Finite Group Databasebeta

← C127×#21491 #44585164

Subgroups — C127×#21491 #44585164

Order 32512.

1094 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C8×D4×C127C212yesmaximal, complemented
2C2×C8×D4×C127C211yesmaximal, characteristic, complemented
3C2×#405×C127C211yesmaximal, characteristic, complemented
4C127×#2392C211yesmaximal, characteristic
5C127×#1955C211yesmaximal, characteristic, complemented
6C127×#1940C211yesmaximal, characteristic, complemented
7C127×#1924C212yesmaximal, complemented
8C127×#1870C212yesmaximal, complemented
9C127×#1798C211yesmaximal, characteristic, complemented
10C8×C4⋊C4×C127C211yesmaximal, characteristic, complemented
11C8×C22⋊C4×C127C212yesmaximal, complemented
12C22×M16×C127C2211yescharacteristic
13C23×C8×C127C2212yes—
14C23×C8×C127C2211yescharacteristic
15C2×C4×D4×C127C2212yes—
16C2×C4×D4×C127C2211yescharacteristic
17C2×#117×C127C2211yescharacteristic
18C8×D4×C127—28no—
19C8×D4×C127—24no—
20C2×C4⋊C8×C127C2212yes—
21C2×C4⋊C8×C127C2211yescharacteristic
22C2×C4⋊C8×C127C2211yescharacteristic
23C2×C22⋊C8×C127C2212yes—
24C2×C22⋊C8×C127C2212yes—
25C2×C22⋊C8×C127C2212yes—
26C2×C22⋊C8×C127C2212yes—
27#405×C127—24no—
28C2×#97×C127C2211yescharacteristic
29C2×#97×C127C2211yescharacteristic
30C2×C4×C8×C127C2211yescharacteristic
31C2×C4×C8×C127C2212yes—
32C2×C4×C8×C127C2211yescharacteristic
33#398×C127C411yescharacteristic
34#397×C127C411yescharacteristic
35#396×C127C412yes—
36#394×C127C412yes—
37#394×C127C411yescharacteristic
38#392×C127C411yescharacteristic
39C4×C4⋊C4×C127C2211yescharacteristic
40C4×C22⋊C4×C127C2212yes—
41#336×C127C2212yes—
42#336×C127C2212yes—
43#336×C127C2212yes—
44C22×D4×C127C2×C411yescharacteristic
45C22×D4×C127C2×C412yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2311yescharacteristic
48C2×M16×C127—22no—
49C2×M16×C127—22no—
50C2×M16×C127—22no—
51C22×C8×C127—22no—
52C22×C8×C127—22no—
53C22×C8×C127—24no—
54C22×C8×C127—24no—
55C22×C8×C127—24no—
56C22×C8×C127D414yescomplemented
57C22×C8×C127C2312yes—
58C22×C8×C127C2312yes—
59C22×C8×C127C2311yescharacteristic
60C22×C8×C127C2311yescharacteristic
61C22×C8×C127C2311yescharacteristic
62C22×C8×C127C2311yescharacteristic
63C4×D4×C127—24no—
64C4×D4×C127—24no—
65C4×D4×C127—22no—
66C4×D4×C127—22no—
67#117×C127—22no—
68#117×C127—22no—
69C2×C4⋊C4×C127C2×C411yescharacteristic
70C2×C4⋊C4×C127C2×C411yescharacteristic
71C2×C4⋊C4×C127C2×C412yes—
72C2×C4⋊C4×C127C2×C411yescharacteristic
73C2×C4⋊C4×C127C2×C412yes—
74C2×C22⋊C4×C127C2×C411yescharacteristic
75C2×C22⋊C4×C127C2×C411yescharacteristic
76C2×C22⋊C4×C127C2×C412yes—
77C2×C22⋊C4×C127C2×C412yes—
78C2×C22⋊C4×C127C2×C412yes—
79C2×C22⋊C4×C127C2×C412yes—
80C2×C22⋊C4×C127C2×C412yes—
81C2×C42×C127C2311yescharacteristic
82C2×C42×C127C2312yes—
83C2×C42×C127C2311yescharacteristic
84C4⋊C8×C127—24no—
85C4⋊C8×C127—22no—
86C4⋊C8×C127—22no—
87C22⋊C8×C127—24no—
88C22⋊C8×C127—24no—
89C22⋊C8×C127—24no—
90C22⋊C8×C127—24no—
91#97×C127—22no—
92#97×C127—22no—
93C4×C8×C127—22no—
94C4×C8×C127—24no—
95C4×C8×C127D414yescomplemented
96#95×C127C2×C412yes—
97#95×C127C2×C412yes—
98#95×C127C2×C411yescharacteristic
99#95×C127C2×C411yescharacteristic
100C24×C127C22×C411yescharacteristic
101C24×C127C22×C412yes—
102C2×D4×C127—24no—
103C2×D4×C127—24no—
104C2×D4×C127—24no—
105C2×D4×C127—22no—
106C2×D4×C127—24no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127C22×C412yes—
118C22×C4×C127C22×C411yescharacteristic
119C22×C4×C127C22×C411yescharacteristic
120C22×C4×C127C22×C412yes—
121C22×C4×C127C22×C411yescharacteristic
122C22×C4×C127C22×C411yescharacteristic
123C22×C4×C127C22×C411yescharacteristic
124C22×C4×C127C22×C412yes—
125C22×C4×C127C2×D412yes—
126C22×C4×C127#4112yes—
127C22×C4×C127C2411yescharacteristic
128M16×C127—28no—
129C2×C8×C127—21no—
130C2×C8×C127—21no—
131C2×C8×C127—21no—
132C2×C8×C127—21no—
133C2×C8×C127—21no—
134C2×C8×C127—21no—
135C2×C8×C127—28no—
136C2×C8×C127—22no—
137C2×C8×C127—22no—
138C2×C8×C127—22no—
139C2×C8×C127—22no—
140C2×C8×C127—22no—
141C2×C8×C127—22no—
142C2×C8×C127—48no—
143C2×C8×C127C2×D412yes—
144C2×C8×C127C2×D412yes—
145C2×C8×C127C2×D412yes—
146C2×C8×C127C2×D412yes—
147C2×C8×C127#4112yes—
148C2×C8×C127#4112yes—
149C4⋊C4×C127—22no—
150C4⋊C4×C127—22no—
151C4⋊C4×C127—24no—
152C4⋊C4×C127—22no—
153C4⋊C4×C127—24no—
154C22⋊C4×C127—24no—
155C22⋊C4×C127—24no—
156C22⋊C4×C127—22no—
157C22⋊C4×C127—22no—
158C22⋊C4×C127—24no—
159C22⋊C4×C127—24no—
160C22⋊C4×C127—24no—
161C42×C127—21no—
162C42×C127—22no—
163C42×C127—21no—
164C42×C127—22no—
165C42×C127C2×D412yes—
166C42×C127#4112yes—
167C23×C127—21no—
168C23×C127—22no—
169C23×C127—22no—
170C23×C127—22no—
171C23×C127—21no—
172C23×C127—22no—
173C23×C127—22no—
174C23×C127—22no—
175C23×C127—22no—
176C23×C127—22no—
177C23×C127C4×D412yes—
178C23×C127#13114yes—
179C23×C127C23×C411yescharacteristic
180D4×C127—28no—
181D4×C127—216no—
182C2×C4×C127—22no—
183C2×C4×C127—21no—
184C2×C4×C127—21no—
185C2×C4×C127—22no—
186C2×C4×C127—22no—
187C2×C4×C127—22no—
188C2×C4×C127—22no—
189C2×C4×C127—22no—
190C2×C4×C127—22no—
191C2×C4×C127—22no—
192C2×C4×C127—22no—
193C2×C4×C127—21no—
194C2×C4×C127—21no—
195C2×C4×C127—22no—
196C2×C4×C127—22no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—42no—
203C2×C4×C127—42no—
204C2×C4×C127—42no—
205C2×C4×C127—42no—
206C2×C4×C127C4×D412yes—
207C2×C4×C127C4×D412yes—
208C2×C4×C127C4×D412yes—
209C2×C4×C127#13114yes—
210C2×C4×C127C22×D411yescharacteristic
211C2×C4×C127C22×D411yescharacteristic
212C2×C4×C127C2×#4111yescharacteristic
213C2×C4×C127C2×#4111yescharacteristic
214C2×C4×C127C2×#4111yescharacteristic
215C2×C4×C127C2×#4111yescharacteristic
216C8×C127—22no—
217C8×C127—22no—
218C8×C127—22no—
219C8×C127—42no—
220C8×C127—42no—
221C8×C127#12114yes—
222C22×C127—24no—
223C22×C127—24no—
224C22×C127—24no—
225C22×C127—24no—
226C22×C127—22no—
227C22×C127—41no—
228C22×C127—42no—
229C22×C127—41no—
230C22×C127—42no—
231C22×C127—42no—
232C22×C127—42no—
233C22×C127—42no—
234C22×C127C2×C4×D411yescharacteristic
235C22×C127C2×C4×D411yescharacteristic
236C22×C127C4×#4111yescharacteristic
237C22×C127C2×#13112yes—
238C22×C127C2×#13112yes—
239C4×C127—22no—
240C4×C127—24no—
241C4×C127—22no—
242C4×C127—22no—
243C4×C127—42no—
244C4×C127—41no—
245C4×C127—41no—
246C4×C127—42no—
247C4×C127C2×#12111yescharacteristic
248C4×C127#52511yescharacteristic
249C4×C127#52911yescharacteristic
250C4×C127#53211yescharacteristic
251#21491C12711yesmaximal, characteristic, direct product factor, Sylow
252C2×C127—42no—
253C2×C127—44no—
254C2×C127C4×#12111yescharacteristic
255C2×C127#292911yescharacteristic
256C2×C127#292912yes—
257C2×C127#293111yescharacteristic
258C2×C127#296612yes—
259C2×C8×D4C2×C12712yescomplemented
260C2×C8×D4C2×C12711yescharacteristic, complemented
261C2×#405C2×C12711yescharacteristic, complemented
262#2392C2×C12711yescharacteristic
263#1955C2×C12711yescharacteristic, complemented
264#1940C2×C12711yescharacteristic, complemented
265#1924C2×C12712yescomplemented
266#1870C2×C12712yescomplemented
267#1798C2×C12711yescharacteristic, complemented
268C8×C4⋊C4C2×C12711yescharacteristic, complemented
269C8×C22⋊C4C2×C12712yescomplemented
270C127#2149111yescharacteristic, direct product factor, Sylow
271C22×M16C22×C12711yescharacteristic
272C23×C8C22×C12712yes—
273C23×C8C22×C12711yescharacteristic
274C2×C4×D4C22×C12712yes—
275C2×C4×D4C22×C12711yescharacteristic
276C2×#117C22×C12711yescharacteristic
277C8×D4—28no—
278C8×D4—24no—
279C2×C4⋊C8C22×C12711yescharacteristic
280C2×C4⋊C8C22×C12711yescharacteristic
281C2×C4⋊C8C22×C12712yes—
282C2×C22⋊C8C22×C12712yes—
283C2×C22⋊C8C22×C12712yes—
284C2×C22⋊C8C22×C12712yes—
285C2×C22⋊C8C22×C12712yes—
286#405—24no—
287C2×#97C22×C12711yescharacteristic
288C2×#97C22×C12711yescharacteristic
289C2×C4×C8C22×C12711yescharacteristic
290C2×C4×C8C22×C12712yes—
291C2×C4×C8C22×C12711yescharacteristic
292#398C4×C12711yescharacteristic
293#397C4×C12711yescharacteristic
294#396C4×C12712yes—
295#394C4×C12712yes—
296#394C4×C12711yescharacteristic
297#392C4×C12711yescharacteristic
298C4×C4⋊C4C22×C12711yescharacteristic
299C4×C22⋊C4C22×C12712yes—
300#336C22×C12712yes—
301#336C22×C12712yes—
302#336C22×C12712yes—
303C22×D4C2×C4×C12711yescharacteristic
304C22×D4C2×C4×C12712yes—
305C23×C4C23×C12712yes—
306C23×C4C23×C12711yescharacteristic
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—24no—
313C22×C8—24no—
314C22×C8—24no—
315C22×C8D4×C12714yescomplemented
316C22×C8C23×C12712yes—
317C22×C8C23×C12712yes—
318C22×C8C23×C12711yescharacteristic
319C22×C8C23×C12711yescharacteristic
320C22×C8C23×C12711yescharacteristic
321C22×C8C23×C12711yescharacteristic
322C4×D4—24no—
323C4×D4—24no—
324C4×D4—22no—
325C4×D4—22no—
326#117—22no—
327#117—22no—
328C2×C4⋊C4C2×C4×C12711yescharacteristic
329C2×C4⋊C4C2×C4×C12711yescharacteristic
330C2×C4⋊C4C2×C4×C12712yes—
331C2×C4⋊C4C2×C4×C12711yescharacteristic
332C2×C4⋊C4C2×C4×C12712yes—
333C2×C22⋊C4C2×C4×C12711yescharacteristic
334C2×C22⋊C4C2×C4×C12711yescharacteristic
335C2×C22⋊C4C2×C4×C12712yes—
336C2×C22⋊C4C2×C4×C12712yes—
337C2×C22⋊C4C2×C4×C12712yes—
338C2×C22⋊C4C2×C4×C12712yes—
339C2×C22⋊C4C2×C4×C12712yes—
340C2×C42C23×C12711yescharacteristic
341C2×C42C23×C12712yes—
342C2×C42C23×C12711yescharacteristic
343C4⋊C8—24no—
344C4⋊C8—22no—
345C4⋊C8—22no—
346C22⋊C8—24no—
347C22⋊C8—24no—
348C22⋊C8—24no—
349C22⋊C8—24no—
350#97—22no—
351#97—22no—
352C4×C8—22no—
353C4×C8—24no—
354C4×C8D4×C12714yescomplemented
355#95C2×C4×C12712yes—
356#95C2×C4×C12712yes—
357#95C2×C4×C12711yescharacteristic
358#95C2×C4×C12711yescharacteristic
359C24C22×C4×C12711yescharacteristic
360C24C22×C4×C12712yes—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—24no—
364C2×D4—22no—
365C2×D4—24no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4C22×C4×C12712yes—
377C22×C4C22×C4×C12711yescharacteristic
378C22×C4C22×C4×C12711yescharacteristic
379C22×C4C22×C4×C12712yes—
380C22×C4C22×C4×C12711yescharacteristic
381C22×C4C22×C4×C12711yescharacteristic
382C22×C4C22×C4×C12711yescharacteristic
383C22×C4C22×C4×C12712yes—
384C22×C4C2×D4×C12712yes—
385C22×C4#41×C12712yes—
386C22×C4C24×C12711yescharacteristic
387M16—28no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—28no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—48no—
402C2×C8C2×D4×C12712yes—
403C2×C8C2×D4×C12712yes—
404C2×C8C2×D4×C12712yes—
405C2×C8C2×D4×C12712yes—
406C2×C8#41×C12712yes—
407C2×C8#41×C12712yes—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—24no—
411C4⋊C4—22no—
412C4⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C42—21no—
421C42—22no—
422C42—21no—
423C42—22no—
424C42C2×D4×C12712yes—
425C42#41×C12712yes—
426C23—21no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—21no—
431C23—22no—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—22no—
436C23C4×D4×C12712yes—
437C23#131×C12714yes—
438C23C23×C4×C12711yescharacteristic
439D4—28no—
440D4—216no—
441C2×C4—22no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4C4×D4×C12712yes—
466C2×C4C4×D4×C12712yes—
467C2×C4C4×D4×C12712yes—
468C2×C4#131×C12714yes—
469C2×C4C22×D4×C12711yescharacteristic
470C2×C4C22×D4×C12711yescharacteristic
471C2×C4C2×#41×C12711yescharacteristic
472C2×C4C2×#41×C12711yescharacteristic
473C2×C4C2×#41×C12711yescharacteristic
474C2×C4C2×#41×C12711yescharacteristic
475C8—22no—
476C8—22no—
477C8—22no—
478C8—42no—
479C8—42no—
480C8#121×C12714yes—
481C22—24no—
482C22—24no—
483C22—24no—
484C22—24no—
485C22—22no—
486C22—41no—
487C22—42no—
488C22—41no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22C2×C4×D4×C12711yescharacteristic
494C22C2×C4×D4×C12711yescharacteristic
495C22C4×#41×C12711yescharacteristic
496C22C2×#131×C12712yes—
497C22C2×#131×C12712yes—
498C4—22no—
499C4—24no—
500C4—22no—
501C4—22no—
502C4—42no—
503C4—41no—
504C4—41no—
505C4—42no—
506C4C2×#121×C12711yescharacteristic
507C4#525×C12711yescharacteristic
508C4#529×C12711yescharacteristic
509C4#532×C12711yescharacteristic
510C2—42no—
511C2—44no—
512C2C4×#121×C12711yescharacteristic
513C2C127×#292911yescharacteristic
514C2C127×#292912yes—
515C2C127×#293111yescharacteristic
516C2C127×#296612yes—
subgroupG/H
centerC22×C8×C127C23
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radical#392×C127C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C8×D4×C127C2semidirect
2. C2×C8×D4×C127C2semidirect
3. C2×#405×C127C2semidirect
5. C127×#1955C2semidirect
6. C127×#1940C2semidirect
7. C127×#1924C2semidirect
8. C127×#1870C2semidirect
9. C127×#1798C2semidirect
10. C8×C4⋊C4×C127C2semidirect
11. C8×C22⋊C4×C127C2semidirect
56. C22×C8×C127D4semidirect
95. C4×C8×C127D4semidirect
251. #21491C127direct (N × H)
259. C2×C8×D4C2×C127semidirect
260. C2×C8×D4C2×C127semidirect
261. C2×#405C2×C127semidirect
263. #1955C2×C127semidirect
264. #1940C2×C127semidirect
265. #1924C2×C127semidirect
266. #1870C2×C127semidirect
267. #1798C2×C127semidirect
268. C8×C4⋊C4C2×C127semidirect
269. C8×C22⋊C4C2×C127semidirect
270. C127#21491direct (N × H)
315. C22×C8D4×C127semidirect
354. C4×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D4×C1272
C2×#405×C1272
C127×#23922
C127×#19552
C127×#19402
C127×#19242
C127×#18702
C127×#17982
C8×C4⋊C4×C1272
C8×C22⋊C4×C1272
#21491127