Finite Group Databasebeta

← C2×C127×#1628 #44582165

Subgroups — C2×C127×#1628 #44582165

Order 32512.

1062 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C127C211yesmaximal, characteristic, complemented
2C2×#486×C127C211yesmaximal, characteristic, complemented
3C2×#460×C127C211yesmaximal, characteristic, complemented
4C2×#459×C127C211yesmaximal, characteristic
5C127×#1628C218yesmaximal, direct product factor
6C2×#332×C127C211yesmaximal, characteristic, complemented
7C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
9C22×SD16×C127—21no—
10C22×D8×C127—21no—
11#556×C127—22no—
12#556×C127—22no—
13#556×C127—22no—
14#556×C127C2214yescomplemented
15C2×C4⋊Q8×C127C2211yescharacteristic
16C2×#127×C127C2211yescharacteristic
17C2×#126×C127—22no—
18C2×#124×C127—21no—
19C2×C22⋊Q8×C127—21no—
20C2×C4×Q8×C127—21no—
21C2×C4×Q8×C127C2211yescharacteristic
22C2×C4×D4×C127C2211yescharacteristic
23C2×#117×C127—21no—
24#486×C127—22no—
25#486×C127C2214yescomplemented
26#460×C127—22no—
27#460×C127C2214yescomplemented
28#459×C127—22no—
29#459×C127C2214yes—
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
37Q8⋊C8×C127C2214yescomplemented
38D4⋊C8×C127C2214yescomplemented
39C22×Q8×C127—21no—
40C22×Q8×C127D411yescharacteristic
41C22×D4×C127—21no—
42C22×D4×C127—21no—
43C22×D4×C127—21no—
44C22×D4×C127D411yescharacteristic
45C23×C4×C127—21no—
46C2×SD16×C127—24no—
47C2×SD16×C127—44no—
48C2×D8×C127—24no—
49C2×D8×C127—44no—
50C22×C8×C127—21no—
51C22×C8×C127—21no—
52C22×C8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127—21no—
55C4⋊Q8×C127D412yes—
56C4⋊Q8×C127C2312yes—
57#127×C127—21no—
58#127×C127—21no—
59#127×C127—21no—
60#127×C127C2312yes—
61#126×C127—28no—
62#126×C127—28no—
63#124×C127—24no—
64#124×C127—24no—
65C22⋊Q8×C127—24no—
66C22⋊Q8×C127—24no—
67C4×Q8×C127—24no—
68C4×Q8×C127—24no—
69C4×Q8×C127—21no—
70C4×Q8×C127—21no—
71C4×Q8×C127D412yes—
72C4×Q8×C127C2312yes—
73C4×D4×C127—21no—
74C4×D4×C127—21no—
75C4×D4×C127D412yes—
76C4×D4×C127C2312yes—
77#117×C127—24no—
78#117×C127—24no—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—21no—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127D411yescharacteristic
83C2×C4⋊C4×C127D411yescharacteristic
84C2×C4⋊C4×C127D412yes—
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—22no—
87C2×C22⋊C4×C127—21no—
88C2×C42×C127—22no—
89C2×C42×C127—21no—
90C2×C42×C127C2311yescharacteristic
91C4⋊C8×C127—21no—
92C4⋊C8×C127—21no—
93C4⋊C8×C127C2312yes—
94C4⋊C8×C127C2312yes—
95#102×C127—24no—
96#102×C127—24no—
97#102×C127—28no—
98C4×C8×C127—21no—
99C4×C8×C127C2312yes—
100C24×C127—21no—
101C24×C127—41no—
102C2×Q8×C127—21no—
103C2×Q8×C127—22no—
104C2×Q8×C127—22no—
105C2×Q8×C127—22no—
106C2×Q8×C127—22no—
107C2×Q8×C127—42no—
108C2×Q8×C127—42no—
109C2×Q8×C127C2×D412yes—
110C2×D4×C127—21no—
111C2×D4×C127—22no—
112C2×D4×C127—22no—
113C2×D4×C127—22no—
114C2×D4×C127—22no—
115C2×D4×C127—22no—
116C2×D4×C127—44no—
117C2×D4×C127—41no—
118C2×D4×C127—41no—
119C2×D4×C127—41no—
120C2×D4×C127—42no—
121C2×D4×C127—42no—
122C2×D4×C127—42no—
123C2×D4×C127—42no—
124C2×D4×C127C2×D412yes—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—42no—
132C22×C4×C127—42no—
133C22×C4×C127C2×D411yescharacteristic
134C22×C4×C127C2×D411yescharacteristic
135C22×C4×C127C2×D411yescharacteristic
136SD16×C127—48no—
137D8×C127—48no—
138C2×C8×C127—22no—
139C2×C8×C127—22no—
140C2×C8×C127—22no—
141C2×C8×C127—42no—
142C2×C8×C127—42no—
143C2×C8×C127—42no—
144C4⋊C4×C127—28no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—21no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—22no—
152C4⋊C4×C127C2×D412yes—
153C4⋊C4×C127C2×D412yes—
154C4⋊C4×C127C2×D414yes—
155C22⋊C4×C127—28no—
156C22⋊C4×C127—28no—
157C22⋊C4×C127—22no—
158C22⋊C4×C127—22no—
159C42×C127—28no—
160C42×C127—22no—
161C42×C127—22no—
162C42×C127C2×D411yescharacteristic
163C42×C127C2×D411yescharacteristic
164C42×C127C2×D411yescharacteristic
165C42×C127C2411yescharacteristic
166C23×C127—22no—
167C23×C127—42no—
168C23×C127—42no—
169C23×C127—42no—
170C23×C127—42no—
171C23×C127—82no—
172C23×C127—82no—
173C23×C127—82no—
174C23×C127#12011yescharacteristic
175Q8×C127—22no—
176Q8×C127—22no—
177Q8×C127—42no—
178Q8×C127—42no—
179Q8×C127—42no—
180Q8×C127—44no—
181D4×C127—22no—
182D4×C127—22no—
183D4×C127—44no—
184D4×C127—42no—
185D4×C127—42no—
186D4×C127—42no—
187D4×C127—42no—
188D4×C127—42no—
189D4×C127—82no—
190D4×C127—82no—
191D4×C127—82no—
192C2×C4×C127—22no—
193C2×C4×C127—22no—
194C2×C4×C127—22no—
195C2×C4×C127—22no—
196C2×C4×C127—24no—
197C2×C4×C127—42no—
198C2×C4×C127—42no—
199C2×C4×C127—44no—
200C2×C4×C127—42no—
201C2×C4×C127—42no—
202C2×C4×C127—42no—
203C2×C4×C127—44no—
204C2×C4×C127#12011yescharacteristic
205C2×C4×C127#12011yescharacteristic
206C2×C4×C127#12011yescharacteristic
207C2×C4×C127#13512yes—
208C2×C4×C127#13512yes—
209C2×C4×C127AGL(1,ℤ/8)12yes—
210C2×C4×C127AGL(1,ℤ/8)12yes—
211C2×C4×C127C22×D411yescharacteristic
212C2×C4×C127C22×D411yescharacteristic
213C2×C4×C127C22×D411yescharacteristic
214C8×C127—42no—
215C8×C127—42no—
216C8×C127—42no—
217C22×C127—42no—
218C22×C127—42no—
219C22×C127—42no—
220C22×C127—84no—
221C22×C127—82no—
222C22×C127—82no—
223C22×C127—82no—
224C22×C127—164no—
225C22×C127#44912yes—
226C22×C127#44912yes—
227C22×C127#45412yes—
228C22×C127C2×#12011yescharacteristic
229C4×C127—21no—
230C4×C127—21no—
231C4×C127—42no—
232C4×C127—42no—
233C4×C127—44no—
234C4×C127—42no—
235C4×C127#44912yes—
236C4×C127#44912yes—
237C4×C127C2×#13511yescharacteristic
238C4×C127C2×#13511yescharacteristic
239C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
240C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
241C2×#1628C12711yesmaximal, characteristic, direct product factor, Sylow
242C2×C127—82no—
243C2×C127—162no—
244C2×C127#162814yesdirect product factor
245C2×C127C2×#44911yescharacteristic
246C2×C127C2×#44911yescharacteristic
247C2×C127C2×#45411yescharacteristic
248C2×#556C2×C12711yescharacteristic, complemented
249C2×#486C2×C12711yescharacteristic, complemented
250C2×#460C2×C12711yescharacteristic, complemented
251C2×#459C2×C12711yescharacteristic
252#1628C2×C12718yesdirect product factor
253C2×#332C2×C12711yescharacteristic, complemented
254C2×Q8⋊C8C2×C12711yescharacteristic, complemented
255C2×D4⋊C8C2×C12711yescharacteristic, complemented
256C127C2×#162811yescharacteristic, direct product factor, Sylow
257C22×SD16—21no—
258C22×D8—21no—
259#556—22no—
260#556—22no—
261#556—22no—
262#556C22×C12714yescomplemented
263C2×C4⋊Q8C22×C12711yescharacteristic
264C2×#127C22×C12711yescharacteristic
265C2×#126—22no—
266C2×#124—21no—
267C2×C22⋊Q8—21no—
268C2×C4×Q8—21no—
269C2×C4×Q8C22×C12711yescharacteristic
270C2×C4×D4C22×C12711yescharacteristic
271C2×#117—21no—
272#486—22no—
273#486C22×C12714yescomplemented
274#460—22no—
275#460C22×C12714yescomplemented
276#459—22no—
277#459C22×C12714yes—
278C2×C4⋊C8C22×C12711yescharacteristic
279C2×C4⋊C8C22×C12711yescharacteristic
280C2×#102—22no—
281C2×#102—21no—
282C2×#102—21no—
283C2×C4×C8C22×C12711yescharacteristic
284#332C22×C12714yescomplemented
285Q8⋊C8C22×C12714yescomplemented
286D4⋊C8C22×C12714yescomplemented
287C22×Q8—21no—
288C22×Q8D4×C12711yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—21no—
292C22×D4D4×C12711yescharacteristic
293C23×C4—21no—
294C2×SD16—24no—
295C2×SD16—44no—
296C2×D8—24no—
297C2×D8—44no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8D4×C12712yes—
304C4⋊Q8C23×C12712yes—
305#127—21no—
306#127—21no—
307#127—21no—
308#127C23×C12712yes—
309#126—28no—
310#126—28no—
311#124—24no—
312#124—24no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C4×Q8—24no—
316C4×Q8—24no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8D4×C12712yes—
320C4×Q8C23×C12712yes—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4D4×C12712yes—
324C4×D4C23×C12712yes—
325#117—24no—
326#117—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4D4×C12711yescharacteristic
331C2×C4⋊C4D4×C12711yescharacteristic
332C2×C4⋊C4D4×C12712yes—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—21no—
336C2×C42—22no—
337C2×C42—21no—
338C2×C42C23×C12711yescharacteristic
339C4⋊C8—21no—
340C4⋊C8—21no—
341C4⋊C8C23×C12712yes—
342C4⋊C8C23×C12712yes—
343#102—24no—
344#102—24no—
345#102—28no—
346C4×C8—21no—
347C4×C8C23×C12712yes—
348C24—21no—
349C24—41no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—42no—
356C2×Q8—42no—
357C2×Q8C2×D4×C12712yes—
358C2×D4—21no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—44no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—42no—
372C2×D4C2×D4×C12712yes—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4C2×D4×C12711yescharacteristic
382C22×C4C2×D4×C12711yescharacteristic
383C22×C4C2×D4×C12711yescharacteristic
384SD16—48no—
385D8—48no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—42no—
390C2×C8—42no—
391C2×C8—42no—
392C4⋊C4—28no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4C2×D4×C12712yes—
401C4⋊C4C2×D4×C12712yes—
402C4⋊C4C2×D4×C12714yes—
403C22⋊C4—28no—
404C22⋊C4—28no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C42—28no—
408C42—22no—
409C42—22no—
410C42C2×D4×C12711yescharacteristic
411C42C2×D4×C12711yescharacteristic
412C42C2×D4×C12711yescharacteristic
413C42C24×C12711yescharacteristic
414C23—22no—
415C23—42no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—82no—
420C23—82no—
421C23—82no—
422C23#120×C12711yescharacteristic
423Q8—22no—
424Q8—22no—
425Q8—42no—
426Q8—42no—
427Q8—42no—
428Q8—44no—
429D4—22no—
430D4—22no—
431D4—44no—
432D4—42no—
433D4—42no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—82no—
438D4—82no—
439D4—82no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4#120×C12711yescharacteristic
453C2×C4#120×C12711yescharacteristic
454C2×C4#120×C12711yescharacteristic
455C2×C4#135×C12712yes—
456C2×C4#135×C12712yes—
457C2×C4AGL(1,ℤ/8)×C12712yes—
458C2×C4AGL(1,ℤ/8)×C12712yes—
459C2×C4C22×D4×C12711yescharacteristic
460C2×C4C22×D4×C12711yescharacteristic
461C2×C4C22×D4×C12711yescharacteristic
462C8—42no—
463C8—42no—
464C8—42no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—84no—
469C22—82no—
470C22—82no—
471C22—82no—
472C22—164no—
473C22#449×C12712yes—
474C22#449×C12712yes—
475C22#454×C12712yes—
476C22C2×#120×C12711yescharacteristic
477C4—21no—
478C4—21no—
479C4—42no—
480C4—42no—
481C4—44no—
482C4—42no—
483C4#449×C12712yes—
484C4#449×C12712yes—
485C4C2×#135×C12711yescharacteristic
486C4C2×#135×C12711yescharacteristic
487C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
488C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
489C2—82no—
490C2—162no—
491C2C127×#162814yesdirect product factor
492C2C2×#449×C12711yescharacteristic
493C2C2×#449×C12711yescharacteristic
494C2C2×#454×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#459×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
1. C2×#556×C127C2semidirect
2. C2×#486×C127C2semidirect
3. C2×#460×C127C2semidirect
5. C127×#1628C2direct (N × H)
6. C2×#332×C127C2semidirect
7. C2×Q8⋊C8×C127C2semidirect
8. C2×D4⋊C8×C127C2semidirect
14. #556×C127C22semidirect
25. #486×C127C22semidirect
27. #460×C127C22semidirect
36. #332×C127C22semidirect
37. Q8⋊C8×C127C22semidirect
38. D4⋊C8×C127C22semidirect
241. C2×#1628C127direct (N × H)
244. C2×C127#1628direct (N × H)
248. C2×#556C2×C127semidirect
249. C2×#486C2×C127semidirect
250. C2×#460C2×C127semidirect
252. #1628C2×C127direct (N × H)
253. C2×#332C2×C127semidirect
254. C2×Q8⋊C8C2×C127semidirect
255. C2×D4⋊C8C2×C127semidirect
256. C127C2×#1628direct (N × H)
262. #556C22×C127semidirect
273. #486C22×C127semidirect
275. #460C22×C127semidirect
284. #332C22×C127semidirect
285. Q8⋊C8C22×C127semidirect
286. D4⋊C8C22×C127semidirect
491. C2C127×#1628direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#556×C1272
C2×#486×C1272
C2×#460×C1272
C2×#459×C1272
C127×#16282
C2×#332×C1272
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
C2×#1628127