Finite Group Databasebeta

← C4×#460×C127 #44585172

Subgroups — C4×#460×C127 #44585172

Order 32512.

1152 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C127C211yesmaximal, characteristic
2C2×C4×SD16×C127C212yesmaximal, complemented
3C4×#127×C127C211yesmaximal, characteristic
4C42×Q8×C127C211yesmaximal, characteristic, complemented
5C127×#1982C211yesmaximal, characteristic
6C127×#1948C211yesmaximal, characteristic, complemented
7C127×#1926C212yesmaximal, complemented
8C127×#1880C212yesmaximal, complemented
9C127×#1803C211yesmaximal, characteristic, complemented
10C4×C4⋊C8×C127C211yesmaximal, characteristic, complemented
11C4×#102×C127C212yesmaximal, complemented
12C22×SD16×C127C2212yes—
13C2×#127×C127C2211yescharacteristic
14C2×C4×Q8×C127C2211yescharacteristic
15C2×C4×Q8×C127C2211yescharacteristic
16C2×C4×Q8×C127C2211yescharacteristic
17C2×C4×D4×C127—21no—
18C2×C4×D4×C127—21no—
19C2×C4×D4×C127C2212yes—
20#460×C127C418yesdirect product factor
21C4×SD16×C127—28no—
22C2×#106×C127C2212yes—
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×C4⋊C8×C127C2211yescharacteristic
25C2×#103×C127C2212yes—
26C2×#102×C127C2212yes—
27C2×#102×C127C2212yes—
28C2×#102×C127C2212yes—
29C2×C4×C8×C127C2212yes—
30#390×C127—21no—
31#390×C127—21no—
32#390×C127C2212yes—
33#384×C127C2211yescharacteristic
34C4×C4⋊C4×C127—21no—
35C4×C4⋊C4×C127—21no—
36C4×C4⋊C4×C127—21no—
37C4×C4⋊C4×C127C2211yescharacteristic
38C4×C4⋊C4×C127C2211yescharacteristic
39C4×C4⋊C4×C127C2211yescharacteristic
40C43×C127—21no—
41C43×C127C2211yescharacteristic
42#340×C127C2212yes—
43#340×C127C2212yes—
44#336×C127C2212yes—
45C22×Q8×C127C2311yescharacteristic
46C22×D4×C127—21no—
47C22×D4×C127—21no—
48C22×D4×C127C2312yes—
49C23×C4×C127—22no—
50C2×SD16×C127—24no—
51C2×SD16×C127—24no—
52C2×SD16×C127C2×C418yescomplemented
53C22×C8×C127C2312yes—
54C22×C8×C127C2312yes—
55#127×C127—22no—
56#127×C127C2×C414yes—
57C4×Q8×C127—22no—
58C4×Q8×C127—22no—
59C4×Q8×C127—22no—
60C4×Q8×C127—22no—
61C4×Q8×C127C2×C414yescomplemented
62C4×Q8×C127D414yescomplemented
63C4×D4×C127—24no—
64C4×D4×C127—24no—
65C4×D4×C127—44no—
66C4×D4×C127—44no—
67C2×C4⋊C4×C127—21no—
68C2×C4⋊C4×C127—21no—
69C2×C4⋊C4×C127—21no—
70C2×C4⋊C4×C127—21no—
71C2×C4⋊C4×C127—21no—
72C2×C4⋊C4×C127C2312yes—
73C2×C4⋊C4×C127C2311yescharacteristic
74C2×C4⋊C4×C127C2311yescharacteristic
75C2×C4⋊C4×C127C2311yescharacteristic
76C2×C22⋊C4×C127—22no—
77C2×C22⋊C4×C127—22no—
78C2×C22⋊C4×C127—22no—
79C2×C42×C127—21no—
80C2×C42×C127—21no—
81C2×C42×C127—21no—
82C2×C42×C127—21no—
83C2×C42×C127—21no—
84C2×C42×C127—21no—
85C2×C42×C127D411yescharacteristic
86C2×C42×C127D411yescharacteristic
87C2×C42×C127D411yescharacteristic
88C2×C42×C127D411yescharacteristic
89C2×C42×C127C2311yescharacteristic
90C2×C42×C127C2311yescharacteristic
91C2×C42×C127C2311yescharacteristic
92#106×C127—24no—
93C4⋊C8×C127—22no—
94C4⋊C8×C127C2×C414yescomplemented
95#103×C127—24no—
96#102×C127—24no—
97#102×C127—24no—
98#102×C127C2×C418yescomplemented
99C4×C8×C127—24no—
100#95×C127—21no—
101#95×C127—21no—
102#95×C127—21no—
103C24×C127—22no—
104C2×Q8×C127—21no—
105C2×Q8×C127—21no—
106C2×Q8×C127—21no—
107C2×Q8×C127C22×C412yes—
108C2×Q8×C127C2×D412yes—
109C2×Q8×C127#4112yes—
110C2×D4×C127—24no—
111C2×D4×C127—24no—
112C2×D4×C127—22no—
113C2×D4×C127—22no—
114C2×D4×C127—22no—
115C2×D4×C127—22no—
116C2×D4×C127—22no—
117C2×D4×C127—42no—
118C2×D4×C127—42no—
119C2×D4×C127—42no—
120C2×D4×C127—42no—
121C2×D4×C127C22×C414yes—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—21no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—44no—
128C22×C4×C127—44no—
129C22×C4×C127—44no—
130C22×C4×C127C2×D411yescharacteristic
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127C2×D411yescharacteristic
133C22×C4×C127C2×D411yescharacteristic
134C22×C4×C127C2×D411yescharacteristic
135C22×C4×C127C2×D411yescharacteristic
136C22×C4×C127C2411yescharacteristic
137SD16×C127—216no—
138C2×C8×C127—22no—
139C2×C8×C127—22no—
140C2×C8×C127—22no—
141C2×C8×C127—22no—
142C2×C8×C127—22no—
143C2×C8×C127C22×C414yes—
144C4⋊C4×C127—24no—
145C4⋊C4×C127—24no—
146C4⋊C4×C127—24no—
147C4⋊C4×C127—21no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127—42no—
153C4⋊C4×C127—42no—
154C4⋊C4×C127C22×C412yes—
155C4⋊C4×C127C2×D412yes—
156C4⋊C4×C127#4112yes—
157C22⋊C4×C127—44no—
158C22⋊C4×C127—44no—
159C22⋊C4×C127—44no—
160C42×C127—24no—
161C42×C127—24no—
162C42×C127—24no—
163C42×C127—22no—
164C42×C127—22no—
165C42×C127—21no—
166C42×C127—21no—
167C42×C127—41no—
168C42×C127—42no—
169C42×C127—42no—
170C42×C127—42no—
171C42×C127SD1614yescomplemented
172C42×C127C22×C412yes—
173C42×C127C2×D412yes—
174C42×C127#4112yes—
175C42×C127#4112yes—
176C23×C127—24no—
177C23×C127—42no—
178C23×C127—42no—
179C23×C127—42no—
180C23×C127—42no—
181C23×C127—42no—
182C23×C127—42no—
183C23×C127C22×D411yescharacteristic
184Q8×C127—22no—
185Q8×C127—22no—
186Q8×C127—22no—
187Q8×C127C4×D414yescomplemented
188D4×C127—24no—
189D4×C127—24no—
190D4×C127—48no—
191D4×C127—42no—
192D4×C127—42no—
193D4×C127—48no—
194C2×C4×C127—22no—
195C2×C4×C127—22no—
196C2×C4×C127—21no—
197C2×C4×C127—22no—
198C2×C4×C127—21no—
199C2×C4×C127—21no—
200C2×C4×C127—21no—
201C2×C4×C127—21no—
202C2×C4×C127—21no—
203C2×C4×C127—22no—
204C2×C4×C127—22no—
205C2×C4×C127—21no—
206C2×C4×C127—22no—
207C2×C4×C127—21no—
208C2×C4×C127—21no—
209C2×C4×C127—41no—
210C2×C4×C127—41no—
211C2×C4×C127—41no—
212C2×C4×C127—41no—
213C2×C4×C127—41no—
214C2×C4×C127—41no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—88no—
219C2×C4×C127C4×D412yes—
220C2×C4×C127C4×D412yes—
221C2×C4×C127#12112yes—
222C2×C4×C127#12112yes—
223C2×C4×C127C2×SD1612yes—
224C2×C4×C127C2×SD1612yes—
225C2×C4×C127C2×SD1612yes—
226C2×C4×C127#13512yes—
227C2×C4×C127AGL(1,ℤ/8)12yes—
228C2×C4×C127C23×C411yescharacteristic
229C2×C4×C127C22×D411yescharacteristic
230C2×C4×C127C2×#4111yescharacteristic
231C2×C4×C127C2×#4111yescharacteristic
232C2×C4×C127C2×#4111yescharacteristic
233C2×C4×C127C2×#4111yescharacteristic
234C8×C127—24no—
235C8×C127—42no—
236C22×C127—44no—
237C22×C127—44no—
238C22×C127—44no—
239C22×C127—82no—
240C22×C127—82no—
241C22×C127—82no—
242C22×C127—82no—
243C22×C127C2×C4×D411yescharacteristic
244C22×C127C2×#12111yescharacteristic
245C22×C127#52511yescharacteristic
246C22×C127C22×SD1611yescharacteristic
247C22×C127C2×#13511yescharacteristic
248C22×C127C2×AGL(1,ℤ/8)11yescharacteristic
249C22×C127#57511yescharacteristic
250C4×C127—22no—
251C4×C127—22no—
252C4×C127—22no—
253C4×C127—24no—
254C4×C127—41no—
255C4×C127—42no—
256C4×C127—42no—
257C4×C127—42no—
258C4×C127—82no—
259C4×C127C4×SD1614yescomplemented
260C4×C127#46014yesdirect product factor
261C4×C127C2×C4×D411yescharacteristic
262C4×C127C4×#4111yescharacteristic
263C4×C127#52911yescharacteristic
264C4×C127#53211yescharacteristic
265C4×#460C12711yesmaximal, characteristic, direct product factor, Sylow
266C2×C127—84no—
267C2×C127C4×#12111yescharacteristic
268C2×C127C2×C4×SD1611yescharacteristic
269C2×C127C4×AGL(1,ℤ/8)11yescharacteristic
270C2×C127C2×#46011yescharacteristic
271C2×C127#303511yescharacteristic
272C2×C127#310311yescharacteristic
273C2×C127#310611yescharacteristic
274C2×#460C2×C12711yescharacteristic
275C2×C4×SD16C2×C12712yescomplemented
276C4×#127C2×C12711yescharacteristic
277C42×Q8C2×C12711yescharacteristic, complemented
278#1982C2×C12711yescharacteristic
279#1948C2×C12711yescharacteristic, complemented
280#1926C2×C12712yescomplemented
281#1880C2×C12712yescomplemented
282#1803C2×C12711yescharacteristic, complemented
283C4×C4⋊C8C2×C12711yescharacteristic, complemented
284C4×#102C2×C12712yescomplemented
285C127C4×#46011yescharacteristic, direct product factor, Sylow
286C22×SD16C22×C12712yes—
287C2×#127C22×C12711yescharacteristic
288C2×C4×Q8C22×C12711yescharacteristic
289C2×C4×Q8C22×C12711yescharacteristic
290C2×C4×Q8C22×C12711yescharacteristic
291C2×C4×D4—21no—
292C2×C4×D4—21no—
293C2×C4×D4C22×C12712yes—
294#460C4×C12718yesdirect product factor
295C4×SD16—28no—
296C2×#106C22×C12712yes—
297C2×C4⋊C8C22×C12711yescharacteristic
298C2×C4⋊C8C22×C12711yescharacteristic
299C2×#103C22×C12712yes—
300C2×#102C22×C12712yes—
301C2×#102C22×C12712yes—
302C2×#102C22×C12712yes—
303C2×C4×C8C22×C12712yes—
304#390—21no—
305#390—21no—
306#390C22×C12712yes—
307#384C22×C12711yescharacteristic
308C4×C4⋊C4—21no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4—21no—
311C4×C4⋊C4C22×C12711yescharacteristic
312C4×C4⋊C4C22×C12711yescharacteristic
313C4×C4⋊C4C22×C12711yescharacteristic
314C43—21no—
315C43C22×C12711yescharacteristic
316#340C22×C12712yes—
317#340C22×C12712yes—
318#336C22×C12712yes—
319C22×Q8C23×C12711yescharacteristic
320C22×D4—21no—
321C22×D4—21no—
322C22×D4C23×C12712yes—
323C23×C4—22no—
324C2×SD16—24no—
325C2×SD16—24no—
326C2×SD16C2×C4×C12718yescomplemented
327C22×C8C23×C12712yes—
328C22×C8C23×C12712yes—
329#127—22no—
330#127C2×C4×C12714yes—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8C2×C4×C12714yescomplemented
336C4×Q8D4×C12714yescomplemented
337C4×D4—24no—
338C4×D4—24no—
339C4×D4—44no—
340C4×D4—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4C23×C12712yes—
347C2×C4⋊C4C23×C12711yescharacteristic
348C2×C4⋊C4C23×C12711yescharacteristic
349C2×C4⋊C4C23×C12711yescharacteristic
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C42—21no—
354C2×C42—21no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42D4×C12711yescharacteristic
360C2×C42D4×C12711yescharacteristic
361C2×C42D4×C12711yescharacteristic
362C2×C42D4×C12711yescharacteristic
363C2×C42C23×C12711yescharacteristic
364C2×C42C23×C12711yescharacteristic
365C2×C42C23×C12711yescharacteristic
366#106—24no—
367C4⋊C8—22no—
368C4⋊C8C2×C4×C12714yescomplemented
369#103—24no—
370#102—24no—
371#102—24no—
372#102C2×C4×C12718yescomplemented
373C4×C8—24no—
374#95—21no—
375#95—21no—
376#95—21no—
377C24—22no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8C22×C4×C12712yes—
382C2×Q8C2×D4×C12712yes—
383C2×Q8#41×C12712yes—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4C22×C4×C12714yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—44no—
402C22×C4—44no—
403C22×C4—44no—
404C22×C4C2×D4×C12711yescharacteristic
405C22×C4C2×D4×C12711yescharacteristic
406C22×C4C2×D4×C12711yescharacteristic
407C22×C4C2×D4×C12711yescharacteristic
408C22×C4C2×D4×C12711yescharacteristic
409C22×C4C2×D4×C12711yescharacteristic
410C22×C4C24×C12711yescharacteristic
411SD16—216no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8C22×C4×C12714yes—
418C4⋊C4—24no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C4⋊C4C22×C4×C12712yes—
429C4⋊C4C2×D4×C12712yes—
430C4⋊C4#41×C12712yes—
431C22⋊C4—44no—
432C22⋊C4—44no—
433C22⋊C4—44no—
434C42—24no—
435C42—24no—
436C42—24no—
437C42—22no—
438C42—22no—
439C42—21no—
440C42—21no—
441C42—41no—
442C42—42no—
443C42—42no—
444C42—42no—
445C42SD16×C12714yescomplemented
446C42C22×C4×C12712yes—
447C42C2×D4×C12712yes—
448C42#41×C12712yes—
449C42#41×C12712yes—
450C23—24no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23C22×D4×C12711yescharacteristic
458Q8—22no—
459Q8—22no—
460Q8—22no—
461Q8C4×D4×C12714yescomplemented
462D4—24no—
463D4—24no—
464D4—48no—
465D4—42no—
466D4—42no—
467D4—48no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—88no—
493C2×C4C4×D4×C12712yes—
494C2×C4C4×D4×C12712yes—
495C2×C4#121×C12712yes—
496C2×C4#121×C12712yes—
497C2×C4C2×SD16×C12712yes—
498C2×C4C2×SD16×C12712yes—
499C2×C4C2×SD16×C12712yes—
500C2×C4#135×C12712yes—
501C2×C4AGL(1,ℤ/8)×C12712yes—
502C2×C4C23×C4×C12711yescharacteristic
503C2×C4C22×D4×C12711yescharacteristic
504C2×C4C2×#41×C12711yescharacteristic
505C2×C4C2×#41×C12711yescharacteristic
506C2×C4C2×#41×C12711yescharacteristic
507C2×C4C2×#41×C12711yescharacteristic
508C8—24no—
509C8—42no—
510C22—44no—
511C22—44no—
512C22—44no—
513C22—82no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22C2×C4×D4×C12711yescharacteristic
518C22C2×#121×C12711yescharacteristic
519C22#525×C12711yescharacteristic
520C22C22×SD16×C12711yescharacteristic
521C22C2×#135×C12711yescharacteristic
522C22C2×AGL(1,ℤ/8)×C12711yescharacteristic
523C22#575×C12711yescharacteristic
524C4—22no—
525C4—22no—
526C4—22no—
527C4—24no—
528C4—41no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—82no—
533C4C4×SD16×C12714yescomplemented
534C4#460×C12714yesdirect product factor
535C4C2×C4×D4×C12711yescharacteristic
536C4C4×#41×C12711yescharacteristic
537C4#529×C12711yescharacteristic
538C4#532×C12711yescharacteristic
539C2—84no—
540C2C4×#121×C12711yescharacteristic
541C2C2×C4×SD16×C12711yescharacteristic
542C2C4×AGL(1,ℤ/8)×C12711yescharacteristic
543C2C2×#460×C12711yescharacteristic
544C2C127×#303511yescharacteristic
545C2C127×#310311yescharacteristic
546C2C127×#310611yescharacteristic
subgroupG/H
centerC22×C4×C127C2×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C22×D4
prime radicalC2×#127×C127C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ C43×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C127C2semidirect
4. C42×Q8×C127C2semidirect
6. C127×#1948C2semidirect
7. C127×#1926C2semidirect
8. C127×#1880C2semidirect
9. C127×#1803C2semidirect
10. C4×C4⋊C8×C127C2semidirect
11. C4×#102×C127C2semidirect
20. #460×C127C4direct (N × H)
52. C2×SD16×C127C2×C4semidirect
61. C4×Q8×C127C2×C4semidirect
62. C4×Q8×C127D4semidirect
94. C4⋊C8×C127C2×C4semidirect
98. #102×C127C2×C4semidirect
171. C42×C127SD16semidirect
187. Q8×C127C4×D4semidirect
259. C4×C127C4×SD16semidirect
260. C4×C127#460direct (N × H)
265. C4×#460C127direct (N × H)
275. C2×C4×SD16C2×C127semidirect
277. C42×Q8C2×C127semidirect
279. #1948C2×C127semidirect
280. #1926C2×C127semidirect
281. #1880C2×C127semidirect
282. #1803C2×C127semidirect
283. C4×C4⋊C8C2×C127semidirect
284. C4×#102C2×C127semidirect
285. C127C4×#460direct (N × H)
294. #460C4×C127direct (N × H)
326. C2×SD16C2×C4×C127semidirect
335. C4×Q8C2×C4×C127semidirect
336. C4×Q8D4×C127semidirect
368. C4⋊C8C2×C4×C127semidirect
372. #102C2×C4×C127semidirect
445. C42SD16×C127semidirect
461. Q8C4×D4×C127semidirect
533. C4C4×SD16×C127semidirect
534. C4#460×C127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#460×C1272
C2×C4×SD16×C1272
C4×#127×C1272
C42×Q8×C1272
C127×#19822
C127×#19482
C127×#19262
C127×#18802
C127×#18032
C4×C4⋊C8×C1272
C4×#102×C1272
C4×#460127