Finite Group Databasebeta

← C2×C127×#1631 #44582178

Subgroups — C2×C127×#1631 #44582178

Order 32512.

1322 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C127C211yesmaximal, characteristic
2C2×#492×C127C211yesmaximal, characteristic, complemented
3C2×#477×C127C211yesmaximal, characteristic, complemented
4C2×#476×C127C211yesmaximal, characteristic, complemented
5C127×#1631C218yesmaximal, 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—22no—
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#492×C127—22no—
24#492×C127C2214yescomplemented
25#477×C127—22no—
26#477×C127C2214yescomplemented
27#476×C127—22no—
28#476×C127C2214yescomplemented
29C2×#107×C127—21no—
30C2×#106×C127—21no—
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×C4⋊C8×C127C2211yescharacteristic
33C2×#103×C127—21no—
34C2×#102×C127—21no—
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—28no—
54C2×SD16×C127—48no—
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#107×C127—24no—
92#106×C127—24no—
93C4⋊C8×C127—21no—
94C4⋊C8×C127—21no—
95C4⋊C8×C127C2312yes—
96C4⋊C8×C127C2312yes—
97#103×C127—24no—
98#102×C127—24no—
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—44no—
110C2×Q8×C127—41no—
111C2×Q8×C127SD1614yescomplemented
112C2×Q8×C127C2×D412yes—
113C2×D4×C127—28no—
114C2×D4×C127—28no—
115C2×D4×C127—21no—
116C2×D4×C127—22no—
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—48no—
124C2×D4×C127—44no—
125C2×D4×C127—42no—
126C2×D4×C127—42no—
127C2×D4×C127—42no—
128C2×D4×C127—42no—
129C2×D4×C127—84no—
130C2×D4×C127C2×D412yes—
131C2×D4×C127C2×D414yes—
132C22×C4×C127—21no—
133C22×C4×C127—28no—
134C22×C4×C127—21no—
135C22×C4×C127—21no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—48no—
139C22×C4×C127—42no—
140C22×C4×C127—42no—
141C22×C4×C127—41no—
142C22×C4×C127C2×D411yescharacteristic
143C22×C4×C127C2×D411yescharacteristic
144C22×C4×C127C2×D411yescharacteristic
145SD16×C127—416no—
146C2×C8×C127—24no—
147C2×C8×C127—22no—
148C2×C8×C127—22no—
149C2×C8×C127—22no—
150C2×C8×C127—42no—
151C2×C8×C127—42no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—21no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127—41no—
159C4⋊C4×C127—41no—
160C4⋊C4×C127C2×D412yes—
161C4⋊C4×C127C2×D412yes—
162C22⋊C4×C127—28no—
163C22⋊C4×C127—22no—
164C22⋊C4×C127—22no—
165C42×C127—22no—
166C42×C127—22no—
167C42×C127C2×D411yescharacteristic
168C42×C127C2×D411yescharacteristic
169C42×C127C2×D411yescharacteristic
170C42×C127C2411yescharacteristic
171C23×C127—22no—
172C23×C127—24no—
173C23×C127—44no—
174C23×C127—42no—
175C23×C127—42no—
176C23×C127—44no—
177C23×C127—44no—
178C23×C127—42no—
179C23×C127#12011yescharacteristic
180Q8×C127—22no—
181Q8×C127—24no—
182Q8×C127—44no—
183Q8×C127—82no—
184Q8×C127C2×SD1614yescomplemented
185D4×C127—22no—
186D4×C127—22no—
187D4×C127—44no—
188D4×C127—416no—
189D4×C127—42no—
190D4×C127—42no—
191D4×C127—42no—
192D4×C127—42no—
193D4×C127—44no—
194D4×C127—42no—
195D4×C127—44no—
196D4×C127—82no—
197D4×C127—88no—
198C2×C4×C127—22no—
199C2×C4×C127—24no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—416no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—44no—
209C2×C4×C127—42no—
210C2×C4×C127—82no—
211C2×C4×C127#12011yescharacteristic
212C2×C4×C127#12011yescharacteristic
213C2×C4×C127#12011yescharacteristic
214C2×C4×C127C2×SD1612yes—
215C2×C4×C127#13512yes—
216C2×C4×C127AGL(1,ℤ/8)12yes—
217C2×C4×C127#13712yes—
218C2×C4×C127C22×D411yescharacteristic
219C2×C4×C127C22×D411yescharacteristic
220C2×C4×C127C22×D411yescharacteristic
221C8×C127—24no—
222C8×C127—42no—
223C8×C127—42no—
224C22×C127—44no—
225C22×C127—42no—
226C22×C127—42no—
227C22×C127—44no—
228C22×C127—44no—
229C22×C127—42no—
230C22×C127—84no—
231C22×C127—88no—
232C22×C127#45012yes—
233C22×C127#45212yes—
234C22×C127#45312yes—
235C22×C127C2×#12011yescharacteristic
236C4×C127—24no—
237C4×C127—21no—
238C4×C127—21no—
239C4×C127—42no—
240C4×C127—42no—
241C4×C127—82no—
242C4×C127#45012yes—
243C4×C127#45212yes—
244C4×C127C22×SD1611yescharacteristic
245C4×C127C2×#13511yescharacteristic
246C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C127C2×#13711yescharacteristic
248C2×#1631C12711yesmaximal, characteristic, direct product factor, Sylow
249C2×C127—82no—
250C2×C127—84no—
251C2×C127#163114yesdirect product factor
252C2×C127C2×#45011yescharacteristic
253C2×C127C2×#45211yescharacteristic
254C2×C127C2×#45311yescharacteristic
255C2×#550C2×C12711yescharacteristic
256C2×#492C2×C12711yescharacteristic, complemented
257C2×#477C2×C12711yescharacteristic, complemented
258C2×#476C2×C12711yescharacteristic, complemented
259#1631C2×C12718yesdirect product factor
260C2×#331C2×C12711yescharacteristic, complemented
261C2×Q8⋊C8C2×C12711yescharacteristic, complemented
262C2×D4⋊C8C2×C12711yescharacteristic, complemented
263C127C2×#163111yescharacteristic, direct product factor, Sylow
264C22×#41—21no—
265C22×SD16—22no—
266#550—22no—
267#550—22no—
268#550—22no—
269#550C22×C12714yes—
270C2×C4⋊Q8C22×C12711yescharacteristic
271C2×#127—21no—
272C2×#127C22×C12711yescharacteristic
273C2×#121—22no—
274C2×#121—21no—
275C2×C4×Q8C22×C12711yescharacteristic
276C2×C4×D4—21no—
277C2×C4×D4C22×C12711yescharacteristic
278#492—22no—
279#492C22×C12714yescomplemented
280#477—22no—
281#477C22×C12714yescomplemented
282#476—22no—
283#476C22×C12714yescomplemented
284C2×#107—21no—
285C2×#106—21no—
286C2×C4⋊C8C22×C12711yescharacteristic
287C2×C4⋊C8C22×C12711yescharacteristic
288C2×#103—21no—
289C2×#102—21no—
290C2×C4×C8C22×C12711yescharacteristic
291#331C22×C12714yescomplemented
292Q8⋊C8C22×C12714yescomplemented
293D4⋊C8C22×C12714yescomplemented
294C2×#41—24no—
295C2×#41—24no—
296C2×#41—44no—
297C2×#41—44no—
298C22×Q8—21no—
299C22×Q8D4×C12711yescharacteristic
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4D4×C12711yescharacteristic
305C22×D4D4×C12712yes—
306C23×C4—22no—
307C23×C4—21no—
308C2×SD16—28no—
309C2×SD16—48no—
310C22×C8—21no—
311C22×C8—21no—
312C22×C8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8C23×C12712yes—
317#127—24no—
318#127—24no—
319#127—21no—
320#127—21no—
321#127D4×C12712yes—
322#127C23×C12712yes—
323#121—24no—
324#121—28no—
325#121—28no—
326#121—24no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8D4×C12712yes—
330C4×Q8C23×C12712yes—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4D4×C12712yes—
336C4×D4C23×C12712yes—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4D4×C12711yescharacteristic
341C2×C4⋊C4D4×C12711yescharacteristic
342C2×C22⋊C4—22no—
343C2×C22⋊C4—21no—
344C2×C42—21no—
345C2×C42C23×C12711yescharacteristic
346#107—24no—
347#106—24no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8C23×C12712yes—
351C4⋊C8C23×C12712yes—
352#103—24no—
353#102—24no—
354C4×C8—21no—
355C4×C8C23×C12712yes—
356C24—21no—
357C24—22no—
358#41—48no—
359#41—416no—
360#41—48no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—44no—
365C2×Q8—41no—
366C2×Q8SD16×C12714yescomplemented
367C2×Q8C2×D4×C12712yes—
368C2×D4—28no—
369C2×D4—28no—
370C2×D4—21no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—48no—
379C2×D4—44no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—84no—
385C2×D4C2×D4×C12712yes—
386C2×D4C2×D4×C12714yes—
387C22×C4—21no—
388C22×C4—28no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—48no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—41no—
397C22×C4C2×D4×C12711yescharacteristic
398C22×C4C2×D4×C12711yescharacteristic
399C22×C4C2×D4×C12711yescharacteristic
400SD16—416no—
401C2×C8—24no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—22no—
405C2×C8—42no—
406C2×C8—42no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4C2×D4×C12712yes—
416C4⋊C4C2×D4×C12712yes—
417C22⋊C4—28no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C42—22no—
421C42—22no—
422C42C2×D4×C12711yescharacteristic
423C42C2×D4×C12711yescharacteristic
424C42C2×D4×C12711yescharacteristic
425C42C24×C12711yescharacteristic
426C23—22no—
427C23—24no—
428C23—44no—
429C23—42no—
430C23—42no—
431C23—44no—
432C23—44no—
433C23—42no—
434C23#120×C12711yescharacteristic
435Q8—22no—
436Q8—24no—
437Q8—44no—
438Q8—82no—
439Q8C2×SD16×C12714yescomplemented
440D4—22no—
441D4—22no—
442D4—44no—
443D4—416no—
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—44no—
449D4—42no—
450D4—44no—
451D4—82no—
452D4—88no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—416no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—42no—
465C2×C4—82no—
466C2×C4#120×C12711yescharacteristic
467C2×C4#120×C12711yescharacteristic
468C2×C4#120×C12711yescharacteristic
469C2×C4C2×SD16×C12712yes—
470C2×C4#135×C12712yes—
471C2×C4AGL(1,ℤ/8)×C12712yes—
472C2×C4#137×C12712yes—
473C2×C4C22×D4×C12711yescharacteristic
474C2×C4C22×D4×C12711yescharacteristic
475C2×C4C22×D4×C12711yescharacteristic
476C8—24no—
477C8—42no—
478C8—42no—
479C22—44no—
480C22—42no—
481C22—42no—
482C22—44no—
483C22—44no—
484C22—42no—
485C22—84no—
486C22—88no—
487C22#450×C12712yes—
488C22#452×C12712yes—
489C22#453×C12712yes—
490C22C2×#120×C12711yescharacteristic
491C4—24no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—42no—
496C4—82no—
497C4#450×C12712yes—
498C4#452×C12712yes—
499C4C22×SD16×C12711yescharacteristic
500C4C2×#135×C12711yescharacteristic
501C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
502C4C2×#137×C12711yescharacteristic
503C2—82no—
504C2—84no—
505C2C127×#163114yesdirect product factor
506C2C2×#450×C12711yescharacteristic
507C2C2×#452×C12711yescharacteristic
508C2C2×#453×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×#492×C127C2semidirect
3. C2×#477×C127C2semidirect
4. C2×#476×C127C2semidirect
5. C127×#1631C2direct (N × H)
6. C2×#331×C127C2semidirect
7. C2×Q8⋊C8×C127C2semidirect
8. C2×D4⋊C8×C127C2semidirect
24. #492×C127C22semidirect
26. #477×C127C22semidirect
28. #476×C127C22semidirect
36. #331×C127C22semidirect
37. Q8⋊C8×C127C22semidirect
38. D4⋊C8×C127C22semidirect
111. C2×Q8×C127SD16semidirect
184. Q8×C127C2×SD16semidirect
248. C2×#1631C127direct (N × H)
251. C2×C127#1631direct (N × H)
256. C2×#492C2×C127semidirect
257. C2×#477C2×C127semidirect
258. C2×#476C2×C127semidirect
259. #1631C2×C127direct (N × H)
260. C2×#331C2×C127semidirect
261. C2×Q8⋊C8C2×C127semidirect
262. C2×D4⋊C8C2×C127semidirect
263. C127C2×#1631direct (N × H)
279. #492C22×C127semidirect
281. #477C22×C127semidirect
283. #476C22×C127semidirect
291. #331C22×C127semidirect
292. Q8⋊C8C22×C127semidirect
293. D4⋊C8C22×C127semidirect
366. C2×Q8SD16×C127semidirect
439. Q8C2×SD16×C127semidirect
505. C2C127×#1631direct (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×#492×C1272
C2×#477×C1272
C2×#476×C1272
C127×#16312
C2×#331×C1272
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
C2×#1631127