Finite Group Databasebeta

← C2×C127×#1643 #44582155

Subgroups — C2×C127×#1643 #44582155

Order 32512.

1022 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C127C211yesmaximal, characteristic
2C2×#487×C127C211yesmaximal, characteristic, complemented
3C2×#475×C127C211yesmaximal, characteristic, complemented
4C2×#461×C127C211yesmaximal, characteristic
5C127×#1643C218yesmaximal, direct product factor
6C2×#333×C127C211yesmaximal, characteristic, complemented
7C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic
9C22×SD16×C127—21no—
10#554×C127—22no—
11#554×C127—22no—
12#554×C127—22no—
13#554×C127C2214yes—
14C2×C4⋊Q8×C127C2211yescharacteristic
15C2×C4⋊Q8×C127C2211yescharacteristic
16C2×#125×C127—21no—
17C2×C22⋊Q8×C127—21no—
18C2×C22⋊Q8×C127—22no—
19C2×C4×Q8×C127C2211yescharacteristic
20C2×C4×D4×C127—21no—
21C2×C4×D4×C127C2211yescharacteristic
22C22×C4⋊C4×C127—21no—
23#487×C127—22no—
24#487×C127C2214yescomplemented
25#475×C127—22no—
26#475×C127C2214yescomplemented
27#461×C127—22no—
28#461×C127C2214yes—
29C2×#106×C127—21no—
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×#103×C127—22no—
33C2×#103×C127—21no—
34C2×#103×C127—21no—
35C2×C4×C8×C127C2211yescharacteristic
36#333×C127C2214yescomplemented
37Q8⋊C8×C127C2214yescomplemented
38D4⋊C8×C127C2214yes—
39C22×Q8×C127—21no—
40C22×Q8×C127D411yescharacteristic
41C22×Q8×C127D412yes—
42C22×D4×C127D411yescharacteristic
43C23×C4×C127—22no—
44C23×C4×C127—21no—
45C2×SD16×C127—24no—
46C2×SD16×C127—44no—
47C22×C8×C127—21no—
48C22×C8×C127—21no—
49C22×C8×C127—21no—
50C4⋊Q8×C127—21no—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127—21no—
55C4⋊Q8×C127D412yes—
56C4⋊Q8×C127C2312yes—
57C4⋊Q8×C127C2312yes—
58#125×C127—24no—
59#125×C127—24no—
60C22⋊Q8×C127—24no—
61C22⋊Q8×C127—28no—
62C22⋊Q8×C127—24no—
63C22⋊Q8×C127—28no—
64C4×Q8×C127—21no—
65C4×Q8×C127—21no—
66C4×Q8×C127D412yes—
67C4×Q8×C127C2312yes—
68C4×D4×C127—24no—
69C4×D4×C127—24no—
70C4×D4×C127—21no—
71C4×D4×C127—21no—
72C4×D4×C127D412yes—
73C4×D4×C127C2312yes—
74C2×C4⋊C4×C127—22no—
75C2×C4⋊C4×C127—24no—
76C2×C4⋊C4×C127—22no—
77C2×C4⋊C4×C127—21no—
78C2×C4⋊C4×C127—21no—
79C2×C4⋊C4×C127—21no—
80C2×C4⋊C4×C127—24no—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127D411yescharacteristic
84C2×C4⋊C4×C127D411yescharacteristic
85C2×C22⋊C4×C127—22no—
86C2×C22⋊C4×C127—21no—
87C2×C42×C127—21no—
88C2×C42×C127C2311yescharacteristic
89#106×C127—24no—
90C4⋊C8×C127—21no—
91C4⋊C8×C127—21no—
92C4⋊C8×C127C2312yes—
93C4⋊C8×C127C2312yes—
94#103×C127—24no—
95#103×C127—28no—
96#103×C127—24no—
97C4×C8×C127—21no—
98C4×C8×C127C2312yes—
99C24×C127—21no—
100C2×Q8×C127—21no—
101C2×Q8×C127—22no—
102C2×Q8×C127—22no—
103C2×Q8×C127—22no—
104C2×Q8×C127—22no—
105C2×Q8×C127—44no—
106C2×Q8×C127—41no—
107C2×Q8×C127—42no—
108C2×Q8×C127—42no—
109C2×Q8×C127C2×D412yes—
110C2×Q8×C127C2×D414yes—
111C2×D4×C127—21no—
112C2×D4×C127—22no—
113C2×D4×C127SD1614yes—
114C2×D4×C127C2×D412yes—
115C22×C4×C127—21no—
116C22×C4×C127—21no—
117C22×C4×C127—21no—
118C22×C4×C127—22no—
119C22×C4×C127—28no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—42no—
123C22×C4×C127—42no—
124C22×C4×C127—41no—
125C22×C4×C127—84no—
126C22×C4×C127C2×D411yescharacteristic
127C22×C4×C127C2×D411yescharacteristic
128C22×C4×C127C2×D411yescharacteristic
129SD16×C127—48no—
130C2×C8×C127—22no—
131C2×C8×C127—22no—
132C2×C8×C127—22no—
133C2×C8×C127—42no—
134C2×C8×C127—42no—
135C2×C8×C127—42no—
136C4⋊C4×C127—28no—
137C4⋊C4×C127—28no—
138C4⋊C4×C127—21no—
139C4⋊C4×C127—22no—
140C4⋊C4×C127—22no—
141C4⋊C4×C127—22no—
142C4⋊C4×C127—21no—
143C4⋊C4×C127—22no—
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—22no—
154C22⋊C4×C127—22no—
155C42×C127—22no—
156C42×C127—22no—
157C42×C127C2×D411yescharacteristic
158C42×C127C2×D411yescharacteristic
159C42×C127C2×D411yescharacteristic
160C42×C127C2411yescharacteristic
161C23×C127—22no—
162C23×C127—24no—
163C23×C127—42no—
164C23×C127—42no—
165C23×C127#12011yescharacteristic
166Q8×C127—22no—
167Q8×C127—22no—
168Q8×C127—44no—
169Q8×C127—42no—
170Q8×C127—42no—
171Q8×C127—42no—
172Q8×C127—82no—
173Q8×C127—82no—
174D4×C127—22no—
175D4×C127—24no—
176D4×C127C2×SD1614yes—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—24no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—44no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—44no—
189C2×C4×C127—42no—
190C2×C4×C127—88no—
191C2×C4×C127—82no—
192C2×C4×C127#12011yescharacteristic
193C2×C4×C127#12011yescharacteristic
194C2×C4×C127#12011yescharacteristic
195C2×C4×C127C2×SD1612yes—
196C2×C4×C127#13512yes—
197C2×C4×C127#13712yes—
198C2×C4×C127#13712yes—
199C2×C4×C127C22×D411yescharacteristic
200C2×C4×C127C22×D411yescharacteristic
201C2×C4×C127C22×D411yescharacteristic
202C8×C127—42no—
203C8×C127—42no—
204C8×C127—42no—
205C22×C127—24no—
206C22×C127—48no—
207C22×C127—42no—
208C22×C127—42no—
209C22×C127#44812yes—
210C22×C127#45212yes—
211C22×C127#45512yes—
212C22×C127C2×#12011yescharacteristic
213C4×C127—21no—
214C4×C127—21no—
215C4×C127—42no—
216C4×C127—42no—
217C4×C127—42no—
218C4×C127—44no—
219C4×C127—82no—
220C4×C127#44812yes—
221C4×C127#45212yes—
222C4×C127C22×SD1611yescharacteristic
223C4×C127C2×#13511yescharacteristic
224C4×C127C2×#13711yescharacteristic
225C4×C127C2×#13711yescharacteristic
226C2×#1643C12711yesmaximal, characteristic, direct product factor, Sylow
227C2×C127—44no—
228C2×C127#164314yesdirect product factor
229C2×C127C2×#44811yescharacteristic
230C2×C127C2×#45211yescharacteristic
231C2×C127C2×#45511yescharacteristic
232C2×#554C2×C12711yescharacteristic
233C2×#487C2×C12711yescharacteristic, complemented
234C2×#475C2×C12711yescharacteristic, complemented
235C2×#461C2×C12711yescharacteristic
236#1643C2×C12718yesdirect product factor
237C2×#333C2×C12711yescharacteristic, complemented
238C2×Q8⋊C8C2×C12711yescharacteristic, complemented
239C2×D4⋊C8C2×C12711yescharacteristic
240C127C2×#164311yescharacteristic, direct product factor, Sylow
241C22×SD16—21no—
242#554—22no—
243#554—22no—
244#554—22no—
245#554C22×C12714yes—
246C2×C4⋊Q8C22×C12711yescharacteristic
247C2×C4⋊Q8C22×C12711yescharacteristic
248C2×#125—21no—
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8—22no—
251C2×C4×Q8C22×C12711yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4C22×C12711yescharacteristic
254C22×C4⋊C4—21no—
255#487—22no—
256#487C22×C12714yescomplemented
257#475—22no—
258#475C22×C12714yescomplemented
259#461—22no—
260#461C22×C12714yes—
261C2×#106—21no—
262C2×C4⋊C8C22×C12711yescharacteristic
263C2×C4⋊C8C22×C12711yescharacteristic
264C2×#103—21no—
265C2×#103—22no—
266C2×#103—21no—
267C2×C4×C8C22×C12711yescharacteristic
268#333C22×C12714yescomplemented
269Q8⋊C8C22×C12714yescomplemented
270D4⋊C8C22×C12714yes—
271C22×Q8—21no—
272C22×Q8D4×C12711yescharacteristic
273C22×Q8D4×C12712yes—
274C22×D4D4×C12711yescharacteristic
275C23×C4—22no—
276C23×C4—21no—
277C2×SD16—24no—
278C2×SD16—44no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8D4×C12712yes—
288C4⋊Q8C23×C12712yes—
289C4⋊Q8C23×C12712yes—
290#125—24no—
291#125—24no—
292C22⋊Q8—24no—
293C22⋊Q8—28no—
294C22⋊Q8—24no—
295C22⋊Q8—28no—
296C4×Q8—21no—
297C4×Q8—21no—
298C4×Q8D4×C12712yes—
299C4×Q8C23×C12712yes—
300C4×D4—24no—
301C4×D4—24no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4D4×C12712yes—
305C4×D4C23×C12712yes—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4D4×C12711yescharacteristic
316C2×C4⋊C4D4×C12711yescharacteristic
317C2×C22⋊C4—22no—
318C2×C22⋊C4—21no—
319C2×C42—21no—
320C2×C42C23×C12711yescharacteristic
321#106—24no—
322C4⋊C8—21no—
323C4⋊C8—21no—
324C4⋊C8C23×C12712yes—
325C4⋊C8C23×C12712yes—
326#103—24no—
327#103—28no—
328#103—24no—
329C4×C8—21no—
330C4×C8C23×C12712yes—
331C24—21no—
332C2×Q8—21no—
333C2×Q8—22no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—44no—
338C2×Q8—41no—
339C2×Q8—42no—
340C2×Q8—42no—
341C2×Q8C2×D4×C12712yes—
342C2×Q8C2×D4×C12714yes—
343C2×D4—21no—
344C2×D4—22no—
345C2×D4SD16×C12714yes—
346C2×D4C2×D4×C12712yes—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—28no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—41no—
357C22×C4—84no—
358C22×C4C2×D4×C12711yescharacteristic
359C22×C4C2×D4×C12711yescharacteristic
360C22×C4C2×D4×C12711yescharacteristic
361SD16—48no—
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—42no—
366C2×C8—42no—
367C2×C8—42no—
368C4⋊C4—28no—
369C4⋊C4—28no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4C2×D4×C12712yes—
383C4⋊C4C2×D4×C12712yes—
384C22⋊C4—28no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—22no—
388C42—22no—
389C42C2×D4×C12711yescharacteristic
390C42C2×D4×C12711yescharacteristic
391C42C2×D4×C12711yescharacteristic
392C42C24×C12711yescharacteristic
393C23—22no—
394C23—24no—
395C23—42no—
396C23—42no—
397C23#120×C12711yescharacteristic
398Q8—22no—
399Q8—22no—
400Q8—44no—
401Q8—42no—
402Q8—42no—
403Q8—42no—
404Q8—82no—
405Q8—82no—
406D4—22no—
407D4—24no—
408D4C2×SD16×C12714yes—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—88no—
423C2×C4—82no—
424C2×C4#120×C12711yescharacteristic
425C2×C4#120×C12711yescharacteristic
426C2×C4#120×C12711yescharacteristic
427C2×C4C2×SD16×C12712yes—
428C2×C4#135×C12712yes—
429C2×C4#137×C12712yes—
430C2×C4#137×C12712yes—
431C2×C4C22×D4×C12711yescharacteristic
432C2×C4C22×D4×C12711yescharacteristic
433C2×C4C22×D4×C12711yescharacteristic
434C8—42no—
435C8—42no—
436C8—42no—
437C22—24no—
438C22—48no—
439C22—42no—
440C22—42no—
441C22#448×C12712yes—
442C22#452×C12712yes—
443C22#455×C12712yes—
444C22C2×#120×C12711yescharacteristic
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—44no—
451C4—82no—
452C4#448×C12712yes—
453C4#452×C12712yes—
454C4C22×SD16×C12711yescharacteristic
455C4C2×#135×C12711yescharacteristic
456C4C2×#137×C12711yescharacteristic
457C4C2×#137×C12711yescharacteristic
458C2—44no—
459C2C127×#164314yesdirect product factor
460C2C2×#448×C12711yescharacteristic
461C2C2×#452×C12711yescharacteristic
462C2C2×#455×C12711yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC22×D4×C127D4
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×#475×C127C2semidirect
5. C127×#1643C2direct (N × H)
6. C2×#333×C127C2semidirect
7. C2×Q8⋊C8×C127C2semidirect
24. #487×C127C22semidirect
26. #475×C127C22semidirect
36. #333×C127C22semidirect
37. Q8⋊C8×C127C22semidirect
226. C2×#1643C127direct (N × H)
228. C2×C127#1643direct (N × H)
233. C2×#487C2×C127semidirect
234. C2×#475C2×C127semidirect
236. #1643C2×C127direct (N × H)
237. C2×#333C2×C127semidirect
238. C2×Q8⋊C8C2×C127semidirect
240. C127C2×#1643direct (N × H)
256. #487C22×C127semidirect
258. #475C22×C127semidirect
268. #333C22×C127semidirect
269. Q8⋊C8C22×C127semidirect
459. C2C127×#1643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#554×C1272
C2×#487×C1272
C2×#475×C1272
C2×#461×C1272
C127×#16432
C2×#333×C1272
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
C2×#1643127