Finite Group Databasebeta

← C127×#17043 #44580716

Subgroups — C127×#17043 #44580716

Order 32512.

1102 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×#389×C127C211yesmaximal, characteristic
2C2×#387×C127C211yesmaximal, characteristic
3C127×#1445C211yesmaximal, characteristic
4C127×#1445C211yesmaximal, characteristic
5C127×#1444C212yesmaximal
6C127×#1444C211yesmaximal, characteristic
7C127×#1443C212yesmaximal
8C127×#1442C211yesmaximal, characteristic
9C127×#1442C212yesmaximal
10C127×#1441C212yesmaximal
11C127×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2212yes—
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C4⋊C4×C127C2212yes—
18C22×C42×C127C2211yescharacteristic
19#389×C127—24no—
20#387×C127—24no—
21C2×#95×C127C2212yes—
22C2×#95×C127C2211yescharacteristic
23C2×#95×C127C2211yescharacteristic
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2212yes—
28C2×#95×C127C2211yescharacteristic
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2311yescharacteristic
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2312yes—
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2311yescharacteristic
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
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—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—42no—
58C2×C4⋊C4×C127—42no—
59C2×C4⋊C4×C127—42no—
60C2×C4⋊C4×C127—42no—
61C2×C4⋊C4×C127—42no—
62C2×C4⋊C4×C127—42no—
63C2×C4⋊C4×C127Q814yes—
64C2×C42×C127—42no—
65C2×C42×C127D414yes—
66#95×C127—22no—
67#95×C127—22no—
68#95×C127—22no—
69#95×C127—22no—
70#95×C127—24no—
71#95×C127—24no—
72#95×C127—22no—
73#95×C127—24no—
74#95×C127—24no—
75#95×C127—24no—
76#95×C127—22no—
77#95×C127—42no—
78#95×C127—42no—
79#95×C127—42no—
80#95×C127—42no—
81#95×C127—42no—
82C24×C127C2411yescharacteristic
83C22×C4×C127—22no—
84C22×C4×C127—22no—
85C22×C4×C127—21no—
86C22×C4×C127—22no—
87C22×C4×C127—21no—
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—21no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—21no—
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—21no—
109C22×C4×C127—21no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
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—21no—
131C22×C4×C127—21no—
132C22×C4×C127—21no—
133C22×C4×C127—22no—
134C22×C4×C127—21no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127C2×D412yes—
138C22×C4×C127C2×D412yes—
139C22×C4×C127C2×D412yes—
140C22×C4×C127C2×Q814yes—
141C22×C4×C127C2×Q812yes—
142C22×C4×C127#4114yes—
143C22×C4×C127#4112yes—
144C22×C4×C127#4112yes—
145C22×C4×C127#4112yes—
146C4⋊C4×C127—28no—
147C4⋊C4×C127—28no—
148C4⋊C4×C127—44no—
149C4⋊C4×C127—44no—
150C4⋊C4×C127—48no—
151C4⋊C4×C127—48no—
152C42×C127—44no—
153C23×C127C22×D411yescharacteristic
154C23×C127C22×Q811yescharacteristic
155C23×C127C2×#4111yescharacteristic
156C23×C127C2×#4111yescharacteristic
157C23×C127C2×#4111yescharacteristic
158C23×C127C2×#4112yes—
159C23×C127H(5,𝔽2)12yes—
160C23×C127H(5,𝔽2)12yes—
161C23×C1272−1+411yescharacteristic
162C23×C1272−1+412yes—
163C23×C1272−1+411yescharacteristic
164C2×C4×C127—22no—
165C2×C4×C127—22no—
166C2×C4×C127—24no—
167C2×C4×C127—24no—
168C2×C4×C127—24no—
169C2×C4×C127—22no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
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—42no—
185C2×C4×C127—41no—
186C2×C4×C127—41no—
187C2×C4×C127—42no—
188C2×C4×C127—41no—
189C2×C4×C127—41no—
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—41no—
204C2×C4×C127—42no—
205C2×C4×C127—41no—
206C2×C4×C127—42no—
207C2×C4×C127—41no—
208C2×C4×C127—41no—
209C2×C4×C127—41no—
210C2×C4×C127—41no—
211C2×C4×C127—42no—
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×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127C22⋊Q814yes—
227C22×C127C2×C22⋊Q811yescharacteristic
228C22×C127#52511yescharacteristic
229C22×C127#53211yescharacteristic
230C22×C127#53411yescharacteristic
231C22×C127#53511yescharacteristic
232C22×C127#53611yescharacteristic
233C22×C127#53611yescharacteristic
234C22×C127#53812yes—
235C22×C127#53912yes—
236C22×C127#53912yes—
237C22×C127#54012yes—
238C22×C127#54212yes—
239C22×C127#54412yes—
240C22×C127#55212yes—
241C22×C127#55212yes—
242C22×C127#55312yes—
243C22×C127#55412yes—
244C22×C127#55611yescharacteristic
245C22×C127#55611yescharacteristic
246C22×C127#55711yescharacteristic
247C22×C127#55711yescharacteristic
248C22×C127#56312yes—
249C22×C127#56312yes—
250C4×C127—24no—
251C4×C127—44no—
252C4×C127—42no—
253C4×C127—42no—
254C4×C127—42no—
255C4×C127—42no—
256C4×C127—44no—
257C4×C127—81no—
258C4×C127—82no—
259C4×C127—81no—
260C4×C127—82no—
261#17043C12711yesmaximal, characteristic, direct product factor, Sylow
262C2×C127#256611yescharacteristic
263C2×C127#258111yescharacteristic
264C2×C127#261111yescharacteristic
265C2×C127#262711yescharacteristic
266C2×C127#263511yescharacteristic
267C2×C127#266311yescharacteristic
268C2×C127#277412yes—
269C2×C127#277712yes—
270C2×C127#278712yes—
271C2×C127#279112yes—
272C2×C127#282111yescharacteristic
273C2×#389C2×C12711yescharacteristic
274C2×#387C2×C12711yescharacteristic
275#1445C2×C12711yescharacteristic
276#1445C2×C12711yescharacteristic
277#1444C2×C12712yes—
278#1444C2×C12711yescharacteristic
279#1443C2×C12712yes—
280#1442C2×C12711yescharacteristic
281#1442C2×C12712yes—
282#1441C2×C12712yes—
283#1434C2×C12711yescharacteristic
284C127#1704311yescharacteristic, direct product factor, Sylow
285C22×C4⋊C4C22×C12711yescharacteristic
286C22×C4⋊C4C22×C12711yescharacteristic
287C22×C4⋊C4C22×C12711yescharacteristic
288C22×C4⋊C4C22×C12712yes—
289C22×C4⋊C4C22×C12711yescharacteristic
290C22×C4⋊C4C22×C12712yes—
291C22×C42C22×C12711yescharacteristic
292#389—24no—
293#387—24no—
294C2×#95C22×C12712yes—
295C2×#95C22×C12711yescharacteristic
296C2×#95C22×C12711yescharacteristic
297C2×#95C22×C12712yes—
298C2×#95C22×C12712yes—
299C2×#95C22×C12711yescharacteristic
300C2×#95C22×C12712yes—
301C2×#95C22×C12711yescharacteristic
302C2×#95C22×C12711yescharacteristic
303C2×#95C22×C12712yes—
304C2×#95C22×C12711yescharacteristic
305C2×#95C22×C12712yes—
306C2×#95C22×C12712yes—
307C2×#95C22×C12712yes—
308C2×#95C22×C12712yes—
309C2×#95C22×C12712yes—
310C23×C4C23×C12712yes—
311C23×C4C23×C12711yescharacteristic
312C23×C4C23×C12711yescharacteristic
313C23×C4C23×C12712yes—
314C23×C4C23×C12711yescharacteristic
315C23×C4C23×C12711yescharacteristic
316C23×C4C23×C12712yes—
317C23×C4C23×C12711yescharacteristic
318C23×C4C23×C12711yescharacteristic
319C23×C4C23×C12712yes—
320C23×C4C23×C12711yescharacteristic
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4Q8×C12714yes—
337C2×C42—42no—
338C2×C42D4×C12714yes—
339#95—22no—
340#95—22no—
341#95—22no—
342#95—22no—
343#95—24no—
344#95—24no—
345#95—22no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—22no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355C24C24×C12711yescharacteristic
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
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×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4C2×D4×C12712yes—
411C22×C4C2×D4×C12712yes—
412C22×C4C2×D4×C12712yes—
413C22×C4C2×Q8×C12714yes—
414C22×C4C2×Q8×C12712yes—
415C22×C4#41×C12714yes—
416C22×C4#41×C12712yes—
417C22×C4#41×C12712yes—
418C22×C4#41×C12712yes—
419C4⋊C4—28no—
420C4⋊C4—28no—
421C4⋊C4—44no—
422C4⋊C4—44no—
423C4⋊C4—48no—
424C4⋊C4—48no—
425C42—44no—
426C23C22×D4×C12711yescharacteristic
427C23C22×Q8×C12711yescharacteristic
428C23C2×#41×C12711yescharacteristic
429C23C2×#41×C12711yescharacteristic
430C23C2×#41×C12711yescharacteristic
431C23C2×#41×C12712yes—
432C23H(5,𝔽2)×C12712yes—
433C23H(5,𝔽2)×C12712yes—
434C232−1+4×C12711yescharacteristic
435C232−1+4×C12712yes—
436C232−1+4×C12711yescharacteristic
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—41no—
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—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4C22⋊Q8×C12714yes—
500C22C2×C22⋊Q8×C12711yescharacteristic
501C22#525×C12711yescharacteristic
502C22#532×C12711yescharacteristic
503C22#534×C12711yescharacteristic
504C22#535×C12711yescharacteristic
505C22#536×C12711yescharacteristic
506C22#536×C12711yescharacteristic
507C22#538×C12712yes—
508C22#539×C12712yes—
509C22#539×C12712yes—
510C22#540×C12712yes—
511C22#542×C12712yes—
512C22#544×C12712yes—
513C22#552×C12712yes—
514C22#552×C12712yes—
515C22#553×C12712yes—
516C22#554×C12712yes—
517C22#556×C12711yescharacteristic
518C22#556×C12711yescharacteristic
519C22#557×C12711yescharacteristic
520C22#557×C12711yescharacteristic
521C22#563×C12712yes—
522C22#563×C12712yes—
523C4—24no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—44no—
529C4—44no—
530C4—82no—
531C4—81no—
532C4—82no—
533C4—81no—
534C2C127×#256611yescharacteristic
535C2C127×#258111yescharacteristic
536C2C127×#261111yescharacteristic
537C2C127×#262711yescharacteristic
538C2C127×#263511yescharacteristic
539C2C127×#266311yescharacteristic
540C2C127×#277412yes—
541C2C127×#277712yes—
542C2C127×#278712yes—
543C2C127×#279112yes—
544C2C127×#282111yescharacteristic
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
261. #17043C127direct (N × H)
284. C127#17043direct (N × H)

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
C127×#14452
C127×#14442
C127×#14432
C127×#14422
C127×#14412
C127×#14342
#17043127