Finite Group Databasebeta

← C2×C127×#1649 #44582171

Subgroups — C2×C127×#1649 #44582171

Order 32512.

1206 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C127C211yesmaximal, characteristic
2C2×#500×C127C211yesmaximal, characteristic, complemented
3C2×#474×C127C211yesmaximal, characteristic
4C2×#462×C127C211yesmaximal, characteristic, complemented
5C127×#1649C218yesmaximal, direct product factor
6C2×#332×C127C211yesmaximal, characteristic, complemented
7C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic
9C23×Q8×C127—21no—
10C22×Q16×C127—21no—
11D4×Q8×C127—22no—
12D4×Q8×C127—22no—
13D4×Q8×C127—22no—
14D4×Q8×C127C2214yes—
15C2×C4⋊Q8×C127—21no—
16C2×C4⋊Q8×C127C2211yescharacteristic
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#500×C127—22no—
24#500×C127C2214yescomplemented
25#474×C127—22no—
26#474×C127C2214yes—
27#462×C127—22no—
28#462×C127C2214yescomplemented
29C2×#107×C127—22no—
30C2×#107×C127—21no—
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×C4⋊C8×C127C2211yescharacteristic
33C2×#103×C127—21no—
34C2×#102×C127—21no—
35C2×C4×C8×C127C2211yescharacteristic
36#332×C127C2214yescomplemented
37Q8⋊C8×C127C2214yescomplemented
38D4⋊C8×C127C2214yes—
39C22×Q8×C127—22no—
40C22×Q8×C127—24no—
41C22×Q8×C127—24no—
42C22×Q8×C127—21no—
43C22×Q8×C127—21no—
44C22×Q8×C127—44no—
45C22×Q8×C127—44no—
46C22×Q8×C127D411yescharacteristic
47C22×D4×C127D411yescharacteristic
48C23×C4×C127—22no—
49C23×C4×C127—21no—
50C2×Q16×C127—24no—
51C2×Q16×C127—44no—
52C22×C8×C127—21no—
53C22×C8×C127—21no—
54C22×C8×C127—21no—
55C4⋊Q8×C127—24no—
56C4⋊Q8×C127—24no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127—21no—
60C4⋊Q8×C127—21no—
61C4⋊Q8×C127—21no—
62C4⋊Q8×C127D412yes—
63C4⋊Q8×C127C2312yes—
64C4⋊Q8×C127C2312yes—
65C22⋊Q8×C127—24no—
66C22⋊Q8×C127—28no—
67C22⋊Q8×C127—24no—
68C22⋊Q8×C127—28no—
69C4×Q8×C127—21no—
70C4×Q8×C127—21no—
71C4×Q8×C127D412yes—
72C4×Q8×C127C2312yes—
73C4×D4×C127—24no—
74C4×D4×C127—24no—
75C4×D4×C127—21no—
76C4×D4×C127—21no—
77C4×D4×C127D412yes—
78C4×D4×C127C2312yes—
79C2×C4⋊C4×C127—22no—
80C2×C4⋊C4×C127—21no—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127—21no—
83C2×C4⋊C4×C127—21no—
84C2×C4⋊C4×C127D411yescharacteristic
85C2×C4⋊C4×C127D411yescharacteristic
86C2×C4⋊C4×C127D412yes—
87C2×C22⋊C4×C127—22no—
88C2×C22⋊C4×C127—21no—
89C2×C42×C127—21no—
90C2×C42×C127C2311yescharacteristic
91#107×C127—28no—
92#107×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—
102C2×Q8×C127—28no—
103C2×Q8×C127—21no—
104C2×Q8×C127—22no—
105C2×Q8×C127—22no—
106C2×Q8×C127—22no—
107C2×Q8×C127—22no—
108C2×Q8×C127—48no—
109C2×Q8×C127—48no—
110C2×Q8×C127—416no—
111C2×Q8×C127—48no—
112C2×Q8×C127—41no—
113C2×Q8×C127—42no—
114C2×Q8×C127—42no—
115C2×Q8×C127—42no—
116C2×Q8×C127—42no—
117C2×Q8×C127D814yes—
118C2×Q8×C127C2×D412yes—
119C2×D4×C127—21no—
120C2×D4×C127—22no—
121C2×D4×C127Q1614yescomplemented
122C2×D4×C127C2×D412yes—
123C22×C4×C127—21no—
124C22×C4×C127—28no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—21no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—48no—
131C22×C4×C127—42no—
132C22×C4×C127—42no—
133C22×C4×C127—41no—
134C22×C4×C127C2×D411yescharacteristic
135C22×C4×C127C2×D411yescharacteristic
136C22×C4×C127C2×D411yescharacteristic
137Q16×C127—48no—
138C2×C8×C127—24no—
139C2×C8×C127—22no—
140C2×C8×C127—22no—
141C2×C8×C127—22no—
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×C127—22no—
153C4⋊C4×C127—22no—
154C4⋊C4×C127—41no—
155C4⋊C4×C127—41no—
156C4⋊C4×C127C2×D412yes—
157C4⋊C4×C127C2×D412yes—
158C4⋊C4×C127C2×D414yes—
159C22⋊C4×C127—28no—
160C22⋊C4×C127—22no—
161C22⋊C4×C127—22no—
162C42×C127—22no—
163C42×C127—22no—
164C42×C127C2×D411yescharacteristic
165C42×C127C2×D411yescharacteristic
166C42×C127C2×D411yescharacteristic
167C42×C127C2411yescharacteristic
168C23×C127—22no—
169C23×C127—24no—
170C23×C127—42no—
171C23×C127—42no—
172C23×C127#12011yescharacteristic
173Q8×C127—22no—
174Q8×C127—24no—
175Q8×C127—416no—
176Q8×C127—42no—
177Q8×C127—42no—
178Q8×C127—44no—
179Q8×C127—42no—
180Q8×C127—42no—
181Q8×C127—82no—
182Q8×C127C2×D814yes—
183D4×C127—22no—
184D4×C127—24no—
185D4×C127C2×Q1614yescomplemented
186C2×C4×C127—22no—
187C2×C4×C127—24no—
188C2×C4×C127—22no—
189C2×C4×C127—22no—
190C2×C4×C127—24no—
191C2×C4×C127—22no—
192C2×C4×C127—416no—
193C2×C4×C127—44no—
194C2×C4×C127—42no—
195C2×C4×C127—42no—
196C2×C4×C127—42no—
197C2×C4×C127—42no—
198C2×C4×C127—44no—
199C2×C4×C127—42no—
200C2×C4×C127—82no—
201C2×C4×C127#12011yescharacteristic
202C2×C4×C127#12011yescharacteristic
203C2×C4×C127#12011yescharacteristic
204C2×C4×C127C2×D812yes—
205C2×C4×C127C2×Q1612yes—
206C2×C4×C127AGL(1,ℤ/8)12yes—
207C2×C4×C127#13712yes—
208C2×C4×C127C22×D411yescharacteristic
209C2×C4×C127C22×D411yescharacteristic
210C2×C4×C127C22×D411yescharacteristic
211C8×C127—24no—
212C8×C127—42no—
213C8×C127—42no—
214C22×C127—24no—
215C22×C127—48no—
216C22×C127—42no—
217C22×C127—42no—
218C22×C127#44712yes—
219C22×C127#45112yes—
220C22×C127#45612yes—
221C22×C127C2×#12011yescharacteristic
222C4×C127—24no—
223C4×C127—21no—
224C4×C127—21no—
225C4×C127—44no—
226C4×C127—42no—
227C4×C127—42no—
228C4×C127—82no—
229C4×C127#44712yes—
230C4×C127#45112yes—
231C4×C127C22×D811yescharacteristic
232C4×C127C22×Q1611yescharacteristic
233C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C127C2×#13711yescharacteristic
235C2×#1649C12711yesmaximal, characteristic, direct product factor, Sylow
236C2×C127—44no—
237C2×C127#164914yesdirect product factor
238C2×C127C2×#44711yescharacteristic
239C2×C127C2×#45111yescharacteristic
240C2×C127C2×#45611yescharacteristic
241C2×D4×Q8C2×C12711yescharacteristic
242C2×#500C2×C12711yescharacteristic, complemented
243C2×#474C2×C12711yescharacteristic
244C2×#462C2×C12711yescharacteristic, complemented
245#1649C2×C12718yesdirect product factor
246C2×#332C2×C12711yescharacteristic, complemented
247C2×Q8⋊C8C2×C12711yescharacteristic, complemented
248C2×D4⋊C8C2×C12711yescharacteristic
249C127C2×#164911yescharacteristic, direct product factor, Sylow
250C23×Q8—21no—
251C22×Q16—21no—
252D4×Q8—22no—
253D4×Q8—22no—
254D4×Q8—22no—
255D4×Q8C22×C12714yes—
256C2×C4⋊Q8—21no—
257C2×C4⋊Q8C22×C12711yescharacteristic
258C2×C4⋊Q8C22×C12711yescharacteristic
259C2×C22⋊Q8—21no—
260C2×C22⋊Q8—22no—
261C2×C4×Q8C22×C12711yescharacteristic
262C2×C4×D4—21no—
263C2×C4×D4C22×C12711yescharacteristic
264#500—22no—
265#500C22×C12714yescomplemented
266#474—22no—
267#474C22×C12714yes—
268#462—22no—
269#462C22×C12714yescomplemented
270C2×#107—22no—
271C2×#107—21no—
272C2×C4⋊C8C22×C12711yescharacteristic
273C2×C4⋊C8C22×C12711yescharacteristic
274C2×#103—21no—
275C2×#102—21no—
276C2×C4×C8C22×C12711yescharacteristic
277#332C22×C12714yescomplemented
278Q8⋊C8C22×C12714yescomplemented
279D4⋊C8C22×C12714yes—
280C22×Q8—22no—
281C22×Q8—24no—
282C22×Q8—24no—
283C22×Q8—21no—
284C22×Q8—21no—
285C22×Q8—44no—
286C22×Q8—44no—
287C22×Q8D4×C12711yescharacteristic
288C22×D4D4×C12711yescharacteristic
289C23×C4—22no—
290C23×C4—21no—
291C2×Q16—24no—
292C2×Q16—44no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C4⋊Q8—24no—
297C4⋊Q8—24no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8D4×C12712yes—
304C4⋊Q8C23×C12712yes—
305C4⋊Q8C23×C12712yes—
306C22⋊Q8—24no—
307C22⋊Q8—28no—
308C22⋊Q8—24no—
309C22⋊Q8—28no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8D4×C12712yes—
313C4×Q8C23×C12712yes—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4D4×C12712yes—
319C4×D4C23×C12712yes—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
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—28no—
334C4⋊C8—21no—
335C4⋊C8—21no—
336C4⋊C8C23×C12712yes—
337C4⋊C8C23×C12712yes—
338#103—24no—
339#102—24no—
340C4×C8—21no—
341C4×C8C23×C12712yes—
342C24—21no—
343C2×Q8—28no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—48no—
350C2×Q8—48no—
351C2×Q8—416no—
352C2×Q8—48no—
353C2×Q8—41no—
354C2×Q8—42no—
355C2×Q8—42no—
356C2×Q8—42no—
357C2×Q8—42no—
358C2×Q8D8×C12714yes—
359C2×Q8C2×D4×C12712yes—
360C2×D4—21no—
361C2×D4—22no—
362C2×D4Q16×C12714yescomplemented
363C2×D4C2×D4×C12712yes—
364C22×C4—21no—
365C22×C4—28no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—48no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—41no—
375C22×C4C2×D4×C12711yescharacteristic
376C22×C4C2×D4×C12711yescharacteristic
377C22×C4C2×D4×C12711yescharacteristic
378Q16—48no—
379C2×C8—24no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—42no—
384C2×C8—42no—
385C4⋊C4—28no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
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—
403C42—22no—
404C42—22no—
405C42C2×D4×C12711yescharacteristic
406C42C2×D4×C12711yescharacteristic
407C42C2×D4×C12711yescharacteristic
408C42C24×C12711yescharacteristic
409C23—22no—
410C23—24no—
411C23—42no—
412C23—42no—
413C23#120×C12711yescharacteristic
414Q8—22no—
415Q8—24no—
416Q8—416no—
417Q8—42no—
418Q8—42no—
419Q8—44no—
420Q8—42no—
421Q8—42no—
422Q8—82no—
423Q8C2×D8×C12714yes—
424D4—22no—
425D4—24no—
426D4C2×Q16×C12714yescomplemented
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—416no—
434C2×C4—44no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—82no—
442C2×C4#120×C12711yescharacteristic
443C2×C4#120×C12711yescharacteristic
444C2×C4#120×C12711yescharacteristic
445C2×C4C2×D8×C12712yes—
446C2×C4C2×Q16×C12712yes—
447C2×C4AGL(1,ℤ/8)×C12712yes—
448C2×C4#137×C12712yes—
449C2×C4C22×D4×C12711yescharacteristic
450C2×C4C22×D4×C12711yescharacteristic
451C2×C4C22×D4×C12711yescharacteristic
452C8—24no—
453C8—42no—
454C8—42no—
455C22—24no—
456C22—48no—
457C22—42no—
458C22—42no—
459C22#447×C12712yes—
460C22#451×C12712yes—
461C22#456×C12712yes—
462C22C2×#120×C12711yescharacteristic
463C4—24no—
464C4—21no—
465C4—21no—
466C4—44no—
467C4—42no—
468C4—42no—
469C4—82no—
470C4#447×C12712yes—
471C4#451×C12712yes—
472C4C22×D8×C12711yescharacteristic
473C4C22×Q16×C12711yescharacteristic
474C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
475C4C2×#137×C12711yescharacteristic
476C2—44no—
477C2C127×#164914yesdirect product factor
478C2C2×#447×C12711yescharacteristic
479C2C2×#451×C12711yescharacteristic
480C2C2×#456×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×#500×C127C2semidirect
4. C2×#462×C127C2semidirect
5. C127×#1649C2direct (N × H)
6. C2×#332×C127C2semidirect
7. C2×Q8⋊C8×C127C2semidirect
24. #500×C127C22semidirect
28. #462×C127C22semidirect
36. #332×C127C22semidirect
37. Q8⋊C8×C127C22semidirect
121. C2×D4×C127Q16semidirect
185. D4×C127C2×Q16semidirect
235. C2×#1649C127direct (N × H)
237. C2×C127#1649direct (N × H)
242. C2×#500C2×C127semidirect
244. C2×#462C2×C127semidirect
245. #1649C2×C127direct (N × H)
246. C2×#332C2×C127semidirect
247. C2×Q8⋊C8C2×C127semidirect
249. C127C2×#1649direct (N × H)
265. #500C22×C127semidirect
269. #462C22×C127semidirect
277. #332C22×C127semidirect
278. Q8⋊C8C22×C127semidirect
362. C2×D4Q16×C127semidirect
426. D4C2×Q16×C127semidirect
477. C2C127×#1649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1272
C2×#500×C1272
C2×#474×C1272
C2×#462×C1272
C127×#16492
C2×#332×C1272
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
C2×#1649127