Finite Group Databasebeta

← C2×C127×#1646 #44582187

Subgroups — C2×C127×#1646 #44582187

Order 32512.

1042 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C127C211yesmaximal, characteristic
2C2×#487×C127C211yesmaximal, characteristic, complemented
3C2×#474×C127C211yesmaximal, characteristic, complemented
4C2×#461×C127C211yesmaximal, characteristic, complemented
5C127×#1646C218yesmaximal, direct product factor
6C2×#333×C127C211yesmaximal, characteristic, complemented
7C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic, complemented
9C22×SD16×C127—21no—
10#555×C127—22no—
11#555×C127—22no—
12#555×C127—22no—
13#555×C127C2214yes—
14C2×C4⋊Q8×C127C2211yescharacteristic
15C2×C4⋊Q8×C127C2211yescharacteristic
16C2×#124×C127—22no—
17C2×#121×C127—21no—
18C2×#121×C127—21no—
19C2×C4×D4×C127C2211yescharacteristic
20C2×C4×D4×C127C2211yescharacteristic
21C2×#117×C127—21no—
22C2×#117×C127—21no—
23#487×C127—22no—
24#487×C127C2214yescomplemented
25#474×C127—22no—
26#474×C127C2214yescomplemented
27#461×C127—22no—
28#461×C127C2214yescomplemented
29C2×#107×C127—21no—
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×#103×C127—22no—
33C2×#103×C127—21no—
34C2×#102×C127—21no—
35C2×C4×C8×C127C2211yescharacteristic
36#333×C127C2214yescomplemented
37D4⋊C8×C127C2214yescomplemented
38D4⋊C8×C127C2214yescomplemented
39C22×Q8×C127—21no—
40C22×Q8×C127D412yes—
41C22×D4×C127—22no—
42C22×D4×C127D411yescharacteristic
43C22×D4×C127D411yescharacteristic
44C23×C4×C127—21no—
45C23×C4×C127—21no—
46C2×SD16×C127—24no—
47C2×SD16×C127—44no—
48C22×C8×C127—21no—
49C22×C8×C127—21no—
50C22×C8×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127—21no—
55C4⋊Q8×C127—21no—
56C4⋊Q8×C127D412yes—
57C4⋊Q8×C127C2312yes—
58C4⋊Q8×C127C2312yes—
59#124×C127—28no—
60#124×C127—28no—
61#121×C127—24no—
62#121×C127—24no—
63#121×C127—24no—
64#121×C127—24no—
65C4×D4×C127—21no—
66C4×D4×C127—21no—
67C4×D4×C127—21no—
68C4×D4×C127—21no—
69C4×D4×C127D412yes—
70C4×D4×C127D412yes—
71C4×D4×C127C2312yes—
72C4×D4×C127C2312yes—
73#117×C127—24no—
74#117×C127—24no—
75#117×C127—24no—
76#117×C127—24no—
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127—21no—
79C2×C4⋊C4×C127—21no—
80C2×C4⋊C4×C127—21no—
81C2×C4⋊C4×C127D411yescharacteristic
82C2×C4⋊C4×C127D411yescharacteristic
83C2×C22⋊C4×C127—22no—
84C2×C22⋊C4×C127—22no—
85C2×C22⋊C4×C127—21no—
86C2×C22⋊C4×C127—21no—
87C2×C42×C127—22no—
88C2×C42×C127C2311yescharacteristic
89#107×C127—24no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127—21no—
92C4⋊C8×C127C2312yes—
93C4⋊C8×C127C2312yes—
94#103×C127—28no—
95#103×C127—24no—
96#102×C127—24no—
97C4×C8×C127—21no—
98C4×C8×C127C2312yes—
99C24×C127—21no—
100C24×C127—21no—
101C2×Q8×C127—22no—
102C2×Q8×C127—22no—
103C2×Q8×C127—44no—
104C2×Q8×C127—41no—
105C2×Q8×C127—42no—
106C2×Q8×C127—42no—
107C2×Q8×C127C2×D414yes—
108C2×D4×C127—28no—
109C2×D4×C127—21no—
110C2×D4×C127—21no—
111C2×D4×C127—22no—
112C2×D4×C127—22no—
113C2×D4×C127—22no—
114C2×D4×C127—22no—
115C2×D4×C127—84no—
116C2×D4×C127C2×D412yes—
117C2×D4×C127C2×D412yes—
118C22×C4×C127—21no—
119C22×C4×C127—21no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—22no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—42no—
126C22×C4×C127—42no—
127C22×C4×C127—42no—
128C22×C4×C127—42no—
129C22×C4×C127—41no—
130C22×C4×C127C2×D411yescharacteristic
131C22×C4×C127C2×D411yescharacteristic
132C22×C4×C127C2×D411yescharacteristic
133SD16×C127—48no—
134C2×C8×C127—22no—
135C2×C8×C127—22no—
136C2×C8×C127—22no—
137C2×C8×C127—42no—
138C2×C8×C127—42no—
139C2×C8×C127—42no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—21no—
144C4⋊C4×C127—22no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—41no—
149C4⋊C4×C127—41no—
150C4⋊C4×C127C2×D412yes—
151C4⋊C4×C127C2×D412yes—
152C22⋊C4×C127—28no—
153C22⋊C4×C127—28no—
154C22⋊C4×C127—22no—
155C22⋊C4×C127—22no—
156C22⋊C4×C127—22no—
157C22⋊C4×C127—22no—
158C42×C127—28no—
159C42×C127C2×D411yescharacteristic
160C42×C127C2×D411yescharacteristic
161C42×C127C2×D411yescharacteristic
162C42×C127C2411yescharacteristic
163C23×C127—22no—
164C23×C127—22no—
165C23×C127—42no—
166C23×C127—42no—
167C23×C127—42no—
168C23×C127—42no—
169C23×C127—42no—
170C23×C127—42no—
171C23×C127#12011yescharacteristic
172Q8×C127—44no—
173Q8×C127—42no—
174Q8×C127—42no—
175Q8×C127—82no—
176Q8×C127—82no—
177D4×C127—22no—
178D4×C127—22no—
179D4×C127—22no—
180D4×C127—22no—
181D4×C127—42no—
182D4×C127—42no—
183D4×C127—88no—
184C2×C4×C127—22no—
185C2×C4×C127—22no—
186C2×C4×C127—22no—
187C2×C4×C127—24no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—44no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—42no—
195C2×C4×C127—44no—
196C2×C4×C127—44no—
197C2×C4×C127—42no—
198C2×C4×C127—82no—
199C2×C4×C127#12011yescharacteristic
200C2×C4×C127#12011yescharacteristic
201C2×C4×C127#12011yescharacteristic
202C2×C4×C127#13512yes—
203C2×C4×C127#13512yes—
204C2×C4×C127AGL(1,ℤ/8)12yes—
205C2×C4×C127#13712yes—
206C2×C4×C127C22×D411yescharacteristic
207C2×C4×C127C22×D411yescharacteristic
208C2×C4×C127C22×D411yescharacteristic
209C8×C127—42no—
210C8×C127—42no—
211C8×C127—42no—
212C22×C127—42no—
213C22×C127—42no—
214C22×C127—42no—
215C22×C127—42no—
216C22×C127—42no—
217C22×C127—42no—
218C22×C127—84no—
219C22×C127—84no—
220C22×C127#44912yes—
221C22×C127#45212yes—
222C22×C127#45512yes—
223C22×C127C2×#12011yescharacteristic
224C4×C127—21no—
225C4×C127—21no—
226C4×C127—42no—
227C4×C127—42no—
228C4×C127—44no—
229C4×C127—82no—
230C4×C127#44912yes—
231C4×C127#45212yes—
232C4×C127C2×#13511yescharacteristic
233C4×C127C2×#13511yescharacteristic
234C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
235C4×C127C2×#13711yescharacteristic
236C2×#1646C12711yesmaximal, characteristic, direct product factor, Sylow
237C2×C127—82no—
238C2×C127—82no—
239C2×C127#164614yesdirect product factor
240C2×C127C2×#44911yescharacteristic
241C2×C127C2×#45211yescharacteristic
242C2×C127C2×#45511yescharacteristic
243C2×#555C2×C12711yescharacteristic
244C2×#487C2×C12711yescharacteristic, complemented
245C2×#474C2×C12711yescharacteristic, complemented
246C2×#461C2×C12711yescharacteristic, complemented
247#1646C2×C12718yesdirect product factor
248C2×#333C2×C12711yescharacteristic, complemented
249C2×D4⋊C8C2×C12711yescharacteristic, complemented
250C2×D4⋊C8C2×C12711yescharacteristic, complemented
251C127C2×#164611yescharacteristic, direct product factor, Sylow
252C22×SD16—21no—
253#555—22no—
254#555—22no—
255#555—22no—
256#555C22×C12714yes—
257C2×C4⋊Q8C22×C12711yescharacteristic
258C2×C4⋊Q8C22×C12711yescharacteristic
259C2×#124—22no—
260C2×#121—21no—
261C2×#121—21no—
262C2×C4×D4C22×C12711yescharacteristic
263C2×C4×D4C22×C12711yescharacteristic
264C2×#117—21no—
265C2×#117—21no—
266#487—22no—
267#487C22×C12714yescomplemented
268#474—22no—
269#474C22×C12714yescomplemented
270#461—22no—
271#461C22×C12714yescomplemented
272C2×#107—21no—
273C2×C4⋊C8C22×C12711yescharacteristic
274C2×C4⋊C8C22×C12711yescharacteristic
275C2×#103—22no—
276C2×#103—21no—
277C2×#102—21no—
278C2×C4×C8C22×C12711yescharacteristic
279#333C22×C12714yescomplemented
280D4⋊C8C22×C12714yescomplemented
281D4⋊C8C22×C12714yescomplemented
282C22×Q8—21no—
283C22×Q8D4×C12712yes—
284C22×D4—22no—
285C22×D4D4×C12711yescharacteristic
286C22×D4D4×C12711yescharacteristic
287C23×C4—21no—
288C23×C4—21no—
289C2×SD16—24no—
290C2×SD16—44no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8D4×C12712yes—
300C4⋊Q8C23×C12712yes—
301C4⋊Q8C23×C12712yes—
302#124—28no—
303#124—28no—
304#121—24no—
305#121—24no—
306#121—24no—
307#121—24no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4D4×C12712yes—
313C4×D4D4×C12712yes—
314C4×D4C23×C12712yes—
315C4×D4C23×C12712yes—
316#117—24no—
317#117—24no—
318#117—24no—
319#117—24no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4D4×C12711yescharacteristic
325C2×C4⋊C4D4×C12711yescharacteristic
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C42—22no—
331C2×C42C23×C12711yescharacteristic
332#107—24no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8C23×C12712yes—
336C4⋊C8C23×C12712yes—
337#103—28no—
338#103—24no—
339#102—24no—
340C4×C8—21no—
341C4×C8C23×C12712yes—
342C24—21no—
343C24—21no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—44no—
347C2×Q8—41no—
348C2×Q8—42no—
349C2×Q8—42no—
350C2×Q8C2×D4×C12714yes—
351C2×D4—28no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—84no—
359C2×D4C2×D4×C12712yes—
360C2×D4C2×D4×C12712yes—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—41no—
373C22×C4C2×D4×C12711yescharacteristic
374C22×C4C2×D4×C12711yescharacteristic
375C22×C4C2×D4×C12711yescharacteristic
376SD16—48no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—42no—
381C2×C8—42no—
382C2×C8—42no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4C2×D4×C12712yes—
394C4⋊C4C2×D4×C12712yes—
395C22⋊C4—28no—
396C22⋊C4—28no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C42—28no—
402C42C2×D4×C12711yescharacteristic
403C42C2×D4×C12711yescharacteristic
404C42C2×D4×C12711yescharacteristic
405C42C24×C12711yescharacteristic
406C23—22no—
407C23—22no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23#120×C12711yescharacteristic
415Q8—44no—
416Q8—42no—
417Q8—42no—
418Q8—82no—
419Q8—82no—
420D4—22no—
421D4—22no—
422D4—22no—
423D4—22no—
424D4—42no—
425D4—42no—
426D4—88no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—82no—
442C2×C4#120×C12711yescharacteristic
443C2×C4#120×C12711yescharacteristic
444C2×C4#120×C12711yescharacteristic
445C2×C4#135×C12712yes—
446C2×C4#135×C12712yes—
447C2×C4AGL(1,ℤ/8)×C12712yes—
448C2×C4#137×C12712yes—
449C2×C4C22×D4×C12711yescharacteristic
450C2×C4C22×D4×C12711yescharacteristic
451C2×C4C22×D4×C12711yescharacteristic
452C8—42no—
453C8—42no—
454C8—42no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—84no—
462C22—84no—
463C22#449×C12712yes—
464C22#452×C12712yes—
465C22#455×C12712yes—
466C22C2×#120×C12711yescharacteristic
467C4—21no—
468C4—21no—
469C4—42no—
470C4—42no—
471C4—44no—
472C4—82no—
473C4#449×C12712yes—
474C4#452×C12712yes—
475C4C2×#135×C12711yescharacteristic
476C4C2×#135×C12711yescharacteristic
477C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
478C4C2×#137×C12711yescharacteristic
479C2—82no—
480C2—82no—
481C2C127×#164614yesdirect product factor
482C2C2×#449×C12711yescharacteristic
483C2C2×#452×C12711yescharacteristic
484C2C2×#455×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#555×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×#487×C127C2semidirect
3. C2×#474×C127C2semidirect
4. C2×#461×C127C2semidirect
5. C127×#1646C2direct (N × H)
6. C2×#333×C127C2semidirect
7. C2×D4⋊C8×C127C2semidirect
8. C2×D4⋊C8×C127C2semidirect
24. #487×C127C22semidirect
26. #474×C127C22semidirect
28. #461×C127C22semidirect
36. #333×C127C22semidirect
37. D4⋊C8×C127C22semidirect
38. D4⋊C8×C127C22semidirect
236. C2×#1646C127direct (N × H)
239. C2×C127#1646direct (N × H)
244. C2×#487C2×C127semidirect
245. C2×#474C2×C127semidirect
246. C2×#461C2×C127semidirect
247. #1646C2×C127direct (N × H)
248. C2×#333C2×C127semidirect
249. C2×D4⋊C8C2×C127semidirect
250. C2×D4⋊C8C2×C127semidirect
251. C127C2×#1646direct (N × H)
267. #487C22×C127semidirect
269. #474C22×C127semidirect
271. #461C22×C127semidirect
279. #333C22×C127semidirect
280. D4⋊C8C22×C127semidirect
281. D4⋊C8C22×C127semidirect
481. C2C127×#1646direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#555×C1272
C2×#487×C1272
C2×#474×C1272
C2×#461×C1272
C127×#16462
C2×#333×C1272
C2×D4⋊C8×C1272
C2×#1646127