Finite Group Databasebeta

← C127×#21419 #44585092

Subgroups — C127×#21419 #44585092

Order 32512.

1122 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3455C211yesmaximal, characteristic
2C127×#2921C211yesmaximal, characteristic, complemented
3C4×#117×C127C211yesmaximal, characteristic, complemented
4C127×#1995C211yesmaximal, characteristic, complemented
5C127×#1994C211yesmaximal, characteristic, complemented
6C127×#1963C211yesmaximal, characteristic, complemented
7C127×#1962C211yesmaximal, characteristic, complemented
8C127×#1897C212yesmaximal, complemented
9C127×#1896C212yesmaximal, complemented
10C127×#1759C212yesmaximal, complemented
11C4×#104×C127C212yesmaximal, complemented
12#542×C127C414yescomplemented
13#541×C127C412yescomplemented
14#540×C127C412yescomplemented
15#539×C127—22no—
16#538×C127—22no—
17#533×C127C2211yescharacteristic
18#532×C127C2211yescharacteristic
19#529×C127—24no—
20#525×C127C2212yes—
21C4×#41×C127C2212yes—
22C2×#117×C127C2211yescharacteristic
23C2×#117×C127C2211yescharacteristic
24C22×C42×C127C2211yescharacteristic
25#433×C127—24no—
26#423×C127C2211yescharacteristic
27#423×C127C2211yescharacteristic
28C2×#104×C127C2212yes—
29C2×#104×C127C2212yes—
30C2×#104×C127C2212yes—
31C2×#104×C127C2212yes—
32#407×C127C2212yes—
33C4×M16×C127C2212yes—
34C4×C4⋊C4×C127—22no—
35C4×C22⋊C4×C127—22no—
36#376×C127C2211yescharacteristic
37#376×C127C2211yescharacteristic
38C43×C127C2211yescharacteristic
39C43×C127C2211yescharacteristic
40#339×C127C2212yes—
41#339×C127C2212yes—
42#339×C127C2212yes—
43#339×C127C2212yes—
44C2×#41×C127C2312yes—
45C23×C4×C127—21no—
46C23×C4×C127C2311yescharacteristic
47C2×M16×C127C2312yes—
48C2×M16×C127C2312yes—
49C4⋊Q8×C127C2×C411yescharacteristic, complemented
50C4⋊Q8×C127C2×C412yescomplemented
51#127×C127C2×C411yescharacteristic, complemented
52#126×C127—24no—
53#126×C127—24no—
54#125×C127—24no—
55#125×C127C2×C412yescomplemented
56#124×C127—24no—
57#124×C127C2×C412yescomplemented
58#123×C127—22no—
59#123×C127—24no—
60#123×C127—24no—
61C22⋊Q8×C127—22no—
62C22⋊Q8×C127—24no—
63C22⋊Q8×C127C2×C414yes—
64#121×C127—22no—
65#121×C127—24no—
66#121×C127C2×C414yes—
67#120×C127—22no—
68C4×Q8×C127—22no—
69C4×Q8×C127C2×C414yescomplemented
70C4×D4×C127—24no—
71C4×D4×C127—24no—
72C4×D4×C127—22no—
73C4×D4×C127C2×C414yescomplemented
74#117×C127—22no—
75#117×C127—22no—
76#117×C127—22no—
77#117×C127C2×C412yes—
78#117×C127C2×C412yes—
79#117×C127D414yes—
80#117×C127C2312yes—
81C2×C4⋊C4×C127—21no—
82C2×C4⋊C4×C127D412yes—
83C2×C22⋊C4×C127—21no—
84C2×C22⋊C4×C127D412yes—
85C2×C42×C127—21no—
86C2×C42×C127—22no—
87C2×C42×C127—22no—
88C2×C42×C127—22no—
89C2×C42×C127—22no—
90C2×C42×C127—22no—
91C2×C42×C127C2311yescharacteristic
92C2×C42×C127C2311yescharacteristic
93C2×C42×C127C2311yescharacteristic
94C2×C42×C127C2311yescharacteristic
95C2×C42×C127C2311yescharacteristic
96C2×C42×C127C2311yescharacteristic
97C4⋊C8×C127—22no—
98C4⋊C8×C127—22no—
99#104×C127—24no—
100#104×C127—24no—
101#104×C127—24no—
102#104×C127—24no—
103C22⋊C8×C127—24no—
104#97×C127—22no—
105C4×C8×C127—22no—
106#95×C127—22no—
107#95×C127—22no—
108C24×C127C2×D411yescharacteristic
109#41×C127—22no—
110#41×C127—22no—
111#41×C127—22no—
112#41×C127—22no—
113C2×Q8×C127—22no—
114C2×Q8×C127C22×C412yes—
115C2×D4×C127—22no—
116C2×D4×C127—24no—
117C2×D4×C127—22no—
118C2×D4×C127C22×C412yes—
119C22×C4×C127—21no—
120C22×C4×C127—21no—
121C22×C4×C127—21no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
124C22×C4×C127—24no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—21no—
128C22×C4×C127—22no—
129C22×C4×C127—24no—
130C22×C4×C127—44no—
131C22×C4×C127C22×C412yes—
132C22×C4×C127C2×D411yescharacteristic
133C22×C4×C127C2×D412yes—
134C22×C4×C127C2×D412yes—
135C22×C4×C127C2×D412yes—
136C22×C4×C127C2411yescharacteristic
137M16×C127—22no—
138M16×C127—22no—
139M16×C127—22no—
140M16×C127—22no—
141C2×C8×C127—22no—
142C2×C8×C127—22no—
143C4⋊C4×C127—24no—
144C4⋊C4×C127—24no—
145C4⋊C4×C127—22no—
146C4⋊C4×C127—24no—
147C4⋊C4×C127—24no—
148C4⋊C4×C127—22no—
149C4⋊C4×C127C22⋊C414yes—
150C4⋊C4×C127C22⋊C414yes—
151C4⋊C4×C127C22×C414yes—
152C22⋊C4×C127—24no—
153C22⋊C4×C127—24no—
154C22⋊C4×C127—22no—
155C22⋊C4×C127—24no—
156C22⋊C4×C127—24no—
157C22⋊C4×C127—24no—
158C22⋊C4×C127C22⋊C414yes—
159C22⋊C4×C127C22⋊C414yes—
160C42×C127—24no—
161C42×C127—24no—
162C42×C127—22no—
163C42×C127—21no—
164C42×C127—21no—
165C42×C127—21no—
166C42×C127—21no—
167C42×C127—44no—
168C42×C127—44no—
169C42×C127C22×C412yes—
170C42×C127C22×C411yescharacteristic
171C42×C127C22×C411yescharacteristic
172C42×C127C2×D412yes—
173C42×C127C2×D412yes—
174C42×C127#4112yes—
175C42×C127#4112yes—
176C42×C127#4112yes—
177C42×C127#4112yes—
178C23×C127—21no—
179C23×C127—21no—
180C23×C127—22no—
181C23×C127—42no—
182C23×C127C2×C22⋊C412yes—
183C23×C127C22×D411yescharacteristic
184Q8×C127—22no—
185Q8×C127—22no—
186Q8×C127—82no—
187D4×C127—22no—
188D4×C127—22no—
189D4×C127—42no—
190D4×C127—42no—
191D4×C127—82no—
192D4×C127—84no—
193C2×C4×C127—24no—
194C2×C4×C127—21no—
195C2×C4×C127—22no—
196C2×C4×C127—21no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—24no—
203C2×C4×C127—22no—
204C2×C4×C127—22no—
205C2×C4×C127—22no—
206C2×C4×C127—42no—
207C2×C4×C127—42no—
208C2×C4×C127—48no—
209C2×C4×C127—42no—
210C2×C4×C127—42no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—84no—
215C2×C4×C127C2×C22⋊C414yes—
216C2×C4×C127C2×C22⋊C412yes—
217C2×C4×C127C2×C22⋊C412yes—
218C2×C4×C127C2×C22⋊C412yes—
219C2×C4×C127C23×C411yescharacteristic
220C2×C4×C127C22×D411yescharacteristic
221C2×C4×C127C2×#4111yescharacteristic
222C2×C4×C127C2×#4111yescharacteristic
223C2×C4×C127C2×#4111yescharacteristic
224C2×C4×C127C2×#4111yescharacteristic
225C8×C127—42no—
226C8×C127—42no—
227C22×C127—22no—
228C22×C127—24no—
229C22×C127—22no—
230C22×C127—42no—
231C22×C127—42no—
232C22×C127—44no—
233C22×C127—42no—
234C22×C127C22×C22⋊C411yescharacteristic
235C22×C127#52511yescharacteristic
236C22×C127#52511yescharacteristic
237C4×C127—24no—
238C4×C127—24no—
239C4×C127—22no—
240C4×C127—22no—
241C4×C127—22no—
242C4×C127—42no—
243C4×C127—42no—
244C4×C127—42no—
245C4×C127—44no—
246C4×C127—42no—
247C4×C127C4×#4111yescharacteristic
248C4×C127C4×#4111yescharacteristic
249C4×C127#53211yescharacteristic
250C4×C127#53211yescharacteristic
251#21419C12711yesmaximal, characteristic, direct product factor, Sylow
252C2×C127—21no—
253C2×C127—21no—
254C2×C127—42no—
255C2×C127—82no—
256C2×C127#229711yescharacteristic
257C2×C127#290112yes—
258#3455C2×C12711yescharacteristic
259#2921C2×C12711yescharacteristic, complemented
260C4×#117C2×C12711yescharacteristic, complemented
261#1995C2×C12711yescharacteristic, complemented
262#1994C2×C12711yescharacteristic, complemented
263#1963C2×C12711yescharacteristic, complemented
264#1962C2×C12711yescharacteristic, complemented
265#1897C2×C12712yescomplemented
266#1896C2×C12712yescomplemented
267#1759C2×C12712yescomplemented
268C4×#104C2×C12712yescomplemented
269C127#2141911yescharacteristic, direct product factor, Sylow
270#542C4×C12714yescomplemented
271#541C4×C12712yescomplemented
272#540C4×C12712yescomplemented
273#539—22no—
274#538—22no—
275#533C22×C12711yescharacteristic
276#532C22×C12711yescharacteristic
277#529—24no—
278#525C22×C12712yes—
279C4×#41C22×C12712yes—
280C2×#117C22×C12711yescharacteristic
281C2×#117C22×C12711yescharacteristic
282C22×C42C22×C12711yescharacteristic
283#433—24no—
284#423C22×C12711yescharacteristic
285#423C22×C12711yescharacteristic
286C2×#104C22×C12712yes—
287C2×#104C22×C12712yes—
288C2×#104C22×C12712yes—
289C2×#104C22×C12712yes—
290#407C22×C12712yes—
291C4×M16C22×C12712yes—
292C4×C4⋊C4—22no—
293C4×C22⋊C4—22no—
294#376C22×C12711yescharacteristic
295#376C22×C12711yescharacteristic
296C43C22×C12711yescharacteristic
297C43C22×C12711yescharacteristic
298#339C22×C12712yes—
299#339C22×C12712yes—
300#339C22×C12712yes—
301#339C22×C12712yes—
302C2×#41C23×C12712yes—
303C23×C4—21no—
304C23×C4C23×C12711yescharacteristic
305C2×M16C23×C12712yes—
306C2×M16C23×C12712yes—
307C4⋊Q8C2×C4×C12711yescharacteristic, complemented
308C4⋊Q8C2×C4×C12712yescomplemented
309#127C2×C4×C12711yescharacteristic, complemented
310#126—24no—
311#126—24no—
312#125—24no—
313#125C2×C4×C12712yescomplemented
314#124—24no—
315#124C2×C4×C12712yescomplemented
316#123—22no—
317#123—24no—
318#123—24no—
319C22⋊Q8—22no—
320C22⋊Q8—24no—
321C22⋊Q8C2×C4×C12714yes—
322#121—22no—
323#121—24no—
324#121C2×C4×C12714yes—
325#120—22no—
326C4×Q8—22no—
327C4×Q8C2×C4×C12714yescomplemented
328C4×D4—24no—
329C4×D4—24no—
330C4×D4—22no—
331C4×D4C2×C4×C12714yescomplemented
332#117—22no—
333#117—22no—
334#117—22no—
335#117C2×C4×C12712yes—
336#117C2×C4×C12712yes—
337#117D4×C12714yes—
338#117C23×C12712yes—
339C2×C4⋊C4—21no—
340C2×C4⋊C4D4×C12712yes—
341C2×C22⋊C4—21no—
342C2×C22⋊C4D4×C12712yes—
343C2×C42—21no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42C23×C12711yescharacteristic
350C2×C42C23×C12711yescharacteristic
351C2×C42C23×C12711yescharacteristic
352C2×C42C23×C12711yescharacteristic
353C2×C42C23×C12711yescharacteristic
354C2×C42C23×C12711yescharacteristic
355C4⋊C8—22no—
356C4⋊C8—22no—
357#104—24no—
358#104—24no—
359#104—24no—
360#104—24no—
361C22⋊C8—24no—
362#97—22no—
363C4×C8—22no—
364#95—22no—
365#95—22no—
366C24C2×D4×C12711yescharacteristic
367#41—22no—
368#41—22no—
369#41—22no—
370#41—22no—
371C2×Q8—22no—
372C2×Q8C22×C4×C12712yes—
373C2×D4—22no—
374C2×D4—24no—
375C2×D4—22no—
376C2×D4C22×C4×C12712yes—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—24no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—24no—
388C22×C4—44no—
389C22×C4C22×C4×C12712yes—
390C22×C4C2×D4×C12711yescharacteristic
391C22×C4C2×D4×C12712yes—
392C22×C4C2×D4×C12712yes—
393C22×C4C2×D4×C12712yes—
394C22×C4C24×C12711yescharacteristic
395M16—22no—
396M16—22no—
397M16—22no—
398M16—22no—
399C2×C8—22no—
400C2×C8—22no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4C22⋊C4×C12714yes—
408C4⋊C4C22⋊C4×C12714yes—
409C4⋊C4C22×C4×C12714yes—
410C22⋊C4—24no—
411C22⋊C4—24no—
412C22⋊C4—22no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4C22⋊C4×C12714yes—
417C22⋊C4C22⋊C4×C12714yes—
418C42—24no—
419C42—24no—
420C42—22no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—21no—
425C42—44no—
426C42—44no—
427C42C22×C4×C12712yes—
428C42C22×C4×C12711yescharacteristic
429C42C22×C4×C12711yescharacteristic
430C42C2×D4×C12712yes—
431C42C2×D4×C12712yes—
432C42#41×C12712yes—
433C42#41×C12712yes—
434C42#41×C12712yes—
435C42#41×C12712yes—
436C23—21no—
437C23—21no—
438C23—22no—
439C23—42no—
440C23C2×C22⋊C4×C12712yes—
441C23C22×D4×C12711yescharacteristic
442Q8—22no—
443Q8—22no—
444Q8—82no—
445D4—22no—
446D4—22no—
447D4—42no—
448D4—42no—
449D4—82no—
450D4—84no—
451C2×C4—24no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—48no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—84no—
473C2×C4C2×C22⋊C4×C12714yes—
474C2×C4C2×C22⋊C4×C12712yes—
475C2×C4C2×C22⋊C4×C12712yes—
476C2×C4C2×C22⋊C4×C12712yes—
477C2×C4C23×C4×C12711yescharacteristic
478C2×C4C22×D4×C12711yescharacteristic
479C2×C4C2×#41×C12711yescharacteristic
480C2×C4C2×#41×C12711yescharacteristic
481C2×C4C2×#41×C12711yescharacteristic
482C2×C4C2×#41×C12711yescharacteristic
483C8—42no—
484C8—42no—
485C22—22no—
486C22—24no—
487C22—22no—
488C22—42no—
489C22—42no—
490C22—44no—
491C22—42no—
492C22C22×C22⋊C4×C12711yescharacteristic
493C22#525×C12711yescharacteristic
494C22#525×C12711yescharacteristic
495C4—24no—
496C4—24no—
497C4—22no—
498C4—22no—
499C4—22no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—44no—
504C4—42no—
505C4C4×#41×C12711yescharacteristic
506C4C4×#41×C12711yescharacteristic
507C4#532×C12711yescharacteristic
508C4#532×C12711yescharacteristic
509C2—21no—
510C2—21no—
511C2—42no—
512C2—82no—
513C2C127×#229711yescharacteristic
514C2C127×#290112yes—
subgroupG/H
centerC2×C4×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC127×#3455C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2921C2semidirect
3. C4×#117×C127C2semidirect
4. C127×#1995C2semidirect
5. C127×#1994C2semidirect
6. C127×#1963C2semidirect
7. C127×#1962C2semidirect
8. C127×#1897C2semidirect
9. C127×#1896C2semidirect
10. C127×#1759C2semidirect
11. C4×#104×C127C2semidirect
12. #542×C127C4semidirect
13. #541×C127C4semidirect
14. #540×C127C4semidirect
49. C4⋊Q8×C127C2×C4semidirect
50. C4⋊Q8×C127C2×C4semidirect
51. #127×C127C2×C4semidirect
55. #125×C127C2×C4semidirect
57. #124×C127C2×C4semidirect
69. C4×Q8×C127C2×C4semidirect
73. C4×D4×C127C2×C4semidirect
251. #21419C127direct (N × H)
259. #2921C2×C127semidirect
260. C4×#117C2×C127semidirect
261. #1995C2×C127semidirect
262. #1994C2×C127semidirect
263. #1963C2×C127semidirect
264. #1962C2×C127semidirect
265. #1897C2×C127semidirect
266. #1896C2×C127semidirect
267. #1759C2×C127semidirect
268. C4×#104C2×C127semidirect
269. C127#21419direct (N × H)
270. #542C4×C127semidirect
271. #541C4×C127semidirect
272. #540C4×C127semidirect
307. C4⋊Q8C2×C4×C127semidirect
308. C4⋊Q8C2×C4×C127semidirect
309. #127C2×C4×C127semidirect
313. #125C2×C4×C127semidirect
315. #124C2×C4×C127semidirect
327. C4×Q8C2×C4×C127semidirect
331. C4×D4C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34552
C127×#29212
C4×#117×C1272
C127×#19952
C127×#19942
C127×#19632
C127×#19622
C127×#18972
C127×#18962
C127×#17592
C4×#104×C1272
#21419127