Finite Group Databasebeta

← C127×#18540 #44582213

Subgroups — C127×#18540 #44582213

Order 32512.

1146 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C127C211yesmaximal, characteristic
2C127×#3165C211yesmaximal, characteristic, complemented
3C127×#3113C211yesmaximal, characteristic, complemented
4C127×#3110C211yesmaximal, characteristic
5C127×#1651C214yesmaximal, complemented
6C127×#1649C214yesmaximal, complemented
7C127×#1556C211yesmaximal, characteristic, complemented
8C127×#1491C211yesmaximal, characteristic, complemented
9C127×#1490C211yesmaximal, characteristic
10C23×Q8×C127—21no—
11D4×Q8×C127—22no—
12D4×Q8×C127—22no—
13D4×Q8×C127—22no—
14D4×Q8×C127C2214yes—
15#533×C127C2211yescharacteristic
16C2×C4⋊Q8×C127—21no—
17C2×C4⋊Q8×C127C2211yescharacteristic
18C2×C22⋊Q8×C127—21no—
19C2×C22⋊Q8×C127—22no—
20C2×C4×Q8×C127C2211yescharacteristic
21C2×C4×D4×C127—21no—
22C2×C4×D4×C127C2211yescharacteristic
23#501×C127—22no—
24#500×C127C2212yescomplemented
25#498×C127C2212yescomplemented
26#484×C127—21no—
27#483×C127—21no—
28#475×C127C2212yescomplemented
29#474×C127C2212yes—
30#462×C127C2212yescomplemented
31#461×C127C2212yes—
32#451×C127—21no—
33#450×C127—21no—
34#441×C127—22no—
35#440×C127—22no—
36#432×C127C2211yescharacteristic
37#432×C127C2211yescharacteristic
38#428×C127—22no—
39C4×M16×C127C2211yescharacteristic
40#332×C127C2214yescomplemented
41Q8⋊C8×C127C2214yescomplemented
42D4⋊C8×C127C2214yes—
43C22×Q8×C127—22no—
44C22×Q8×C127—24no—
45C22×Q8×C127—24no—
46C22×Q8×C127—21no—
47C22×Q8×C127—48no—
48C22×Q8×C127D411yescharacteristic
49C22×D4×C127D411yescharacteristic
50C23×C4×C127—22no—
51C23×C4×C127—21no—
52C2×Q16×C127—22no—
53C2×SD16×C127—22no—
54C2×M16×C127—21no—
55C4⋊Q8×C127—24no—
56C4⋊Q8×C127—24no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127D412yes—
60C4⋊Q8×C127C2311yescharacteristic
61C4⋊Q8×C127C2311yescharacteristic
62C4⋊Q8×C127C2312yes—
63#125×C127—21no—
64C22⋊Q8×C127—24no—
65C22⋊Q8×C127—28no—
66C22⋊Q8×C127—24no—
67C22⋊Q8×C127—28no—
68C22⋊Q8×C127—21no—
69C22⋊Q8×C127—21no—
70C4×Q8×C127—21no—
71C4×Q8×C127—21no—
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—
82#117×C127—21no—
83C2×C4⋊C4×C127—22no—
84C2×C4⋊C4×C127—21no—
85C2×C4⋊C4×C127—21no—
86C2×C4⋊C4×C127D411yescharacteristic
87C2×C4⋊C4×C127D411yescharacteristic
88C2×C4⋊C4×C127D412yes—
89C2×C22⋊C4×C127—22no—
90C2×C22⋊C4×C127—21no—
91C2×C42×C127—21no—
92C2×C42×C127C2311yescharacteristic
93#107×C127—24no—
94#107×C127—22no—
95#106×C127—24no—
96#106×C127—22no—
97C4⋊C8×C127C2312yes—
98C4⋊C8×C127C2312yes—
99#103×C127—22no—
100#103×C127—22no—
101#103×C127—22no—
102#102×C127—22no—
103C22⋊C8×C127—21no—
104C22⋊C8×C127—21no—
105#97×C127—21no—
106#97×C127—21no—
107#97×C127—21no—
108C4×C8×C127C2312yes—
109C24×C127—21no—
110C2×Q8×C127—24no—
111C2×Q8×C127—28no—
112C2×Q8×C127—21no—
113C2×Q8×C127—22no—
114C2×Q8×C127—22no—
115C2×Q8×C127—21no—
116C2×Q8×C127—21no—
117C2×Q8×C127—48no—
118C2×Q8×C127—44no—
119C2×Q8×C127—416no—
120C2×Q8×C127—48no—
121C2×Q8×C127—48no—
122C2×Q8×C127C2×D412yes—
123C2×D4×C127—24no—
124C2×D4×C127—21no—
125C2×D4×C127C2×D412yes—
126C22×C4×C127—21no—
127C22×C4×C127—28no—
128C22×C4×C127—21no—
129C22×C4×C127—22no—
130C22×C4×C127—21no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—48no—
134C22×C4×C127—44no—
135C22×C4×C127C2×D411yescharacteristic
136C22×C4×C127C2×D411yescharacteristic
137C22×C4×C127C2×D411yescharacteristic
138Q16×C127—44no—
139SD16×C127—44no—
140M16×C127—24no—
141C2×C8×C127—22no—
142C2×C8×C127—22no—
143C2×C8×C127—22no—
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×C127—21no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—21no—
155C4⋊C4×C127—21no—
156C4⋊C4×C127—41no—
157C4⋊C4×C127—41no—
158C4⋊C4×C127C2×D412yes—
159C4⋊C4×C127C2×D412yes—
160C4⋊C4×C127C2×D414yes—
161C22⋊C4×C127—28no—
162C22⋊C4×C127—22no—
163C22⋊C4×C127—22no—
164C22⋊C4×C127—41no—
165C42×C127—22no—
166C42×C127—22no—
167C42×C127—41no—
168C42×C127C2×D411yescharacteristic
169C42×C127C2×D411yescharacteristic
170C42×C127C2×D411yescharacteristic
171C42×C127C2411yescharacteristic
172C23×C127—24no—
173C23×C127—22no—
174C23×C127—42no—
175C23×C127—42no—
176C23×C127#12011yescharacteristic
177Q8×C127—24no—
178Q8×C127—22no—
179Q8×C127—416no—
180Q8×C127—44no—
181Q8×C127—44no—
182Q8×C127—42no—
183Q8×C127—42no—
184Q8×C127AGL(1,ℤ/8)14yes—
185D4×C127—24no—
186D4×C127—22no—
187D4×C127#13714yes—
188C2×C4×C127—24no—
189C2×C4×C127—22no—
190C2×C4×C127—22no—
191C2×C4×C127—22no—
192C2×C4×C127—22no—
193C2×C4×C127—22no—
194C2×C4×C127—24no—
195C2×C4×C127—22no—
196C2×C4×C127—416no—
197C2×C4×C127—44no—
198C2×C4×C127—44no—
199C2×C4×C127—42no—
200C2×C4×C127—42no—
201C2×C4×C127—44no—
202C2×C4×C127—41no—
203C2×C4×C127—41no—
204C2×C4×C127#12011yescharacteristic
205C2×C4×C127#12011yescharacteristic
206C2×C4×C127#12011yescharacteristic
207C2×C4×C127C22×D411yescharacteristic
208C2×C4×C127C22×D411yescharacteristic
209C2×C4×C127C22×D411yescharacteristic
210C8×C127—24no—
211C8×C127—42no—
212C8×C127—42no—
213C22×C127—21no—
214C22×C127—21no—
215C22×C127—24no—
216C22×C127—48no—
217C22×C127—42no—
218C22×C127—42no—
219C22×C127#45612yes—
220C22×C127C2×#12011yescharacteristic
221C4×C127—24no—
222C4×C127—21no—
223C4×C127—21no—
224C4×C127—21no—
225C4×C127—21no—
226C4×C127—44no—
227C4×C127—42no—
228C4×C127—42no—
229C4×C127—81no—
230C4×C127—81no—
231C4×C127C2×AGL(1,ℤ/8)12yes—
232C4×C127C2×#13712yes—
233#18540C12711yesmaximal, characteristic, direct product factor, Sylow
234C2×C127—22no—
235C2×C127—44no—
236C2×C127#300311yescharacteristic
237C2×C127#300411yescharacteristic
238C2×C127C2×#45611yescharacteristic
239C2×D4×Q8C2×C12711yescharacteristic
240#3165C2×C12711yescharacteristic, complemented
241#3113C2×C12711yescharacteristic, complemented
242#3110C2×C12711yescharacteristic
243#1651C2×C12714yescomplemented
244#1649C2×C12714yescomplemented
245#1556C2×C12711yescharacteristic, complemented
246#1491C2×C12711yescharacteristic, complemented
247#1490C2×C12711yescharacteristic
248C127#1854011yescharacteristic, direct product factor, Sylow
249C23×Q8—21no—
250D4×Q8—22no—
251D4×Q8—22no—
252D4×Q8—22no—
253D4×Q8C22×C12714yes—
254#533C22×C12711yescharacteristic
255C2×C4⋊Q8—21no—
256C2×C4⋊Q8C22×C12711yescharacteristic
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8—22no—
259C2×C4×Q8C22×C12711yescharacteristic
260C2×C4×D4—21no—
261C2×C4×D4C22×C12711yescharacteristic
262#501—22no—
263#500C22×C12712yescomplemented
264#498C22×C12712yescomplemented
265#484—21no—
266#483—21no—
267#475C22×C12712yescomplemented
268#474C22×C12712yes—
269#462C22×C12712yescomplemented
270#461C22×C12712yes—
271#451—21no—
272#450—21no—
273#441—22no—
274#440—22no—
275#432C22×C12711yescharacteristic
276#432C22×C12711yescharacteristic
277#428—22no—
278C4×M16C22×C12711yescharacteristic
279#332C22×C12714yescomplemented
280Q8⋊C8C22×C12714yescomplemented
281D4⋊C8C22×C12714yes—
282C22×Q8—22no—
283C22×Q8—24no—
284C22×Q8—24no—
285C22×Q8—21no—
286C22×Q8—48no—
287C22×Q8D4×C12711yescharacteristic
288C22×D4D4×C12711yescharacteristic
289C23×C4—22no—
290C23×C4—21no—
291C2×Q16—22no—
292C2×SD16—22no—
293C2×M16—21no—
294C4⋊Q8—24no—
295C4⋊Q8—24no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8D4×C12712yes—
299C4⋊Q8C23×C12711yescharacteristic
300C4⋊Q8C23×C12711yescharacteristic
301C4⋊Q8C23×C12712yes—
302#125—21no—
303C22⋊Q8—24no—
304C22⋊Q8—28no—
305C22⋊Q8—24no—
306C22⋊Q8—28no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8D4×C12712yes—
314C4×Q8C23×C12712yes—
315C4×D4—24no—
316C4×D4—24no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4D4×C12712yes—
320C4×D4C23×C12712yes—
321#117—21no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4D4×C12711yescharacteristic
326C2×C4⋊C4D4×C12711yescharacteristic
327C2×C4⋊C4D4×C12712yes—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—21no—
330C2×C42—21no—
331C2×C42C23×C12711yescharacteristic
332#107—24no—
333#107—22no—
334#106—24no—
335#106—22no—
336C4⋊C8C23×C12712yes—
337C4⋊C8C23×C12712yes—
338#103—22no—
339#103—22no—
340#103—22no—
341#102—22no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344#97—21no—
345#97—21no—
346#97—21no—
347C4×C8C23×C12712yes—
348C24—21no—
349C2×Q8—24no—
350C2×Q8—28no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—48no—
357C2×Q8—44no—
358C2×Q8—416no—
359C2×Q8—48no—
360C2×Q8—48no—
361C2×Q8C2×D4×C12712yes—
362C2×D4—24no—
363C2×D4—21no—
364C2×D4C2×D4×C12712yes—
365C22×C4—21no—
366C22×C4—28no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—48no—
373C22×C4—44no—
374C22×C4C2×D4×C12711yescharacteristic
375C22×C4C2×D4×C12711yescharacteristic
376C22×C4C2×D4×C12711yescharacteristic
377Q16—44no—
378SD16—44no—
379M16—24no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C4⋊C4—28no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4C2×D4×C12712yes—
398C4⋊C4C2×D4×C12712yes—
399C4⋊C4C2×D4×C12714yes—
400C22⋊C4—28no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—41no—
404C42—22no—
405C42—22no—
406C42—41no—
407C42C2×D4×C12711yescharacteristic
408C42C2×D4×C12711yescharacteristic
409C42C2×D4×C12711yescharacteristic
410C42C24×C12711yescharacteristic
411C23—24no—
412C23—22no—
413C23—42no—
414C23—42no—
415C23#120×C12711yescharacteristic
416Q8—24no—
417Q8—22no—
418Q8—416no—
419Q8—44no—
420Q8—44no—
421Q8—42no—
422Q8—42no—
423Q8AGL(1,ℤ/8)×C12714yes—
424D4—24no—
425D4—22no—
426D4#137×C12714yes—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—416no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4#120×C12711yescharacteristic
444C2×C4#120×C12711yescharacteristic
445C2×C4#120×C12711yescharacteristic
446C2×C4C22×D4×C12711yescharacteristic
447C2×C4C22×D4×C12711yescharacteristic
448C2×C4C22×D4×C12711yescharacteristic
449C8—24no—
450C8—42no—
451C8—42no—
452C22—21no—
453C22—21no—
454C22—24no—
455C22—48no—
456C22—42no—
457C22—42no—
458C22#456×C12712yes—
459C22C2×#120×C12711yescharacteristic
460C4—24no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—44no—
466C4—42no—
467C4—42no—
468C4—81no—
469C4—81no—
470C4C2×AGL(1,ℤ/8)×C12712yes—
471C4C2×#137×C12712yes—
472C2—22no—
473C2—44no—
474C2C127×#300311yescharacteristic
475C2C127×#300411yescharacteristic
476C2C2×#456×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC22×D4×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C127×#3165C2semidirect
3. C127×#3113C2semidirect
5. C127×#1651C2semidirect
6. C127×#1649C2semidirect
7. C127×#1556C2semidirect
8. C127×#1491C2semidirect
24. #500×C127C22semidirect
25. #498×C127C22semidirect
28. #475×C127C22semidirect
30. #462×C127C22semidirect
40. #332×C127C22semidirect
41. Q8⋊C8×C127C22semidirect
233. #18540C127direct (N × H)
240. #3165C2×C127semidirect
241. #3113C2×C127semidirect
243. #1651C2×C127semidirect
244. #1649C2×C127semidirect
245. #1556C2×C127semidirect
246. #1491C2×C127semidirect
248. C127#18540direct (N × H)
263. #500C22×C127semidirect
264. #498C22×C127semidirect
267. #475C22×C127semidirect
269. #462C22×C127semidirect
279. #332C22×C127semidirect
280. Q8⋊C8C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1272
C127×#31652
C127×#31132
C127×#31102
C127×#16512
C127×#16492
C127×#15562
C127×#14912
C127×#14902
#18540127