Finite Group Databasebeta

← C127×#20984 #44584657

Subgroups — C127×#20984 #44584657

Order 32512.

2102 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C127C211yesmaximal, characteristic
2C2×#518×C127C211yesmaximal, characteristic, complemented
3C22×#99×C127C212yesmaximal, complemented
4C127×#2308C211yesmaximal, characteristic, complemented
5C127×#1899C214yesmaximal, complemented
6C127×#1898C214yesmaximal, complemented
7C2×#342×C127C212yesmaximal, complemented
8C23×D4×C127C2211yescharacteristic
9C23×D4×C127C2211yescharacteristic
10#534×C127—24no—
11#534×C127—24no—
12C2×#123×C127C412yescomplemented
13C2×#123×C127C2212yes—
14C2×#121×C127C414yescomplemented
15C2×#120×C127C412yescomplemented
16C2×#120×C127C2212yes—
17#518×C127—28no—
18C2×C4×D4×C127—24no—
19C2×#117×C127C2212yescomplemented
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2211yescharacteristic
22C22×C22⋊C4×C127C2212yes—
23C22×C22⋊C4×C127C2212yescomplemented
24C2×#99×C127—28no—
25C2×#99×C127C2218yes—
26#386×C127—24no—
27#381×C127C2212yescomplemented
28#379×C127C2212yescomplemented
29#342×C127C2218yescomplemented
30C25×C127C2×C411yescharacteristic, complemented
31C25×C127C2311yescharacteristic
32C25×C127C2311yescharacteristic
33C22×D4×C127—24no—
34C22×D4×C127—24no—
35C22×D4×C127—22no—
36C22×D4×C127—22no—
37C22×D4×C127—24no—
38C22×D4×C127—24no—
39C22×D4×C127C2×C412yes—
40C22×D4×C127C2×C412yes—
41C22×D4×C127C2×C412yescomplemented
42C22×D4×C127C2×C414yescomplemented
43C22×D4×C127D414yes—
44C22×D4×C127D414yes—
45C22×D4×C127C2312yes—
46C23×C4×C127—22no—
47C23×C4×C127—22no—
48C23×C4×C127—22no—
49C23×C4×C127C2×C411yescharacteristic, complemented
50C23×C4×C127C2×C412yescomplemented
51C23×C4×C127C2311yescharacteristic
52#123×C127—28no—
53#123×C127—24no—
54#123×C127—24no—
55#121×C127—216no—
56#120×C127—24no—
57#120×C127—24no—
58#120×C127—28no—
59C4×D4×C127—232no—
60#117×C127—28no—
61C2×C4⋊C4×C127—22no—
62C2×C4⋊C4×C127C2×C414yescomplemented
63C2×C22⋊C4×C127—22no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—22no—
66C2×C22⋊C4×C127—22no—
67C2×C22⋊C4×C127—22no—
68C2×C22⋊C4×C127—28no—
69C2×C22⋊C4×C127—24no—
70C2×C22⋊C4×C127—24no—
71C2×C22⋊C4×C127—22no—
72C2×C22⋊C4×C127—24no—
73C2×C22⋊C4×C127C2×C412yescomplemented
74C2×C22⋊C4×C127C2×C414yescomplemented
75C2×C22⋊C4×C127C2×C414yescomplemented
76C2×C22⋊C4×C127D418yescomplemented
77C2×C22⋊C4×C127C2314yes—
78C2×C22⋊C4×C127C2312yes—
79C2×C22⋊C4×C127C2314yes—
80C2×C42×C127—22no—
81#99×C127—216no—
82#95×C127—24no—
83C24×C127—22no—
84C24×C127—22no—
85C24×C127—22no—
86C24×C127—24no—
87C24×C127—82no—
88C24×C127—82no—
89C24×C127—82no—
90C24×C127C22×C412yes—
91C24×C127C22×C412yes—
92C24×C127C22×C411yescharacteristic
93C24×C127C22×C411yescharacteristic
94C24×C127C2×D412yes—
95C24×C127C2×D412yes—
96C24×C127C2×D412yes—
97C24×C127C2×D412yes—
98C24×C127C2×D414yes—
99C24×C127#4114yes—
100C24×C127C2411yescharacteristic
101C2×D4×C127—28no—
102C2×D4×C127—28no—
103C2×D4×C127—28no—
104C2×D4×C127—28no—
105C2×D4×C127—28no—
106C2×D4×C127—28no—
107C2×D4×C127—24no—
108C2×D4×C127—28no—
109C2×D4×C127—24no—
110C2×D4×C127—22no—
111C2×D4×C127—22no—
112C2×D4×C127—24no—
113C2×D4×C127—28no—
114C2×D4×C127—44no—
115C2×D4×C127—44no—
116C2×D4×C127—44no—
117C2×D4×C127—44no—
118C2×D4×C127—84no—
119C2×D4×C127C22⋊C418yes—
120C2×D4×C127C22⋊C418yes—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—24no—
125C22×C4×C127—24no—
126C22×C4×C127—28no—
127C22×C4×C127—24no—
128C22×C4×C127—28no—
129C22×C4×C127—24no—
130C22×C4×C127—44no—
131C22×C4×C127—84no—
132C22×C4×C127—84no—
133C22×C4×C127—84no—
134C22×C4×C127—82no—
135C22×C4×C127C22×C412yes—
136C22×C4×C127C22×C412yes—
137C22×C4×C127C22×C414yes—
138C22×C4×C127C2×D412yes—
139C22×C4×C127C2×D412yes—
140C4⋊C4×C127—28no—
141C4⋊C4×C127—28no—
142C22⋊C4×C127—28no—
143C22⋊C4×C127—24no—
144C22⋊C4×C127—28no—
145C22⋊C4×C127—28no—
146C22⋊C4×C127—24no—
147C22⋊C4×C127—22no—
148C22⋊C4×C127—22no—
149C22⋊C4×C127—28no—
150C22⋊C4×C127—24no—
151C22⋊C4×C127—24no—
152C22⋊C4×C127—44no—
153C22⋊C4×C127—84no—
154C22⋊C4×C127C2×D418yes—
155C42×C127—28no—
156C23×C127—22no—
157C23×C127—22no—
158C23×C127—24no—
159C23×C127—24no—
160C23×C127—22no—
161C23×C127—24no—
162C23×C127—42no—
163C23×C127—44no—
164C23×C127—44no—
165C23×C127—44no—
166C23×C127—42no—
167C23×C127—42no—
168C23×C127—44no—
169C23×C127—44no—
170C23×C127—44no—
171C23×C127—44no—
172C23×C127—84no—
173C23×C127—84no—
174C23×C127—84no—
175C23×C127—84no—
176C23×C127—84no—
177C23×C127—88no—
178C23×C127C2×C22⋊C414yes—
179C23×C127C2×C22⋊C412yes—
180C23×C127C2×C22⋊C412yes—
181C23×C127C4×D414yes—
182C23×C127C4×D414yes—
183C23×C127#12014yes—
184C23×C127#12114yes—
185C23×C127#12114yes—
186C23×C127#12314yes—
187C23×C127C23×C411yescharacteristic
188C23×C127C22×D411yescharacteristic
189C23×C127C22×D411yescharacteristic
190C23×C127C22×D412yes—
191C23×C127C2×#4112yes—
192D4×C127—216no—
193D4×C127—216no—
194D4×C127—42no—
195D4×C127—44no—
196D4×C127—42no—
197D4×C127—48no—
198D4×C127—88no—
199C2×C4×C127—24no—
200C2×C4×C127—22no—
201C2×C4×C127—24no—
202C2×C4×C127—22no—
203C2×C4×C127—24no—
204C2×C4×C127—22no—
205C2×C4×C127—24no—
206C2×C4×C127—28no—
207C2×C4×C127—48no—
208C2×C4×C127—44no—
209C2×C4×C127—44no—
210C2×C4×C127—48no—
211C2×C4×C127—44no—
212C2×C4×C127—84no—
213C2×C4×C127—88no—
214C2×C4×C127—88no—
215C2×C4×C127—88no—
216C2×C4×C127C2×C22⋊C414yes—
217C22×C127—22no—
218C22×C127—22no—
219C22×C127—22no—
220C22×C127—24no—
221C22×C127—24no—
222C22×C127—28no—
223C22×C127—24no—
224C22×C127—44no—
225C22×C127—44no—
226C22×C127—44no—
227C22×C127—42no—
228C22×C127—42no—
229C22×C127—44no—
230C22×C127—44no—
231C22×C127—44no—
232C22×C127—44no—
233C22×C127—44no—
234C22×C127—44no—
235C22×C127—42no—
236C22×C127—84no—
237C22×C127—84no—
238C22×C127—84no—
239C22×C127—88no—
240C22×C127#38614yes—
241C22×C127#38614yes—
242C22×C127C22×C22⋊C411yescharacteristic
243C22×C127C2×C4×D412yes—
244C22×C127C2×#12011yescharacteristic
245C22×C127C2×#12112yes—
246C22×C127C2×#12311yescharacteristic
247C4×C127—24no—
248C4×C127—48no—
249C4×C127—44no—
250C4×C127—42no—
251C4×C127—84no—
252#20984C12711yesmaximal, characteristic, direct product factor, Sylow
253C2×C127—21no—
254C2×C127—22no—
255C2×C127—21no—
256C2×C127—22no—
257C2×C127—24no—
258C2×C127—24no—
259C2×C127—44no—
260C2×C127—82no—
261C2×C127C2×#38611yescharacteristic
262C2×C127#288312yes—
263C2×#534C2×C12711yescharacteristic
264C2×#518C2×C12711yescharacteristic, complemented
265C22×#99C2×C12712yescomplemented
266#2308C2×C12711yescharacteristic, complemented
267#1899C2×C12714yescomplemented
268#1898C2×C12714yescomplemented
269C2×#342C2×C12712yescomplemented
270C127#2098411yescharacteristic, direct product factor, Sylow
271C23×D4C22×C12711yescharacteristic
272C23×D4C22×C12711yescharacteristic
273#534—24no—
274#534—24no—
275C2×#123C4×C12712yescomplemented
276C2×#123C22×C12712yes—
277C2×#121C4×C12714yescomplemented
278C2×#120C4×C12712yescomplemented
279C2×#120C22×C12712yes—
280#518—28no—
281C2×C4×D4—24no—
282C2×#117C22×C12712yescomplemented
283C22×C22⋊C4C22×C12712yes—
284C22×C22⋊C4C22×C12711yescharacteristic
285C22×C22⋊C4C22×C12712yes—
286C22×C22⋊C4C22×C12712yescomplemented
287C2×#99—28no—
288C2×#99C22×C12718yes—
289#386—24no—
290#381C22×C12712yescomplemented
291#379C22×C12712yescomplemented
292#342C22×C12718yescomplemented
293C25C2×C4×C12711yescharacteristic, complemented
294C25C23×C12711yescharacteristic
295C25C23×C12711yescharacteristic
296C22×D4—24no—
297C22×D4—24no—
298C22×D4—22no—
299C22×D4—22no—
300C22×D4—24no—
301C22×D4—24no—
302C22×D4C2×C4×C12712yes—
303C22×D4C2×C4×C12712yes—
304C22×D4C2×C4×C12712yescomplemented
305C22×D4C2×C4×C12714yescomplemented
306C22×D4D4×C12714yes—
307C22×D4D4×C12714yes—
308C22×D4C23×C12712yes—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4C2×C4×C12711yescharacteristic, complemented
313C23×C4C2×C4×C12712yescomplemented
314C23×C4C23×C12711yescharacteristic
315#123—28no—
316#123—24no—
317#123—24no—
318#121—216no—
319#120—24no—
320#120—24no—
321#120—28no—
322C4×D4—232no—
323#117—28no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4C2×C4×C12714yescomplemented
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4C2×C4×C12712yescomplemented
337C2×C22⋊C4C2×C4×C12714yescomplemented
338C2×C22⋊C4C2×C4×C12714yescomplemented
339C2×C22⋊C4D4×C12718yescomplemented
340C2×C22⋊C4C23×C12714yes—
341C2×C22⋊C4C23×C12712yes—
342C2×C22⋊C4C23×C12714yes—
343C2×C42—22no—
344#99—216no—
345#95—24no—
346C24—22no—
347C24—22no—
348C24—22no—
349C24—24no—
350C24—82no—
351C24—82no—
352C24—82no—
353C24C22×C4×C12712yes—
354C24C22×C4×C12712yes—
355C24C22×C4×C12711yescharacteristic
356C24C22×C4×C12711yescharacteristic
357C24C2×D4×C12712yes—
358C24C2×D4×C12712yes—
359C24C2×D4×C12712yes—
360C24C2×D4×C12712yes—
361C24C2×D4×C12714yes—
362C24#41×C12714yes—
363C24C24×C12711yescharacteristic
364C2×D4—28no—
365C2×D4—28no—
366C2×D4—28no—
367C2×D4—28no—
368C2×D4—28no—
369C2×D4—28no—
370C2×D4—24no—
371C2×D4—28no—
372C2×D4—24no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—24no—
376C2×D4—28no—
377C2×D4—44no—
378C2×D4—44no—
379C2×D4—44no—
380C2×D4—44no—
381C2×D4—84no—
382C2×D4C22⋊C4×C12718yes—
383C2×D4C22⋊C4×C12718yes—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—28no—
390C22×C4—24no—
391C22×C4—28no—
392C22×C4—24no—
393C22×C4—44no—
394C22×C4—84no—
395C22×C4—84no—
396C22×C4—84no—
397C22×C4—82no—
398C22×C4C22×C4×C12712yes—
399C22×C4C22×C4×C12712yes—
400C22×C4C22×C4×C12714yes—
401C22×C4C2×D4×C12712yes—
402C22×C4C2×D4×C12712yes—
403C4⋊C4—28no—
404C4⋊C4—28no—
405C22⋊C4—28no—
406C22⋊C4—24no—
407C22⋊C4—28no—
408C22⋊C4—28no—
409C22⋊C4—24no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—28no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—44no—
416C22⋊C4—84no—
417C22⋊C4C2×D4×C12718yes—
418C42—28no—
419C23—22no—
420C23—22no—
421C23—24no—
422C23—24no—
423C23—22no—
424C23—24no—
425C23—42no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—42no—
430C23—42no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—84no—
436C23—84no—
437C23—84no—
438C23—84no—
439C23—84no—
440C23—88no—
441C23C2×C22⋊C4×C12714yes—
442C23C2×C22⋊C4×C12712yes—
443C23C2×C22⋊C4×C12712yes—
444C23C4×D4×C12714yes—
445C23C4×D4×C12714yes—
446C23#120×C12714yes—
447C23#121×C12714yes—
448C23#121×C12714yes—
449C23#123×C12714yes—
450C23C23×C4×C12711yescharacteristic
451C23C22×D4×C12711yescharacteristic
452C23C22×D4×C12711yescharacteristic
453C23C22×D4×C12712yes—
454C23C2×#41×C12712yes—
455D4—216no—
456D4—216no—
457D4—42no—
458D4—44no—
459D4—42no—
460D4—48no—
461D4—88no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—28no—
470C2×C4—48no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—48no—
474C2×C4—44no—
475C2×C4—84no—
476C2×C4—88no—
477C2×C4—88no—
478C2×C4—88no—
479C2×C4C2×C22⋊C4×C12714yes—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—24no—
484C22—24no—
485C22—28no—
486C22—24no—
487C22—44no—
488C22—44no—
489C22—44no—
490C22—42no—
491C22—42no—
492C22—44no—
493C22—44no—
494C22—44no—
495C22—44no—
496C22—44no—
497C22—44no—
498C22—42no—
499C22—84no—
500C22—84no—
501C22—84no—
502C22—88no—
503C22#386×C12714yes—
504C22#386×C12714yes—
505C22C22×C22⋊C4×C12711yescharacteristic
506C22C2×C4×D4×C12712yes—
507C22C2×#120×C12711yescharacteristic
508C22C2×#121×C12712yes—
509C22C2×#123×C12711yescharacteristic
510C4—24no—
511C4—48no—
512C4—44no—
513C4—42no—
514C4—84no—
515C2—21no—
516C2—22no—
517C2—21no—
518C2—22no—
519C2—24no—
520C2—24no—
521C2—44no—
522C2—82no—
523C2C2×#386×C12711yescharacteristic
524C2C127×#288312yes—
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×#534×C127C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#518×C127C2semidirect
3. C22×#99×C127C2semidirect
4. C127×#2308C2semidirect
5. C127×#1899C2semidirect
6. C127×#1898C2semidirect
7. C2×#342×C127C2semidirect
12. C2×#123×C127C4semidirect
14. C2×#121×C127C4semidirect
15. C2×#120×C127C4semidirect
19. C2×#117×C127C22semidirect
23. C22×C22⋊C4×C127C22semidirect
27. #381×C127C22semidirect
28. #379×C127C22semidirect
29. #342×C127C22semidirect
30. C25×C127C2×C4semidirect
41. C22×D4×C127C2×C4semidirect
42. C22×D4×C127C2×C4semidirect
49. C23×C4×C127C2×C4semidirect
50. C23×C4×C127C2×C4semidirect
62. C2×C4⋊C4×C127C2×C4semidirect
73. C2×C22⋊C4×C127C2×C4semidirect
74. C2×C22⋊C4×C127C2×C4semidirect
75. C2×C22⋊C4×C127C2×C4semidirect
76. C2×C22⋊C4×C127D4semidirect
252. #20984C127direct (N × H)
264. C2×#518C2×C127semidirect
265. C22×#99C2×C127semidirect
266. #2308C2×C127semidirect
267. #1899C2×C127semidirect
268. #1898C2×C127semidirect
269. C2×#342C2×C127semidirect
270. C127#20984direct (N × H)
275. C2×#123C4×C127semidirect
277. C2×#121C4×C127semidirect
278. C2×#120C4×C127semidirect
282. C2×#117C22×C127semidirect
286. C22×C22⋊C4C22×C127semidirect
290. #381C22×C127semidirect
291. #379C22×C127semidirect
292. #342C22×C127semidirect
293. C25C2×C4×C127semidirect
304. C22×D4C2×C4×C127semidirect
305. C22×D4C2×C4×C127semidirect
312. C23×C4C2×C4×C127semidirect
313. C23×C4C2×C4×C127semidirect
325. C2×C4⋊C4C2×C4×C127semidirect
336. C2×C22⋊C4C2×C4×C127semidirect
337. C2×C22⋊C4C2×C4×C127semidirect
338. C2×C22⋊C4C2×C4×C127semidirect
339. C2×C22⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1272
C2×#518×C1272
C22×#99×C1272
C127×#23082
C127×#18992
C127×#18982
C2×#342×C1272
#20984127