496C22#551×C12712yes—
497C22#554×C12712yes—
498C22#554×C12712yes—
499C22#556×C12712yes—
500C22Q82×C12711yescharacteristic
501C4—28no—
502C4—24no—
503C4—24no—
504C4—42no—
505C4—44no—
506C4—44no—
507C4—44no—
508C4—44no—
509C4—82no—
510C2C127×#239911yescharacteristic
511C2C127×#246512yes—
512C2C127×#247212yes—
513C2C127×#249212yes—
514C2C127×#254911yescharacteristic
515C2C127×#254911yescharacteristic
516C2C127×#255111yescharacteristic
517C2C127×#258612yes—
518C2C127×#260511yescharacteristic
519C2C127×#266511yescharacteristic
520C2C127×#286211yescharacteristic
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
62. C2×C42×C127Q8semidirect
76. #95×C127Q8semidirect
77. #95×C127Q8semidirect
249. #15011C127direct (N × H)
270. C127#15011direct (N × H)
323. C2×C42Q8×C127semidirect
337. #95Q8×C127semidirect
338. #95Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1272
C2×#391×C1272
C127×#14462
C127×#14422
C127×#14412
C127×#14362
C127×C4⋊#952
C127×#14342
C4×#95×C1272
#15011127