Finite Group Databasebeta

← C2×C127×#1637 #44582162

Subgroups — C2×C127×#1637 #44582162

Order 32512.

1174 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C127C211yesmaximal, characteristic
2C2×#487×C127C211yesmaximal, characteristic, complemented
3C2×#477×C127C211yesmaximal, characteristic, complemented
4C2×#476×C127C211yesmaximal, characteristic
5C127×#1637C218yesmaximal, direct product factor
6C2×#332×C127C211yesmaximal, characteristic, complemented
7C2×Q8⋊C8×C127C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C127C211yesmaximal, characteristic
9C23×Q8×C127—21no—
10D4×Q8×C127—22no—
11D4×Q8×C127—22no—
12D4×Q8×C127—22no—
13D4×Q8×C127C2214yes—
14C2×C4⋊Q8×C127—21no—
15C2×C4⋊Q8×C127C2211yescharacteristic
16C2×C4⋊Q8×C127C2211yescharacteristic
17C2×C22⋊Q8×C127—21no—
18C2×C22⋊Q8×C127—22no—
19C2×C4×Q8×C127C2211yescharacteristic
20C2×C4×D4×C127—21no—
21C2×C4×D4×C127C2211yescharacteristic
22#487×C127—22no—
23#487×C127C2214yescomplemented
24#477×C127—22no—
25#477×C127C2214yescomplemented
26#476×C127—22no—
27#476×C127C2214yes—
28C2×#107×C127—21no—
29C2×#106×C127—21no—
30C2×C4⋊C8×C127C2211yescharacteristic
31C2×C4⋊C8×C127C2211yescharacteristic
32C2×#103×C127—21no—
33C2×#103×C127—22no—
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—
50C22×C8×C127—21no—
51C22×C8×C127—21no—
52C22×C8×C127—21no—
53C4⋊Q8×C127—24no—
54C4⋊Q8×C127—24no—
55C4⋊Q8×C127—21no—
56C4⋊Q8×C127—21no—
57C4⋊Q8×C127—21no—
58C4⋊Q8×C127—21no—
59C4⋊Q8×C127—21no—
60C4⋊Q8×C127D412yes—
61C4⋊Q8×C127C2312yes—
62C4⋊Q8×C127C2312yes—
63C22⋊Q8×C127—24no—
64C22⋊Q8×C127—28no—
65C22⋊Q8×C127—24no—
66C22⋊Q8×C127—28no—
67C4×Q8×C127—21no—
68C4×Q8×C127—21no—
69C4×Q8×C127D412yes—
70C4×Q8×C127C2312yes—
71C4×D4×C127—24no—
72C4×D4×C127—24no—
73C4×D4×C127—21no—
74C4×D4×C127—21no—
75C4×D4×C127D412yes—
76C4×D4×C127C2312yes—
77C2×C4⋊C4×C127—22no—
78C2×C4⋊C4×C127—21no—
79C2×C4⋊C4×C127—21no—
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—21no—
87C2×C42×C127—21no—
88C2×C42×C127C2311yescharacteristic
89#107×C127—24no—
90#106×C127—24no—
91C4⋊C8×C127—21no—
92C4⋊C8×C127—21no—
93C4⋊C8×C127C2312yes—
94C4⋊C8×C127C2312yes—
95#103×C127—24no—
96#103×C127—28no—
97#102×C127—24no—
98C4×C8×C127—21no—
99C4×C8×C127C2312yes—
100C24×C127—21no—
101C2×Q8×C127—28no—
102C2×Q8×C127—21no—
103C2×Q8×C127—22no—
104C2×Q8×C127—22no—
105C2×Q8×C127—22no—
106C2×Q8×C127—22no—
107C2×Q8×C127—48no—
108C2×Q8×C127—44no—
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×C127SD1614yes—
116C2×Q8×C127C2×D412yes—
117C2×D4×C127—21no—
118C2×D4×C127—22no—
119C2×D4×C127Q1614yes—
120C2×D4×C127C2×D412yes—
121C22×C4×C127—21no—
122C22×C4×C127—28no—
123C22×C4×C127—21no—
124C22×C4×C127—22no—
125C22×C4×C127—21no—
126C22×C4×C127—22no—
127C22×C4×C127—22no—
128C22×C4×C127—48no—
129C22×C4×C127—42no—
130C22×C4×C127—42no—
131C22×C4×C127—41no—
132C22×C4×C127C2×D411yescharacteristic
133C22×C4×C127C2×D411yescharacteristic
134C22×C4×C127C2×D411yescharacteristic
135C2×C8×C127—22no—
136C2×C8×C127—22no—
137C2×C8×C127—22no—
138C2×C8×C127—42no—
139C2×C8×C127—42no—
140C2×C8×C127—42no—
141C4⋊C4×C127—28no—
142C4⋊C4×C127—22no—
143C4⋊C4×C127—22no—
144C4⋊C4×C127—21no—
145C4⋊C4×C127—21no—
146C4⋊C4×C127—22no—
147C4⋊C4×C127—22no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—41no—
152C4⋊C4×C127—41no—
153C4⋊C4×C127C2×D414yes—
154C4⋊C4×C127C2×D412yes—
155C4⋊C4×C127C2×D412yes—
156C22⋊C4×C127—28no—
157C22⋊C4×C127—22no—
158C22⋊C4×C127—22no—
159C42×C127—22no—
160C42×C127—22no—
161C42×C127C2×D411yescharacteristic
162C42×C127C2×D411yescharacteristic
163C42×C127C2×D411yescharacteristic
164C42×C127C2411yescharacteristic
165C23×C127—22no—
166C23×C127—24no—
167C23×C127—42no—
168C23×C127—42no—
169C23×C127#12011yescharacteristic
170Q8×C127—22no—
171Q8×C127—24no—
172Q8×C127—416no—
173Q8×C127—44no—
174Q8×C127—42no—
175Q8×C127—42no—
176Q8×C127—44no—
177Q8×C127—82no—
178Q8×C127C2×SD1614yes—
179D4×C127—22no—
180D4×C127—24no—
181D4×C127C2×Q1614yes—
182C2×C4×C127—22no—
183C2×C4×C127—24no—
184C2×C4×C127—22no—
185C2×C4×C127—22no—
186C2×C4×C127—24no—
187C2×C4×C127—22no—
188C2×C4×C127—416no—
189C2×C4×C127—44no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—44no—
195C2×C4×C127—42no—
196C2×C4×C127—82no—
197C2×C4×C127#12011yescharacteristic
198C2×C4×C127#12011yescharacteristic
199C2×C4×C127#12011yescharacteristic
200C2×C4×C127C2×SD1612yes—
201C2×C4×C127C2×Q1612yes—
202C2×C4×C127AGL(1,ℤ/8)12yes—
203C2×C4×C127#13712yes—
204C2×C4×C127C22×D411yescharacteristic
205C2×C4×C127C22×D411yescharacteristic
206C2×C4×C127C22×D411yescharacteristic
207C8×C127—42no—
208C8×C127—42no—
209C8×C127—42no—
210C22×C127—24no—
211C22×C127—48no—
212C22×C127—42no—
213C22×C127—42no—
214C22×C127#45012yes—
215C22×C127#45112yes—
216C22×C127#45412yes—
217C22×C127C2×#12011yescharacteristic
218C4×C127—24no—
219C4×C127—21no—
220C4×C127—21no—
221C4×C127—44no—
222C4×C127—42no—
223C4×C127—42no—
224C4×C127—82no—
225C4×C127#45012yes—
226C4×C127#45112yes—
227C4×C127C22×SD1611yescharacteristic
228C4×C127C22×Q1611yescharacteristic
229C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
230C4×C127C2×#13711yescharacteristic
231C2×#1637C12711yesmaximal, characteristic, direct product factor, Sylow
232C2×C127—44no—
233C2×C127#163714yesdirect product factor
234C2×C127C2×#45011yescharacteristic
235C2×C127C2×#45111yescharacteristic
236C2×C127C2×#45411yescharacteristic
237C2×D4×Q8C2×C12711yescharacteristic
238C2×#487C2×C12711yescharacteristic, complemented
239C2×#477C2×C12711yescharacteristic, complemented
240C2×#476C2×C12711yescharacteristic
241#1637C2×C12718yesdirect product factor
242C2×#332C2×C12711yescharacteristic, complemented
243C2×Q8⋊C8C2×C12711yescharacteristic, complemented
244C2×D4⋊C8C2×C12711yescharacteristic
245C127C2×#163711yescharacteristic, direct product factor, Sylow
246C23×Q8—21no—
247D4×Q8—22no—
248D4×Q8—22no—
249D4×Q8—22no—
250D4×Q8C22×C12714yes—
251C2×C4⋊Q8—21no—
252C2×C4⋊Q8C22×C12711yescharacteristic
253C2×C4⋊Q8C22×C12711yescharacteristic
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—22no—
256C2×C4×Q8C22×C12711yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4C22×C12711yescharacteristic
259#487—22no—
260#487C22×C12714yescomplemented
261#477—22no—
262#477C22×C12714yescomplemented
263#476—22no—
264#476C22×C12714yes—
265C2×#107—21no—
266C2×#106—21no—
267C2×C4⋊C8C22×C12711yescharacteristic
268C2×C4⋊C8C22×C12711yescharacteristic
269C2×#103—21no—
270C2×#103—22no—
271C2×#102—21no—
272C2×C4×C8C22×C12711yescharacteristic
273#332C22×C12714yescomplemented
274Q8⋊C8C22×C12714yescomplemented
275D4⋊C8C22×C12714yes—
276C22×Q8—22no—
277C22×Q8—24no—
278C22×Q8—24no—
279C22×Q8—21no—
280C22×Q8—21no—
281C22×Q8—44no—
282C22×Q8—44no—
283C22×Q8D4×C12711yescharacteristic
284C22×D4D4×C12711yescharacteristic
285C23×C4—22no—
286C23×C4—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C4⋊Q8—24no—
291C4⋊Q8—24no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8D4×C12712yes—
298C4⋊Q8C23×C12712yes—
299C4⋊Q8C23×C12712yes—
300C22⋊Q8—24no—
301C22⋊Q8—28no—
302C22⋊Q8—24no—
303C22⋊Q8—28no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8D4×C12712yes—
307C4×Q8C23×C12712yes—
308C4×D4—24no—
309C4×D4—24no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4D4×C12712yes—
313C4×D4C23×C12712yes—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4D4×C12711yescharacteristic
320C2×C4⋊C4D4×C12711yescharacteristic
321C2×C4⋊C4D4×C12712yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—21no—
324C2×C42—21no—
325C2×C42C23×C12711yescharacteristic
326#107—24no—
327#106—24no—
328C4⋊C8—21no—
329C4⋊C8—21no—
330C4⋊C8C23×C12712yes—
331C4⋊C8C23×C12712yes—
332#103—24no—
333#103—28no—
334#102—24no—
335C4×C8—21no—
336C4×C8C23×C12712yes—
337C24—21no—
338C2×Q8—28no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—48no—
345C2×Q8—44no—
346C2×Q8—48no—
347C2×Q8—416no—
348C2×Q8—48no—
349C2×Q8—41no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8SD16×C12714yes—
353C2×Q8C2×D4×C12712yes—
354C2×D4—21no—
355C2×D4—22no—
356C2×D4Q16×C12714yes—
357C2×D4C2×D4×C12712yes—
358C22×C4—21no—
359C22×C4—28no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—48no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—41no—
369C22×C4C2×D4×C12711yescharacteristic
370C22×C4C2×D4×C12711yescharacteristic
371C22×C4C2×D4×C12711yescharacteristic
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—42no—
376C2×C8—42no—
377C2×C8—42no—
378C4⋊C4—28no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4C2×D4×C12714yes—
391C4⋊C4C2×D4×C12712yes—
392C4⋊C4C2×D4×C12712yes—
393C22⋊C4—28no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C42—22no—
397C42—22no—
398C42C2×D4×C12711yescharacteristic
399C42C2×D4×C12711yescharacteristic
400C42C2×D4×C12711yescharacteristic
401C42C24×C12711yescharacteristic
402C23—22no—
403C23—24no—
404C23—42no—
405C23—42no—
406C23#120×C12711yescharacteristic
407Q8—22no—
408Q8—24no—
409Q8—416no—
410Q8—44no—
411Q8—42no—
412Q8—42no—
413Q8—44no—
414Q8—82no—
415Q8C2×SD16×C12714yes—
416D4—22no—
417D4—24no—
418D4C2×Q16×C12714yes—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—416no—
426C2×C4—44no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—44no—
432C2×C4—42no—
433C2×C4—82no—
434C2×C4#120×C12711yescharacteristic
435C2×C4#120×C12711yescharacteristic
436C2×C4#120×C12711yescharacteristic
437C2×C4C2×SD16×C12712yes—
438C2×C4C2×Q16×C12712yes—
439C2×C4AGL(1,ℤ/8)×C12712yes—
440C2×C4#137×C12712yes—
441C2×C4C22×D4×C12711yescharacteristic
442C2×C4C22×D4×C12711yescharacteristic
443C2×C4C22×D4×C12711yescharacteristic
444C8—42no—
445C8—42no—
446C8—42no—
447C22—24no—
448C22—48no—
449C22—42no—
450C22—42no—
451C22#450×C12712yes—
452C22#451×C12712yes—
453C22#454×C12712yes—
454C22C2×#120×C12711yescharacteristic
455C4—24no—
456C4—21no—
457C4—21no—
458C4—44no—
459C4—42no—
460C4—42no—
461C4—82no—
462C4#450×C12712yes—
463C4#451×C12712yes—
464C4C22×SD16×C12711yescharacteristic
465C4C22×Q16×C12711yescharacteristic
466C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
467C4C2×#137×C12711yescharacteristic
468C2—44no—
469C2C127×#163714yesdirect product factor
470C2C2×#450×C12711yescharacteristic
471C2C2×#451×C12711yescharacteristic
472C2C2×#454×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×#477×C127C2semidirect
5. C127×#1637C2direct (N × H)
6. C2×#332×C127C2semidirect
7. C2×Q8⋊C8×C127C2semidirect
23. #487×C127C22semidirect
25. #477×C127C22semidirect
36. #332×C127C22semidirect
37. Q8⋊C8×C127C22semidirect
231. C2×#1637C127direct (N × H)
233. C2×C127#1637direct (N × H)
238. C2×#487C2×C127semidirect
239. C2×#477C2×C127semidirect
241. #1637C2×C127direct (N × H)
242. C2×#332C2×C127semidirect
243. C2×Q8⋊C8C2×C127semidirect
245. C127C2×#1637direct (N × H)
260. #487C22×C127semidirect
262. #477C22×C127semidirect
273. #332C22×C127semidirect
274. Q8⋊C8C22×C127semidirect
469. C2C127×#1637direct (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×#487×C1272
C2×#477×C1272
C2×#476×C1272
C127×#16372
C2×#332×C1272
C2×Q8⋊C8×C1272
C2×D4⋊C8×C1272
C2×#1637127