Finite Group Databasebeta

← C2×C127×#1642 #44582185

Subgroups — C2×C127×#1642 #44582185

Order 32512.

1290 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C127C211yesmaximal, characteristic
2C2×#486×C127C211yesmaximal, characteristic, complemented
3C2×#475×C127C211yesmaximal, characteristic, complemented
4C2×#461×C127C211yesmaximal, characteristic, complemented
5C127×#1642C218yesmaximal, direct product factor
6C2×#331×C127C211yesmaximal, characteristic, complemented
7C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
9C22×#41×C127—21no—
10C22×SD16×C127—21no—
11#550×C127—22no—
12#550×C127—22no—
13#550×C127—22no—
14#550×C127C2214yes—
15C2×C4⋊Q8×C127C2211yescharacteristic
16C2×#127×C127—21no—
17C2×#127×C127C2211yescharacteristic
18C2×#121×C127—22no—
19C2×#121×C127—21no—
20C2×C4×Q8×C127C2211yescharacteristic
21C2×C4×D4×C127—21no—
22C2×C4×D4×C127C2211yescharacteristic
23#486×C127—22no—
24#486×C127C2214yescomplemented
25#475×C127—22no—
26#475×C127C2214yescomplemented
27#461×C127—22no—
28#461×C127C2214yescomplemented
29C2×#106×C127—21no—
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×#103×C127—21no—
33C2×#103×C127—21no—
34C2×#102×C127—22no—
35C2×C4×C8×C127C2211yescharacteristic
36#331×C127C2214yescomplemented
37Q8⋊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×Q8×C127D411yescharacteristic
45C22×D4×C127—22no—
46C22×D4×C127—22no—
47C22×D4×C127—21no—
48C22×D4×C127—21no—
49C22×D4×C127D411yescharacteristic
50C22×D4×C127D412yes—
51C23×C4×C127—22no—
52C23×C4×C127—21no—
53C2×SD16×C127—24no—
54C2×SD16×C127—44no—
55C22×C8×C127—21no—
56C22×C8×C127—21no—
57C22×C8×C127—21no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127—21no—
60C4⋊Q8×C127—21no—
61C4⋊Q8×C127C2312yes—
62#127×C127—24no—
63#127×C127—24no—
64#127×C127—21no—
65#127×C127—21no—
66#127×C127D412yes—
67#127×C127C2312yes—
68#121×C127—24no—
69#121×C127—28no—
70#121×C127—28no—
71#121×C127—24no—
72C4×Q8×C127—21no—
73C4×Q8×C127—21no—
74C4×Q8×C127D412yes—
75C4×Q8×C127C2312yes—
76C4×D4×C127—24no—
77C4×D4×C127—24no—
78C4×D4×C127—21no—
79C4×D4×C127—21no—
80C4×D4×C127D412yes—
81C4×D4×C127C2312yes—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127—21no—
84C2×C4⋊C4×C127—21no—
85C2×C4⋊C4×C127D411yescharacteristic
86C2×C4⋊C4×C127D411yescharacteristic
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—21no—
89C2×C42×C127—21no—
90C2×C42×C127C2311yescharacteristic
91#106×C127—24no—
92C4⋊C8×C127—21no—
93C4⋊C8×C127—21no—
94C4⋊C8×C127C2312yes—
95C4⋊C8×C127C2312yes—
96#103×C127—24no—
97#103×C127—24no—
98#102×C127—28no—
99C4×C8×C127—21no—
100C4×C8×C127C2312yes—
101C24×C127—21no—
102C24×C127—22no—
103#41×C127—48no—
104#41×C127—416no—
105#41×C127—48no—
106C2×Q8×C127—21no—
107C2×Q8×C127—22no—
108C2×Q8×C127—22no—
109C2×Q8×C127—41no—
110C2×Q8×C127—42no—
111C2×Q8×C127—42no—
112C2×Q8×C127SD1614yescomplemented
113C2×Q8×C127C2×D412yes—
114C2×D4×C127—28no—
115C2×D4×C127—28no—
116C2×D4×C127—21no—
117C2×D4×C127—22no—
118C2×D4×C127—22no—
119C2×D4×C127—22no—
120C2×D4×C127—22no—
121C2×D4×C127—22no—
122C2×D4×C127—22no—
123C2×D4×C127—22no—
124C2×D4×C127—48no—
125C2×D4×C127—44no—
126C2×D4×C127—42no—
127C2×D4×C127—42no—
128C2×D4×C127—42no—
129C2×D4×C127—42no—
130C2×D4×C127—84no—
131C2×D4×C127C2×D412yes—
132C2×D4×C127C2×D414yes—
133C22×C4×C127—21no—
134C22×C4×C127—28no—
135C22×C4×C127—21no—
136C22×C4×C127—21no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—48no—
140C22×C4×C127—42no—
141C22×C4×C127—42no—
142C22×C4×C127—41no—
143C22×C4×C127C2×D411yescharacteristic
144C22×C4×C127C2×D411yescharacteristic
145C22×C4×C127C2×D411yescharacteristic
146SD16×C127—48no—
147C2×C8×C127—22no—
148C2×C8×C127—22no—
149C2×C8×C127—22no—
150C2×C8×C127—42no—
151C2×C8×C127—42no—
152C2×C8×C127—42no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—21no—
155C4⋊C4×C127—21no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127—22no—
159C4⋊C4×C127—41no—
160C4⋊C4×C127—41no—
161C4⋊C4×C127C2×D412yes—
162C4⋊C4×C127C2×D412yes—
163C22⋊C4×C127—28no—
164C22⋊C4×C127—22no—
165C22⋊C4×C127—22no—
166C42×C127—22no—
167C42×C127—22no—
168C42×C127C2×D411yescharacteristic
169C42×C127C2×D411yescharacteristic
170C42×C127C2×D411yescharacteristic
171C42×C127C2411yescharacteristic
172C23×C127—22no—
173C23×C127—24no—
174C23×C127—42no—
175C23×C127—44no—
176C23×C127—44no—
177C23×C127—42no—
178C23×C127—44no—
179C23×C127—42no—
180C23×C127#12011yescharacteristic
181Q8×C127—22no—
182Q8×C127—24no—
183Q8×C127—42no—
184Q8×C127—42no—
185Q8×C127—82no—
186Q8×C127C2×SD1614yescomplemented
187D4×C127—22no—
188D4×C127—22no—
189D4×C127—44no—
190D4×C127—416no—
191D4×C127—42no—
192D4×C127—42no—
193D4×C127—42no—
194D4×C127—42no—
195D4×C127—42no—
196D4×C127—44no—
197D4×C127—44no—
198D4×C127—82no—
199D4×C127—88no—
200C2×C4×C127—22no—
201C2×C4×C127—24no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—22no—
205C2×C4×C127—416no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—42no—
209C2×C4×C127—42no—
210C2×C4×C127—44no—
211C2×C4×C127—42no—
212C2×C4×C127—82no—
213C2×C4×C127#12011yescharacteristic
214C2×C4×C127#12011yescharacteristic
215C2×C4×C127#12011yescharacteristic
216C2×C4×C127C2×SD1612yes—
217C2×C4×C127#13512yes—
218C2×C4×C127AGL(1,ℤ/8)12yes—
219C2×C4×C127AGL(1,ℤ/8)12yes—
220C2×C4×C127C22×D411yescharacteristic
221C2×C4×C127C22×D411yescharacteristic
222C2×C4×C127C22×D411yescharacteristic
223C8×C127—42no—
224C8×C127—42no—
225C8×C127—42no—
226C22×C127—44no—
227C22×C127—42no—
228C22×C127—42no—
229C22×C127—44no—
230C22×C127—44no—
231C22×C127—42no—
232C22×C127—84no—
233C22×C127—88no—
234C22×C127#44912yes—
235C22×C127#45012yes—
236C22×C127#45512yes—
237C22×C127C2×#12011yescharacteristic
238C4×C127—24no—
239C4×C127—21no—
240C4×C127—21no—
241C4×C127—42no—
242C4×C127—42no—
243C4×C127—82no—
244C4×C127#44912yes—
245C4×C127#45012yes—
246C4×C127C22×SD1611yescharacteristic
247C4×C127C2×#13511yescharacteristic
248C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
249C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
250C2×#1642C12711yesmaximal, characteristic, direct product factor, Sylow
251C2×C127—82no—
252C2×C127—84no—
253C2×C127#164214yesdirect product factor
254C2×C127C2×#45011yescharacteristic
255C2×C127C2×#44911yescharacteristic
256C2×C127C2×#45511yescharacteristic
257C2×#550C2×C12711yescharacteristic
258C2×#486C2×C12711yescharacteristic, complemented
259C2×#475C2×C12711yescharacteristic, complemented
260C2×#461C2×C12711yescharacteristic, complemented
261#1642C2×C12718yesdirect product factor
262C2×#331C2×C12711yescharacteristic, complemented
263C2×Q8⋊C8C2×C12711yescharacteristic, complemented
264C2×D4⋊C8C2×C12711yescharacteristic, complemented
265C127C2×#164211yescharacteristic, direct product factor, Sylow
266C22×#41—21no—
267C22×SD16—21no—
268#550—22no—
269#550—22no—
270#550—22no—
271#550C22×C12714yes—
272C2×C4⋊Q8C22×C12711yescharacteristic
273C2×#127—21no—
274C2×#127C22×C12711yescharacteristic
275C2×#121—22no—
276C2×#121—21no—
277C2×C4×Q8C22×C12711yescharacteristic
278C2×C4×D4—21no—
279C2×C4×D4C22×C12711yescharacteristic
280#486—22no—
281#486C22×C12714yescomplemented
282#475—22no—
283#475C22×C12714yescomplemented
284#461—22no—
285#461C22×C12714yescomplemented
286C2×#106—21no—
287C2×C4⋊C8C22×C12711yescharacteristic
288C2×C4⋊C8C22×C12711yescharacteristic
289C2×#103—21no—
290C2×#103—21no—
291C2×#102—22no—
292C2×C4×C8C22×C12711yescharacteristic
293#331C22×C12714yescomplemented
294Q8⋊C8C22×C12714yescomplemented
295D4⋊C8C22×C12714yescomplemented
296C2×#41—24no—
297C2×#41—24no—
298C2×#41—44no—
299C2×#41—44no—
300C22×Q8—21no—
301C22×Q8D4×C12711yescharacteristic
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4D4×C12711yescharacteristic
307C22×D4D4×C12712yes—
308C23×C4—22no—
309C23×C4—21no—
310C2×SD16—24no—
311C2×SD16—44no—
312C22×C8—21no—
313C22×C8—21no—
314C22×C8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8C23×C12712yes—
319#127—24no—
320#127—24no—
321#127—21no—
322#127—21no—
323#127D4×C12712yes—
324#127C23×C12712yes—
325#121—24no—
326#121—28no—
327#121—28no—
328#121—24no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×Q8D4×C12712yes—
332C4×Q8C23×C12712yes—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4D4×C12712yes—
338C4×D4C23×C12712yes—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4D4×C12711yescharacteristic
343C2×C4⋊C4D4×C12711yescharacteristic
344C2×C22⋊C4—22no—
345C2×C22⋊C4—21no—
346C2×C42—21no—
347C2×C42C23×C12711yescharacteristic
348#106—24no—
349C4⋊C8—21no—
350C4⋊C8—21no—
351C4⋊C8C23×C12712yes—
352C4⋊C8C23×C12712yes—
353#103—24no—
354#103—24no—
355#102—28no—
356C4×C8—21no—
357C4×C8C23×C12712yes—
358C24—21no—
359C24—22no—
360#41—48no—
361#41—416no—
362#41—48no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—41no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8SD16×C12714yescomplemented
370C2×Q8C2×D4×C12712yes—
371C2×D4—28no—
372C2×D4—28no—
373C2×D4—21no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—48no—
382C2×D4—44no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—84no—
388C2×D4C2×D4×C12712yes—
389C2×D4C2×D4×C12714yes—
390C22×C4—21no—
391C22×C4—28no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—48no—
397C22×C4—42no—
398C22×C4—42no—
399C22×C4—41no—
400C22×C4C2×D4×C12711yescharacteristic
401C22×C4C2×D4×C12711yescharacteristic
402C22×C4C2×D4×C12711yescharacteristic
403SD16—48no—
404C2×C8—22no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—42no—
408C2×C8—42no—
409C2×C8—42no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4C2×D4×C12712yes—
419C4⋊C4C2×D4×C12712yes—
420C22⋊C4—28no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C42—22no—
424C42—22no—
425C42C2×D4×C12711yescharacteristic
426C42C2×D4×C12711yescharacteristic
427C42C2×D4×C12711yescharacteristic
428C42C24×C12711yescharacteristic
429C23—22no—
430C23—24no—
431C23—42no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—44no—
436C23—42no—
437C23#120×C12711yescharacteristic
438Q8—22no—
439Q8—24no—
440Q8—42no—
441Q8—42no—
442Q8—82no—
443Q8C2×SD16×C12714yescomplemented
444D4—22no—
445D4—22no—
446D4—44no—
447D4—416no—
448D4—42no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—44no—
454D4—44no—
455D4—82no—
456D4—88no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—416no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—82no—
470C2×C4#120×C12711yescharacteristic
471C2×C4#120×C12711yescharacteristic
472C2×C4#120×C12711yescharacteristic
473C2×C4C2×SD16×C12712yes—
474C2×C4#135×C12712yes—
475C2×C4AGL(1,ℤ/8)×C12712yes—
476C2×C4AGL(1,ℤ/8)×C12712yes—
477C2×C4C22×D4×C12711yescharacteristic
478C2×C4C22×D4×C12711yescharacteristic
479C2×C4C22×D4×C12711yescharacteristic
480C8—42no—
481C8—42no—
482C8—42no—
483C22—44no—
484C22—42no—
485C22—42no—
486C22—44no—
487C22—44no—
488C22—42no—
489C22—84no—
490C22—88no—
491C22#449×C12712yes—
492C22#450×C12712yes—
493C22#455×C12712yes—
494C22C2×#120×C12711yescharacteristic
495C4—24no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—42no—
500C4—82no—
501C4#449×C12712yes—
502C4#450×C12712yes—
503C4C22×SD16×C12711yescharacteristic
504C4C2×#135×C12711yescharacteristic
505C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
506C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
507C2—82no—
508C2—84no—
509C2C127×#164214yesdirect product factor
510C2C2×#450×C12711yescharacteristic
511C2C2×#449×C12711yescharacteristic
512C2C2×#455×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#550×C127C2
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
2. C2×#486×C127C2semidirect
3. C2×#475×C127C2semidirect
4. C2×#461×C127C2semidirect
5. C127×#1642C2direct (N × H)
6. C2×#331×C127C2semidirect
7. C2×Q8⋊C8×C127C2semidirect
8. C2×D4⋊C8×C127C2semidirect
24. #486×C127C22semidirect
26. #475×C127C22semidirect
28. #461×C127C22semidirect
36. #331×C127C22semidirect
37. Q8⋊C8×C127C22semidirect
38. D4⋊C8×C127C22semidirect
112. C2×Q8×C127SD16semidirect
186. Q8×C127C2×SD16semidirect
250. C2×#1642C127direct (N × H)
253. C2×C127#1642direct (N × H)
258. C2×#486C2×C127semidirect
259. C2×#475C2×C127semidirect
260. C2×#461C2×C127semidirect
261. #1642C2×C127direct (N × H)
262. C2×#331C2×C127semidirect
263. C2×Q8⋊C8C2×C127semidirect
264. C2×D4⋊C8C2×C127semidirect
265. C127C2×#1642direct (N × H)
281. #486C22×C127semidirect
283. #475C22×C127semidirect
285. #461C22×C127semidirect
293. #331C22×C127semidirect
294. Q8⋊C8C22×C127semidirect
295. D4⋊C8C22×C127semidirect
369. C2×Q8SD16×C127semidirect
443. Q8C2×SD16×C127semidirect
509. C2C127×#1642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#550×C1272
C2×#486×C1272
C2×#475×C1272
C2×#461×C1272
C127×#16422
C2×#331×C1272
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
C2×#1642127