Finite Group Databasebeta

← C4×#466×C127 #44585194

Subgroups — C4×#466×C127 #44585194

Order 32512.

1222 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C127C211yesmaximal, characteristic
2C2×C4×D8×C127C211yesmaximal, characteristic, complemented
3C22×C4×C8×C127C211yesmaximal, characteristic, complemented
4C4×#121×C127C212yesmaximal, complemented
5C127×#1970C211yesmaximal, characteristic, complemented
6C127×#1942C211yesmaximal, characteristic, complemented
7C127×#1934C212yesmaximal, complemented
8C127×#1893C212yesmaximal, complemented
9C127×#1808C211yesmaximal, characteristic, complemented
10C4×#107×C127C211yesmaximal, characteristic, complemented
11C4×#102×C127C212yesmaximal, complemented
12C22×D8×C127C2211yescharacteristic
13C23×C8×C127C2211yescharacteristic
14C23×C8×C127C2211yescharacteristic
15C2×#121×C127C2212yes—
16C2×C4×D4×C127—22no—
17C2×C4×D4×C127C2212yes—
18C22×C42×C127C2211yescharacteristic
19#466×C127C418yesdirect product factor
20C4×D8×C127—24no—
21C2×#107×C127C2211yescharacteristic
22C2×#107×C127C2211yescharacteristic
23C2×#107×C127C2211yescharacteristic
24C2×#102×C127C2212yes—
25C2×#102×C127C2212yes—
26C2×#102×C127C2212yes—
27C2×C4×C8×C127—24no—
28C2×C4×C8×C127C2211yescharacteristic
29C2×C4×C8×C127C2211yescharacteristic
30C2×C4×C8×C127C2211yescharacteristic
31C2×C4×C8×C127C2211yescharacteristic
32#390×C127C2212yes—
33#389×C127C2212yes—
34#388×C127—22no—
35#386×C127—22no—
36#380×C127C2212yes—
37C4×C4⋊C4×C127C2212yes—
38C4×C22⋊C4×C127—22no—
39#340×C127C2212yes—
40#340×C127C2212yes—
41#340×C127C2212yes—
42C22×D4×C127—22no—
43C22×D4×C127C2312yes—
44C23×C4×C127—22no—
45C23×C4×C127D411yescharacteristic
46C23×C4×C127D411yescharacteristic
47C23×C4×C127C2311yescharacteristic
48C2×D8×C127—22no—
49C2×D8×C127—22no—
50C2×D8×C127C2×C414yescomplemented
51C22×C8×C127—22no—
52C22×C8×C127—22no—
53C22×C8×C127—22no—
54C22×C8×C127—22no—
55C22×C8×C127—22no—
56C22×C8×C127C2×C414yescomplemented
57C22×C8×C127C2311yescharacteristic
58C22×C8×C127C2311yescharacteristic
59C22×C8×C127C2311yescharacteristic
60C22×C8×C127C2311yescharacteristic
61#121×C127—24no—
62#121×C127C2×C418yescomplemented
63C4×D4×C127—24no—
64C4×D4×C127—24no—
65C4×D4×C127—48no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127C2312yes—
68C2×C4⋊C4×C127C2312yes—
69C2×C4⋊C4×C127C2312yes—
70C2×C22⋊C4×C127—22no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—22no—
73C2×C22⋊C4×C127—22no—
74C2×C22⋊C4×C127—22no—
75C2×C42×C127—22no—
76C2×C42×C127—22no—
77C2×C42×C127—22no—
78C2×C42×C127D411yescharacteristic
79C2×C42×C127D411yescharacteristic
80C2×C42×C127C2311yescharacteristic
81C2×C42×C127C2311yescharacteristic
82#107×C127—22no—
83#107×C127—22no—
84#107×C127C2×C414yescomplemented
85#102×C127—24no—
86#102×C127—24no—
87#102×C127C2×C418yescomplemented
88C4×C8×C127—22no—
89C4×C8×C127—22no—
90C4×C8×C127—22no—
91C4×C8×C127D414yescomplemented
92#95×C127—22no—
93#95×C127—22no—
94#95×C127—22no—
95C24×C127—22no—
96C24×C127C2×D411yescharacteristic
97C2×D4×C127—28no—
98C2×D4×C127—22no—
99C2×D4×C127—22no—
100C2×D4×C127—22no—
101C2×D4×C127—22no—
102C2×D4×C127—22no—
103C2×D4×C127—44no—
104C2×D4×C127—44no—
105C2×D4×C127C22×C414yes—
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—21no—
113C22×C4×C127—21no—
114C22×C4×C127—21no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—44no—
119C22×C4×C127—44no—
120C22×C4×C127—44no—
121C22×C4×C127D814yescomplemented
122C22×C4×C127C22×C412yes—
123C22×C4×C127C2×D411yescharacteristic
124C22×C4×C127C2×D411yescharacteristic
125C22×C4×C127C2×D411yescharacteristic
126C22×C4×C127C2×D411yescharacteristic
127C22×C4×C127C2×D411yescharacteristic
128C22×C4×C127#4112yes—
129C22×C4×C127C2411yescharacteristic
130D8×C127—28no—
131C2×C8×C127—28no—
132C2×C8×C127—21no—
133C2×C8×C127—21no—
134C2×C8×C127—21no—
135C2×C8×C127—21no—
136C2×C8×C127—21no—
137C2×C8×C127—21no—
138C2×C8×C127—28no—
139C2×C8×C127C22×C412yes—
140C2×C8×C127C22×C412yes—
141C2×C8×C127C2×D412yes—
142C2×C8×C127C2×D412yes—
143C2×C8×C127#4112yes—
144C2×C8×C127#4112yes—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—44no—
151C4⋊C4×C127C22×C414yes—
152C22⋊C4×C127—28no—
153C22⋊C4×C127—44no—
154C22⋊C4×C127—44no—
155C22⋊C4×C127—44no—
156C22⋊C4×C127—44no—
157C42×C127—22no—
158C42×C127—22no—
159C42×C127—21no—
160C42×C127—21no—
161C42×C127—44no—
162C42×C127C2×D412yes—
163C42×C127#4112yes—
164C23×C127—21no—
165C23×C127—21no—
166C23×C127—21no—
167C23×C127—21no—
168C23×C127—24no—
169C23×C127—42no—
170C23×C127—42no—
171C23×C127—42no—
172C23×C127—42no—
173C23×C127—42no—
174C23×C127—42no—
175C23×C127C4×D412yes—
176C23×C127C2×D812yes—
177C23×C127#13512yes—
178C23×C127C22×D411yescharacteristic
179D4×C127—24no—
180D4×C127—24no—
181D4×C127—416no—
182D4×C127—42no—
183D4×C127—42no—
184C2×C4×C127—28no—
185C2×C4×C127—21no—
186C2×C4×C127—21no—
187C2×C4×C127—21no—
188C2×C4×C127—21no—
189C2×C4×C127—21no—
190C2×C4×C127—21no—
191C2×C4×C127—21no—
192C2×C4×C127—21no—
193C2×C4×C127—22no—
194C2×C4×C127—22no—
195C2×C4×C127—22no—
196C2×C4×C127—22no—
197C2×C4×C127—28no—
198C2×C4×C127—24no—
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—88no—
208C2×C4×C127C4×D412yes—
209C2×C4×C127#12112yes—
210C2×C4×C127#12112yes—
211C2×C4×C127C2×D812yes—
212C2×C4×C127C2×D812yes—
213C2×C4×C127#13512yes—
214C2×C4×C127#13512yes—
215C2×C4×C127C23×C411yescharacteristic
216C2×C4×C127C22×D411yescharacteristic
217C2×C4×C127C2×#4111yescharacteristic
218C2×C4×C127C2×#4111yescharacteristic
219C2×C4×C127C2×#4111yescharacteristic
220C2×C4×C127C2×#4111yescharacteristic
221C8×C127—22no—
222C8×C127—22no—
223C8×C127—22no—
224C8×C127C4×D414yescomplemented
225C22×C127—22no—
226C22×C127—22no—
227C22×C127—22no—
228C22×C127—22no—
229C22×C127—22no—
230C22×C127—22no—
231C22×C127—44no—
232C22×C127—44no—
233C22×C127—44no—
234C22×C127—82no—
235C22×C127—82no—
236C22×C127—82no—
237C22×C127—82no—
238C22×C127C4×D814yescomplemented
239C22×C127C2×C4×D411yescharacteristic
240C22×C127C2×#12111yescharacteristic
241C22×C127#53211yescharacteristic
242C22×C127C22×D811yescharacteristic
243C22×C127C2×#13511yescharacteristic
244C22×C127C2×#13511yescharacteristic
245C22×C127C2×#13511yescharacteristic
246C4×C127—22no—
247C4×C127—22no—
248C4×C127—22no—
249C4×C127—22no—
250C4×C127—44no—
251C4×C127—82no—
252C4×C127—82no—
253C4×C127#46614yesdirect product factor
254C4×C127C2×C4×D411yescharacteristic
255C4×C127C4×#4111yescharacteristic
256C4×C127#52511yescharacteristic
257C4×C127#52911yescharacteristic
258C4×#466C12711yesmaximal, characteristic, direct product factor, Sylow
259C2×C127—24no—
260C2×C127—84no—
261C2×C127C4×#12111yescharacteristic
262C2×C127C2×C4×D811yescharacteristic
263C2×C127C4×#13511yescharacteristic
264C2×C127C2×#46611yescharacteristic
265C2×C127#305011yescharacteristic
266C2×C127#316811yescharacteristic
267C2×C127#316911yescharacteristic
268C2×#466C2×C12711yescharacteristic
269C2×C4×D8C2×C12711yescharacteristic, complemented
270C22×C4×C8C2×C12711yescharacteristic, complemented
271C4×#121C2×C12712yescomplemented
272#1970C2×C12711yescharacteristic, complemented
273#1942C2×C12711yescharacteristic, complemented
274#1934C2×C12712yescomplemented
275#1893C2×C12712yescomplemented
276#1808C2×C12711yescharacteristic, complemented
277C4×#107C2×C12711yescharacteristic, complemented
278C4×#102C2×C12712yescomplemented
279C127C4×#46611yescharacteristic, direct product factor, Sylow
280C22×D8C22×C12711yescharacteristic
281C23×C8C22×C12711yescharacteristic
282C23×C8C22×C12711yescharacteristic
283C2×#121C22×C12712yes—
284C2×C4×D4—22no—
285C2×C4×D4C22×C12712yes—
286C22×C42C22×C12711yescharacteristic
287#466C4×C12718yesdirect product factor
288C4×D8—24no—
289C2×#107C22×C12711yescharacteristic
290C2×#107C22×C12711yescharacteristic
291C2×#107C22×C12711yescharacteristic
292C2×#102C22×C12712yes—
293C2×#102C22×C12712yes—
294C2×#102C22×C12712yes—
295C2×C4×C8—24no—
296C2×C4×C8C22×C12711yescharacteristic
297C2×C4×C8C22×C12711yescharacteristic
298C2×C4×C8C22×C12711yescharacteristic
299C2×C4×C8C22×C12711yescharacteristic
300#390C22×C12712yes—
301#389C22×C12712yes—
302#388—22no—
303#386—22no—
304#380C22×C12712yes—
305C4×C4⋊C4C22×C12712yes—
306C4×C22⋊C4—22no—
307#340C22×C12712yes—
308#340C22×C12712yes—
309#340C22×C12712yes—
310C22×D4—22no—
311C22×D4C23×C12712yes—
312C23×C4—22no—
313C23×C4D4×C12711yescharacteristic
314C23×C4D4×C12711yescharacteristic
315C23×C4C23×C12711yescharacteristic
316C2×D8—22no—
317C2×D8—22no—
318C2×D8C2×C4×C12714yescomplemented
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8C2×C4×C12714yescomplemented
325C22×C8C23×C12711yescharacteristic
326C22×C8C23×C12711yescharacteristic
327C22×C8C23×C12711yescharacteristic
328C22×C8C23×C12711yescharacteristic
329#121—24no—
330#121C2×C4×C12718yescomplemented
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—48no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4C23×C12712yes—
336C2×C4⋊C4C23×C12712yes—
337C2×C4⋊C4C23×C12712yes—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42D4×C12711yescharacteristic
347C2×C42D4×C12711yescharacteristic
348C2×C42C23×C12711yescharacteristic
349C2×C42C23×C12711yescharacteristic
350#107—22no—
351#107—22no—
352#107C2×C4×C12714yescomplemented
353#102—24no—
354#102—24no—
355#102C2×C4×C12718yescomplemented
356C4×C8—22no—
357C4×C8—22no—
358C4×C8—22no—
359C4×C8D4×C12714yescomplemented
360#95—22no—
361#95—22no—
362#95—22no—
363C24—22no—
364C24C2×D4×C12711yescharacteristic
365C2×D4—28no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—44no—
372C2×D4—44no—
373C2×D4C22×C4×C12714yes—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—44no—
387C22×C4—44no—
388C22×C4—44no—
389C22×C4D8×C12714yescomplemented
390C22×C4C22×C4×C12712yes—
391C22×C4C2×D4×C12711yescharacteristic
392C22×C4C2×D4×C12711yescharacteristic
393C22×C4C2×D4×C12711yescharacteristic
394C22×C4C2×D4×C12711yescharacteristic
395C22×C4C2×D4×C12711yescharacteristic
396C22×C4#41×C12712yes—
397C22×C4C24×C12711yescharacteristic
398D8—28no—
399C2×C8—28no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—28no—
407C2×C8C22×C4×C12712yes—
408C2×C8C22×C4×C12712yes—
409C2×C8C2×D4×C12712yes—
410C2×C8C2×D4×C12712yes—
411C2×C8#41×C12712yes—
412C2×C8#41×C12712yes—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—44no—
419C4⋊C4C22×C4×C12714yes—
420C22⋊C4—28no—
421C22⋊C4—44no—
422C22⋊C4—44no—
423C22⋊C4—44no—
424C22⋊C4—44no—
425C42—22no—
426C42—22no—
427C42—21no—
428C42—21no—
429C42—44no—
430C42C2×D4×C12712yes—
431C42#41×C12712yes—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—24no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23C4×D4×C12712yes—
444C23C2×D8×C12712yes—
445C23#135×C12712yes—
446C23C22×D4×C12711yescharacteristic
447D4—24no—
448D4—24no—
449D4—416no—
450D4—42no—
451D4—42no—
452C2×C4—28no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—28no—
466C2×C4—24no—
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—88no—
476C2×C4C4×D4×C12712yes—
477C2×C4#121×C12712yes—
478C2×C4#121×C12712yes—
479C2×C4C2×D8×C12712yes—
480C2×C4C2×D8×C12712yes—
481C2×C4#135×C12712yes—
482C2×C4#135×C12712yes—
483C2×C4C23×C4×C12711yescharacteristic
484C2×C4C22×D4×C12711yescharacteristic
485C2×C4C2×#41×C12711yescharacteristic
486C2×C4C2×#41×C12711yescharacteristic
487C2×C4C2×#41×C12711yescharacteristic
488C2×C4C2×#41×C12711yescharacteristic
489C8—22no—
490C8—22no—
491C8—22no—
492C8C4×D4×C12714yescomplemented
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—44no—
500C22—44no—
501C22—44no—
502C22—82no—
503C22—82no—
504C22—82no—
505C22—82no—
506C22C4×D8×C12714yescomplemented
507C22C2×C4×D4×C12711yescharacteristic
508C22C2×#121×C12711yescharacteristic
509C22#532×C12711yescharacteristic
510C22C22×D8×C12711yescharacteristic
511C22C2×#135×C12711yescharacteristic
512C22C2×#135×C12711yescharacteristic
513C22C2×#135×C12711yescharacteristic
514C4—22no—
515C4—22no—
516C4—22no—
517C4—22no—
518C4—44no—
519C4—82no—
520C4—82no—
521C4#466×C12714yesdirect product factor
522C4C2×C4×D4×C12711yescharacteristic
523C4C4×#41×C12711yescharacteristic
524C4#525×C12711yescharacteristic
525C4#529×C12711yescharacteristic
526C2—24no—
527C2—84no—
528C2C4×#121×C12711yescharacteristic
529C2C2×C4×D8×C12711yescharacteristic
530C2C4×#135×C12711yescharacteristic
531C2C2×#466×C12711yescharacteristic
532C2C127×#305011yescharacteristic
533C2C127×#316811yescharacteristic
534C2C127×#316911yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C22×D4
prime radicalC2×#466×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D8×C127C2semidirect
3. C22×C4×C8×C127C2semidirect
4. C4×#121×C127C2semidirect
5. C127×#1970C2semidirect
6. C127×#1942C2semidirect
7. C127×#1934C2semidirect
8. C127×#1893C2semidirect
9. C127×#1808C2semidirect
10. C4×#107×C127C2semidirect
11. C4×#102×C127C2semidirect
19. #466×C127C4direct (N × H)
50. C2×D8×C127C2×C4semidirect
56. C22×C8×C127C2×C4semidirect
62. #121×C127C2×C4semidirect
84. #107×C127C2×C4semidirect
87. #102×C127C2×C4semidirect
91. C4×C8×C127D4semidirect
121. C22×C4×C127D8semidirect
224. C8×C127C4×D4semidirect
238. C22×C127C4×D8semidirect
253. C4×C127#466direct (N × H)
258. C4×#466C127direct (N × H)
269. C2×C4×D8C2×C127semidirect
270. C22×C4×C8C2×C127semidirect
271. C4×#121C2×C127semidirect
272. #1970C2×C127semidirect
273. #1942C2×C127semidirect
274. #1934C2×C127semidirect
275. #1893C2×C127semidirect
276. #1808C2×C127semidirect
277. C4×#107C2×C127semidirect
278. C4×#102C2×C127semidirect
279. C127C4×#466direct (N × H)
287. #466C4×C127direct (N × H)
318. C2×D8C2×C4×C127semidirect
324. C22×C8C2×C4×C127semidirect
330. #121C2×C4×C127semidirect
352. #107C2×C4×C127semidirect
355. #102C2×C4×C127semidirect
359. C4×C8D4×C127semidirect
389. C22×C4D8×C127semidirect
492. C8C4×D4×C127semidirect
506. C22C4×D8×C127semidirect
521. C4#466×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#466×C1272
C2×C4×D8×C1272
C22×C4×C8×C1272
C4×#121×C1272
C127×#19702
C127×#19422
C127×#19342
C127×#18932
C127×#18082
C4×#107×C1272
C4×#102×C1272
C4×#466127