Finite Group Databasebeta

← C127×#17071 #44580744

Subgroups — C127×#17071 #44580744

Order 32512.

1810 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×#399×C127C212yesmaximal, complemented
2C2×#396×C127C214yesmaximal, complemented
3C2×#390×C127C211yesmaximal, characteristic
4C2×#389×C127C211yesmaximal, characteristic, complemented
5C127×#1444C212yesmaximal, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1438C212yesmaximal
8C127×C4⋊#95C211yesmaximal, characteristic, complemented
9C23×D4×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2214yes—
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2214yes—
19C22×C22⋊C4×C127C2214yes—
20C22×C42×C127C2211yescharacteristic
21#399×C127—28no—
22#396×C127—216no—
23#390×C127—24no—
24#389×C127—24no—
25C2×#95×C127C2214yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C25×C127C2312yes—
30C22×D4×C127—22no—
31C22×D4×C127—22no—
32C22×D4×C127—42no—
33C22×D4×C127—42no—
34C22×D4×C127Q814yes—
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2314yes—
39C23×C4×C127C2311yescharacteristic
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2311yescharacteristic
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127—22no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—22no—
47C2×C4⋊C4×C127—28no—
48C2×C4⋊C4×C127—28no—
49C2×C4⋊C4×C127—28no—
50C2×C4⋊C4×C127—42no—
51C2×C4⋊C4×C127—42no—
52C2×C4⋊C4×C127—44no—
53C2×C4⋊C4×C127—42no—
54C2×C4⋊C4×C127—42no—
55C2×C4⋊C4×C127D414yescomplemented
56C2×C4⋊C4×C127D418yescomplemented
57C2×C22⋊C4×C127—24no—
58C2×C22⋊C4×C127—24no—
59C2×C22⋊C4×C127—28no—
60C2×C22⋊C4×C127—28no—
61C2×C22⋊C4×C127—28no—
62C2×C22⋊C4×C127—28no—
63C2×C22⋊C4×C127—24no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—44no—
66C2×C22⋊C4×C127—44no—
67C2×C22⋊C4×C127—44no—
68C2×C42×C127—42no—
69C2×C42×C127D414yes—
70#95×C127—24no—
71#95×C127—28no—
72#95×C127—24no—
73#95×C127—24no—
74C24×C127—22no—
75C24×C127—24no—
76C24×C127—22no—
77C24×C127—22no—
78C24×C127—22no—
79C24×C127—22no—
80C24×C127—24no—
81C24×C127—24no—
82C24×C127—24no—
83C24×C127—22no—
84C24×C127C2×Q814yes—
85C24×C127C2411yescharacteristic
86C2×D4×C127—28no—
87C2×D4×C127—48no—
88C2×D4×C127—44no—
89C2×D4×C127—44no—
90C2×D4×C127—48no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—21no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—21no—
98C22×C4×C127—24no—
99C22×C4×C127—22no—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127—22no—
103C22×C4×C127—24no—
104C22×C4×C127—24no—
105C22×C4×C127—24no—
106C22×C4×C127—24no—
107C22×C4×C127—24no—
108C22×C4×C127—24no—
109C22×C4×C127—24no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—24no—
116C22×C4×C127—24no—
117C22×C4×C127—22no—
118C22×C4×C127C2×D418yes—
119C22×C4×C127C2×D414yes—
120C22×C4×C127C2×D412yes—
121C22×C4×C127C2×D412yes—
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D412yes—
124C22×C4×C127C2×D414yes—
125C22×C4×C127C2×Q812yes—
126C22×C4×C127#4112yes—
127C22×C4×C127#4112yes—
128C4⋊C4×C127—28no—
129C4⋊C4×C127—48no—
130C4⋊C4×C127—416no—
131C4⋊C4×C127—44no—
132C4⋊C4×C127—44no—
133C4⋊C4×C127—48no—
134C22⋊C4×C127—416no—
135C22⋊C4×C127—416no—
136C22⋊C4×C127—48no—
137C22⋊C4×C127—48no—
138C42×C127—44no—
139C23×C127—24no—
140C23×C127—28no—
141C23×C127—24no—
142C23×C127—28no—
143C23×C127—24no—
144C23×C127—42no—
145C23×C127—42no—
146C23×C127—44no—
147C23×C127—42no—
148C23×C127—42no—
149C23×C127—42no—
150C23×C127—44no—
151C23×C127—44no—
152C23×C127—42no—
153C23×C127—44no—
154C23×C127—44no—
155C23×C127—44no—
156C23×C127—44no—
157C23×C127—44no—
158C23×C127—42no—
159C23×C127—42no—
160C23×C127—44no—
161C23×C127—44no—
162C23×C127C22×D411yescharacteristic
163C23×C127C22×D411yescharacteristic
164C23×C127C22×D412yes—
165C23×C127C22×Q811yescharacteristic
166C23×C127C2×#4111yescharacteristic
167C23×C127C2×#4111yescharacteristic
168C23×C127H(5,𝔽2)12yes—
169C23×C127H(5,𝔽2)11yescharacteristic
170C23×C127H(5,𝔽2)12yes—
171C23×C1272−1+412yes—
172C23×C1272−1+411yescharacteristic
173D4×C127—416no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—24no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—24no—
181C2×C4×C127—22no—
182C2×C4×C127—24no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—24no—
187C2×C4×C127—28no—
188C2×C4×C127—28no—
189C2×C4×C127—28no—
190C2×C4×C127—28no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—44no—
194C2×C4×C127—44no—
195C2×C4×C127—44no—
196C2×C4×C127—44no—
197C2×C4×C127—44no—
198C2×C4×C127—42no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—44no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—44no—
206C2×C4×C127—44no—
207C2×C4×C127—44no—
208C2×C4×C127#12114yes—
209C2×C4×C127C22⋊Q814yes—
210C2×C4×C127#12714yes—
211C22×C127—44no—
212C22×C127—48no—
213C22×C127—48no—
214C22×C127—44no—
215C22×C127—44no—
216C22×C127—82no—
217C22×C127—82no—
218C22×C127—82no—
219C22×C127—84no—
220C22×C127—84no—
221C22×C127—82no—
222C22×C127C2×#12111yescharacteristic
223C22×C127C2×C22⋊Q811yescharacteristic
224C22×C127C2×#12711yescharacteristic
225C22×C127#53411yescharacteristic
226C22×C127#53412yes—
227C22×C127#53511yescharacteristic
228C22×C127#53611yescharacteristic
229C22×C127#53711yescharacteristic
230C22×C127#53712yes—
231C22×C127#53712yes—
232C22×C127#53812yes—
233C22×C127#53912yes—
234C22×C127#54312yes—
235C22×C127D4212yes—
236C22×C127#54712yes—
237C22×C127D4×Q811yescharacteristic
238C22×C127D4×Q812yes—
239C22×C127#55011yescharacteristic
240C22×C127#55012yes—
241C22×C127#55411yescharacteristic
242C22×C127#55611yescharacteristic
243C22×C127#56212yes—
244C22×C127#56312yes—
245C4×C127—24no—
246C4×C127—24no—
247C4×C127—24no—
248C4×C127—48no—
249C4×C127—44no—
250C4×C127—82no—
251C4×C127—82no—
252#17071C12711yesmaximal, characteristic, direct product factor, Sylow
253C2×C127—84no—
254C2×C127#253811yescharacteristic
255C2×C127#254111yescharacteristic
256C2×C127#254211yescharacteristic
257C2×C127#261811yescharacteristic
258C2×C127#262611yescharacteristic
259C2×C127#265611yescharacteristic
260C2×C127#268212yes—
261C2×C127#268312yes—
262C2×C127#272712yes—
263C2×C127#273212yes—
264C2×C127#282011yescharacteristic
265C2×#399C2×C12712yescomplemented
266C2×#396C2×C12714yescomplemented
267C2×#390C2×C12711yescharacteristic
268C2×#389C2×C12711yescharacteristic, complemented
269#1444C2×C12712yescomplemented
270#1439C2×C12712yescomplemented
271#1438C2×C12712yes—
272C4⋊#95C2×C12711yescharacteristic, complemented
273C127#1707111yescharacteristic, direct product factor, Sylow
274C23×D4C22×C12711yescharacteristic
275C22×C4⋊C4C22×C12712yes—
276C22×C4⋊C4C22×C12714yes—
277C22×C4⋊C4C22×C12711yescharacteristic
278C22×C4⋊C4C22×C12711yescharacteristic
279C22×C4⋊C4C22×C12711yescharacteristic
280C22×C4⋊C4C22×C12712yes—
281C22×C22⋊C4C22×C12712yes—
282C22×C22⋊C4C22×C12712yes—
283C22×C22⋊C4C22×C12714yes—
284C22×C22⋊C4C22×C12714yes—
285C22×C42C22×C12711yescharacteristic
286#399—28no—
287#396—216no—
288#390—24no—
289#389—24no—
290C2×#95C22×C12714yes—
291C2×#95C22×C12712yes—
292C2×#95C22×C12712yes—
293C2×#95C22×C12712yes—
294C25C23×C12712yes—
295C22×D4—22no—
296C22×D4—22no—
297C22×D4—42no—
298C22×D4—42no—
299C22×D4Q8×C12714yes—
300C23×C4C23×C12712yes—
301C23×C4C23×C12712yes—
302C23×C4C23×C12712yes—
303C23×C4C23×C12714yes—
304C23×C4C23×C12711yescharacteristic
305C23×C4C23×C12711yescharacteristic
306C23×C4C23×C12711yescharacteristic
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4D4×C12714yescomplemented
321C2×C4⋊C4D4×C12718yescomplemented
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C42—42no—
334C2×C42D4×C12714yes—
335#95—24no—
336#95—28no—
337#95—24no—
338#95—24no—
339C24—22no—
340C24—24no—
341C24—22no—
342C24—22no—
343C24—22no—
344C24—22no—
345C24—24no—
346C24—24no—
347C24—24no—
348C24—22no—
349C24C2×Q8×C12714yes—
350C24C24×C12711yescharacteristic
351C2×D4—28no—
352C2×D4—48no—
353C2×D4—44no—
354C2×D4—44no—
355C2×D4—48no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—24no—
364C22×C4—22no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4C2×D4×C12718yes—
384C22×C4C2×D4×C12714yes—
385C22×C4C2×D4×C12712yes—
386C22×C4C2×D4×C12712yes—
387C22×C4C2×D4×C12712yes—
388C22×C4C2×D4×C12712yes—
389C22×C4C2×D4×C12714yes—
390C22×C4C2×Q8×C12712yes—
391C22×C4#41×C12712yes—
392C22×C4#41×C12712yes—
393C4⋊C4—28no—
394C4⋊C4—48no—
395C4⋊C4—416no—
396C4⋊C4—44no—
397C4⋊C4—44no—
398C4⋊C4—48no—
399C22⋊C4—416no—
400C22⋊C4—416no—
401C22⋊C4—48no—
402C22⋊C4—48no—
403C42—44no—
404C23—24no—
405C23—28no—
406C23—24no—
407C23—28no—
408C23—24no—
409C23—42no—
410C23—42no—
411C23—44no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—44no—
416C23—44no—
417C23—42no—
418C23—44no—
419C23—44no—
420C23—44no—
421C23—44no—
422C23—44no—
423C23—42no—
424C23—42no—
425C23—44no—
426C23—44no—
427C23C22×D4×C12711yescharacteristic
428C23C22×D4×C12711yescharacteristic
429C23C22×D4×C12712yes—
430C23C22×Q8×C12711yescharacteristic
431C23C2×#41×C12711yescharacteristic
432C23C2×#41×C12711yescharacteristic
433C23H(5,𝔽2)×C12712yes—
434C23H(5,𝔽2)×C12711yescharacteristic
435C23H(5,𝔽2)×C12712yes—
436C232−1+4×C12712yes—
437C232−1+4×C12711yescharacteristic
438D4—416no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—28no—
453C2×C4—28no—
454C2×C4—28no—
455C2×C4—28no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4#121×C12714yes—
474C2×C4C22⋊Q8×C12714yes—
475C2×C4#127×C12714yes—
476C22—44no—
477C22—48no—
478C22—48no—
479C22—44no—
480C22—44no—
481C22—82no—
482C22—82no—
483C22—84no—
484C22—84no—
485C22—82no—
486C22—82no—
487C22C2×#121×C12711yescharacteristic
488C22C2×C22⋊Q8×C12711yescharacteristic
489C22C2×#127×C12711yescharacteristic
490C22#534×C12711yescharacteristic
491C22#534×C12712yes—
492C22#535×C12711yescharacteristic
493C22#536×C12711yescharacteristic
494C22#537×C12712yes—
495C22#537×C12712yes—
496C22#537×C12711yescharacteristic
497C22#538×C12712yes—
498C22#539×C12712yes—
499C22#543×C12712yes—
500C22D42×C12712yes—
501C22#547×C12712yes—
502C22D4×Q8×C12711yescharacteristic
503C22D4×Q8×C12712yes—
504C22#550×C12711yescharacteristic
505C22#550×C12712yes—
506C22#554×C12711yescharacteristic
507C22#556×C12711yescharacteristic
508C22#562×C12712yes—
509C22#563×C12712yes—
510C4—24no—
511C4—24no—
512C4—24no—
513C4—48no—
514C4—44no—
515C4—82no—
516C4—82no—
517C2—84no—
518C2C127×#253811yescharacteristic
519C2C127×#254111yescharacteristic
520C2C127×#254211yescharacteristic
521C2C127×#261811yescharacteristic
522C2C127×#262611yescharacteristic
523C2C127×#265611yescharacteristic
524C2C127×#268212yes—
525C2C127×#268312yes—
526C2C127×#272712yes—
527C2C127×#273212yes—
528C2C127×#282011yescharacteristic
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#399×C127C2semidirect
2. C2×#396×C127C2semidirect
4. C2×#389×C127C2semidirect
5. C127×#1444C2semidirect
6. C127×#1439C2semidirect
8. C127×C4⋊#95C2semidirect
55. C2×C4⋊C4×C127D4semidirect
56. C2×C4⋊C4×C127D4semidirect
252. #17071C127direct (N × H)
265. C2×#399C2×C127semidirect
266. C2×#396C2×C127semidirect
268. C2×#389C2×C127semidirect
269. #1444C2×C127semidirect
270. #1439C2×C127semidirect
272. C4⋊#95C2×C127semidirect
273. C127#17071direct (N × H)
320. C2×C4⋊C4D4×C127semidirect
321. C2×C4⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1272
C2×#396×C1272
C2×#390×C1272
C2×#389×C1272
C127×#14442
C127×#14392
C127×#14382
C127×C4⋊#952
#17071127