Finite Group Databasebeta

← C127×#16877 #44580550

Subgroups — C127×#16877 #44580550

Order 32512.

1170 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C127C212yesmaximal
2C2×#398×C127C212yesmaximal
3C127×#1444C212yesmaximal
4C127×#1443C212yesmaximal
5C127×#1441C211yesmaximal, characteristic
6C127×#1441C212yesmaximal
7C127×#1441C211yesmaximal, characteristic
8C127×#1436C212yesmaximal
9C127×C4⋊#95C211yesmaximal, characteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C42×C127C2211yescharacteristic
18#400×C127—28no—
19#398×C127—28no—
20C2×#95×C127C2212yes—
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×C127C2212yes—
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2211yescharacteristic
32C2×#95×C127C2212yes—
33C23×C4×C127C2312yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2311yescharacteristic
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2312yes—
41C23×C4×C127C2311yescharacteristic
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—24no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—22no—
51C2×C4⋊C4×C127—41no—
52C2×C4⋊C4×C127—41no—
53C2×C4⋊C4×C127—42no—
54C2×C4⋊C4×C127—41no—
55C2×C4⋊C4×C127—41no—
56C2×C4⋊C4×C127—42no—
57C2×C4⋊C4×C127—42no—
58C2×C4⋊C4×C127—41no—
59C2×C4⋊C4×C127—41no—
60C2×C4⋊C4×C127Q814yes—
61C2×C42×C127—22no—
62C2×C42×C127—41no—
63C2×C42×C127—41no—
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—24no—
71#95×C127—24no—
72#95×C127—24no—
73#95×C127—41no—
74#95×C127—42no—
75#95×C127—41no—
76#95×C127D418yes—
77C24×C127C2411yescharacteristic
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
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—22no—
96C22×C4×C127—21no—
97C22×C4×C127—21no—
98C22×C4×C127—22no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
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×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×C127C2×D414yes—
129C22×C4×C127C2×D414yes—
130C22×C4×C127C2×D414yes—
131C22×C4×C127C2×Q812yes—
132C22×C4×C127C2×Q812yes—
133C22×C4×C127C2×Q812yes—
134C22×C4×C127#4114yes—
135C22×C4×C127#4112yes—
136C22×C4×C127#4112yes—
137C4⋊C4×C127—44no—
138C4⋊C4×C127—44no—
139C4⋊C4×C127—44no—
140C4⋊C4×C127—48no—
141C4⋊C4×C127—48no—
142C4⋊C4×C127—48no—
143C4⋊C4×C127—44no—
144C42×C127—44no—
145C23×C127C22×D412yes—
146C23×C127C22×Q811yescharacteristic
147C23×C127C2×#4111yescharacteristic
148C23×C127C2×#4111yescharacteristic
149C23×C127C2×#4112yes—
150C23×C127H(5,𝔽2)11yescharacteristic
151C23×C127H(5,𝔽2)11yescharacteristic
152C23×C127H(5,𝔽2)11yescharacteristic
153C23×C1272−1+411yescharacteristic
154C23×C1272−1+412yes—
155C23×C1272−1+412yes—
156C2×C4×C127—22no—
157C2×C4×C127—22no—
158C2×C4×C127—22no—
159C2×C4×C127—22no—
160C2×C4×C127—22no—
161C2×C4×C127—22no—
162C2×C4×C127—24no—
163C2×C4×C127—24no—
164C2×C4×C127—24no—
165C2×C4×C127—24no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
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—24no—
177C2×C4×C127—24no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—42no—
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—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—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#12514yes—
215C22×C127C2×#12511yescharacteristic
216C22×C127#53212yes—
217C22×C127#53612yes—
218C22×C127#53712yes—
219C22×C127#53811yescharacteristic
220C22×C127#53811yescharacteristic
221C22×C127#53911yescharacteristic
222C22×C127#53911yescharacteristic
223C22×C127#53912yes—
224C22×C127#54112yes—
225C22×C127#54112yes—
226C22×C127#54311yescharacteristic
227C22×C127#54411yescharacteristic
228C22×C127D4211yescharacteristic
229C22×C127#54612yes—
230C22×C127#54712yes—
231C22×C127D4×Q812yes—
232C22×C127#55212yes—
233C22×C127#55511yescharacteristic
234C22×C127#55712yes—
235C22×C127#56311yescharacteristic
236C22×C127#56311yescharacteristic
237C22×C127#56312yes—
238C4×C127—24no—
239C4×C127—44no—
240C4×C127—42no—
241C4×C127—42no—
242C4×C127—44no—
243C4×C127—44no—
244C4×C127—44no—
245C4×C127—82no—
246C4×C127—82no—
247#16877C12711yesmaximal, characteristic, direct product factor, Sylow
248C2×C127#250612yes—
249C2×C127#255511yescharacteristic
250C2×C127#264611yescharacteristic
251C2×C127#266412yes—
252C2×C127#268011yescharacteristic
253C2×C127#268311yescharacteristic
254C2×C127#269512yes—
255C2×C127#271312yes—
256C2×C127#276911yescharacteristic
257C2×C127#280911yescharacteristic
258C2×C127#283311yescharacteristic
259C2×#400C2×C12712yes—
260C2×#398C2×C12712yes—
261#1444C2×C12712yes—
262#1443C2×C12712yes—
263#1441C2×C12711yescharacteristic
264#1441C2×C12712yes—
265#1441C2×C12711yescharacteristic
266#1436C2×C12712yes—
267C4⋊#95C2×C12711yescharacteristic
268C127#1687711yescharacteristic, direct product factor, Sylow
269C22×C4⋊C4C22×C12711yescharacteristic
270C22×C4⋊C4C22×C12712yes—
271C22×C4⋊C4C22×C12712yes—
272C22×C4⋊C4C22×C12712yes—
273C22×C4⋊C4C22×C12711yescharacteristic
274C22×C4⋊C4C22×C12711yescharacteristic
275C22×C4⋊C4C22×C12711yescharacteristic
276C22×C42C22×C12711yescharacteristic
277#400—28no—
278#398—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×C12712yes—
288C2×#95C22×C12712yes—
289C2×#95C22×C12711yescharacteristic
290C2×#95C22×C12711yescharacteristic
291C2×#95C22×C12712yes—
292C23×C4C23×C12712yes—
293C23×C4C23×C12712yes—
294C23×C4C23×C12712yes—
295C23×C4C23×C12712yes—
296C23×C4C23×C12712yes—
297C23×C4C23×C12711yescharacteristic
298C23×C4C23×C12711yescharacteristic
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—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4Q8×C12714yes—
320C2×C42—22no—
321C2×C42—41no—
322C2×C42—41no—
323#95—24no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—24no—
329#95—24no—
330#95—24no—
331#95—24no—
332#95—41no—
333#95—42no—
334#95—41no—
335#95D4×C12718yes—
336C24C24×C12711yescharacteristic
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
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—22no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
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×C4—22no—
376C22×C4—22no—
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×C4C2×D4×C12714yes—
388C22×C4C2×D4×C12714yes—
389C22×C4C2×D4×C12714yes—
390C22×C4C2×Q8×C12712yes—
391C22×C4C2×Q8×C12712yes—
392C22×C4C2×Q8×C12712yes—
393C22×C4#41×C12714yes—
394C22×C4#41×C12712yes—
395C22×C4#41×C12712yes—
396C4⋊C4—44no—
397C4⋊C4—44no—
398C4⋊C4—44no—
399C4⋊C4—48no—
400C4⋊C4—48no—
401C4⋊C4—48no—
402C4⋊C4—44no—
403C42—44no—
404C23C22×D4×C12712yes—
405C23C22×Q8×C12711yescharacteristic
406C23C2×#41×C12711yescharacteristic
407C23C2×#41×C12711yescharacteristic
408C23C2×#41×C12712yes—
409C23H(5,𝔽2)×C12711yescharacteristic
410C23H(5,𝔽2)×C12711yescharacteristic
411C23H(5,𝔽2)×C12711yescharacteristic
412C232−1+4×C12711yescharacteristic
413C232−1+4×C12712yes—
414C232−1+4×C12712yes—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
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—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
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#125×C12714yes—
474C22C2×#125×C12711yescharacteristic
475C22#532×C12712yes—
476C22#536×C12712yes—
477C22#537×C12712yes—
478C22#538×C12711yescharacteristic
479C22#538×C12711yescharacteristic
480C22#539×C12711yescharacteristic
481C22#539×C12711yescharacteristic
482C22#539×C12712yes—
483C22#541×C12712yes—
484C22#541×C12712yes—
485C22#543×C12711yescharacteristic
486C22#544×C12711yescharacteristic
487C22D42×C12711yescharacteristic
488C22#546×C12712yes—
489C22#547×C12712yes—
490C22D4×Q8×C12712yes—
491C22#552×C12712yes—
492C22#555×C12711yescharacteristic
493C22#557×C12712yes—
494C22#563×C12711yescharacteristic
495C22#563×C12711yescharacteristic
496C22#563×C12712yes—
497C4—24no—
498C4—44no—
499C4—42no—
500C4—42no—
501C4—44no—
502C4—44no—
503C4—44no—
504C4—82no—
505C4—82no—
506C2C127×#250612yes—
507C2C127×#255511yescharacteristic
508C2C127×#264611yescharacteristic
509C2C127×#266412yes—
510C2C127×#268011yescharacteristic
511C2C127×#268311yescharacteristic
512C2C127×#269512yes—
513C2C127×#271312yes—
514C2C127×#276911yescharacteristic
515C2C127×#280911yescharacteristic
516C2C127×#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
247. #16877C127direct (N × H)
268. C127#16877direct (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×#398×C1272
C127×#14442
C127×#14432
C127×#14412
C127×#14362
C127×C4⋊#952
#16877127