Finite Group Databasebeta

← C127×#16653 #44580326

Subgroups — C127×#16653 #44580326

Order 32512.

1158 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C127C211yesmaximal, characteristic
2C2×#391×C127C211yesmaximal, characteristic
3C127×#1446C212yesmaximal
4C127×#1445C212yesmaximal
5C127×#1443C212yesmaximal
6C127×#1442C212yesmaximal
7C127×#1441C212yesmaximal
8C127×#1441C211yesmaximal, characteristic
9C127×#1436C212yesmaximal
10C23×Q8×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C42×C127C2211yescharacteristic
16#400×C127—24no—
17#391×C127—24no—
18C2×#95×C127C2212yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2211yescharacteristic
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2212yes—
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C22×Q8×C127—22no—
34C22×Q8×C127—22no—
35C22×Q8×C127—41no—
36C22×Q8×C127—41no—
37C22×Q8×C127—41no—
38C22×Q8×C127—41no—
39C22×Q8×C127Q814yes—
40C23×C4×C127C2312yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2312yes—
48C23×C4×C127C2311yescharacteristic
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—41no—
54C2×C4⋊C4×C127—41no—
55C2×C4⋊C4×C127—41no—
56C2×C4⋊C4×C127—42no—
57C2×C4⋊C4×C127—41no—
58C2×C4⋊C4×C127—41no—
59C2×C4⋊C4×C127D414yes—
60C2×C42×C127—22no—
61C2×C42×C127—41no—
62C2×C42×C127—41no—
63#95×C127—24no—
64#95×C127—24no—
65#95×C127—22no—
66#95×C127—24no—
67#95×C127—24no—
68#95×C127—24no—
69#95×C127—24no—
70#95×C127—24no—
71#95×C127—24no—
72#95×C127—42no—
73#95×C127—42no—
74#95×C127—42no—
75#95×C127—41no—
76#95×C127—42no—
77#95×C127—42no—
78C24×C127C2411yescharacteristic
79C2×Q8×C127—28no—
80C2×Q8×C127—44no—
81C2×Q8×C127—44no—
82C2×Q8×C127—44no—
83C2×Q8×C127—44no—
84C2×Q8×C127—44no—
85C2×Q8×C127—44no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—21no—
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—21no—
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—21no—
110C22×C4×C127—21no—
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—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×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#4114yes—
144C22×C4×C127#4112yes—
145C4⋊C4×C127—44no—
146C4⋊C4×C127—44no—
147C4⋊C4×C127—48no—
148C4⋊C4×C127—44no—
149C42×C127—44no—
150C23×C127C22×D411yescharacteristic
151C23×C127C22×Q811yescharacteristic
152C23×C127C2×#4111yescharacteristic
153C23×C127C2×#4112yes—
154C23×C127C2×#4112yes—
155C23×C127H(5,𝔽2)11yescharacteristic
156C23×C127H(5,𝔽2)11yescharacteristic
157C23×C127H(5,𝔽2)11yescharacteristic
158C23×C127H(5,𝔽2)11yescharacteristic
159C23×C1272−1+412yes—
160C23×C1272−1+412yes—
161Q8×C127—416no—
162C2×C4×C127—22no—
163C2×C4×C127—22no—
164C2×C4×C127—22no—
165C2×C4×C127—22no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
168C2×C4×C127—24no—
169C2×C4×C127—24no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
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—42no—
182C2×C4×C127—42no—
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—41no—
193C2×C4×C127—42no—
194C2×C4×C127—41no—
195C2×C4×C127—42no—
196C2×C4×C127—41no—
197C2×C4×C127—41no—
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—42no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127C22⋊Q814yes—
221C22×C127C2×C22⋊Q811yescharacteristic
222C22×C127#52912yes—
223C22×C127#53411yescharacteristic
224C22×C127#53511yescharacteristic
225C22×C127#53811yescharacteristic
226C22×C127#53811yescharacteristic
227C22×C127#53912yes—
228C22×C127#54112yes—
229C22×C127#54212yes—
230C22×C127#54212yes—
231C22×C127#54212yes—
232C22×C127#54311yescharacteristic
233C22×C127#54311yescharacteristic
234C22×C127#54712yes—
235C22×C127#54812yes—
236C22×C127#55111yescharacteristic
237C22×C127#55112yes—
238C22×C127#55511yescharacteristic
239C22×C127#55712yes—
240C22×C127#55712yes—
241C22×C127#56311yescharacteristic
242C22×C127#56312yes—
243C22×C127#56311yescharacteristic
244C4×C127—24no—
245C4×C127—44no—
246C4×C127—44no—
247C4×C127—42no—
248C4×C127—42no—
249C4×C127—44no—
250C4×C127—82no—
251C4×C127—82no—
252C4×C127—82no—
253#16653C12711yesmaximal, characteristic, direct product factor, Sylow
254C2×C127#245312yes—
255C2×C127#257211yescharacteristic
256C2×C127#262611yescharacteristic
257C2×C127#265012yes—
258C2×C127#271711yescharacteristic
259C2×C127#272312yes—
260C2×C127#273111yescharacteristic
261C2×C127#279912yes—
262C2×C127#279911yescharacteristic
263C2×C127#280911yescharacteristic
264C2×C127#283311yescharacteristic
265C2×#400C2×C12711yescharacteristic
266C2×#391C2×C12711yescharacteristic
267#1446C2×C12712yes—
268#1445C2×C12712yes—
269#1443C2×C12712yes—
270#1442C2×C12712yes—
271#1441C2×C12712yes—
272#1441C2×C12711yescharacteristic
273#1436C2×C12712yes—
274C127#1665311yescharacteristic, direct product factor, Sylow
275C23×Q8C22×C12711yescharacteristic
276C22×C4⋊C4C22×C12712yes—
277C22×C4⋊C4C22×C12711yescharacteristic
278C22×C4⋊C4C22×C12711yescharacteristic
279C22×C4⋊C4C22×C12711yescharacteristic
280C22×C42C22×C12711yescharacteristic
281#400—24no—
282#391—24no—
283C2×#95C22×C12712yes—
284C2×#95C22×C12712yes—
285C2×#95C22×C12711yescharacteristic
286C2×#95C22×C12712yes—
287C2×#95C22×C12712yes—
288C2×#95C22×C12712yes—
289C2×#95C22×C12712yes—
290C2×#95C22×C12712yes—
291C2×#95C22×C12712yes—
292C2×#95C22×C12712yes—
293C2×#95C22×C12712yes—
294C2×#95C22×C12711yescharacteristic
295C2×#95C22×C12712yes—
296C2×#95C22×C12712yes—
297C2×#95C22×C12712yes—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—41no—
301C22×Q8—41no—
302C22×Q8—41no—
303C22×Q8—41no—
304C22×Q8Q8×C12714yes—
305C23×C4C23×C12712yes—
306C23×C4C23×C12712yes—
307C23×C4C23×C12712yes—
308C23×C4C23×C12711yescharacteristic
309C23×C4C23×C12711yescharacteristic
310C23×C4C23×C12712yes—
311C23×C4C23×C12712yes—
312C23×C4C23×C12712yes—
313C23×C4C23×C12711yescharacteristic
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4D4×C12714yes—
325C2×C42—22no—
326C2×C42—41no—
327C2×C42—41no—
328#95—24no—
329#95—24no—
330#95—22no—
331#95—24no—
332#95—24no—
333#95—24no—
334#95—24no—
335#95—24no—
336#95—24no—
337#95—42no—
338#95—42no—
339#95—42no—
340#95—41no—
341#95—42no—
342#95—42no—
343C24C24×C12711yescharacteristic
344C2×Q8—28no—
345C2×Q8—44no—
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—44no—
349C2×Q8—44no—
350C2×Q8—44no—
351C22×C4—21no—
352C22×C4—21no—
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—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
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×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4C2×D4×C12712yes—
403C22×C4C2×D4×C12712yes—
404C22×C4C2×D4×C12712yes—
405C22×C4C2×Q8×C12714yes—
406C22×C4C2×Q8×C12712yes—
407C22×C4#41×C12714yes—
408C22×C4#41×C12714yes—
409C22×C4#41×C12712yes—
410C4⋊C4—44no—
411C4⋊C4—44no—
412C4⋊C4—48no—
413C4⋊C4—44no—
414C42—44no—
415C23C22×D4×C12711yescharacteristic
416C23C22×Q8×C12711yescharacteristic
417C23C2×#41×C12711yescharacteristic
418C23C2×#41×C12712yes—
419C23C2×#41×C12712yes—
420C23H(5,𝔽2)×C12711yescharacteristic
421C23H(5,𝔽2)×C12711yescharacteristic
422C23H(5,𝔽2)×C12711yescharacteristic
423C23H(5,𝔽2)×C12711yescharacteristic
424C232−1+4×C12712yes—
425C232−1+4×C12712yes—
426Q8—416no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—22no—
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—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
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—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4C22⋊Q8×C12714yes—
486C22C2×C22⋊Q8×C12711yescharacteristic
487C22#529×C12712yes—
488C22#534×C12711yescharacteristic
489C22#535×C12711yescharacteristic
490C22#538×C12711yescharacteristic
491C22#538×C12711yescharacteristic
492C22#539×C12712yes—
493C22#541×C12712yes—
494C22#542×C12712yes—
495C22#542×C12712yes—
496C22#542×C12712yes—
497C22#543×C12711yescharacteristic
498C22#543×C12711yescharacteristic
499C22#547×C12712yes—
500C22#548×C12712yes—
501C22#551×C12711yescharacteristic
502C22#551×C12712yes—
503C22#555×C12711yescharacteristic
504C22#557×C12712yes—
505C22#557×C12712yes—
506C22#563×C12711yescharacteristic
507C22#563×C12712yes—
508C22#563×C12711yescharacteristic
509C4—24no—
510C4—44no—
511C4—44no—
512C4—42no—
513C4—42no—
514C4—44no—
515C4—82no—
516C4—82no—
517C4—82no—
518C2C127×#245312yes—
519C2C127×#257211yescharacteristic
520C2C127×#262611yescharacteristic
521C2C127×#265012yes—
522C2C127×#271711yescharacteristic
523C2C127×#272312yes—
524C2C127×#273111yescharacteristic
525C2C127×#279912yes—
526C2C127×#279911yescharacteristic
527C2C127×#280911yescharacteristic
528C2C127×#283311yescharacteristic
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
253. #16653C127direct (N × H)
274. C127#16653direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#400×C1272
C2×#391×C1272
C127×#14462
C127×#14452
C127×#14432
C127×#14422
C127×#14412
C127×#14362
#16653127