Finite Group Databasebeta

← C2×C127×#1625 #44582159

Subgroups — C2×C127×#1625 #44582159

Order 32512.

1322 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×#547×C127C211yesmaximal, characteristic, complemented
2C2×#486×C127C211yesmaximal, characteristic, complemented
3C2×#459×C127C211yesmaximal, characteristic, complemented
4C2×#459×C127C211yesmaximal, characteristic, complemented
5C127×#1625C218yesmaximal, direct product factor
6C2×#332×C127C211yesmaximal, characteristic, complemented
7C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
9C22×#41×C127—21no—
10C22×D8×C127—21no—
11C22×D8×C127—21no—
12#547×C127—22no—
13#547×C127—22no—
14#547×C127—22no—
15#547×C127C2214yescomplemented
16C2×C4⋊Q8×C127C2211yescharacteristic
17C2×#127×C127C2211yescharacteristic
18C2×#123×C127—22no—
19C2×C22⋊Q8×C127—21no—
20C2×#121×C127—21no—
21C2×C4×D4×C127C2211yescharacteristic
22C2×C4×D4×C127C2211yescharacteristic
23C22×C4⋊C4×C127—21no—
24#486×C127—22no—
25#486×C127C2214yescomplemented
26#459×C127—22no—
27#459×C127—22no—
28#459×C127C2214yescomplemented
29#459×C127C2214yescomplemented
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×#102×C127—22no—
33C2×#102×C127—21no—
34C2×#102×C127—21no—
35C2×C4×C8×C127C2211yescharacteristic
36#332×C127C2214yescomplemented
37D4⋊C8×C127C2214yescomplemented
38D4⋊C8×C127C2214yescomplemented
39C2×#41×C127—24no—
40C2×#41×C127—24no—
41C2×#41×C127—44no—
42C2×#41×C127—44no—
43C22×Q8×C127—21no—
44C22×D4×C127—22no—
45C22×D4×C127—21no—
46C22×D4×C127—21no—
47C22×D4×C127—21no—
48C22×D4×C127D411yescharacteristic
49C22×D4×C127D411yescharacteristic
50C23×C4×C127—22no—
51C23×C4×C127—21no—
52C23×C4×C127—21no—
53C2×D8×C127—24no—
54C2×D8×C127—24no—
55C2×D8×C127—44no—
56C2×D8×C127—44no—
57C22×C8×C127—21no—
58C22×C8×C127—21no—
59C22×C8×C127—21no—
60C4⋊Q8×C127—21no—
61C4⋊Q8×C127—21no—
62C4⋊Q8×C127D412yes—
63C4⋊Q8×C127C2312yes—
64#127×C127—21no—
65#127×C127—21no—
66#127×C127—21no—
67#127×C127C2312yes—
68#123×C127—28no—
69#123×C127—28no—
70C22⋊Q8×C127—24no—
71C22⋊Q8×C127—24no—
72#121×C127—24no—
73#121×C127—24no—
74C4×D4×C127—21no—
75C4×D4×C127—21no—
76C4×D4×C127—21no—
77C4×D4×C127—21no—
78C4×D4×C127D412yes—
79C4×D4×C127D412yes—
80C4×D4×C127C2312yes—
81C4×D4×C127C2312yes—
82C2×C4⋊C4×C127—22no—
83C2×C4⋊C4×C127—24no—
84C2×C4⋊C4×C127—21no—
85C2×C4⋊C4×C127—24no—
86C2×C4⋊C4×C127D411yescharacteristic
87C2×C4⋊C4×C127D411yescharacteristic
88C2×C4⋊C4×C127D412yes—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—21no—
91C2×C22⋊C4×C127—21no—
92C2×C42×C127C2311yescharacteristic
93C4⋊C8×C127—21no—
94C4⋊C8×C127—21no—
95C4⋊C8×C127C2312yes—
96C4⋊C8×C127C2312yes—
97#102×C127—24no—
98#102×C127—24no—
99#102×C127—28no—
100C4×C8×C127—21no—
101C4×C8×C127C2312yes—
102C24×C127—21no—
103C24×C127—21no—
104C24×C127—41no—
105#41×C127—48no—
106#41×C127—416no—
107#41×C127—48no—
108C2×Q8×C127—22no—
109C2×Q8×C127—22no—
110C2×Q8×C127—42no—
111C2×Q8×C127—42no—
112C2×D4×C127—28no—
113C2×D4×C127—21no—
114C2×D4×C127—21no—
115C2×D4×C127—22no—
116C2×D4×C127—22no—
117C2×D4×C127—22no—
118C2×D4×C127—22no—
119C2×D4×C127—22no—
120C2×D4×C127—22no—
121C2×D4×C127—44no—
122C2×D4×C127—48no—
123C2×D4×C127—41no—
124C2×D4×C127—41no—
125C2×D4×C127—41no—
126C2×D4×C127—42no—
127C2×D4×C127—42no—
128C2×D4×C127—42no—
129C2×D4×C127—42no—
130C2×D4×C127D814yescomplemented
131C2×D4×C127C2×D412yes—
132C2×D4×C127C2×D412yes—
133C22×C4×C127—28no—
134C22×C4×C127—21no—
135C22×C4×C127—21no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—48no—
142C22×C4×C127—42no—
143C22×C4×C127—42no—
144C22×C4×C127—42no—
145C22×C4×C127—42no—
146C22×C4×C127C2×D411yescharacteristic
147C22×C4×C127C2×D411yescharacteristic
148C22×C4×C127C2×D411yescharacteristic
149D8×C127—48no—
150D8×C127—48no—
151C2×C8×C127—22no—
152C2×C8×C127—22no—
153C2×C8×C127—22no—
154C2×C8×C127—42no—
155C2×C8×C127—42no—
156C2×C8×C127—42no—
157C4⋊C4×C127—28no—
158C4⋊C4×C127—21no—
159C4⋊C4×C127—22no—
160C4⋊C4×C127—21no—
161C4⋊C4×C127—22no—
162C4⋊C4×C127—22no—
163C4⋊C4×C127C2×D412yes—
164C4⋊C4×C127C2×D412yes—
165C4⋊C4×C127C2×D414yes—
166C22⋊C4×C127—28no—
167C22⋊C4×C127—22no—
168C22⋊C4×C127—22no—
169C22⋊C4×C127—22no—
170C22⋊C4×C127—22no—
171C42×C127C2×D411yescharacteristic
172C42×C127C2×D411yescharacteristic
173C42×C127C2×D411yescharacteristic
174C42×C127C2411yescharacteristic
175C23×C127—22no—
176C23×C127—24no—
177C23×C127—22no—
178C23×C127—42no—
179C23×C127—42no—
180C23×C127—42no—
181C23×C127—42no—
182C23×C127—42no—
183C23×C127—42no—
184C23×C127—82no—
185C23×C127—82no—
186C23×C127—82no—
187C23×C127#12011yescharacteristic
188Q8×C127—42no—
189Q8×C127—42no—
190Q8×C127—44no—
191D4×C127—22no—
192D4×C127—22no—
193D4×C127—22no—
194D4×C127—24no—
195D4×C127—44no—
196D4×C127—416no—
197D4×C127—42no—
198D4×C127—42no—
199D4×C127—42no—
200D4×C127—42no—
201D4×C127—42no—
202D4×C127—82no—
203D4×C127—82no—
204D4×C127—82no—
205D4×C127C2×D814yescomplemented
206C2×C4×C127—22no—
207C2×C4×C127—22no—
208C2×C4×C127—22no—
209C2×C4×C127—24no—
210C2×C4×C127—416no—
211C2×C4×C127—42no—
212C2×C4×C127—44no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—44no—
219C2×C4×C127—44no—
220C2×C4×C127#12011yescharacteristic
221C2×C4×C127#12011yescharacteristic
222C2×C4×C127#12011yescharacteristic
223C2×C4×C127C2×D812yes—
224C2×C4×C127#13512yes—
225C2×C4×C127AGL(1,ℤ/8)12yes—
226C2×C4×C127AGL(1,ℤ/8)12yes—
227C2×C4×C127C22×D411yescharacteristic
228C2×C4×C127C22×D411yescharacteristic
229C2×C4×C127C22×D411yescharacteristic
230C8×C127—42no—
231C8×C127—42no—
232C8×C127—42no—
233C22×C127—24no—
234C22×C127—48no—
235C22×C127—42no—
236C22×C127—42no—
237C22×C127—42no—
238C22×C127—42no—
239C22×C127—42no—
240C22×C127—84no—
241C22×C127—82no—
242C22×C127—82no—
243C22×C127—82no—
244C22×C127—164no—
245C22×C127#44712yes—
246C22×C127#44912yes—
247C22×C127#45412yes—
248C22×C127C2×#12011yescharacteristic
249C4×C127—21no—
250C4×C127—21no—
251C4×C127—42no—
252C4×C127—44no—
253C4×C127—42no—
254C4×C127#44712yes—
255C4×C127#44912yes—
256C4×C127C22×D811yescharacteristic
257C4×C127C2×#13511yescharacteristic
258C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
259C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
260C2×#1625C12711yesmaximal, characteristic, direct product factor, Sylow
261C2×C127—44no—
262C2×C127—82no—
263C2×C127—162no—
264C2×C127#162514yesdirect product factor
265C2×C127C2×#44711yescharacteristic
266C2×C127C2×#44911yescharacteristic
267C2×C127C2×#45411yescharacteristic
268C2×#547C2×C12711yescharacteristic, complemented
269C2×#486C2×C12711yescharacteristic, complemented
270C2×#459C2×C12711yescharacteristic, complemented
271C2×#459C2×C12711yescharacteristic, complemented
272#1625C2×C12718yesdirect product factor
273C2×#332C2×C12711yescharacteristic, complemented
274C2×D4⋊C8C2×C12711yescharacteristic, complemented
275C2×D4⋊C8C2×C12711yescharacteristic, complemented
276C127C2×#162511yescharacteristic, direct product factor, Sylow
277C22×#41—21no—
278C22×D8—21no—
279C22×D8—21no—
280#547—22no—
281#547—22no—
282#547—22no—
283#547C22×C12714yescomplemented
284C2×C4⋊Q8C22×C12711yescharacteristic
285C2×#127C22×C12711yescharacteristic
286C2×#123—22no—
287C2×C22⋊Q8—21no—
288C2×#121—21no—
289C2×C4×D4C22×C12711yescharacteristic
290C2×C4×D4C22×C12711yescharacteristic
291C22×C4⋊C4—21no—
292#486—22no—
293#486C22×C12714yescomplemented
294#459—22no—
295#459—22no—
296#459C22×C12714yescomplemented
297#459C22×C12714yescomplemented
298C2×C4⋊C8C22×C12711yescharacteristic
299C2×C4⋊C8C22×C12711yescharacteristic
300C2×#102—22no—
301C2×#102—21no—
302C2×#102—21no—
303C2×C4×C8C22×C12711yescharacteristic
304#332C22×C12714yescomplemented
305D4⋊C8C22×C12714yescomplemented
306D4⋊C8C22×C12714yescomplemented
307C2×#41—24no—
308C2×#41—24no—
309C2×#41—44no—
310C2×#41—44no—
311C22×Q8—21no—
312C22×D4—22no—
313C22×D4—21no—
314C22×D4—21no—
315C22×D4—21no—
316C22×D4D4×C12711yescharacteristic
317C22×D4D4×C12711yescharacteristic
318C23×C4—22no—
319C23×C4—21no—
320C23×C4—21no—
321C2×D8—24no—
322C2×D8—24no—
323C2×D8—44no—
324C2×D8—44no—
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8D4×C12712yes—
331C4⋊Q8C23×C12712yes—
332#127—21no—
333#127—21no—
334#127—21no—
335#127C23×C12712yes—
336#123—28no—
337#123—28no—
338C22⋊Q8—24no—
339C22⋊Q8—24no—
340#121—24no—
341#121—24no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4D4×C12712yes—
347C4×D4D4×C12712yes—
348C4×D4C23×C12712yes—
349C4×D4C23×C12712yes—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4D4×C12711yescharacteristic
355C2×C4⋊C4D4×C12711yescharacteristic
356C2×C4⋊C4D4×C12712yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C42C23×C12711yescharacteristic
361C4⋊C8—21no—
362C4⋊C8—21no—
363C4⋊C8C23×C12712yes—
364C4⋊C8C23×C12712yes—
365#102—24no—
366#102—24no—
367#102—28no—
368C4×C8—21no—
369C4×C8C23×C12712yes—
370C24—21no—
371C24—21no—
372C24—41no—
373#41—48no—
374#41—416no—
375#41—48no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×D4—28no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—44no—
390C2×D4—48no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4D8×C12714yescomplemented
399C2×D4C2×D4×C12712yes—
400C2×D4C2×D4×C12712yes—
401C22×C4—28no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—48no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4C2×D4×C12711yescharacteristic
415C22×C4C2×D4×C12711yescharacteristic
416C22×C4C2×D4×C12711yescharacteristic
417D8—48no—
418D8—48no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—42no—
423C2×C8—42no—
424C2×C8—42no—
425C4⋊C4—28no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4C2×D4×C12712yes—
432C4⋊C4C2×D4×C12712yes—
433C4⋊C4C2×D4×C12714yes—
434C22⋊C4—28no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C42C2×D4×C12711yescharacteristic
440C42C2×D4×C12711yescharacteristic
441C42C2×D4×C12711yescharacteristic
442C42C24×C12711yescharacteristic
443C23—22no—
444C23—24no—
445C23—22no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—82no—
453C23—82no—
454C23—82no—
455C23#120×C12711yescharacteristic
456Q8—42no—
457Q8—42no—
458Q8—44no—
459D4—22no—
460D4—22no—
461D4—22no—
462D4—24no—
463D4—44no—
464D4—416no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—82no—
471D4—82no—
472D4—82no—
473D4C2×D8×C12714yescomplemented
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—416no—
479C2×C4—42no—
480C2×C4—44no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4#120×C12711yescharacteristic
489C2×C4#120×C12711yescharacteristic
490C2×C4#120×C12711yescharacteristic
491C2×C4C2×D8×C12712yes—
492C2×C4#135×C12712yes—
493C2×C4AGL(1,ℤ/8)×C12712yes—
494C2×C4AGL(1,ℤ/8)×C12712yes—
495C2×C4C22×D4×C12711yescharacteristic
496C2×C4C22×D4×C12711yescharacteristic
497C2×C4C22×D4×C12711yescharacteristic
498C8—42no—
499C8—42no—
500C8—42no—
501C22—24no—
502C22—48no—
503C22—42no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—84no—
509C22—82no—
510C22—82no—
511C22—82no—
512C22—164no—
513C22#447×C12712yes—
514C22#449×C12712yes—
515C22#454×C12712yes—
516C22C2×#120×C12711yescharacteristic
517C4—21no—
518C4—21no—
519C4—42no—
520C4—44no—
521C4—42no—
522C4#447×C12712yes—
523C4#449×C12712yes—
524C4C22×D8×C12711yescharacteristic
525C4C2×#135×C12711yescharacteristic
526C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
527C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
528C2—44no—
529C2—82no—
530C2—162no—
531C2C127×#162514yesdirect product factor
532C2C2×#447×C12711yescharacteristic
533C2C2×#449×C12711yescharacteristic
534C2C2×#454×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#547×C127C2semidirect
2. C2×#486×C127C2semidirect
3. C2×#459×C127C2semidirect
4. C2×#459×C127C2semidirect
5. C127×#1625C2direct (N × H)
6. C2×#332×C127C2semidirect
7. C2×D4⋊C8×C127C2semidirect
8. C2×D4⋊C8×C127C2semidirect
15. #547×C127C22semidirect
25. #486×C127C22semidirect
28. #459×C127C22semidirect
29. #459×C127C22semidirect
36. #332×C127C22semidirect
37. D4⋊C8×C127C22semidirect
38. D4⋊C8×C127C22semidirect
130. C2×D4×C127D8semidirect
205. D4×C127C2×D8semidirect
260. C2×#1625C127direct (N × H)
264. C2×C127#1625direct (N × H)
268. C2×#547C2×C127semidirect
269. C2×#486C2×C127semidirect
270. C2×#459C2×C127semidirect
271. C2×#459C2×C127semidirect
272. #1625C2×C127direct (N × H)
273. C2×#332C2×C127semidirect
274. C2×D4⋊C8C2×C127semidirect
275. C2×D4⋊C8C2×C127semidirect
276. C127C2×#1625direct (N × H)
283. #547C22×C127semidirect
293. #486C22×C127semidirect
296. #459C22×C127semidirect
297. #459C22×C127semidirect
304. #332C22×C127semidirect
305. D4⋊C8C22×C127semidirect
306. D4⋊C8C22×C127semidirect
398. C2×D4D8×C127semidirect
473. D4C2×D8×C127semidirect
531. C2C127×#1625direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#547×C1272
C2×#486×C1272
C2×#459×C1272
C127×#16252
C2×#332×C1272
C2×D4⋊C8×C1272
C2×#1625127